[ { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Recently the city revisited its pickup plan: decide which transfer stations should be in operation and for every block pick a single active station that will collect its rubbish. No station can be given more than it can deal with, and every block must be assigned to exactly one open station. What counts as a better plan is a lower overall expense — add up the startup cost of every station that gets switched on and the hauling cost for every block’s trip to its station; the total should be as small as possible. The exact figures and options are shown underneath.\n\n# num_stations=9\n# num_blocks=19\n# STATIONS\nstation_id,startup_cost,handling_capacity\nF1,400.0,300.0\nF2,400.0,300.0\nF3,400.0,300.0\nF4,400.0,300.0\nF5,400.0,300.0\nF6,400.0,300.0\nF7,400.0,300.0\nF8,400.0,300.0\nF9,400.0,300.0\n# BLOCKS\nblock_id,waste_amount\n0,25.0\n1,18.0\n2,24.0\n3,12.0\n4,19.0\n5,11.0\n6,12.0\n7,27.0\n8,14.0\n9,24.0\n10,17.0\n11,24.0\n12,13.0\n13,27.0\n14,18.0\n15,18.0\n16,13.0\n17,16.0\n18,18.0\n# HAULS\nstation_id,block_id,haul_cost\nF1,0,71.0\nF1,1,46.0\nF1,2,76.0\nF1,3,69.0\nF1,4,197.0\nF1,5,22.0\nF1,6,43.0\nF1,7,509.0\nF1,8,145.0\nF1,9,339.0\nF1,10,80.0\nF1,11,49.0\nF1,12,613.0\nF1,13,273.0\nF1,14,39.0\nF1,15,46.0\nF1,16,151.0\nF1,17,81.0\nF1,18,146.0\nF2,0,1087.0\nF2,1,446.0\nF2,2,216.0\nF2,3,913.0\nF2,4,1185.0\nF2,5,1542.0\nF2,6,269.0\nF2,7,820.0\nF2,8,1287.0\nF2,9,438.0\nF2,10,1131.0\nF2,11,671.0\nF2,12,1271.0\nF2,13,895.0\nF2,14,37.0\nF2,15,1086.0\nF2,16,475.0\nF2,17,1305.0\nF2,18,1944.0\nF3,0,285.0\nF3,1,42.0\nF3,2,124.0\nF3,3,25.0\nF3,4,131.0\nF3,5,448.0\nF3,6,99.0\nF3,7,428.0\nF3,8,112.0\nF3,9,261.0\nF3,10,52.0\nF3,11,87.0\nF3,12,574.0\nF3,13,482.0\nF3,14,36.0\nF3,15,242.0\nF3,16,79.0\nF3,17,415.0\nF3,18,769.0\nF4,0,1241.0\nF4,1,607.0\nF4,2,378.0\nF4,3,974.0\nF4,4,1167.0\nF4,5,1631.0\nF4,6,472.0\nF4,7,495.0\nF4,8,1297.0\nF4,9,48.0\nF4,10,1184.0\nF4,11,825.0\nF4,12,1032.0\nF4,13,1108.0\nF4,14,59.0\nF4,15,1229.0\nF4,16,458.0\nF4,17,1453.0\nF4,18,1986.0\nF5,0,110.0\nF5,1,44.0\nF5,2,84.0\nF5,3,78.0\nF5,4,269.0\nF5,5,180.0\nF5,6,51.0\nF5,7,551.0\nF5,8,228.0\nF5,9,353.0\nF5,10,102.0\nF5,11,48.0\nF5,12,712.0\nF5,13,337.0\nF5,14,38.0\nF5,15,72.0\nF5,16,162.0\nF5,17,178.0\nF5,18,602.0\nF6,0,1136.0\nF6,1,499.0\nF6,2,307.0\nF6,3,887.0\nF6,4,1105.0\nF6,5,1541.0\nF6,6,380.0\nF6,7,573.0\nF6,8,1228.0\nF6,9,192.0\nF6,10,1101.0\nF6,11,718.0\nF6,12,1064.0\nF6,13,1005.0\nF6,14,47.0\nF6,15,1126.0\nF6,16,374.0\nF6,17,1350.0\nF6,18,1911.0\nF7,0,106.0\nF7,1,37.0\nF7,2,90.0\nF7,3,39.0\nF7,4,132.0\nF7,5,51.0\nF7,6,57.0\nF7,7,445.0\nF7,8,84.0\nF7,9,294.0\nF7,10,47.0\nF7,11,50.0\nF7,12,527.0\nF7,13,326.0\nF7,14,37.0\nF7,15,73.0\nF7,16,112.0\nF7,17,136.0\nF7,18,36.0\nF8,0,377.0\nF8,1,41.0\nF8,2,124.0\nF8,3,24.0\nF8,4,354.0\nF8,5,681.0\nF8,6,102.0\nF8,7,509.0\nF8,8,413.0\nF8,9,299.0\nF8,10,242.0\nF8,11,97.0\nF8,12,729.0\nF8,13,519.0\nF8,14,36.0\nF8,15,342.0\nF8,16,109.0\nF8,17,552.0\nF8,18,1057.0\nF9,0,756.0\nF9,1,210.0\nF9,2,223.0\nF9,3,429.0\nF9,4,590.0\nF9,5,1077.0\nF9,6,241.0\nF9,7,332.0\nF9,8,722.0\nF9,9,155.0\nF9,10,624.0\nF9,11,378.0\nF9,12,634.0\nF9,13,784.0\nF9,14,40.0\nF9,15,730.0\nF9,16,34.0\nF9,17,949.0\nF9,18,1412.0\n\nOne more thing — when you send back the plan, please use this simple JSON shape so it's easy to check:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list the transfer stations you decide to turn on. \"assignments\" is a list (in block order) showing which open station each block is assigned to. Think of it like filling out a form: a short list of active sites and then, for every block, the one chosen station.\n\nThis is just a sketch of the expected shape — not the actual answer.\n\nPlease use the exact identifiers from the instance input, with no renaming and no invented labels. For example:\nValid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "connection_costs": [ [ 71.0, 46.0, 76.0, 69.0, 197.0, 22.0, 43.0, 509.0, 145.0, 339.0, 80.0, 49.0, 613.0, 273.0, 39.0, 46.0, 151.0, 81.0, 146.0 ], [ 1087.0, 446.0, 216.0, 913.0, 1185.0, 1542.0, 269.0, 820.0, 1287.0, 438.0, 1131.0, 671.0, 1271.0, 895.0, 37.0, 1086.0, 475.0, 1305.0, 1944.0 ], [ 285.0, 42.0, 124.0, 25.0, 131.0, 448.0, 99.0, 428.0, 112.0, 261.0, 52.0, 87.0, 574.0, 482.0, 36.0, 242.0, 79.0, 415.0, 769.0 ], [ 1241.0, 607.0, 378.0, 974.0, 1167.0, 1631.0, 472.0, 495.0, 1297.0, 48.0, 1184.0, 825.0, 1032.0, 1108.0, 59.0, 1229.0, 458.0, 1453.0, 1986.0 ], [ 110.0, 44.0, 84.0, 78.0, 269.0, 180.0, 51.0, 551.0, 228.0, 353.0, 102.0, 48.0, 712.0, 337.0, 38.0, 72.0, 162.0, 178.0, 602.0 ], [ 1136.0, 499.0, 307.0, 887.0, 1105.0, 1541.0, 380.0, 573.0, 1228.0, 192.0, 1101.0, 718.0, 1064.0, 1005.0, 47.0, 1126.0, 374.0, 1350.0, 1911.0 ], [ 106.0, 37.0, 90.0, 39.0, 132.0, 51.0, 57.0, 445.0, 84.0, 294.0, 47.0, 50.0, 527.0, 326.0, 37.0, 73.0, 112.0, 136.0, 36.0 ], [ 377.0, 41.0, 124.0, 24.0, 354.0, 681.0, 102.0, 509.0, 413.0, 299.0, 242.0, 97.0, 729.0, 519.0, 36.0, 342.0, 109.0, 552.0, 1057.0 ], [ 756.0, 210.0, 223.0, 429.0, 590.0, 1077.0, 241.0, 332.0, 722.0, 155.0, 624.0, 378.0, 634.0, 784.0, 40.0, 730.0, 34.0, 949.0, 1412.0 ] ], "demands": [ 25.0, 18.0, 24.0, 12.0, 19.0, 11.0, 12.0, 27.0, 14.0, 24.0, 17.0, 24.0, 13.0, 27.0, 18.0, 18.0, 13.0, 16.0, 18.0 ], "objective": 3149.0 }, "solution": { "open_facilities": [ 6, 8 ], "assignments": [ 6, 6, 6, 6, 6, 6, 6, 8, 6, 8, 6, 6, 6, 6, 6, 6, 8, 6, 6 ] }, "obj": 3149.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 9, "num_customers": 19, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 300.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 300.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 300.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 300.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 300.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 300.0 }, { "id": "F7", "opening_cost": 400.0, "capacity": 300.0 }, { "id": "F8", "opening_cost": 400.0, "capacity": 300.0 }, { "id": "F9", "opening_cost": 400.0, "capacity": 300.0 } ], "customers": [ { "id": 0, "demand": 25.0 }, { "id": 1, "demand": 18.0 }, { "id": 2, "demand": 24.0 }, { "id": 3, "demand": 12.0 }, { "id": 4, "demand": 19.0 }, { "id": 5, "demand": 11.0 }, { "id": 6, "demand": 12.0 }, { "id": 7, "demand": 27.0 }, { "id": 8, "demand": 14.0 }, { "id": 9, "demand": 24.0 }, { "id": 10, "demand": 17.0 }, { "id": 11, "demand": 24.0 }, { "id": 12, "demand": 13.0 }, { "id": 13, "demand": 27.0 }, { "id": 14, "demand": 18.0 }, { "id": 15, "demand": 18.0 }, { "id": 16, "demand": 13.0 }, { "id": 17, "demand": 16.0 }, { "id": 18, "demand": 18.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 71.0 }, { "facility": "F1", "customer": 1, "cost": 46.0 }, { "facility": "F1", "customer": 2, "cost": 76.0 }, { "facility": "F1", "customer": 3, "cost": 69.0 }, { "facility": "F1", "customer": 4, "cost": 197.0 }, { "facility": "F1", "customer": 5, "cost": 22.0 }, { "facility": "F1", "customer": 6, "cost": 43.0 }, { "facility": "F1", "customer": 7, "cost": 509.0 }, { "facility": "F1", "customer": 8, "cost": 145.0 }, { "facility": "F1", "customer": 9, "cost": 339.0 }, { "facility": "F1", "customer": 10, "cost": 80.0 }, { "facility": "F1", "customer": 11, "cost": 49.0 }, { "facility": "F1", "customer": 12, "cost": 613.0 }, { "facility": "F1", "customer": 13, "cost": 273.0 }, { "facility": "F1", "customer": 14, "cost": 39.0 }, { "facility": "F1", "customer": 15, "cost": 46.0 }, { "facility": "F1", "customer": 16, "cost": 151.0 }, { "facility": "F1", "customer": 17, "cost": 81.0 }, { "facility": "F1", "customer": 18, "cost": 146.0 }, { "facility": "F2", "customer": 0, "cost": 1087.0 }, { "facility": "F2", "customer": 1, "cost": 446.0 }, { "facility": "F2", "customer": 2, "cost": 216.0 }, { "facility": "F2", "customer": 3, "cost": 913.0 }, { "facility": "F2", "customer": 4, "cost": 1185.0 }, { "facility": "F2", "customer": 5, "cost": 1542.0 }, { "facility": "F2", "customer": 6, "cost": 269.0 }, { "facility": "F2", "customer": 7, "cost": 820.0 }, { "facility": "F2", "customer": 8, "cost": 1287.0 }, { "facility": "F2", "customer": 9, "cost": 438.0 }, { "facility": "F2", "customer": 10, "cost": 1131.0 }, { "facility": "F2", "customer": 11, "cost": 671.0 }, { "facility": "F2", "customer": 12, "cost": 1271.0 }, { "facility": "F2", "customer": 13, "cost": 895.0 }, { "facility": "F2", "customer": 14, "cost": 37.0 }, { "facility": "F2", "customer": 15, "cost": 1086.0 }, { "facility": "F2", "customer": 16, "cost": 475.0 }, { "facility": "F2", "customer": 17, "cost": 1305.0 }, { "facility": "F2", "customer": 18, "cost": 1944.0 }, { "facility": "F3", "customer": 0, "cost": 285.0 }, { "facility": "F3", "customer": 1, "cost": 42.0 }, { "facility": "F3", "customer": 2, "cost": 124.0 }, { "facility": "F3", "customer": 3, "cost": 25.0 }, { "facility": "F3", "customer": 4, "cost": 131.0 }, { "facility": "F3", "customer": 5, "cost": 448.0 }, { "facility": "F3", "customer": 6, "cost": 99.0 }, { "facility": "F3", "customer": 7, "cost": 428.0 }, { "facility": "F3", "customer": 8, "cost": 112.0 }, { "facility": "F3", "customer": 9, "cost": 261.0 }, { "facility": "F3", "customer": 10, "cost": 52.0 }, { "facility": "F3", "customer": 11, "cost": 87.0 }, { "facility": "F3", "customer": 12, "cost": 574.0 }, { "facility": "F3", "customer": 13, "cost": 482.0 }, { "facility": "F3", "customer": 14, "cost": 36.0 }, { "facility": "F3", "customer": 15, "cost": 242.0 }, { "facility": "F3", "customer": 16, "cost": 79.0 }, { "facility": "F3", "customer": 17, "cost": 415.0 }, { "facility": "F3", "customer": 18, "cost": 769.0 }, { "facility": "F4", "customer": 0, "cost": 1241.0 }, { "facility": "F4", "customer": 1, "cost": 607.0 }, { "facility": "F4", "customer": 2, "cost": 378.0 }, { "facility": "F4", "customer": 3, "cost": 974.0 }, { "facility": "F4", "customer": 4, "cost": 1167.0 }, { "facility": "F4", "customer": 5, "cost": 1631.0 }, { "facility": "F4", "customer": 6, "cost": 472.0 }, { "facility": "F4", "customer": 7, "cost": 495.0 }, { "facility": "F4", "customer": 8, "cost": 1297.0 }, { "facility": "F4", "customer": 9, "cost": 48.0 }, { "facility": "F4", "customer": 10, "cost": 1184.0 }, { "facility": "F4", "customer": 11, "cost": 825.0 }, { "facility": "F4", "customer": 12, "cost": 1032.0 }, { "facility": "F4", "customer": 13, "cost": 1108.0 }, { "facility": "F4", "customer": 14, "cost": 59.0 }, { "facility": "F4", "customer": 15, "cost": 1229.0 }, { "facility": "F4", "customer": 16, "cost": 458.0 }, { "facility": "F4", "customer": 17, "cost": 1453.0 }, { "facility": "F4", "customer": 18, "cost": 1986.0 }, { "facility": "F5", "customer": 0, "cost": 110.0 }, { "facility": "F5", "customer": 1, "cost": 44.0 }, { "facility": "F5", "customer": 2, "cost": 84.0 }, { "facility": "F5", "customer": 3, "cost": 78.0 }, { "facility": "F5", "customer": 4, "cost": 269.0 }, { "facility": "F5", "customer": 5, "cost": 180.0 }, { "facility": "F5", "customer": 6, "cost": 51.0 }, { "facility": "F5", "customer": 7, "cost": 551.0 }, { "facility": "F5", "customer": 8, "cost": 228.0 }, { "facility": "F5", "customer": 9, "cost": 353.0 }, { "facility": "F5", "customer": 10, "cost": 102.0 }, { "facility": "F5", "customer": 11, "cost": 48.0 }, { "facility": "F5", "customer": 12, "cost": 712.0 }, { "facility": "F5", "customer": 13, "cost": 337.0 }, { "facility": "F5", "customer": 14, "cost": 38.0 }, { "facility": "F5", "customer": 15, "cost": 72.0 }, { "facility": "F5", "customer": 16, "cost": 162.0 }, { "facility": "F5", "customer": 17, "cost": 178.0 }, { "facility": "F5", "customer": 18, "cost": 602.0 }, { "facility": "F6", "customer": 0, "cost": 1136.0 }, { "facility": "F6", "customer": 1, "cost": 499.0 }, { "facility": "F6", "customer": 2, "cost": 307.0 }, { "facility": "F6", "customer": 3, "cost": 887.0 }, { "facility": "F6", "customer": 4, "cost": 1105.0 }, { "facility": "F6", "customer": 5, "cost": 1541.0 }, { "facility": "F6", "customer": 6, "cost": 380.0 }, { "facility": "F6", "customer": 7, "cost": 573.0 }, { "facility": "F6", "customer": 8, "cost": 1228.0 }, { "facility": "F6", "customer": 9, "cost": 192.0 }, { "facility": "F6", "customer": 10, "cost": 1101.0 }, { "facility": "F6", "customer": 11, "cost": 718.0 }, { "facility": "F6", "customer": 12, "cost": 1064.0 }, { "facility": "F6", "customer": 13, "cost": 1005.0 }, { "facility": "F6", "customer": 14, "cost": 47.0 }, { "facility": "F6", "customer": 15, "cost": 1126.0 }, { "facility": "F6", "customer": 16, "cost": 374.0 }, { "facility": "F6", "customer": 17, "cost": 1350.0 }, { "facility": "F6", "customer": 18, "cost": 1911.0 }, { "facility": "F7", "customer": 0, "cost": 106.0 }, { "facility": "F7", "customer": 1, "cost": 37.0 }, { "facility": "F7", "customer": 2, "cost": 90.0 }, { "facility": "F7", "customer": 3, "cost": 39.0 }, { "facility": "F7", "customer": 4, "cost": 132.0 }, { "facility": "F7", "customer": 5, "cost": 51.0 }, { "facility": "F7", "customer": 6, "cost": 57.0 }, { "facility": "F7", "customer": 7, "cost": 445.0 }, { "facility": "F7", "customer": 8, "cost": 84.0 }, { "facility": "F7", "customer": 9, "cost": 294.0 }, { "facility": "F7", "customer": 10, "cost": 47.0 }, { "facility": "F7", "customer": 11, "cost": 50.0 }, { "facility": "F7", "customer": 12, "cost": 527.0 }, { "facility": "F7", "customer": 13, "cost": 326.0 }, { "facility": "F7", "customer": 14, "cost": 37.0 }, { "facility": "F7", "customer": 15, "cost": 73.0 }, { "facility": "F7", "customer": 16, "cost": 112.0 }, { "facility": "F7", "customer": 17, "cost": 136.0 }, { "facility": "F7", "customer": 18, "cost": 36.0 }, { "facility": "F8", "customer": 0, "cost": 377.0 }, { "facility": "F8", "customer": 1, "cost": 41.0 }, { "facility": "F8", "customer": 2, "cost": 124.0 }, { "facility": "F8", "customer": 3, "cost": 24.0 }, { "facility": "F8", "customer": 4, "cost": 354.0 }, { "facility": "F8", "customer": 5, "cost": 681.0 }, { "facility": "F8", "customer": 6, "cost": 102.0 }, { "facility": "F8", "customer": 7, "cost": 509.0 }, { "facility": "F8", "customer": 8, "cost": 413.0 }, { "facility": "F8", "customer": 9, "cost": 299.0 }, { "facility": "F8", "customer": 10, "cost": 242.0 }, { "facility": "F8", "customer": 11, "cost": 97.0 }, { "facility": "F8", "customer": 12, "cost": 729.0 }, { "facility": "F8", "customer": 13, "cost": 519.0 }, { "facility": "F8", "customer": 14, "cost": 36.0 }, { "facility": "F8", "customer": 15, "cost": 342.0 }, { "facility": "F8", "customer": 16, "cost": 109.0 }, { "facility": "F8", "customer": 17, "cost": 552.0 }, { "facility": "F8", "customer": 18, "cost": 1057.0 }, { "facility": "F9", "customer": 0, "cost": 756.0 }, { "facility": "F9", "customer": 1, "cost": 210.0 }, { "facility": "F9", "customer": 2, "cost": 223.0 }, { "facility": "F9", "customer": 3, "cost": 429.0 }, { "facility": "F9", "customer": 4, "cost": 590.0 }, { "facility": "F9", "customer": 5, "cost": 1077.0 }, { "facility": "F9", "customer": 6, "cost": 241.0 }, { "facility": "F9", "customer": 7, "cost": 332.0 }, { "facility": "F9", "customer": 8, "cost": 722.0 }, { "facility": "F9", "customer": 9, "cost": 155.0 }, { "facility": "F9", "customer": 10, "cost": 624.0 }, { "facility": "F9", "customer": 11, "cost": 378.0 }, { "facility": "F9", "customer": 12, "cost": 634.0 }, { "facility": "F9", "customer": 13, "cost": 784.0 }, { "facility": "F9", "customer": 14, "cost": 40.0 }, { "facility": "F9", "customer": 15, "cost": 730.0 }, { "facility": "F9", "customer": 16, "cost": 34.0 }, { "facility": "F9", "customer": 17, "cost": 949.0 }, { "facility": "F9", "customer": 18, "cost": 1412.0 } ], "objective": 3149.0 }, "solution_variant": { "selected": [ "F7", "F9" ], "assignments": [ "F7", "F7", "F7", "F7", "F7", "F7", "F7", "F9", "F7", "F9", "F7", "F7", "F7", "F7", "F7", "F7", "F9", "F7", "F7" ] }, "context_index": 1, "input_format": "csv", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Recently the team sat down with a map of stores and candidate depots and boiled the task down: open some depots, and send each store’s whole order to a single open depot (no partial shipments, all stores covered), while not overloading any depot beyond its capacity. The way to judge plans is by their total cost — just add up depot activation fees and the delivery costs to the stores — and pick the smallest. The concrete details will be shown below.\n\nThere are 6 depots and 17 stores in this instance.\n\n**Depots**\n| depot_id | activation_fee | handling_capacity |\n|---|---|---|\n| F1 | 400.0 | 1382.0 |\n| F2 | 400.0 | 1335.0 |\n| F3 | 400.0 | 1400.0 |\n| F4 | 400.0 | 1105.0 |\n| F5 | 400.0 | 898.0 |\n| F6 | 400.0 | 1331.0 |\n\n**Stores**\n| store_id | store_demand |\n|---|---|\n| A | 39.0 |\n| B | 11.0 |\n| C | 25.0 |\n| D | 36.0 |\n| E | 32.0 |\n| F | 42.0 |\n| G | 38.0 |\n| H | 17.0 |\n| I | 31.0 |\n| J | 32.0 |\n| K | 44.0 |\n| L | 45.0 |\n| M | 46.0 |\n| N | 27.0 |\n| O | 40.0 |\n| P | 34.0 |\n| Q | 40.0 |\n\n**Delivery Cost**\n| depot_id | store_id | delivery_cost |\n|---|---|---|\n| F1 | A | 692.0 |\n| F1 | B | 262.0 |\n| F1 | C | 468.0 |\n| F1 | D | 569.0 |\n| F1 | E | 802.0 |\n| F1 | F | 487.0 |\n| F1 | G | 501.0 |\n| F1 | H | 734.0 |\n| F1 | I | 364.0 |\n| F1 | J | 97.0 |\n| F1 | K | 574.0 |\n| F1 | L | 200.0 |\n| F1 | M | 562.0 |\n| F1 | N | 190.0 |\n| F1 | O | 417.0 |\n| F1 | P | 224.0 |\n| F1 | Q | 535.0 |\n| F2 | A | 313.0 |\n| F2 | B | 686.0 |\n| F2 | C | 603.0 |\n| F2 | D | 501.0 |\n| F2 | E | 4.0 |\n| F2 | F | 342.0 |\n| F2 | G | 299.0 |\n| F2 | H | 114.0 |\n| F2 | I | 502.0 |\n| F2 | J | 877.0 |\n| F2 | K | 233.0 |\n| F2 | L | 600.0 |\n| F2 | M | 265.0 |\n| F2 | N | 635.0 |\n| F2 | O | 583.0 |\n| F2 | P | 577.0 |\n| F2 | Q | 274.0 |\n| F3 | A | 658.0 |\n| F3 | B | 94.0 |\n| F3 | C | 296.0 |\n| F3 | D | 586.0 |\n| F3 | E | 701.0 |\n| F3 | F | 362.0 |\n| F3 | G | 403.0 |\n| F3 | H | 616.0 |\n| F3 | I | 361.0 |\n| F3 | J | 268.0 |\n| F3 | K | 465.0 |\n| F3 | L | 168.0 |\n| F3 | M | 495.0 |\n| F3 | N | 72.0 |\n| F3 | O | 246.0 |\n| F3 | P | 152.0 |\n| F3 | Q | 424.0 |\n| F4 | A | 453.0 |\n| F4 | B | 474.0 |\n| F4 | C | 353.0 |\n| F4 | D | 566.0 |\n| F4 | E | 261.0 |\n| F4 | F | 163.0 |\n| F4 | G | 205.0 |\n| F4 | H | 144.0 |\n| F4 | I | 456.0 |\n| F4 | J | 738.0 |\n| F4 | K | 142.0 |\n| F4 | L | 466.0 |\n| F4 | M | 290.0 |\n| F4 | N | 461.0 |\n| F4 | O | 342.0 |\n| F4 | P | 429.0 |\n| F4 | Q | 153.0 |\n| F5 | A | 490.0 |\n| F5 | B | 200.0 |\n| F5 | C | 261.0 |\n| F5 | D | 466.0 |\n| F5 | E | 508.0 |\n| F5 | F | 173.0 |\n| F5 | G | 210.0 |\n| F5 | H | 425.0 |\n| F5 | I | 255.0 |\n| F5 | J | 408.0 |\n| F5 | K | 272.0 |\n| F5 | L | 148.0 |\n| F5 | M | 313.0 |\n| F5 | N | 133.0 |\n| F5 | O | 204.0 |\n| F5 | P | 105.0 |\n| F5 | Q | 231.0 |\n| F6 | A | 156.0 |\n| F6 | B | 544.0 |\n| F6 | C | 545.0 |\n| F6 | D | 258.0 |\n| F6 | E | 265.0 |\n| F6 | F | 256.0 |\n| F6 | G | 161.0 |\n| F6 | H | 269.0 |\n| F6 | I | 247.0 |\n| F6 | J | 648.0 |\n| F6 | K | 179.0 |\n| F6 | L | 387.0 |\n| F6 | M | 34.0 |\n| F6 | N | 452.0 |\n| F6 | O | 503.0 |\n| F6 | P | 378.0 |\n| F6 | Q | 191.0 |\n\nAnd just so we're on the same page about the output format, please return your plan using this simple JSON layout below — it’s just the shape I expect, nothing fancy.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of depots you decide to open, and \"assignments\" as, for each store (in the same order they appear in the instance), which open depot will handle that store. Easy, informal — like filling out a short form.\n\nThis JSON is only a sketch of the expected shape, not the actual answer. Also, please use the exact identifiers from the instance input — do not rename them or invent new labels. For example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 1382.0, 1335.0, 1400.0, 1105.0, 898.0, 1331.0 ], "connection_costs": [ [ 692.0, 262.0, 468.0, 569.0, 802.0, 487.0, 501.0, 734.0, 364.0, 97.0, 574.0, 200.0, 562.0, 190.0, 417.0, 224.0, 535.0 ], [ 313.0, 686.0, 603.0, 501.0, 4.0, 342.0, 299.0, 114.0, 502.0, 877.0, 233.0, 600.0, 265.0, 635.0, 583.0, 577.0, 274.0 ], [ 658.0, 94.0, 296.0, 586.0, 701.0, 362.0, 403.0, 616.0, 361.0, 268.0, 465.0, 168.0, 495.0, 72.0, 246.0, 152.0, 424.0 ], [ 453.0, 474.0, 353.0, 566.0, 261.0, 163.0, 205.0, 144.0, 456.0, 738.0, 142.0, 466.0, 290.0, 461.0, 342.0, 429.0, 153.0 ], [ 490.0, 200.0, 261.0, 466.0, 508.0, 173.0, 210.0, 425.0, 255.0, 408.0, 272.0, 148.0, 313.0, 133.0, 204.0, 105.0, 231.0 ], [ 156.0, 544.0, 545.0, 258.0, 265.0, 256.0, 161.0, 269.0, 247.0, 648.0, 179.0, 387.0, 34.0, 452.0, 503.0, 378.0, 191.0 ] ], "demands": [ 39.0, 11.0, 25.0, 36.0, 32.0, 42.0, 38.0, 17.0, 31.0, 32.0, 44.0, 45.0, 46.0, 27.0, 40.0, 34.0, 40.0 ], "objective": 4096.0 }, "solution": { "open_facilities": [ 1, 2, 5 ], "assignments": [ 5, 2, 2, 5, 1, 5, 5, 1, 5, 2, 5, 2, 5, 2, 2, 2, 5 ] }, "obj": 4096.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 6, "num_customers": 17, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 1382.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 1335.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 1400.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 1105.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 898.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 1331.0 } ], "customers": [ { "id": "A", "demand": 39.0 }, { "id": "B", "demand": 11.0 }, { "id": "C", "demand": 25.0 }, { "id": "D", "demand": 36.0 }, { "id": "E", "demand": 32.0 }, { "id": "F", "demand": 42.0 }, { "id": "G", "demand": 38.0 }, { "id": "H", "demand": 17.0 }, { "id": "I", "demand": 31.0 }, { "id": "J", "demand": 32.0 }, { "id": "K", "demand": 44.0 }, { "id": "L", "demand": 45.0 }, { "id": "M", "demand": 46.0 }, { "id": "N", "demand": 27.0 }, { "id": "O", "demand": 40.0 }, { "id": "P", "demand": 34.0 }, { "id": "Q", "demand": 40.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 692.0 }, { "facility": "F1", "customer": "B", "cost": 262.0 }, { "facility": "F1", "customer": "C", "cost": 468.0 }, { "facility": "F1", "customer": "D", "cost": 569.0 }, { "facility": "F1", "customer": "E", "cost": 802.0 }, { "facility": "F1", "customer": "F", "cost": 487.0 }, { "facility": "F1", "customer": "G", "cost": 501.0 }, { "facility": "F1", "customer": "H", "cost": 734.0 }, { "facility": "F1", "customer": "I", "cost": 364.0 }, { "facility": "F1", "customer": "J", "cost": 97.0 }, { "facility": "F1", "customer": "K", "cost": 574.0 }, { "facility": "F1", "customer": "L", "cost": 200.0 }, { "facility": "F1", "customer": "M", "cost": 562.0 }, { "facility": "F1", "customer": "N", "cost": 190.0 }, { "facility": "F1", "customer": "O", "cost": 417.0 }, { "facility": "F1", "customer": "P", "cost": 224.0 }, { "facility": "F1", "customer": "Q", "cost": 535.0 }, { "facility": "F2", "customer": "A", "cost": 313.0 }, { "facility": "F2", "customer": "B", "cost": 686.0 }, { "facility": "F2", "customer": "C", "cost": 603.0 }, { "facility": "F2", "customer": "D", "cost": 501.0 }, { "facility": "F2", "customer": "E", "cost": 4.0 }, { "facility": "F2", "customer": "F", "cost": 342.0 }, { "facility": "F2", "customer": "G", "cost": 299.0 }, { "facility": "F2", "customer": "H", "cost": 114.0 }, { "facility": "F2", "customer": "I", "cost": 502.0 }, { "facility": "F2", "customer": "J", "cost": 877.0 }, { "facility": "F2", "customer": "K", "cost": 233.0 }, { "facility": "F2", "customer": "L", "cost": 600.0 }, { "facility": "F2", "customer": "M", "cost": 265.0 }, { "facility": "F2", "customer": "N", "cost": 635.0 }, { "facility": "F2", "customer": "O", "cost": 583.0 }, { "facility": "F2", "customer": "P", "cost": 577.0 }, { "facility": "F2", "customer": "Q", "cost": 274.0 }, { "facility": "F3", "customer": "A", "cost": 658.0 }, { "facility": "F3", "customer": "B", "cost": 94.0 }, { "facility": "F3", "customer": "C", "cost": 296.0 }, { "facility": "F3", "customer": "D", "cost": 586.0 }, { "facility": "F3", "customer": "E", "cost": 701.0 }, { "facility": "F3", "customer": "F", "cost": 362.0 }, { "facility": "F3", "customer": "G", "cost": 403.0 }, { "facility": "F3", "customer": "H", "cost": 616.0 }, { "facility": "F3", "customer": "I", "cost": 361.0 }, { "facility": "F3", "customer": "J", "cost": 268.0 }, { "facility": "F3", "customer": "K", "cost": 465.0 }, { "facility": "F3", "customer": "L", "cost": 168.0 }, { "facility": "F3", "customer": "M", "cost": 495.0 }, { "facility": "F3", "customer": "N", "cost": 72.0 }, { "facility": "F3", "customer": "O", "cost": 246.0 }, { "facility": "F3", "customer": "P", "cost": 152.0 }, { "facility": "F3", "customer": "Q", "cost": 424.0 }, { "facility": "F4", "customer": "A", "cost": 453.0 }, { "facility": "F4", "customer": "B", "cost": 474.0 }, { "facility": "F4", "customer": "C", "cost": 353.0 }, { "facility": "F4", "customer": "D", "cost": 566.0 }, { "facility": "F4", "customer": "E", "cost": 261.0 }, { "facility": "F4", "customer": "F", "cost": 163.0 }, { "facility": "F4", "customer": "G", "cost": 205.0 }, { "facility": "F4", "customer": "H", "cost": 144.0 }, { "facility": "F4", "customer": "I", "cost": 456.0 }, { "facility": "F4", "customer": "J", "cost": 738.0 }, { "facility": "F4", "customer": "K", "cost": 142.0 }, { "facility": "F4", "customer": "L", "cost": 466.0 }, { "facility": "F4", "customer": "M", "cost": 290.0 }, { "facility": "F4", "customer": "N", "cost": 461.0 }, { "facility": "F4", "customer": "O", "cost": 342.0 }, { "facility": "F4", "customer": "P", "cost": 429.0 }, { "facility": "F4", "customer": "Q", "cost": 153.0 }, { "facility": "F5", "customer": "A", "cost": 490.0 }, { "facility": "F5", "customer": "B", "cost": 200.0 }, { "facility": "F5", "customer": "C", "cost": 261.0 }, { "facility": "F5", "customer": "D", "cost": 466.0 }, { "facility": "F5", "customer": "E", "cost": 508.0 }, { "facility": "F5", "customer": "F", "cost": 173.0 }, { "facility": "F5", "customer": "G", "cost": 210.0 }, { "facility": "F5", "customer": "H", "cost": 425.0 }, { "facility": "F5", "customer": "I", "cost": 255.0 }, { "facility": "F5", "customer": "J", "cost": 408.0 }, { "facility": "F5", "customer": "K", "cost": 272.0 }, { "facility": "F5", "customer": "L", "cost": 148.0 }, { "facility": "F5", "customer": "M", "cost": 313.0 }, { "facility": "F5", "customer": "N", "cost": 133.0 }, { "facility": "F5", "customer": "O", "cost": 204.0 }, { "facility": "F5", "customer": "P", "cost": 105.0 }, { "facility": "F5", "customer": "Q", "cost": 231.0 }, { "facility": "F6", "customer": "A", "cost": 156.0 }, { "facility": "F6", "customer": "B", "cost": 544.0 }, { "facility": "F6", "customer": "C", "cost": 545.0 }, { "facility": "F6", "customer": "D", "cost": 258.0 }, { "facility": "F6", "customer": "E", "cost": 265.0 }, { "facility": "F6", "customer": "F", "cost": 256.0 }, { "facility": "F6", "customer": "G", "cost": 161.0 }, { "facility": "F6", "customer": "H", "cost": 269.0 }, { "facility": "F6", "customer": "I", "cost": 247.0 }, { "facility": "F6", "customer": "J", "cost": 648.0 }, { "facility": "F6", "customer": "K", "cost": 179.0 }, { "facility": "F6", "customer": "L", "cost": 387.0 }, { "facility": "F6", "customer": "M", "cost": 34.0 }, { "facility": "F6", "customer": "N", "cost": 452.0 }, { "facility": "F6", "customer": "O", "cost": 503.0 }, { "facility": "F6", "customer": "P", "cost": 378.0 }, { "facility": "F6", "customer": "Q", "cost": 191.0 } ], "objective": 4096.0 }, "solution_variant": { "selected": [ "F2", "F3", "F6" ], "assignments": [ "F6", "F3", "F3", "F6", "F2", "F6", "F6", "F2", "F6", "F3", "F6", "F3", "F6", "F3", "F3", "F3", "F6" ] }, "context_index": 2, "input_format": "markdown_table", "input_index_base": "names" }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "As the person running the lunch operation, the job is to decide which kitchens to staff and which single kitchen will serve each school. No school can be split between kitchens and each kitchen only has so much output it can produce. Plans are compared by their total cost — just add the staffing bill for the kitchens that are staffed to the food-transport costs for all school deliveries — smaller totals win. No school may be left unserved and no kitchen may go over its production limit; the actual figures are provided below.\n\nBelow are the 7 candidate kitchens and the 16 schools with their figures.\nKitchen F1: staffing cost 243.0, production capacity 376.0.\nKitchen F2: staffing cost 468.0, production capacity 425.0.\nKitchen F3: staffing cost 201.0, production capacity 378.0.\nKitchen F4: staffing cost 573.0, production capacity 434.0.\nKitchen F5: staffing cost 209.0, production capacity 259.0.\nKitchen F6: staffing cost 405.0, production capacity 490.0.\nKitchen F7: staffing cost 462.0, production capacity 403.0.\nSchool 0: meal demand 12.0.\nSchool 1: meal demand 26.0.\nSchool 2: meal demand 25.0.\nSchool 3: meal demand 28.0.\nSchool 4: meal demand 17.0.\nSchool 5: meal demand 29.0.\nSchool 6: meal demand 14.0.\nSchool 7: meal demand 19.0.\nSchool 8: meal demand 19.0.\nSchool 9: meal demand 13.0.\nSchool 10: meal demand 23.0.\nSchool 11: meal demand 16.0.\nSchool 12: meal demand 27.0.\nSchool 13: meal demand 20.0.\nSchool 14: meal demand 27.0.\nSchool 15: meal demand 13.0.\nIf staffed, kitchen F1 can serve school 0 at delivery cost 76.0.\nIf staffed, kitchen F1 can serve school 1 at delivery cost 59.0.\nIf staffed, kitchen F1 can serve school 2 at delivery cost 334.0.\nIf staffed, kitchen F1 can serve school 3 at delivery cost 506.0.\nIf staffed, kitchen F1 can serve school 4 at delivery cost 590.0.\nIf staffed, kitchen F1 can serve school 5 at delivery cost 315.0.\nIf staffed, kitchen F1 can serve school 6 at delivery cost 35.0.\nIf staffed, kitchen F1 can serve school 7 at delivery cost 63.0.\nIf staffed, kitchen F1 can serve school 8 at delivery cost 524.0.\nIf staffed, kitchen F1 can serve school 9 at delivery cost 46.0.\nIf staffed, kitchen F1 can serve school 10 at delivery cost 474.0.\nIf staffed, kitchen F1 can serve school 11 at delivery cost 43.0.\nIf staffed, kitchen F1 can serve school 12 at delivery cost 447.0.\nIf staffed, kitchen F1 can serve school 13 at delivery cost 403.0.\nIf staffed, kitchen F1 can serve school 14 at delivery cost 136.0.\nIf staffed, kitchen F1 can serve school 15 at delivery cost 58.0.\nIf staffed, kitchen F2 can serve school 0 at delivery cost 618.0.\nIf staffed, kitchen F2 can serve school 1 at delivery cost 1022.0.\nIf staffed, kitchen F2 can serve school 2 at delivery cost 2126.0.\nIf staffed, kitchen F2 can serve school 3 at delivery cost 1562.0.\nIf staffed, kitchen F2 can serve school 4 at delivery cost 2010.0.\nIf staffed, kitchen F2 can serve school 5 at delivery cost 910.0.\nIf staffed, kitchen F2 can serve school 6 at delivery cost 1311.0.\nIf staffed, kitchen F2 can serve school 7 at delivery cost 1563.0.\nIf staffed, kitchen F2 can serve school 8 at delivery cost 2617.0.\nIf staffed, kitchen F2 can serve school 9 at delivery cost 214.0.\nIf staffed, kitchen F2 can serve school 10 at delivery cost 1280.0.\nIf staffed, kitchen F2 can serve school 11 at delivery cost 1583.0.\nIf staffed, kitchen F2 can serve school 12 at delivery cost 2293.0.\nIf staffed, kitchen F2 can serve school 13 at delivery cost 1333.0.\nIf staffed, kitchen F2 can serve school 14 at delivery cost 612.0.\nIf staffed, kitchen F2 can serve school 15 at delivery cost 1354.0.\nIf staffed, kitchen F3 can serve school 0 at delivery cost 60.0.\nIf staffed, kitchen F3 can serve school 1 at delivery cost 54.0.\nIf staffed, kitchen F3 can serve school 2 at delivery cost 147.0.\nIf staffed, kitchen F3 can serve school 3 at delivery cost 388.0.\nIf staffed, kitchen F3 can serve school 4 at delivery cost 518.0.\nIf staffed, kitchen F3 can serve school 5 at delivery cost 264.0.\nIf staffed, kitchen F3 can serve school 6 at delivery cost 41.0.\nIf staffed, kitchen F3 can serve school 7 at delivery cost 69.0.\nIf staffed, kitchen F3 can serve school 8 at delivery cost 128.0.\nIf staffed, kitchen F3 can serve school 9 at delivery cost 50.0.\nIf staffed, kitchen F3 can serve school 10 at delivery cost 385.0.\nIf staffed, kitchen F3 can serve school 11 at delivery cost 33.0.\nIf staffed, kitchen F3 can serve school 12 at delivery cost 189.0.\nIf staffed, kitchen F3 can serve school 13 at delivery cost 391.0.\nIf staffed, kitchen F3 can serve school 14 at delivery cost 143.0.\nIf staffed, kitchen F3 can serve school 15 at delivery cost 64.0.\nIf staffed, kitchen F4 can serve school 0 at delivery cost 60.0.\nIf staffed, kitchen F4 can serve school 1 at delivery cost 250.0.\nIf staffed, kitchen F4 can serve school 2 at delivery cost 619.0.\nIf staffed, kitchen F4 can serve school 3 at delivery cost 56.0.\nIf staffed, kitchen F4 can serve school 4 at delivery cost 1302.0.\nIf staffed, kitchen F4 can serve school 5 at delivery cost 61.0.\nIf staffed, kitchen F4 can serve school 6 at delivery cost 458.0.\nIf staffed, kitchen F4 can serve school 7 at delivery cost 625.0.\nIf staffed, kitchen F4 can serve school 8 at delivery cost 1278.0.\nIf staffed, kitchen F4 can serve school 9 at delivery cost 153.0.\nIf staffed, kitchen F4 can serve school 10 at delivery cost 62.0.\nIf staffed, kitchen F4 can serve school 11 at delivery cost 468.0.\nIf staffed, kitchen F4 can serve school 12 at delivery cost 732.0.\nIf staffed, kitchen F4 can serve school 13 at delivery cost 906.0.\nIf staffed, kitchen F4 can serve school 14 at delivery cost 382.0.\nIf staffed, kitchen F4 can serve school 15 at delivery cost 543.0.\nIf staffed, kitchen F5 can serve school 0 at delivery cost 197.0.\nIf staffed, kitchen F5 can serve school 1 at delivery cost 209.0.\nIf staffed, kitchen F5 can serve school 2 at delivery cost 1197.0.\nIf staffed, kitchen F5 can serve school 3 at delivery cost 986.0.\nIf staffed, kitchen F5 can serve school 4 at delivery cost 952.0.\nIf staffed, kitchen F5 can serve school 5 at delivery cost 558.0.\nIf staffed, kitchen F5 can serve school 6 at delivery cost 249.0.\nIf staffed, kitchen F5 can serve school 7 at delivery cost 467.0.\nIf staffed, kitchen F5 can serve school 8 at delivery cost 1542.0.\nIf staffed, kitchen F5 can serve school 9 at delivery cost 32.0.\nIf staffed, kitchen F5 can serve school 10 at delivery cost 839.0.\nIf staffed, kitchen F5 can serve school 11 at delivery cost 589.0.\nIf staffed, kitchen F5 can serve school 12 at delivery cost 1359.0.\nIf staffed, kitchen F5 can serve school 13 at delivery cost 471.0.\nIf staffed, kitchen F5 can serve school 14 at delivery cost 105.0.\nIf staffed, kitchen F5 can serve school 15 at delivery cost 244.0.\nIf staffed, kitchen F6 can serve school 0 at delivery cost 341.0.\nIf staffed, kitchen F6 can serve school 1 at delivery cost 410.0.\nIf staffed, kitchen F6 can serve school 2 at delivery cost 1407.0.\nIf staffed, kitchen F6 can serve school 3 at delivery cost 1199.0.\nIf staffed, kitchen F6 can serve school 4 at delivery cost 889.0.\nIf staffed, kitchen F6 can serve school 5 at delivery cost 727.0.\nIf staffed, kitchen F6 can serve school 6 at delivery cost 464.0.\nIf staffed, kitchen F6 can serve school 7 at delivery cost 642.0.\nIf staffed, kitchen F6 can serve school 8 at delivery cost 1689.0.\nIf staffed, kitchen F6 can serve school 9 at delivery cost 27.0.\nIf staffed, kitchen F6 can serve school 10 at delivery cost 1033.0.\nIf staffed, kitchen F6 can serve school 11 at delivery cost 801.0.\nIf staffed, kitchen F6 can serve school 12 at delivery cost 1566.0.\nIf staffed, kitchen F6 can serve school 13 at delivery cost 301.0.\nIf staffed, kitchen F6 can serve school 14 at delivery cost 56.0.\nIf staffed, kitchen F6 can serve school 15 at delivery cost 428.0.\nIf staffed, kitchen F7 can serve school 0 at delivery cost 172.0.\nIf staffed, kitchen F7 can serve school 1 at delivery cost 150.0.\nIf staffed, kitchen F7 can serve school 2 at delivery cost 885.0.\nIf staffed, kitchen F7 can serve school 3 at delivery cost 842.0.\nIf staffed, kitchen F7 can serve school 4 at delivery cost 601.0.\nIf staffed, kitchen F7 can serve school 5 at delivery cost 500.0.\nIf staffed, kitchen F7 can serve school 6 at delivery cost 79.0.\nIf staffed, kitchen F7 can serve school 7 at delivery cost 121.0.\nIf staffed, kitchen F7 can serve school 8 at delivery cost 1115.0.\nIf staffed, kitchen F7 can serve school 9 at delivery cost 30.0.\nIf staffed, kitchen F7 can serve school 10 at delivery cost 741.0.\nIf staffed, kitchen F7 can serve school 11 at delivery cost 317.0.\nIf staffed, kitchen F7 can serve school 12 at delivery cost 1034.0.\nIf staffed, kitchen F7 can serve school 13 at delivery cost 318.0.\nIf staffed, kitchen F7 can serve school 14 at delivery cost 88.0.\nIf staffed, kitchen F7 can serve school 15 at delivery cost 37.0.\nUse these figures to choose which kitchens to staff and assign every one of the 16 schools without exceeding any kitchen's capacity, minimizing total cost.\n\nAlso, when you hand me a plan, please use this little JSON layout so it's quick to check and compare plans — nothing fancy, just a predictable shape.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list the kitchens you plan to staff (one entry per kitchen). \"assignments\" is where you list, for each school in the order they appear in the instance, the single staffed kitchen that will serve it. Think of the JSON as a simple form: the first array says which kitchens are open, the second array says who serves which school. It's just a sketch of the expected shape — not the final plan.\n\nPlease be sure to use the exact identifiers from the instance input when you fill this in — do not rename them or invent new labels. Valid identifiers look like plain numbers such as \"1\" or \"23\", single capital letters like \"A\" or \"B\", or a capital letter followed by digits like \"A1\" or \"X7\".", "instance": { "opening_costs": [ 243.0, 468.0, 201.0, 573.0, 209.0, 405.0, 462.0 ], "capacities": [ 376.0, 425.0, 378.0, 434.0, 259.0, 490.0, 403.0 ], "connection_costs": [ [ 76.0, 59.0, 334.0, 506.0, 590.0, 315.0, 35.0, 63.0, 524.0, 46.0, 474.0, 43.0, 447.0, 403.0, 136.0, 58.0 ], [ 618.0, 1022.0, 2126.0, 1562.0, 2010.0, 910.0, 1311.0, 1563.0, 2617.0, 214.0, 1280.0, 1583.0, 2293.0, 1333.0, 612.0, 1354.0 ], [ 60.0, 54.0, 147.0, 388.0, 518.0, 264.0, 41.0, 69.0, 128.0, 50.0, 385.0, 33.0, 189.0, 391.0, 143.0, 64.0 ], [ 60.0, 250.0, 619.0, 56.0, 1302.0, 61.0, 458.0, 625.0, 1278.0, 153.0, 62.0, 468.0, 732.0, 906.0, 382.0, 543.0 ], [ 197.0, 209.0, 1197.0, 986.0, 952.0, 558.0, 249.0, 467.0, 1542.0, 32.0, 839.0, 589.0, 1359.0, 471.0, 105.0, 244.0 ], [ 341.0, 410.0, 1407.0, 1199.0, 889.0, 727.0, 464.0, 642.0, 1689.0, 27.0, 1033.0, 801.0, 1566.0, 301.0, 56.0, 428.0 ], [ 172.0, 150.0, 885.0, 842.0, 601.0, 500.0, 79.0, 121.0, 1115.0, 30.0, 741.0, 317.0, 1034.0, 318.0, 88.0, 37.0 ] ], "demands": [ 12.0, 26.0, 25.0, 28.0, 17.0, 29.0, 14.0, 19.0, 19.0, 13.0, 23.0, 16.0, 27.0, 20.0, 27.0, 13.0 ], "objective": 2840.0 }, "solution": { "open_facilities": [ 2, 3 ], "assignments": [ 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2 ] }, "obj": 2840.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 16, "facilities": [ { "id": "F1", "opening_cost": 243.0, "capacity": 376.0 }, { "id": "F2", "opening_cost": 468.0, "capacity": 425.0 }, { "id": "F3", "opening_cost": 201.0, "capacity": 378.0 }, { "id": "F4", "opening_cost": 573.0, "capacity": 434.0 }, { "id": "F5", "opening_cost": 209.0, "capacity": 259.0 }, { "id": "F6", "opening_cost": 405.0, "capacity": 490.0 }, { "id": "F7", "opening_cost": 462.0, "capacity": 403.0 } ], "customers": [ { "id": 0, "demand": 12.0 }, { "id": 1, "demand": 26.0 }, { "id": 2, "demand": 25.0 }, { "id": 3, "demand": 28.0 }, { "id": 4, "demand": 17.0 }, { "id": 5, "demand": 29.0 }, { "id": 6, "demand": 14.0 }, { "id": 7, "demand": 19.0 }, { "id": 8, "demand": 19.0 }, { "id": 9, "demand": 13.0 }, { "id": 10, "demand": 23.0 }, { "id": 11, "demand": 16.0 }, { "id": 12, "demand": 27.0 }, { "id": 13, "demand": 20.0 }, { "id": 14, "demand": 27.0 }, { "id": 15, "demand": 13.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 76.0 }, { "facility": "F1", "customer": 1, "cost": 59.0 }, { "facility": "F1", "customer": 2, "cost": 334.0 }, { "facility": "F1", "customer": 3, "cost": 506.0 }, { "facility": "F1", "customer": 4, "cost": 590.0 }, { "facility": "F1", "customer": 5, "cost": 315.0 }, { "facility": "F1", "customer": 6, "cost": 35.0 }, { "facility": "F1", "customer": 7, "cost": 63.0 }, { "facility": "F1", "customer": 8, "cost": 524.0 }, { "facility": "F1", "customer": 9, "cost": 46.0 }, { "facility": "F1", "customer": 10, "cost": 474.0 }, { "facility": "F1", "customer": 11, "cost": 43.0 }, { "facility": "F1", "customer": 12, "cost": 447.0 }, { "facility": "F1", "customer": 13, "cost": 403.0 }, { "facility": "F1", "customer": 14, "cost": 136.0 }, { "facility": "F1", "customer": 15, "cost": 58.0 }, { "facility": "F2", "customer": 0, "cost": 618.0 }, { "facility": "F2", "customer": 1, "cost": 1022.0 }, { "facility": "F2", "customer": 2, "cost": 2126.0 }, { "facility": "F2", "customer": 3, "cost": 1562.0 }, { "facility": "F2", "customer": 4, "cost": 2010.0 }, { "facility": "F2", "customer": 5, "cost": 910.0 }, { "facility": "F2", "customer": 6, "cost": 1311.0 }, { "facility": "F2", "customer": 7, "cost": 1563.0 }, { "facility": "F2", "customer": 8, "cost": 2617.0 }, { "facility": "F2", "customer": 9, "cost": 214.0 }, { "facility": "F2", "customer": 10, "cost": 1280.0 }, { "facility": "F2", "customer": 11, "cost": 1583.0 }, { "facility": "F2", "customer": 12, "cost": 2293.0 }, { "facility": "F2", "customer": 13, "cost": 1333.0 }, { "facility": "F2", "customer": 14, "cost": 612.0 }, { "facility": "F2", "customer": 15, "cost": 1354.0 }, { "facility": "F3", "customer": 0, "cost": 60.0 }, { "facility": "F3", "customer": 1, "cost": 54.0 }, { "facility": "F3", "customer": 2, "cost": 147.0 }, { "facility": "F3", "customer": 3, "cost": 388.0 }, { "facility": "F3", "customer": 4, "cost": 518.0 }, { "facility": "F3", "customer": 5, "cost": 264.0 }, { "facility": "F3", "customer": 6, "cost": 41.0 }, { "facility": "F3", "customer": 7, "cost": 69.0 }, { "facility": "F3", "customer": 8, "cost": 128.0 }, { "facility": "F3", "customer": 9, "cost": 50.0 }, { "facility": "F3", "customer": 10, "cost": 385.0 }, { "facility": "F3", "customer": 11, "cost": 33.0 }, { "facility": "F3", "customer": 12, "cost": 189.0 }, { "facility": "F3", "customer": 13, "cost": 391.0 }, { "facility": "F3", "customer": 14, "cost": 143.0 }, { "facility": "F3", "customer": 15, "cost": 64.0 }, { "facility": "F4", "customer": 0, "cost": 60.0 }, { "facility": "F4", "customer": 1, "cost": 250.0 }, { "facility": "F4", "customer": 2, "cost": 619.0 }, { "facility": "F4", "customer": 3, "cost": 56.0 }, { "facility": "F4", "customer": 4, "cost": 1302.0 }, { "facility": "F4", "customer": 5, "cost": 61.0 }, { "facility": "F4", "customer": 6, "cost": 458.0 }, { "facility": "F4", "customer": 7, "cost": 625.0 }, { "facility": "F4", "customer": 8, "cost": 1278.0 }, { "facility": "F4", "customer": 9, "cost": 153.0 }, { "facility": "F4", "customer": 10, "cost": 62.0 }, { "facility": "F4", "customer": 11, "cost": 468.0 }, { "facility": "F4", "customer": 12, "cost": 732.0 }, { "facility": "F4", "customer": 13, "cost": 906.0 }, { "facility": "F4", "customer": 14, "cost": 382.0 }, { "facility": "F4", "customer": 15, "cost": 543.0 }, { "facility": "F5", "customer": 0, "cost": 197.0 }, { "facility": "F5", "customer": 1, "cost": 209.0 }, { "facility": "F5", "customer": 2, "cost": 1197.0 }, { "facility": "F5", "customer": 3, "cost": 986.0 }, { "facility": "F5", "customer": 4, "cost": 952.0 }, { "facility": "F5", "customer": 5, "cost": 558.0 }, { "facility": "F5", "customer": 6, "cost": 249.0 }, { "facility": "F5", "customer": 7, "cost": 467.0 }, { "facility": "F5", "customer": 8, "cost": 1542.0 }, { "facility": "F5", "customer": 9, "cost": 32.0 }, { "facility": "F5", "customer": 10, "cost": 839.0 }, { "facility": "F5", "customer": 11, "cost": 589.0 }, { "facility": "F5", "customer": 12, "cost": 1359.0 }, { "facility": "F5", "customer": 13, "cost": 471.0 }, { "facility": "F5", "customer": 14, "cost": 105.0 }, { "facility": "F5", "customer": 15, "cost": 244.0 }, { "facility": "F6", "customer": 0, "cost": 341.0 }, { "facility": "F6", "customer": 1, "cost": 410.0 }, { "facility": "F6", "customer": 2, "cost": 1407.0 }, { "facility": "F6", "customer": 3, "cost": 1199.0 }, { "facility": "F6", "customer": 4, "cost": 889.0 }, { "facility": "F6", "customer": 5, "cost": 727.0 }, { "facility": "F6", "customer": 6, "cost": 464.0 }, { "facility": "F6", "customer": 7, "cost": 642.0 }, { "facility": "F6", "customer": 8, "cost": 1689.0 }, { "facility": "F6", "customer": 9, "cost": 27.0 }, { "facility": "F6", "customer": 10, "cost": 1033.0 }, { "facility": "F6", "customer": 11, "cost": 801.0 }, { "facility": "F6", "customer": 12, "cost": 1566.0 }, { "facility": "F6", "customer": 13, "cost": 301.0 }, { "facility": "F6", "customer": 14, "cost": 56.0 }, { "facility": "F6", "customer": 15, "cost": 428.0 }, { "facility": "F7", "customer": 0, "cost": 172.0 }, { "facility": "F7", "customer": 1, "cost": 150.0 }, { "facility": "F7", "customer": 2, "cost": 885.0 }, { "facility": "F7", "customer": 3, "cost": 842.0 }, { "facility": "F7", "customer": 4, "cost": 601.0 }, { "facility": "F7", "customer": 5, "cost": 500.0 }, { "facility": "F7", "customer": 6, "cost": 79.0 }, { "facility": "F7", "customer": 7, "cost": 121.0 }, { "facility": "F7", "customer": 8, "cost": 1115.0 }, { "facility": "F7", "customer": 9, "cost": 30.0 }, { "facility": "F7", "customer": 10, "cost": 741.0 }, { "facility": "F7", "customer": 11, "cost": 317.0 }, { "facility": "F7", "customer": 12, "cost": 1034.0 }, { "facility": "F7", "customer": 13, "cost": 318.0 }, { "facility": "F7", "customer": 14, "cost": 88.0 }, { "facility": "F7", "customer": 15, "cost": 37.0 } ], "objective": 2840.0 }, "solution_variant": { "selected": [ "F3", "F4" ], "assignments": [ "F3", "F3", "F3", "F4", "F3", "F4", "F3", "F3", "F3", "F3", "F4", "F3", "F3", "F3", "F3", "F3" ] }, "context_index": 3, "input_format": "nl", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Imagine running the hospital network for a region and having to pick a handful of outpatient clinics to operate while assigning every neighborhood’s patients to one of them. Every clinic you flip on carries a fixed opening cost, each neighborhood has a travel price to each clinic, and every clinic can only accept so many patients. What makes one choice better than another is the total price tag — add the opening costs of all chosen clinics to the travel costs for all neighborhoods to calculate it, and the aim is to keep that total as small as possible. No neighborhood can be left unassigned or split between clinics, and no clinic may exceed its capacity. The full list of clinics, capacities and travel costs appears below.\n\nThere are 8 clinics and 18 neighborhoods in this instance.\n\n**Clinics**\n| clinic_id | clinic_opening_cost | clinic_capacity |\n|---|---|---|\n| F1 | 300.0 | 500.0 |\n| F2 | 300.0 | 500.0 |\n| F3 | 300.0 | 500.0 |\n| F4 | 300.0 | 500.0 |\n| F5 | 300.0 | 500.0 |\n| F6 | 300.0 | 500.0 |\n| F7 | 300.0 | 500.0 |\n| F8 | 300.0 | 500.0 |\n\n**Neighborhoods**\n| neighborhood_id | neighborhood_patient_count |\n|---|---|\n| 0 | 14.0 |\n| 1 | 13.0 |\n| 2 | 20.0 |\n| 3 | 24.0 |\n| 4 | 19.0 |\n| 5 | 11.0 |\n| 6 | 25.0 |\n| 7 | 12.0 |\n| 8 | 19.0 |\n| 9 | 13.0 |\n| 10 | 26.0 |\n| 11 | 17.0 |\n| 12 | 24.0 |\n| 13 | 10.0 |\n| 14 | 16.0 |\n| 15 | 18.0 |\n| 16 | 27.0 |\n| 17 | 23.0 |\n\n**Assignment Travel Cost**\n| clinic_id | neighborhood_id | assignment_travel_cost |\n|---|---|---|\n| F1 | 0 | 349.0 |\n| F1 | 1 | 279.0 |\n| F1 | 2 | 165.0 |\n| F1 | 3 | 122.0 |\n| F1 | 4 | 197.0 |\n| F1 | 5 | 22.0 |\n| F1 | 6 | 312.0 |\n| F1 | 7 | 43.0 |\n| F1 | 8 | 39.0 |\n| F1 | 9 | 42.0 |\n| F1 | 10 | 283.0 |\n| F1 | 11 | 101.0 |\n| F1 | 12 | 49.0 |\n| F1 | 13 | 65.0 |\n| F1 | 14 | 316.0 |\n| F1 | 15 | 36.0 |\n| F1 | 16 | 60.0 |\n| F1 | 17 | 114.0 |\n| F2 | 0 | 89.0 |\n| F2 | 1 | 1000.0 |\n| F2 | 2 | 728.0 |\n| F2 | 3 | 366.0 |\n| F2 | 4 | 386.0 |\n| F2 | 5 | 923.0 |\n| F2 | 6 | 522.0 |\n| F2 | 7 | 253.0 |\n| F2 | 8 | 1216.0 |\n| F2 | 9 | 125.0 |\n| F2 | 10 | 53.0 |\n| F2 | 11 | 316.0 |\n| F2 | 12 | 349.0 |\n| F2 | 13 | 48.0 |\n| F2 | 14 | 1076.0 |\n| F2 | 15 | 417.0 |\n| F2 | 16 | 151.0 |\n| F2 | 17 | 611.0 |\n| F3 | 0 | 1030.0 |\n| F3 | 1 | 1569.0 |\n| F3 | 2 | 1257.0 |\n| F3 | 3 | 436.0 |\n| F3 | 4 | 1790.0 |\n| F3 | 5 | 2059.0 |\n| F3 | 6 | 2026.0 |\n| F3 | 7 | 478.0 |\n| F3 | 8 | 2409.0 |\n| F3 | 9 | 39.0 |\n| F3 | 10 | 1236.0 |\n| F3 | 11 | 337.0 |\n| F3 | 12 | 1179.0 |\n| F3 | 13 | 651.0 |\n| F3 | 14 | 1664.0 |\n| F3 | 15 | 1247.0 |\n| F3 | 16 | 54.0 |\n| F3 | 17 | 1176.0 |\n| F4 | 0 | 171.0 |\n| F4 | 1 | 712.0 |\n| F4 | 2 | 484.0 |\n| F4 | 3 | 258.0 |\n| F4 | 4 | 50.0 |\n| F4 | 5 | 506.0 |\n| F4 | 6 | 50.0 |\n| F4 | 7 | 147.0 |\n| F4 | 8 | 765.0 |\n| F4 | 9 | 86.0 |\n| F4 | 10 | 107.0 |\n| F4 | 11 | 221.0 |\n| F4 | 12 | 153.0 |\n| F4 | 13 | 20.0 |\n| F4 | 14 | 776.0 |\n| F4 | 15 | 191.0 |\n| F4 | 16 | 104.0 |\n| F4 | 17 | 382.0 |\n| F5 | 0 | 226.0 |\n| F5 | 1 | 1355.0 |\n| F5 | 2 | 1039.0 |\n| F5 | 3 | 473.0 |\n| F5 | 4 | 1105.0 |\n| F5 | 5 | 1541.0 |\n| F5 | 6 | 1314.0 |\n| F5 | 7 | 380.0 |\n| F5 | 8 | 1880.0 |\n| F5 | 9 | 151.0 |\n| F5 | 10 | 422.0 |\n| F5 | 11 | 406.0 |\n| F5 | 12 | 718.0 |\n| F5 | 13 | 133.0 |\n| F5 | 14 | 1443.0 |\n| F5 | 15 | 808.0 |\n| F5 | 16 | 190.0 |\n| F5 | 17 | 921.0 |\n| F6 | 0 | 300.0 |\n| F6 | 1 | 353.0 |\n| F6 | 2 | 217.0 |\n| F6 | 3 | 146.0 |\n| F6 | 4 | 132.0 |\n| F6 | 5 | 51.0 |\n| F6 | 6 | 227.0 |\n| F6 | 7 | 57.0 |\n| F6 | 8 | 128.0 |\n| F6 | 9 | 50.0 |\n| F6 | 10 | 232.0 |\n| F6 | 11 | 122.0 |\n| F6 | 12 | 50.0 |\n| F6 | 13 | 46.0 |\n| F6 | 14 | 394.0 |\n| F6 | 15 | 45.0 |\n| F6 | 16 | 66.0 |\n| F6 | 17 | 154.0 |\n| F7 | 0 | 312.0 |\n| F7 | 1 | 697.0 |\n| F7 | 2 | 443.0 |\n| F7 | 3 | 210.0 |\n| F7 | 4 | 354.0 |\n| F7 | 5 | 681.0 |\n| F7 | 6 | 594.0 |\n| F7 | 7 | 102.0 |\n| F7 | 8 | 1017.0 |\n| F7 | 9 | 65.0 |\n| F7 | 10 | 257.0 |\n| F7 | 11 | 176.0 |\n| F7 | 12 | 97.0 |\n| F7 | 13 | 33.0 |\n| F7 | 14 | 770.0 |\n| F7 | 15 | 137.0 |\n| F7 | 16 | 80.0 |\n| F7 | 17 | 335.0 |\n| F8 | 0 | 658.0 |\n| F8 | 1 | 756.0 |\n| F8 | 2 | 436.0 |\n| F8 | 3 | 108.0 |\n| F8 | 4 | 1037.0 |\n| F8 | 5 | 1194.0 |\n| F8 | 6 | 1278.0 |\n| F8 | 7 | 27.0 |\n| F8 | 8 | 1542.0 |\n| F8 | 9 | 32.0 |\n| F8 | 10 | 706.0 |\n| F8 | 11 | 84.0 |\n| F8 | 12 | 365.0 |\n| F8 | 13 | 211.0 |\n| F8 | 14 | 848.0 |\n| F8 | 15 | 400.0 |\n| F8 | 16 | 54.0 |\n| F8 | 17 | 323.0 |\n\nAlso, when you send back the actual choices, please use this little JSON layout so it's easy to read and automatic tools can pick it up:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of clinics you decide to flip on, and \"assignments\" as, for each neighborhood in the same order they were given, the clinic you routed that neighborhood's patients to. Super casual: it's just a form—one list of open clinics and one list saying who goes where.\n\nThis is just a sketch of the expected shape, not the actual answer. Please make sure all identifiers you put in there match the instance input exactly — no renaming, no invented labels.\n\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 349.0, 279.0, 165.0, 122.0, 197.0, 22.0, 312.0, 43.0, 39.0, 42.0, 283.0, 101.0, 49.0, 65.0, 316.0, 36.0, 60.0, 114.0 ], [ 89.0, 1000.0, 728.0, 366.0, 386.0, 923.0, 522.0, 253.0, 1216.0, 125.0, 53.0, 316.0, 349.0, 48.0, 1076.0, 417.0, 151.0, 611.0 ], [ 1030.0, 1569.0, 1257.0, 436.0, 1790.0, 2059.0, 2026.0, 478.0, 2409.0, 39.0, 1236.0, 337.0, 1179.0, 651.0, 1664.0, 1247.0, 54.0, 1176.0 ], [ 171.0, 712.0, 484.0, 258.0, 50.0, 506.0, 50.0, 147.0, 765.0, 86.0, 107.0, 221.0, 153.0, 20.0, 776.0, 191.0, 104.0, 382.0 ], [ 226.0, 1355.0, 1039.0, 473.0, 1105.0, 1541.0, 1314.0, 380.0, 1880.0, 151.0, 422.0, 406.0, 718.0, 133.0, 1443.0, 808.0, 190.0, 921.0 ], [ 300.0, 353.0, 217.0, 146.0, 132.0, 51.0, 227.0, 57.0, 128.0, 50.0, 232.0, 122.0, 50.0, 46.0, 394.0, 45.0, 66.0, 154.0 ], [ 312.0, 697.0, 443.0, 210.0, 354.0, 681.0, 594.0, 102.0, 1017.0, 65.0, 257.0, 176.0, 97.0, 33.0, 770.0, 137.0, 80.0, 335.0 ], [ 658.0, 756.0, 436.0, 108.0, 1037.0, 1194.0, 1278.0, 27.0, 1542.0, 32.0, 706.0, 84.0, 365.0, 211.0, 848.0, 400.0, 54.0, 323.0 ] ], "demands": [ 14.0, 13.0, 20.0, 24.0, 19.0, 11.0, 25.0, 12.0, 19.0, 13.0, 26.0, 17.0, 24.0, 10.0, 16.0, 18.0, 27.0, 23.0 ], "objective": 2386.0 }, "solution": { "open_facilities": [ 0, 3 ], "assignments": [ 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0 ] }, "obj": 2386.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 18, "facilities": [ { "id": "F1", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F2", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F3", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F4", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F5", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F6", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F7", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F8", "opening_cost": 300.0, "capacity": 500.0 } ], "customers": [ { "id": 0, "demand": 14.0 }, { "id": 1, "demand": 13.0 }, { "id": 2, "demand": 20.0 }, { "id": 3, "demand": 24.0 }, { "id": 4, "demand": 19.0 }, { "id": 5, "demand": 11.0 }, { "id": 6, "demand": 25.0 }, { "id": 7, "demand": 12.0 }, { "id": 8, "demand": 19.0 }, { "id": 9, "demand": 13.0 }, { "id": 10, "demand": 26.0 }, { "id": 11, "demand": 17.0 }, { "id": 12, "demand": 24.0 }, { "id": 13, "demand": 10.0 }, { "id": 14, "demand": 16.0 }, { "id": 15, "demand": 18.0 }, { "id": 16, "demand": 27.0 }, { "id": 17, "demand": 23.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 349.0 }, { "facility": "F1", "customer": 1, "cost": 279.0 }, { "facility": "F1", "customer": 2, "cost": 165.0 }, { "facility": "F1", "customer": 3, "cost": 122.0 }, { "facility": "F1", "customer": 4, "cost": 197.0 }, { "facility": "F1", "customer": 5, "cost": 22.0 }, { "facility": "F1", "customer": 6, "cost": 312.0 }, { "facility": "F1", "customer": 7, "cost": 43.0 }, { "facility": "F1", "customer": 8, "cost": 39.0 }, { "facility": "F1", "customer": 9, "cost": 42.0 }, { "facility": "F1", "customer": 10, "cost": 283.0 }, { "facility": "F1", "customer": 11, "cost": 101.0 }, { "facility": "F1", "customer": 12, "cost": 49.0 }, { "facility": "F1", "customer": 13, "cost": 65.0 }, { "facility": "F1", "customer": 14, "cost": 316.0 }, { "facility": "F1", "customer": 15, "cost": 36.0 }, { "facility": "F1", "customer": 16, "cost": 60.0 }, { "facility": "F1", "customer": 17, "cost": 114.0 }, { "facility": "F2", "customer": 0, "cost": 89.0 }, { "facility": "F2", "customer": 1, "cost": 1000.0 }, { "facility": "F2", "customer": 2, "cost": 728.0 }, { "facility": "F2", "customer": 3, "cost": 366.0 }, { "facility": "F2", "customer": 4, "cost": 386.0 }, { "facility": "F2", "customer": 5, "cost": 923.0 }, { "facility": "F2", "customer": 6, "cost": 522.0 }, { "facility": "F2", "customer": 7, "cost": 253.0 }, { "facility": "F2", "customer": 8, "cost": 1216.0 }, { "facility": "F2", "customer": 9, "cost": 125.0 }, { "facility": "F2", "customer": 10, "cost": 53.0 }, { "facility": "F2", "customer": 11, "cost": 316.0 }, { "facility": "F2", "customer": 12, "cost": 349.0 }, { "facility": "F2", "customer": 13, "cost": 48.0 }, { "facility": "F2", "customer": 14, "cost": 1076.0 }, { "facility": "F2", "customer": 15, "cost": 417.0 }, { "facility": "F2", "customer": 16, "cost": 151.0 }, { "facility": "F2", "customer": 17, "cost": 611.0 }, { "facility": "F3", "customer": 0, "cost": 1030.0 }, { "facility": "F3", "customer": 1, "cost": 1569.0 }, { "facility": "F3", "customer": 2, "cost": 1257.0 }, { "facility": "F3", "customer": 3, "cost": 436.0 }, { "facility": "F3", "customer": 4, "cost": 1790.0 }, { "facility": "F3", "customer": 5, "cost": 2059.0 }, { "facility": "F3", "customer": 6, "cost": 2026.0 }, { "facility": "F3", "customer": 7, "cost": 478.0 }, { "facility": "F3", "customer": 8, "cost": 2409.0 }, { "facility": "F3", "customer": 9, "cost": 39.0 }, { "facility": "F3", "customer": 10, "cost": 1236.0 }, { "facility": "F3", "customer": 11, "cost": 337.0 }, { "facility": "F3", "customer": 12, "cost": 1179.0 }, { "facility": "F3", "customer": 13, "cost": 651.0 }, { "facility": "F3", "customer": 14, "cost": 1664.0 }, { "facility": "F3", "customer": 15, "cost": 1247.0 }, { "facility": "F3", "customer": 16, "cost": 54.0 }, { "facility": "F3", "customer": 17, "cost": 1176.0 }, { "facility": "F4", "customer": 0, "cost": 171.0 }, { "facility": "F4", "customer": 1, "cost": 712.0 }, { "facility": "F4", "customer": 2, "cost": 484.0 }, { "facility": "F4", "customer": 3, "cost": 258.0 }, { "facility": "F4", "customer": 4, "cost": 50.0 }, { "facility": "F4", "customer": 5, "cost": 506.0 }, { "facility": "F4", "customer": 6, "cost": 50.0 }, { "facility": "F4", "customer": 7, "cost": 147.0 }, { "facility": "F4", "customer": 8, "cost": 765.0 }, { "facility": "F4", "customer": 9, "cost": 86.0 }, { "facility": "F4", "customer": 10, "cost": 107.0 }, { "facility": "F4", "customer": 11, "cost": 221.0 }, { "facility": "F4", "customer": 12, "cost": 153.0 }, { "facility": "F4", "customer": 13, "cost": 20.0 }, { "facility": "F4", "customer": 14, "cost": 776.0 }, { "facility": "F4", "customer": 15, "cost": 191.0 }, { "facility": "F4", "customer": 16, "cost": 104.0 }, { "facility": "F4", "customer": 17, "cost": 382.0 }, { "facility": "F5", "customer": 0, "cost": 226.0 }, { "facility": "F5", "customer": 1, "cost": 1355.0 }, { "facility": "F5", "customer": 2, "cost": 1039.0 }, { "facility": "F5", "customer": 3, "cost": 473.0 }, { "facility": "F5", "customer": 4, "cost": 1105.0 }, { "facility": "F5", "customer": 5, "cost": 1541.0 }, { "facility": "F5", "customer": 6, "cost": 1314.0 }, { "facility": "F5", "customer": 7, "cost": 380.0 }, { "facility": "F5", "customer": 8, "cost": 1880.0 }, { "facility": "F5", "customer": 9, "cost": 151.0 }, { "facility": "F5", "customer": 10, "cost": 422.0 }, { "facility": "F5", "customer": 11, "cost": 406.0 }, { "facility": "F5", "customer": 12, "cost": 718.0 }, { "facility": "F5", "customer": 13, "cost": 133.0 }, { "facility": "F5", "customer": 14, "cost": 1443.0 }, { "facility": "F5", "customer": 15, "cost": 808.0 }, { "facility": "F5", "customer": 16, "cost": 190.0 }, { "facility": "F5", "customer": 17, "cost": 921.0 }, { "facility": "F6", "customer": 0, "cost": 300.0 }, { "facility": "F6", "customer": 1, "cost": 353.0 }, { "facility": "F6", "customer": 2, "cost": 217.0 }, { "facility": "F6", "customer": 3, "cost": 146.0 }, { "facility": "F6", "customer": 4, "cost": 132.0 }, { "facility": "F6", "customer": 5, "cost": 51.0 }, { "facility": "F6", "customer": 6, "cost": 227.0 }, { "facility": "F6", "customer": 7, "cost": 57.0 }, { "facility": "F6", "customer": 8, "cost": 128.0 }, { "facility": "F6", "customer": 9, "cost": 50.0 }, { "facility": "F6", "customer": 10, "cost": 232.0 }, { "facility": "F6", "customer": 11, "cost": 122.0 }, { "facility": "F6", "customer": 12, "cost": 50.0 }, { "facility": "F6", "customer": 13, "cost": 46.0 }, { "facility": "F6", "customer": 14, "cost": 394.0 }, { "facility": "F6", "customer": 15, "cost": 45.0 }, { "facility": "F6", "customer": 16, "cost": 66.0 }, { "facility": "F6", "customer": 17, "cost": 154.0 }, { "facility": "F7", "customer": 0, "cost": 312.0 }, { "facility": "F7", "customer": 1, "cost": 697.0 }, { "facility": "F7", "customer": 2, "cost": 443.0 }, { "facility": "F7", "customer": 3, "cost": 210.0 }, { "facility": "F7", "customer": 4, "cost": 354.0 }, { "facility": "F7", "customer": 5, "cost": 681.0 }, { "facility": "F7", "customer": 6, "cost": 594.0 }, { "facility": "F7", "customer": 7, "cost": 102.0 }, { "facility": "F7", "customer": 8, "cost": 1017.0 }, { "facility": "F7", "customer": 9, "cost": 65.0 }, { "facility": "F7", "customer": 10, "cost": 257.0 }, { "facility": "F7", "customer": 11, "cost": 176.0 }, { "facility": "F7", "customer": 12, "cost": 97.0 }, { "facility": "F7", "customer": 13, "cost": 33.0 }, { "facility": "F7", "customer": 14, "cost": 770.0 }, { "facility": "F7", "customer": 15, "cost": 137.0 }, { "facility": "F7", "customer": 16, "cost": 80.0 }, { "facility": "F7", "customer": 17, "cost": 335.0 }, { "facility": "F8", "customer": 0, "cost": 658.0 }, { "facility": "F8", "customer": 1, "cost": 756.0 }, { "facility": "F8", "customer": 2, "cost": 436.0 }, { "facility": "F8", "customer": 3, "cost": 108.0 }, { "facility": "F8", "customer": 4, "cost": 1037.0 }, { "facility": "F8", "customer": 5, "cost": 1194.0 }, { "facility": "F8", "customer": 6, "cost": 1278.0 }, { "facility": "F8", "customer": 7, "cost": 27.0 }, { "facility": "F8", "customer": 8, "cost": 1542.0 }, { "facility": "F8", "customer": 9, "cost": 32.0 }, { "facility": "F8", "customer": 10, "cost": 706.0 }, { "facility": "F8", "customer": 11, "cost": 84.0 }, { "facility": "F8", "customer": 12, "cost": 365.0 }, { "facility": "F8", "customer": 13, "cost": 211.0 }, { "facility": "F8", "customer": 14, "cost": 848.0 }, { "facility": "F8", "customer": 15, "cost": 400.0 }, { "facility": "F8", "customer": 16, "cost": 54.0 }, { "facility": "F8", "customer": 17, "cost": 323.0 } ], "objective": 2386.0 }, "solution_variant": { "selected": [ "F1", "F4" ], "assignments": [ "F4", "F1", "F1", "F1", "F4", "F1", "F4", "F1", "F1", "F1", "F4", "F1", "F1", "F4", "F1", "F1", "F1", "F1" ] }, "context_index": 4, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "I’m running the food area for a neighborhood festival and need to decide which food stalls to actually set up and which vendor crowds to point to each stall. Each stall costs money to put up and can only serve so many people, and every time a vendor’s customer area is assigned to a stall there’s a serving cost based on distance or effort. The plan has to send each vendor’s customer area to exactly one of the stalls that get set up, make sure no stall serves more people than it can handle, and keep the total bill — the sum of all stall setup costs plus all those serving/distance costs — as low as possible. The specific stall options, costs, capacities, and vendor customer areas are listed below.\n\nI have 7 candidate stalls and 17 vendor areas to consider.\nFor stall F1 I would pay 600.0 to set it up and it can serve up to 700.0 people.\nFor stall F2 I would pay 600.0 to set it up and it can serve up to 700.0 people.\nFor stall F3 I would pay 600.0 to set it up and it can serve up to 700.0 people.\nFor stall F4 I would pay 600.0 to set it up and it can serve up to 700.0 people.\nFor stall F5 I would pay 600.0 to set it up and it can serve up to 700.0 people.\nFor stall F6 I would pay 600.0 to set it up and it can serve up to 700.0 people.\nFor stall F7 I would pay 600.0 to set it up and it can serve up to 700.0 people.\nVendor area 1 has 26.0 people that I need to assign to one open stall.\nVendor area 2 has 23.0 people that I need to assign to one open stall.\nVendor area 3 has 20.0 people that I need to assign to one open stall.\nVendor area 4 has 12.0 people that I need to assign to one open stall.\nVendor area 5 has 20.0 people that I need to assign to one open stall.\nVendor area 6 has 30.0 people that I need to assign to one open stall.\nVendor area 7 has 20.0 people that I need to assign to one open stall.\nVendor area 8 has 19.0 people that I need to assign to one open stall.\nVendor area 9 has 19.0 people that I need to assign to one open stall.\nVendor area 10 has 20.0 people that I need to assign to one open stall.\nVendor area 11 has 16.0 people that I need to assign to one open stall.\nVendor area 12 has 19.0 people that I need to assign to one open stall.\nVendor area 13 has 11.0 people that I need to assign to one open stall.\nVendor area 14 has 17.0 people that I need to assign to one open stall.\nVendor area 15 has 19.0 people that I need to assign to one open stall.\nVendor area 16 has 11.0 people that I need to assign to one open stall.\nVendor area 17 has 13.0 people that I need to assign to one open stall.\nIf I assign vendor area 1 to stall F1 it costs 62.0 to serve them.\nIf I assign vendor area 2 to stall F1 it costs 104.0 to serve them.\nIf I assign vendor area 3 to stall F1 it costs 87.0 to serve them.\nIf I assign vendor area 4 to stall F1 it costs 24.0 to serve them.\nIf I assign vendor area 5 to stall F1 it costs 165.0 to serve them.\nIf I assign vendor area 6 to stall F1 it costs 168.0 to serve them.\nIf I assign vendor area 7 to stall F1 it costs 281.0 to serve them.\nIf I assign vendor area 8 to stall F1 it costs 248.0 to serve them.\nIf I assign vendor area 9 to stall F1 it costs 39.0 to serve them.\nIf I assign vendor area 10 to stall F1 it costs 77.0 to serve them.\nIf I assign vendor area 11 to stall F1 it costs 49.0 to serve them.\nIf I assign vendor area 12 to stall F1 it costs 142.0 to serve them.\nIf I assign vendor area 13 to stall F1 it costs 157.0 to serve them.\nIf I assign vendor area 14 to stall F1 it costs 332.0 to serve them.\nIf I assign vendor area 15 to stall F1 it costs 40.0 to serve them.\nIf I assign vendor area 16 to stall F1 it costs 24.0 to serve them.\nIf I assign vendor area 17 to stall F1 it costs 42.0 to serve them.\nIf I assign vendor area 1 to stall F2 it costs 1022.0 to serve them.\nIf I assign vendor area 2 to stall F2 it costs 2332.0 to serve them.\nIf I assign vendor area 3 to stall F2 it costs 1197.0 to serve them.\nIf I assign vendor area 4 to stall F2 it costs 1110.0 to serve them.\nIf I assign vendor area 5 to stall F2 it costs 1523.0 to serve them.\nIf I assign vendor area 6 to stall F2 it costs 317.0 to serve them.\nIf I assign vendor area 7 to stall F2 it costs 1279.0 to serve them.\nIf I assign vendor area 8 to stall F2 it costs 1904.0 to serve them.\nIf I assign vendor area 9 to stall F2 it costs 2617.0 to serve them.\nIf I assign vendor area 10 to stall F2 it costs 707.0 to serve them.\nIf I assign vendor area 11 to stall F2 it costs 1600.0 to serve them.\nIf I assign vendor area 12 to stall F2 it costs 683.0 to serve them.\nIf I assign vendor area 13 to stall F2 it costs 705.0 to serve them.\nIf I assign vendor area 14 to stall F2 it costs 1902.0 to serve them.\nIf I assign vendor area 15 to stall F2 it costs 1087.0 to serve them.\nIf I assign vendor area 16 to stall F2 it costs 2445.0 to serve them.\nIf I assign vendor area 17 to stall F2 it costs 1354.0 to serve them.\nIf I assign vendor area 1 to stall F3 it costs 518.0 to serve them.\nIf I assign vendor area 2 to stall F3 it costs 1568.0 to serve them.\nIf I assign vendor area 3 to stall F3 it costs 722.0 to serve them.\nIf I assign vendor area 4 to stall F3 it costs 466.0 to serve them.\nIf I assign vendor area 5 to stall F3 it costs 461.0 to serve them.\nIf I assign vendor area 6 to stall F3 it costs 405.0 to serve them.\nIf I assign vendor area 7 to stall F3 it costs 40.0 to serve them.\nIf I assign vendor area 8 to stall F3 it costs 796.0 to serve them.\nIf I assign vendor area 9 to stall F3 it costs 1740.0 to serve them.\nIf I assign vendor area 10 to stall F3 it costs 441.0 to serve them.\nIf I assign vendor area 11 to stall F3 it costs 926.0 to serve them.\nIf I assign vendor area 12 to stall F3 it costs 546.0 to serve them.\nIf I assign vendor area 13 to stall F3 it costs 587.0 to serve them.\nIf I assign vendor area 14 to stall F3 it costs 1439.0 to serve them.\nIf I assign vendor area 15 to stall F3 it costs 495.0 to serve them.\nIf I assign vendor area 16 to stall F3 it costs 1570.0 to serve them.\nIf I assign vendor area 17 to stall F3 it costs 524.0 to serve them.\nIf I assign vendor area 1 to stall F4 it costs 391.0 to serve them.\nIf I assign vendor area 2 to stall F4 it costs 1556.0 to serve them.\nIf I assign vendor area 3 to stall F4 it costs 447.0 to serve them.\nIf I assign vendor area 4 to stall F4 it costs 517.0 to serve them.\nIf I assign vendor area 5 to stall F4 it costs 1039.0 to serve them.\nIf I assign vendor area 6 to stall F4 it costs 68.0 to serve them.\nIf I assign vendor area 7 to stall F4 it costs 952.0 to serve them.\nIf I assign vendor area 8 to stall F4 it costs 1382.0 to serve them.\nIf I assign vendor area 9 to stall F4 it costs 1880.0 to serve them.\nIf I assign vendor area 10 to stall F4 it costs 132.0 to serve them.\nIf I assign vendor area 11 to stall F4 it costs 864.0 to serve them.\nIf I assign vendor area 12 to stall F4 it costs 44.0 to serve them.\nIf I assign vendor area 13 to stall F4 it costs 22.0 to serve them.\nIf I assign vendor area 14 to stall F4 it costs 1031.0 to serve them.\nIf I assign vendor area 15 to stall F4 it costs 477.0 to serve them.\nIf I assign vendor area 16 to stall F4 it costs 1717.0 to serve them.\nIf I assign vendor area 17 to stall F4 it costs 780.0 to serve them.\nIf I assign vendor area 1 to stall F5 it costs 54.0 to serve them.\nIf I assign vendor area 2 to stall F5 it costs 701.0 to serve them.\nIf I assign vendor area 3 to stall F5 it costs 48.0 to serve them.\nIf I assign vendor area 4 to stall F5 it costs 62.0 to serve them.\nIf I assign vendor area 5 to stall F5 it costs 443.0 to serve them.\nIf I assign vendor area 6 to stall F5 it costs 134.0 to serve them.\nIf I assign vendor area 7 to stall F5 it costs 507.0 to serve them.\nIf I assign vendor area 8 to stall F5 it costs 690.0 to serve them.\nIf I assign vendor area 9 to stall F5 it costs 1017.0 to serve them.\nIf I assign vendor area 10 to stall F5 it costs 49.0 to serve them.\nIf I assign vendor area 11 to stall F5 it costs 68.0 to serve them.\nIf I assign vendor area 12 to stall F5 it costs 100.0 to serve them.\nIf I assign vendor area 13 to stall F5 it costs 113.0 to serve them.\nIf I assign vendor area 14 to stall F5 it costs 459.0 to serve them.\nIf I assign vendor area 15 to stall F5 it costs 57.0 to serve them.\nIf I assign vendor area 16 to stall F5 it costs 854.0 to serve them.\nIf I assign vendor area 17 to stall F5 it costs 185.0 to serve them.\nIf I assign vendor area 1 to stall F6 it costs 275.0 to serve them.\nIf I assign vendor area 2 to stall F6 it costs 979.0 to serve them.\nIf I assign vendor area 3 to stall F6 it costs 421.0 to serve them.\nIf I assign vendor area 4 to stall F6 it costs 194.0 to serve them.\nIf I assign vendor area 5 to stall F6 it costs 57.0 to serve them.\nIf I assign vendor area 6 to stall F6 it costs 317.0 to serve them.\nIf I assign vendor area 7 to stall F6 it costs 77.0 to serve them.\nIf I assign vendor area 8 to stall F6 it costs 103.0 to serve them.\nIf I assign vendor area 9 to stall F6 it costs 1075.0 to serve them.\nIf I assign vendor area 10 to stall F6 it costs 272.0 to serve them.\nIf I assign vendor area 11 to stall F6 it costs 489.0 to serve them.\nIf I assign vendor area 12 to stall F6 it costs 380.0 to serve them.\nIf I assign vendor area 13 to stall F6 it costs 416.0 to serve them.\nIf I assign vendor area 14 to stall F6 it costs 1017.0 to serve them.\nIf I assign vendor area 15 to stall F6 it costs 231.0 to serve them.\nIf I assign vendor area 16 to stall F6 it costs 918.0 to serve them.\nIf I assign vendor area 17 to stall F6 it costs 162.0 to serve them.\nIf I assign vendor area 1 to stall F7 it costs 105.0 to serve them.\nIf I assign vendor area 2 to stall F7 it costs 763.0 to serve them.\nIf I assign vendor area 3 to stall F7 it costs 196.0 to serve them.\nIf I assign vendor area 4 to stall F7 it costs 39.0 to serve them.\nIf I assign vendor area 5 to stall F7 it costs 182.0 to serve them.\nIf I assign vendor area 6 to stall F7 it costs 213.0 to serve them.\nIf I assign vendor area 7 to stall F7 it costs 289.0 to serve them.\nIf I assign vendor area 8 to stall F7 it costs 388.0 to serve them.\nIf I assign vendor area 9 to stall F7 it costs 960.0 to serve them.\nIf I assign vendor area 10 to stall F7 it costs 128.0 to serve them.\nIf I assign vendor area 11 to stall F7 it costs 213.0 to serve them.\nIf I assign vendor area 12 to stall F7 it costs 220.0 to serve them.\nIf I assign vendor area 13 to stall F7 it costs 247.0 to serve them.\nIf I assign vendor area 14 to stall F7 it costs 736.0 to serve them.\nIf I assign vendor area 15 to stall F7 it costs 67.0 to serve them.\nIf I assign vendor area 16 to stall F7 it costs 787.0 to serve them.\nIf I assign vendor area 17 to stall F7 it costs 27.0 to serve them.\nI'll pick which stalls to open and assign every vendor area so the sum of stall setup costs and serving costs is as low as possible.\n\nOh, and one more thing — when you send the plan back, please put it in this little JSON sketch so I can read it programmatically. Just follow the layout below; it's just a simple form that says which stalls to open and which stall each vendor is sent to.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of stall locations you decide to set up, and \"assignments\" as, for each vendor/customer area in the order they were given, the stall you point them to. Super casual — it's just a template of the shape I need, not the final answer itself.\n\nPlease make sure to use the exact identifiers from the instance input — don’t rename them or invent new labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 62.0, 104.0, 87.0, 24.0, 165.0, 168.0, 281.0, 248.0, 39.0, 77.0, 49.0, 142.0, 157.0, 332.0, 40.0, 24.0, 42.0 ], [ 1022.0, 2332.0, 1197.0, 1110.0, 1523.0, 317.0, 1279.0, 1904.0, 2617.0, 707.0, 1600.0, 683.0, 705.0, 1902.0, 1087.0, 2445.0, 1354.0 ], [ 518.0, 1568.0, 722.0, 466.0, 461.0, 405.0, 40.0, 796.0, 1740.0, 441.0, 926.0, 546.0, 587.0, 1439.0, 495.0, 1570.0, 524.0 ], [ 391.0, 1556.0, 447.0, 517.0, 1039.0, 68.0, 952.0, 1382.0, 1880.0, 132.0, 864.0, 44.0, 22.0, 1031.0, 477.0, 1717.0, 780.0 ], [ 54.0, 701.0, 48.0, 62.0, 443.0, 134.0, 507.0, 690.0, 1017.0, 49.0, 68.0, 100.0, 113.0, 459.0, 57.0, 854.0, 185.0 ], [ 275.0, 979.0, 421.0, 194.0, 57.0, 317.0, 77.0, 103.0, 1075.0, 272.0, 489.0, 380.0, 416.0, 1017.0, 231.0, 918.0, 162.0 ], [ 105.0, 763.0, 196.0, 39.0, 182.0, 213.0, 289.0, 388.0, 960.0, 128.0, 213.0, 220.0, 247.0, 736.0, 67.0, 787.0, 27.0 ] ], "demands": [ 26.0, 23.0, 20.0, 12.0, 20.0, 30.0, 20.0, 19.0, 19.0, 20.0, 16.0, 19.0, 11.0, 17.0, 19.0, 11.0, 13.0 ], "objective": 2641.0 }, "solution": { "open_facilities": [ 0 ], "assignments": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] }, "obj": 2641.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 17, "facilities": [ { "id": "F1", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F2", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F3", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F4", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F5", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F6", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F7", "opening_cost": 600.0, "capacity": 700.0 } ], "customers": [ { "id": 1, "demand": 26.0 }, { "id": 2, "demand": 23.0 }, { "id": 3, "demand": 20.0 }, { "id": 4, "demand": 12.0 }, { "id": 5, "demand": 20.0 }, { "id": 6, "demand": 30.0 }, { "id": 7, "demand": 20.0 }, { "id": 8, "demand": 19.0 }, { "id": 9, "demand": 19.0 }, { "id": 10, "demand": 20.0 }, { "id": 11, "demand": 16.0 }, { "id": 12, "demand": 19.0 }, { "id": 13, "demand": 11.0 }, { "id": 14, "demand": 17.0 }, { "id": 15, "demand": 19.0 }, { "id": 16, "demand": 11.0 }, { "id": 17, "demand": 13.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 62.0 }, { "facility": "F1", "customer": 2, "cost": 104.0 }, { "facility": "F1", "customer": 3, "cost": 87.0 }, { "facility": "F1", "customer": 4, "cost": 24.0 }, { "facility": "F1", "customer": 5, "cost": 165.0 }, { "facility": "F1", "customer": 6, "cost": 168.0 }, { "facility": "F1", "customer": 7, "cost": 281.0 }, { "facility": "F1", "customer": 8, "cost": 248.0 }, { "facility": "F1", "customer": 9, "cost": 39.0 }, { "facility": "F1", "customer": 10, "cost": 77.0 }, { "facility": "F1", "customer": 11, "cost": 49.0 }, { "facility": "F1", "customer": 12, "cost": 142.0 }, { "facility": "F1", "customer": 13, "cost": 157.0 }, { "facility": "F1", "customer": 14, "cost": 332.0 }, { "facility": "F1", "customer": 15, "cost": 40.0 }, { "facility": "F1", "customer": 16, "cost": 24.0 }, { "facility": "F1", "customer": 17, "cost": 42.0 }, { "facility": "F2", "customer": 1, "cost": 1022.0 }, { "facility": "F2", "customer": 2, "cost": 2332.0 }, { "facility": "F2", "customer": 3, "cost": 1197.0 }, { "facility": "F2", "customer": 4, "cost": 1110.0 }, { "facility": "F2", "customer": 5, "cost": 1523.0 }, { "facility": "F2", "customer": 6, "cost": 317.0 }, { "facility": "F2", "customer": 7, "cost": 1279.0 }, { "facility": "F2", "customer": 8, "cost": 1904.0 }, { "facility": "F2", "customer": 9, "cost": 2617.0 }, { "facility": "F2", "customer": 10, "cost": 707.0 }, { "facility": "F2", "customer": 11, "cost": 1600.0 }, { "facility": "F2", "customer": 12, "cost": 683.0 }, { "facility": "F2", "customer": 13, "cost": 705.0 }, { "facility": "F2", "customer": 14, "cost": 1902.0 }, { "facility": "F2", "customer": 15, "cost": 1087.0 }, { "facility": "F2", "customer": 16, "cost": 2445.0 }, { "facility": "F2", "customer": 17, "cost": 1354.0 }, { "facility": "F3", "customer": 1, "cost": 518.0 }, { "facility": "F3", "customer": 2, "cost": 1568.0 }, { "facility": "F3", "customer": 3, "cost": 722.0 }, { "facility": "F3", "customer": 4, "cost": 466.0 }, { "facility": "F3", "customer": 5, "cost": 461.0 }, { "facility": "F3", "customer": 6, "cost": 405.0 }, { "facility": "F3", "customer": 7, "cost": 40.0 }, { "facility": "F3", "customer": 8, "cost": 796.0 }, { "facility": "F3", "customer": 9, "cost": 1740.0 }, { "facility": "F3", "customer": 10, "cost": 441.0 }, { "facility": "F3", "customer": 11, "cost": 926.0 }, { "facility": "F3", "customer": 12, "cost": 546.0 }, { "facility": "F3", "customer": 13, "cost": 587.0 }, { "facility": "F3", "customer": 14, "cost": 1439.0 }, { "facility": "F3", "customer": 15, "cost": 495.0 }, { "facility": "F3", "customer": 16, "cost": 1570.0 }, { "facility": "F3", "customer": 17, "cost": 524.0 }, { "facility": "F4", "customer": 1, "cost": 391.0 }, { "facility": "F4", "customer": 2, "cost": 1556.0 }, { "facility": "F4", "customer": 3, "cost": 447.0 }, { "facility": "F4", "customer": 4, "cost": 517.0 }, { "facility": "F4", "customer": 5, "cost": 1039.0 }, { "facility": "F4", "customer": 6, "cost": 68.0 }, { "facility": "F4", "customer": 7, "cost": 952.0 }, { "facility": "F4", "customer": 8, "cost": 1382.0 }, { "facility": "F4", "customer": 9, "cost": 1880.0 }, { "facility": "F4", "customer": 10, "cost": 132.0 }, { "facility": "F4", "customer": 11, "cost": 864.0 }, { "facility": "F4", "customer": 12, "cost": 44.0 }, { "facility": "F4", "customer": 13, "cost": 22.0 }, { "facility": "F4", "customer": 14, "cost": 1031.0 }, { "facility": "F4", "customer": 15, "cost": 477.0 }, { "facility": "F4", "customer": 16, "cost": 1717.0 }, { "facility": "F4", "customer": 17, "cost": 780.0 }, { "facility": "F5", "customer": 1, "cost": 54.0 }, { "facility": "F5", "customer": 2, "cost": 701.0 }, { "facility": "F5", "customer": 3, "cost": 48.0 }, { "facility": "F5", "customer": 4, "cost": 62.0 }, { "facility": "F5", "customer": 5, "cost": 443.0 }, { "facility": "F5", "customer": 6, "cost": 134.0 }, { "facility": "F5", "customer": 7, "cost": 507.0 }, { "facility": "F5", "customer": 8, "cost": 690.0 }, { "facility": "F5", "customer": 9, "cost": 1017.0 }, { "facility": "F5", "customer": 10, "cost": 49.0 }, { "facility": "F5", "customer": 11, "cost": 68.0 }, { "facility": "F5", "customer": 12, "cost": 100.0 }, { "facility": "F5", "customer": 13, "cost": 113.0 }, { "facility": "F5", "customer": 14, "cost": 459.0 }, { "facility": "F5", "customer": 15, "cost": 57.0 }, { "facility": "F5", "customer": 16, "cost": 854.0 }, { "facility": "F5", "customer": 17, "cost": 185.0 }, { "facility": "F6", "customer": 1, "cost": 275.0 }, { "facility": "F6", "customer": 2, "cost": 979.0 }, { "facility": "F6", "customer": 3, "cost": 421.0 }, { "facility": "F6", "customer": 4, "cost": 194.0 }, { "facility": "F6", "customer": 5, "cost": 57.0 }, { "facility": "F6", "customer": 6, "cost": 317.0 }, { "facility": "F6", "customer": 7, "cost": 77.0 }, { "facility": "F6", "customer": 8, "cost": 103.0 }, { "facility": "F6", "customer": 9, "cost": 1075.0 }, { "facility": "F6", "customer": 10, "cost": 272.0 }, { "facility": "F6", "customer": 11, "cost": 489.0 }, { "facility": "F6", "customer": 12, "cost": 380.0 }, { "facility": "F6", "customer": 13, "cost": 416.0 }, { "facility": "F6", "customer": 14, "cost": 1017.0 }, { "facility": "F6", "customer": 15, "cost": 231.0 }, { "facility": "F6", "customer": 16, "cost": 918.0 }, { "facility": "F6", "customer": 17, "cost": 162.0 }, { "facility": "F7", "customer": 1, "cost": 105.0 }, { "facility": "F7", "customer": 2, "cost": 763.0 }, { "facility": "F7", "customer": 3, "cost": 196.0 }, { "facility": "F7", "customer": 4, "cost": 39.0 }, { "facility": "F7", "customer": 5, "cost": 182.0 }, { "facility": "F7", "customer": 6, "cost": 213.0 }, { "facility": "F7", "customer": 7, "cost": 289.0 }, { "facility": "F7", "customer": 8, "cost": 388.0 }, { "facility": "F7", "customer": 9, "cost": 960.0 }, { "facility": "F7", "customer": 10, "cost": 128.0 }, { "facility": "F7", "customer": 11, "cost": 213.0 }, { "facility": "F7", "customer": 12, "cost": 220.0 }, { "facility": "F7", "customer": 13, "cost": 247.0 }, { "facility": "F7", "customer": 14, "cost": 736.0 }, { "facility": "F7", "customer": 15, "cost": 67.0 }, { "facility": "F7", "customer": 16, "cost": 787.0 }, { "facility": "F7", "customer": 17, "cost": 27.0 } ], "objective": 2641.0 }, "solution_variant": { "selected": [ "F1" ], "assignments": [ "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1" ] }, "context_index": 5, "input_format": "nl", "input_index_base": 1 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "We’ve got a handful of data centers that can be spun up and a bunch of applications that need service; the job is to pick which centers to activate and then point each app’s traffic to a single active center. Each center costs money to bring online and has a hard bandwidth ceiling, and connecting an app to a center also costs something. A better plan is simply the cheaper one: total expense equals the sum of the centers’ startup charges plus all the routing fees, provided every app is covered by exactly one center and no center’s bandwidth limit is exceeded. The exact numbers and limits follow below.\n\n# num_data_centers=6\n# num_applications=16\n# DATA_CENTERS\ndata_center_id,activation_cost,bandwidth_capacity\nF1,300.0,700.0\nF2,300.0,700.0\nF3,300.0,700.0\nF4,300.0,700.0\nF5,300.0,700.0\nF6,300.0,700.0\n# APPLICATIONS\napplication_id,bandwidth_demand\nA,25.0\nB,24.0\nC,12.0\nD,28.0\nE,25.0\nF,23.0\nG,28.0\nH,15.0\nI,14.0\nJ,13.0\nK,14.0\nL,19.0\nM,17.0\nN,17.0\nO,14.0\nP,19.0\n# ROUTINGS\ndata_center_id,application_id,routing_cost\nF1,A,52.0\nF1,B,228.0\nF1,C,108.0\nF1,D,324.0\nF1,E,389.0\nF1,F,288.0\nF1,G,80.0\nF1,H,43.0\nF1,I,290.0\nF1,J,26.0\nF1,K,30.0\nF1,L,38.0\nF1,M,80.0\nF1,N,171.0\nF1,O,28.0\nF1,P,274.0\nF2,A,384.0\nF2,B,818.0\nF2,C,25.0\nF2,D,66.0\nF2,E,120.0\nF2,F,420.0\nF2,G,409.0\nF2,H,200.0\nF2,I,120.0\nF2,J,99.0\nF2,K,172.0\nF2,L,273.0\nF2,M,73.0\nF2,N,146.0\nF2,O,159.0\nF2,P,70.0\nF3,A,1136.0\nF3,B,1670.0\nF3,C,65.0\nF3,D,663.0\nF3,E,1300.0\nF3,F,1556.0\nF3,G,1049.0\nF3,H,520.0\nF3,I,1228.0\nF3,J,292.0\nF3,K,699.0\nF3,L,935.0\nF3,M,542.0\nF3,N,1101.0\nF3,O,587.0\nF3,P,181.0\nF4,A,781.0\nF4,B,1276.0\nF4,C,60.0\nF4,D,186.0\nF4,E,619.0\nF4,F,930.0\nF4,G,769.0\nF4,H,414.0\nF4,I,598.0\nF4,J,242.0\nF4,K,458.0\nF4,L,625.0\nF4,M,295.0\nF4,N,573.0\nF4,O,406.0\nF4,P,56.0\nF5,A,665.0\nF5,B,1148.0\nF5,C,197.0\nF5,D,764.0\nF5,E,1197.0\nF5,F,1310.0\nF5,G,498.0\nF5,H,40.0\nF5,I,1087.0\nF5,J,29.0\nF5,K,249.0\nF5,L,467.0\nF5,M,337.0\nF5,N,894.0\nF5,O,98.0\nF5,P,516.0\nF6,A,1329.0\nF6,B,1771.0\nF6,C,507.0\nF6,D,1318.0\nF6,E,1837.0\nF6,F,1975.0\nF6,G,1143.0\nF6,H,463.0\nF6,I,1733.0\nF6,J,288.0\nF6,K,908.0\nF6,L,1136.0\nF6,M,929.0\nF6,N,1546.0\nF6,O,735.0\nF6,P,948.0\n\nAlso, when you send the plan back, please use this simple JSON layout so it's easy to parse — just a quick sketch of the shape we expect:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nPretty straightforward: \"selected\" is the list of data centers you decide to spin up, and \"assignments\" lists, in the same order as the applications were given, which spun-up center each app is pointed to. Think of it like filling out a short form — which centers are active, and which active center each app uses.\n\nThis JSON is just the shape I want to receive, not the actual answer. Please make sure to use the exact identifiers from the instance input — do not rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 52.0, 228.0, 108.0, 324.0, 389.0, 288.0, 80.0, 43.0, 290.0, 26.0, 30.0, 38.0, 80.0, 171.0, 28.0, 274.0 ], [ 384.0, 818.0, 25.0, 66.0, 120.0, 420.0, 409.0, 200.0, 120.0, 99.0, 172.0, 273.0, 73.0, 146.0, 159.0, 70.0 ], [ 1136.0, 1670.0, 65.0, 663.0, 1300.0, 1556.0, 1049.0, 520.0, 1228.0, 292.0, 699.0, 935.0, 542.0, 1101.0, 587.0, 181.0 ], [ 781.0, 1276.0, 60.0, 186.0, 619.0, 930.0, 769.0, 414.0, 598.0, 242.0, 458.0, 625.0, 295.0, 573.0, 406.0, 56.0 ], [ 665.0, 1148.0, 197.0, 764.0, 1197.0, 1310.0, 498.0, 40.0, 1087.0, 29.0, 249.0, 467.0, 337.0, 894.0, 98.0, 516.0 ], [ 1329.0, 1771.0, 507.0, 1318.0, 1837.0, 1975.0, 1143.0, 463.0, 1733.0, 288.0, 908.0, 1136.0, 929.0, 1546.0, 735.0, 948.0 ] ], "demands": [ 25.0, 24.0, 12.0, 28.0, 25.0, 23.0, 28.0, 15.0, 14.0, 13.0, 14.0, 19.0, 17.0, 17.0, 14.0, 19.0 ], "objective": 2033.0 }, "solution": { "open_facilities": [ 0, 1 ], "assignments": [ 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1 ] }, "obj": 2033.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 6, "num_customers": 16, "facilities": [ { "id": "F1", "opening_cost": 300.0, "capacity": 700.0 }, { "id": "F2", "opening_cost": 300.0, "capacity": 700.0 }, { "id": "F3", "opening_cost": 300.0, "capacity": 700.0 }, { "id": "F4", "opening_cost": 300.0, "capacity": 700.0 }, { "id": "F5", "opening_cost": 300.0, "capacity": 700.0 }, { "id": "F6", "opening_cost": 300.0, "capacity": 700.0 } ], "customers": [ { "id": "A", "demand": 25.0 }, { "id": "B", "demand": 24.0 }, { "id": "C", "demand": 12.0 }, { "id": "D", "demand": 28.0 }, { "id": "E", "demand": 25.0 }, { "id": "F", "demand": 23.0 }, { "id": "G", "demand": 28.0 }, { "id": "H", "demand": 15.0 }, { "id": "I", "demand": 14.0 }, { "id": "J", "demand": 13.0 }, { "id": "K", "demand": 14.0 }, { "id": "L", "demand": 19.0 }, { "id": "M", "demand": 17.0 }, { "id": "N", "demand": 17.0 }, { "id": "O", "demand": 14.0 }, { "id": "P", "demand": 19.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 52.0 }, { "facility": "F1", "customer": "B", "cost": 228.0 }, { "facility": "F1", "customer": "C", "cost": 108.0 }, { "facility": "F1", "customer": "D", "cost": 324.0 }, { "facility": "F1", "customer": "E", "cost": 389.0 }, { "facility": "F1", "customer": "F", "cost": 288.0 }, { "facility": "F1", "customer": "G", "cost": 80.0 }, { "facility": "F1", "customer": "H", "cost": 43.0 }, { "facility": "F1", "customer": "I", "cost": 290.0 }, { "facility": "F1", "customer": "J", "cost": 26.0 }, { "facility": "F1", "customer": "K", "cost": 30.0 }, { "facility": "F1", "customer": "L", "cost": 38.0 }, { "facility": "F1", "customer": "M", "cost": 80.0 }, { "facility": "F1", "customer": "N", "cost": 171.0 }, { "facility": "F1", "customer": "O", "cost": 28.0 }, { "facility": "F1", "customer": "P", "cost": 274.0 }, { "facility": "F2", "customer": "A", "cost": 384.0 }, { "facility": "F2", "customer": "B", "cost": 818.0 }, { "facility": "F2", "customer": "C", "cost": 25.0 }, { "facility": "F2", "customer": "D", "cost": 66.0 }, { "facility": "F2", "customer": "E", "cost": 120.0 }, { "facility": "F2", "customer": "F", "cost": 420.0 }, { "facility": "F2", "customer": "G", "cost": 409.0 }, { "facility": "F2", "customer": "H", "cost": 200.0 }, { "facility": "F2", "customer": "I", "cost": 120.0 }, { "facility": "F2", "customer": "J", "cost": 99.0 }, { "facility": "F2", "customer": "K", "cost": 172.0 }, { "facility": "F2", "customer": "L", "cost": 273.0 }, { "facility": "F2", "customer": "M", "cost": 73.0 }, { "facility": "F2", "customer": "N", "cost": 146.0 }, { "facility": "F2", "customer": "O", "cost": 159.0 }, { "facility": "F2", "customer": "P", "cost": 70.0 }, { "facility": "F3", "customer": "A", "cost": 1136.0 }, { "facility": "F3", "customer": "B", "cost": 1670.0 }, { "facility": "F3", "customer": "C", "cost": 65.0 }, { "facility": "F3", "customer": "D", "cost": 663.0 }, { "facility": "F3", "customer": "E", "cost": 1300.0 }, { "facility": "F3", "customer": "F", "cost": 1556.0 }, { "facility": "F3", "customer": "G", "cost": 1049.0 }, { "facility": "F3", "customer": "H", "cost": 520.0 }, { "facility": "F3", "customer": "I", "cost": 1228.0 }, { "facility": "F3", "customer": "J", "cost": 292.0 }, { "facility": "F3", "customer": "K", "cost": 699.0 }, { "facility": "F3", "customer": "L", "cost": 935.0 }, { "facility": "F3", "customer": "M", "cost": 542.0 }, { "facility": "F3", "customer": "N", "cost": 1101.0 }, { "facility": "F3", "customer": "O", "cost": 587.0 }, { "facility": "F3", "customer": "P", "cost": 181.0 }, { "facility": "F4", "customer": "A", "cost": 781.0 }, { "facility": "F4", "customer": "B", "cost": 1276.0 }, { "facility": "F4", "customer": "C", "cost": 60.0 }, { "facility": "F4", "customer": "D", "cost": 186.0 }, { "facility": "F4", "customer": "E", "cost": 619.0 }, { "facility": "F4", "customer": "F", "cost": 930.0 }, { "facility": "F4", "customer": "G", "cost": 769.0 }, { "facility": "F4", "customer": "H", "cost": 414.0 }, { "facility": "F4", "customer": "I", "cost": 598.0 }, { "facility": "F4", "customer": "J", "cost": 242.0 }, { "facility": "F4", "customer": "K", "cost": 458.0 }, { "facility": "F4", "customer": "L", "cost": 625.0 }, { "facility": "F4", "customer": "M", "cost": 295.0 }, { "facility": "F4", "customer": "N", "cost": 573.0 }, { "facility": "F4", "customer": "O", "cost": 406.0 }, { "facility": "F4", "customer": "P", "cost": 56.0 }, { "facility": "F5", "customer": "A", "cost": 665.0 }, { "facility": "F5", "customer": "B", "cost": 1148.0 }, { "facility": "F5", "customer": "C", "cost": 197.0 }, { "facility": "F5", "customer": "D", "cost": 764.0 }, { "facility": "F5", "customer": "E", "cost": 1197.0 }, { "facility": "F5", "customer": "F", "cost": 1310.0 }, { "facility": "F5", "customer": "G", "cost": 498.0 }, { "facility": "F5", "customer": "H", "cost": 40.0 }, { "facility": "F5", "customer": "I", "cost": 1087.0 }, { "facility": "F5", "customer": "J", "cost": 29.0 }, { "facility": "F5", "customer": "K", "cost": 249.0 }, { "facility": "F5", "customer": "L", "cost": 467.0 }, { "facility": "F5", "customer": "M", "cost": 337.0 }, { "facility": "F5", "customer": "N", "cost": 894.0 }, { "facility": "F5", "customer": "O", "cost": 98.0 }, { "facility": "F5", "customer": "P", "cost": 516.0 }, { "facility": "F6", "customer": "A", "cost": 1329.0 }, { "facility": "F6", "customer": "B", "cost": 1771.0 }, { "facility": "F6", "customer": "C", "cost": 507.0 }, { "facility": "F6", "customer": "D", "cost": 1318.0 }, { "facility": "F6", "customer": "E", "cost": 1837.0 }, { "facility": "F6", "customer": "F", "cost": 1975.0 }, { "facility": "F6", "customer": "G", "cost": 1143.0 }, { "facility": "F6", "customer": "H", "cost": 463.0 }, { "facility": "F6", "customer": "I", "cost": 1733.0 }, { "facility": "F6", "customer": "J", "cost": 288.0 }, { "facility": "F6", "customer": "K", "cost": 908.0 }, { "facility": "F6", "customer": "L", "cost": 1136.0 }, { "facility": "F6", "customer": "M", "cost": 929.0 }, { "facility": "F6", "customer": "N", "cost": 1546.0 }, { "facility": "F6", "customer": "O", "cost": 735.0 }, { "facility": "F6", "customer": "P", "cost": 948.0 } ], "objective": 2033.0 }, "solution_variant": { "selected": [ "F1", "F2" ], "assignments": [ "F1", "F1", "F2", "F2", "F2", "F1", "F1", "F1", "F2", "F1", "F1", "F1", "F2", "F2", "F1", "F2" ] }, "context_index": 6, "input_format": "csv", "input_index_base": "names" }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Someone in charge of the mobile library has to decide which vans to operate and then assign every neighborhood to one of those active vans. Assignments are exclusive — one neighborhood, one van — and vans cannot be overloaded beyond their book limits. What makes one choice nicer than another is simple math: total up the van deployment fees plus the delivery effort for serving the neighborhoods, and aim for the smallest total possible. The actual numbers for van costs, capacities and neighborhood demands follow below.\n\nThere are 7 vans and 16 neighborhoods in this instance.\n\n**Vans**\n| van_id | deployment_cost | book_capacity |\n|---|---|---|\n| F1 | 600.0 | 300.0 |\n| F2 | 600.0 | 300.0 |\n| F3 | 600.0 | 300.0 |\n| F4 | 600.0 | 300.0 |\n| F5 | 600.0 | 300.0 |\n| F6 | 600.0 | 300.0 |\n| F7 | 600.0 | 300.0 |\n\n**Neighborhoods**\n| neighborhood_id | book_demand |\n|---|---|\n| 0 | 21.0 |\n| 1 | 28.0 |\n| 2 | 24.0 |\n| 3 | 12.0 |\n| 4 | 13.0 |\n| 5 | 13.0 |\n| 6 | 22.0 |\n| 7 | 17.0 |\n| 8 | 23.0 |\n| 9 | 12.0 |\n| 10 | 23.0 |\n| 11 | 11.0 |\n| 12 | 13.0 |\n| 13 | 23.0 |\n| 14 | 27.0 |\n| 15 | 19.0 |\n\n**Delivery Effort**\n| van_id | neighborhood_id | delivery_effort |\n|---|---|---|\n| F1 | 0 | 815.0 |\n| F1 | 1 | 478.0 |\n| F1 | 2 | 93.0 |\n| F1 | 3 | 660.0 |\n| F1 | 4 | 717.0 |\n| F1 | 5 | 412.0 |\n| F1 | 6 | 1103.0 |\n| F1 | 7 | 583.0 |\n| F1 | 8 | 480.0 |\n| F1 | 9 | 563.0 |\n| F1 | 10 | 352.0 |\n| F1 | 11 | 352.0 |\n| F1 | 12 | 282.0 |\n| F1 | 13 | 985.0 |\n| F1 | 14 | 728.0 |\n| F1 | 15 | 175.0 |\n| F2 | 0 | 715.0 |\n| F2 | 1 | 722.0 |\n| F2 | 2 | 378.0 |\n| F2 | 3 | 705.0 |\n| F2 | 4 | 1463.0 |\n| F2 | 5 | 1187.0 |\n| F2 | 6 | 1089.0 |\n| F2 | 7 | 1184.0 |\n| F2 | 8 | 1040.0 |\n| F2 | 9 | 1334.0 |\n| F2 | 10 | 900.0 |\n| F2 | 11 | 1122.0 |\n| F2 | 12 | 458.0 |\n| F2 | 13 | 1391.0 |\n| F2 | 14 | 1483.0 |\n| F2 | 15 | 105.0 |\n| F3 | 0 | 1400.0 |\n| F3 | 1 | 1095.0 |\n| F3 | 2 | 81.0 |\n| F3 | 3 | 1264.0 |\n| F3 | 4 | 692.0 |\n| F3 | 5 | 831.0 |\n| F3 | 6 | 1719.0 |\n| F3 | 7 | 1193.0 |\n| F3 | 8 | 1113.0 |\n| F3 | 9 | 946.0 |\n| F3 | 10 | 992.0 |\n| F3 | 11 | 662.0 |\n| F3 | 12 | 846.0 |\n| F3 | 13 | 1616.0 |\n| F3 | 14 | 754.0 |\n| F3 | 15 | 546.0 |\n| F4 | 0 | 444.0 |\n| F4 | 1 | 175.0 |\n| F4 | 2 | 90.0 |\n| F4 | 3 | 291.0 |\n| F4 | 4 | 353.0 |\n| F4 | 5 | 77.0 |\n| F4 | 6 | 584.0 |\n| F4 | 7 | 47.0 |\n| F4 | 8 | 69.0 |\n| F4 | 9 | 102.0 |\n| F4 | 10 | 67.0 |\n| F4 | 11 | 105.0 |\n| F4 | 12 | 112.0 |\n| F4 | 13 | 228.0 |\n| F4 | 14 | 350.0 |\n| F4 | 15 | 116.0 |\n| F5 | 0 | 962.0 |\n| F5 | 1 | 858.0 |\n| F5 | 2 | 333.0 |\n| F5 | 3 | 907.0 |\n| F5 | 4 | 1455.0 |\n| F5 | 5 | 1214.0 |\n| F5 | 6 | 1331.0 |\n| F5 | 7 | 1274.0 |\n| F5 | 8 | 1131.0 |\n| F5 | 9 | 1367.0 |\n| F5 | 10 | 982.0 |\n| F5 | 11 | 1132.0 |\n| F5 | 12 | 559.0 |\n| F5 | 13 | 1540.0 |\n| F5 | 14 | 1478.0 |\n| F5 | 15 | 59.0 |\n| F6 | 0 | 1182.0 |\n| F6 | 1 | 924.0 |\n| F6 | 2 | 102.0 |\n| F6 | 3 | 1066.0 |\n| F6 | 4 | 1130.0 |\n| F6 | 5 | 973.0 |\n| F6 | 6 | 1523.0 |\n| F6 | 7 | 1176.0 |\n| F6 | 8 | 1054.0 |\n| F6 | 9 | 1126.0 |\n| F6 | 10 | 907.0 |\n| F6 | 11 | 853.0 |\n| F6 | 12 | 642.0 |\n| F6 | 13 | 1544.0 |\n| F6 | 14 | 1160.0 |\n| F6 | 15 | 306.0 |\n| F7 | 0 | 791.0 |\n| F7 | 1 | 447.0 |\n| F7 | 2 | 58.0 |\n| F7 | 3 | 625.0 |\n| F7 | 4 | 270.0 |\n| F7 | 5 | 32.0 |\n| F7 | 6 | 1027.0 |\n| F7 | 7 | 343.0 |\n| F7 | 8 | 329.0 |\n| F7 | 9 | 26.0 |\n| F7 | 10 | 274.0 |\n| F7 | 11 | 27.0 |\n| F7 | 12 | 305.0 |\n| F7 | 13 | 755.0 |\n| F7 | 14 | 267.0 |\n| F7 | 15 | 224.0 |\n\nOh, and when you give the final pick and assignments, just stick to this simple JSON shape so it's easy to read and check:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is the list of vans you'll run (one identifier per van). \"assignments\" lists, in neighborhood order, which of those running vans is assigned to serve each neighborhood. Think of it like filling out a short form: pick the vans, then write next to each neighborhood which picked van will visit it.\n\nThis JSON is just a sketch of the expected shape — not the actual answer. Please be sure to use the exact identifiers from the instance input — don't rename them or invent new labels.\n\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "connection_costs": [ [ 815.0, 478.0, 93.0, 660.0, 717.0, 412.0, 1103.0, 583.0, 480.0, 563.0, 352.0, 352.0, 282.0, 985.0, 728.0, 175.0 ], [ 715.0, 722.0, 378.0, 705.0, 1463.0, 1187.0, 1089.0, 1184.0, 1040.0, 1334.0, 900.0, 1122.0, 458.0, 1391.0, 1483.0, 105.0 ], [ 1400.0, 1095.0, 81.0, 1264.0, 692.0, 831.0, 1719.0, 1193.0, 1113.0, 946.0, 992.0, 662.0, 846.0, 1616.0, 754.0, 546.0 ], [ 444.0, 175.0, 90.0, 291.0, 353.0, 77.0, 584.0, 47.0, 69.0, 102.0, 67.0, 105.0, 112.0, 228.0, 350.0, 116.0 ], [ 962.0, 858.0, 333.0, 907.0, 1455.0, 1214.0, 1331.0, 1274.0, 1131.0, 1367.0, 982.0, 1132.0, 559.0, 1540.0, 1478.0, 59.0 ], [ 1182.0, 924.0, 102.0, 1066.0, 1130.0, 973.0, 1523.0, 1176.0, 1054.0, 1126.0, 907.0, 853.0, 642.0, 1544.0, 1160.0, 306.0 ], [ 791.0, 447.0, 58.0, 625.0, 270.0, 32.0, 1027.0, 343.0, 329.0, 26.0, 274.0, 27.0, 305.0, 755.0, 267.0, 224.0 ] ], "demands": [ 21.0, 28.0, 24.0, 12.0, 13.0, 13.0, 22.0, 17.0, 23.0, 12.0, 23.0, 11.0, 13.0, 23.0, 27.0, 19.0 ], "objective": 4013.0 }, "solution": { "open_facilities": [ 3, 6 ], "assignments": [ 3, 3, 6, 3, 6, 6, 3, 3, 3, 6, 3, 6, 3, 3, 6, 3 ] }, "obj": 4013.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 16, "facilities": [ { "id": "F1", "opening_cost": 600.0, "capacity": 300.0 }, { "id": "F2", "opening_cost": 600.0, "capacity": 300.0 }, { "id": "F3", "opening_cost": 600.0, "capacity": 300.0 }, { "id": "F4", "opening_cost": 600.0, "capacity": 300.0 }, { "id": "F5", "opening_cost": 600.0, "capacity": 300.0 }, { "id": "F6", "opening_cost": 600.0, "capacity": 300.0 }, { "id": "F7", "opening_cost": 600.0, "capacity": 300.0 } ], "customers": [ { "id": 0, "demand": 21.0 }, { "id": 1, "demand": 28.0 }, { "id": 2, "demand": 24.0 }, { "id": 3, "demand": 12.0 }, { "id": 4, "demand": 13.0 }, { "id": 5, "demand": 13.0 }, { "id": 6, "demand": 22.0 }, { "id": 7, "demand": 17.0 }, { "id": 8, "demand": 23.0 }, { "id": 9, "demand": 12.0 }, { "id": 10, "demand": 23.0 }, { "id": 11, "demand": 11.0 }, { "id": 12, "demand": 13.0 }, { "id": 13, "demand": 23.0 }, { "id": 14, "demand": 27.0 }, { "id": 15, "demand": 19.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 815.0 }, { "facility": "F1", "customer": 1, "cost": 478.0 }, { "facility": "F1", "customer": 2, "cost": 93.0 }, { "facility": "F1", "customer": 3, "cost": 660.0 }, { "facility": "F1", "customer": 4, "cost": 717.0 }, { "facility": "F1", "customer": 5, "cost": 412.0 }, { "facility": "F1", "customer": 6, "cost": 1103.0 }, { "facility": "F1", "customer": 7, "cost": 583.0 }, { "facility": "F1", "customer": 8, "cost": 480.0 }, { "facility": "F1", "customer": 9, "cost": 563.0 }, { "facility": "F1", "customer": 10, "cost": 352.0 }, { "facility": "F1", "customer": 11, "cost": 352.0 }, { "facility": "F1", "customer": 12, "cost": 282.0 }, { "facility": "F1", "customer": 13, "cost": 985.0 }, { "facility": "F1", "customer": 14, "cost": 728.0 }, { "facility": "F1", "customer": 15, "cost": 175.0 }, { "facility": "F2", "customer": 0, "cost": 715.0 }, { "facility": "F2", "customer": 1, "cost": 722.0 }, { "facility": "F2", "customer": 2, "cost": 378.0 }, { "facility": "F2", "customer": 3, "cost": 705.0 }, { "facility": "F2", "customer": 4, "cost": 1463.0 }, { "facility": "F2", "customer": 5, "cost": 1187.0 }, { "facility": "F2", "customer": 6, "cost": 1089.0 }, { "facility": "F2", "customer": 7, "cost": 1184.0 }, { "facility": "F2", "customer": 8, "cost": 1040.0 }, { "facility": "F2", "customer": 9, "cost": 1334.0 }, { "facility": "F2", "customer": 10, "cost": 900.0 }, { "facility": "F2", "customer": 11, "cost": 1122.0 }, { "facility": "F2", "customer": 12, "cost": 458.0 }, { "facility": "F2", "customer": 13, "cost": 1391.0 }, { "facility": "F2", "customer": 14, "cost": 1483.0 }, { "facility": "F2", "customer": 15, "cost": 105.0 }, { "facility": "F3", "customer": 0, "cost": 1400.0 }, { "facility": "F3", "customer": 1, "cost": 1095.0 }, { "facility": "F3", "customer": 2, "cost": 81.0 }, { "facility": "F3", "customer": 3, "cost": 1264.0 }, { "facility": "F3", "customer": 4, "cost": 692.0 }, { "facility": "F3", "customer": 5, "cost": 831.0 }, { "facility": "F3", "customer": 6, "cost": 1719.0 }, { "facility": "F3", "customer": 7, "cost": 1193.0 }, { "facility": "F3", "customer": 8, "cost": 1113.0 }, { "facility": "F3", "customer": 9, "cost": 946.0 }, { "facility": "F3", "customer": 10, "cost": 992.0 }, { "facility": "F3", "customer": 11, "cost": 662.0 }, { "facility": "F3", "customer": 12, "cost": 846.0 }, { "facility": "F3", "customer": 13, "cost": 1616.0 }, { "facility": "F3", "customer": 14, "cost": 754.0 }, { "facility": "F3", "customer": 15, "cost": 546.0 }, { "facility": "F4", "customer": 0, "cost": 444.0 }, { "facility": "F4", "customer": 1, "cost": 175.0 }, { "facility": "F4", "customer": 2, "cost": 90.0 }, { "facility": "F4", "customer": 3, "cost": 291.0 }, { "facility": "F4", "customer": 4, "cost": 353.0 }, { "facility": "F4", "customer": 5, "cost": 77.0 }, { "facility": "F4", "customer": 6, "cost": 584.0 }, { "facility": "F4", "customer": 7, "cost": 47.0 }, { "facility": "F4", "customer": 8, "cost": 69.0 }, { "facility": "F4", "customer": 9, "cost": 102.0 }, { "facility": "F4", "customer": 10, "cost": 67.0 }, { "facility": "F4", "customer": 11, "cost": 105.0 }, { "facility": "F4", "customer": 12, "cost": 112.0 }, { "facility": "F4", "customer": 13, "cost": 228.0 }, { "facility": "F4", "customer": 14, "cost": 350.0 }, { "facility": "F4", "customer": 15, "cost": 116.0 }, { "facility": "F5", "customer": 0, "cost": 962.0 }, { "facility": "F5", "customer": 1, "cost": 858.0 }, { "facility": "F5", "customer": 2, "cost": 333.0 }, { "facility": "F5", "customer": 3, "cost": 907.0 }, { "facility": "F5", "customer": 4, "cost": 1455.0 }, { "facility": "F5", "customer": 5, "cost": 1214.0 }, { "facility": "F5", "customer": 6, "cost": 1331.0 }, { "facility": "F5", "customer": 7, "cost": 1274.0 }, { "facility": "F5", "customer": 8, "cost": 1131.0 }, { "facility": "F5", "customer": 9, "cost": 1367.0 }, { "facility": "F5", "customer": 10, "cost": 982.0 }, { "facility": "F5", "customer": 11, "cost": 1132.0 }, { "facility": "F5", "customer": 12, "cost": 559.0 }, { "facility": "F5", "customer": 13, "cost": 1540.0 }, { "facility": "F5", "customer": 14, "cost": 1478.0 }, { "facility": "F5", "customer": 15, "cost": 59.0 }, { "facility": "F6", "customer": 0, "cost": 1182.0 }, { "facility": "F6", "customer": 1, "cost": 924.0 }, { "facility": "F6", "customer": 2, "cost": 102.0 }, { "facility": "F6", "customer": 3, "cost": 1066.0 }, { "facility": "F6", "customer": 4, "cost": 1130.0 }, { "facility": "F6", "customer": 5, "cost": 973.0 }, { "facility": "F6", "customer": 6, "cost": 1523.0 }, { "facility": "F6", "customer": 7, "cost": 1176.0 }, { "facility": "F6", "customer": 8, "cost": 1054.0 }, { "facility": "F6", "customer": 9, "cost": 1126.0 }, { "facility": "F6", "customer": 10, "cost": 907.0 }, { "facility": "F6", "customer": 11, "cost": 853.0 }, { "facility": "F6", "customer": 12, "cost": 642.0 }, { "facility": "F6", "customer": 13, "cost": 1544.0 }, { "facility": "F6", "customer": 14, "cost": 1160.0 }, { "facility": "F6", "customer": 15, "cost": 306.0 }, { "facility": "F7", "customer": 0, "cost": 791.0 }, { "facility": "F7", "customer": 1, "cost": 447.0 }, { "facility": "F7", "customer": 2, "cost": 58.0 }, { "facility": "F7", "customer": 3, "cost": 625.0 }, { "facility": "F7", "customer": 4, "cost": 270.0 }, { "facility": "F7", "customer": 5, "cost": 32.0 }, { "facility": "F7", "customer": 6, "cost": 1027.0 }, { "facility": "F7", "customer": 7, "cost": 343.0 }, { "facility": "F7", "customer": 8, "cost": 329.0 }, { "facility": "F7", "customer": 9, "cost": 26.0 }, { "facility": "F7", "customer": 10, "cost": 274.0 }, { "facility": "F7", "customer": 11, "cost": 27.0 }, { "facility": "F7", "customer": 12, "cost": 305.0 }, { "facility": "F7", "customer": 13, "cost": 755.0 }, { "facility": "F7", "customer": 14, "cost": 267.0 }, { "facility": "F7", "customer": 15, "cost": 224.0 } ], "objective": 4013.0 }, "solution_variant": { "selected": [ "F4", "F7" ], "assignments": [ "F4", "F4", "F7", "F4", "F7", "F7", "F4", "F4", "F4", "F7", "F4", "F7", "F4", "F4", "F7", "F4" ] }, "context_index": 7, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "I’m the emergency planner trying to set up a handful of supply hubs after a disaster, and the job is to pick which hubs to open and then link every relief site to one of those open hubs. Each hub costs money to establish and can only hold so much inventory, and sending supplies from a hub to a site adds shipping costs. The goal is to choose hubs and assignments so the total bill — the hubs’ setup costs plus all shipment costs — is as small as possible, while making sure every relief site is assigned to exactly one open hub and no hub’s stock limit is exceeded. The specific sites, hub options, capacities, and costs are shown below.\n\nI can consider 8 candidate hubs and must serve 16 relief sites.\nHub F1 would cost 600.0 to open, and I can stock up to 700.0 units there.\nHub F2 would cost 600.0 to open, and I can stock up to 700.0 units there.\nHub F3 would cost 600.0 to open, and I can stock up to 700.0 units there.\nHub F4 would cost 600.0 to open, and I can stock up to 700.0 units there.\nHub F5 would cost 600.0 to open, and I can stock up to 700.0 units there.\nHub F6 would cost 600.0 to open, and I can stock up to 700.0 units there.\nHub F7 would cost 600.0 to open, and I can stock up to 700.0 units there.\nHub F8 would cost 600.0 to open, and I can stock up to 700.0 units there.\nRelief site 0 needs 28.0 units that I must assign to one open hub.\nRelief site 1 needs 23.0 units that I must assign to one open hub.\nRelief site 2 needs 28.0 units that I must assign to one open hub.\nRelief site 3 needs 18.0 units that I must assign to one open hub.\nRelief site 4 needs 12.0 units that I must assign to one open hub.\nRelief site 5 needs 20.0 units that I must assign to one open hub.\nRelief site 6 needs 29.0 units that I must assign to one open hub.\nRelief site 7 needs 22.0 units that I must assign to one open hub.\nRelief site 8 needs 18.0 units that I must assign to one open hub.\nRelief site 9 needs 27.0 units that I must assign to one open hub.\nRelief site 10 needs 23.0 units that I must assign to one open hub.\nRelief site 11 needs 21.0 units that I must assign to one open hub.\nRelief site 12 needs 11.0 units that I must assign to one open hub.\nRelief site 13 needs 11.0 units that I must assign to one open hub.\nRelief site 14 needs 29.0 units that I must assign to one open hub.\nRelief site 15 needs 11.0 units that I must assign to one open hub.\nIf I assign site 0 to hub F1, shipping costs 83.0.\nIf I assign site 1 to hub F1, shipping costs 120.0.\nIf I assign site 2 to hub F1, shipping costs 145.0.\nIf I assign site 3 to hub F1, shipping costs 42.0.\nIf I assign site 4 to hub F1, shipping costs 282.0.\nIf I assign site 5 to hub F1, shipping costs 477.0.\nIf I assign site 6 to hub F1, shipping costs 231.0.\nIf I assign site 7 to hub F1, shipping costs 832.0.\nIf I assign site 8 to hub F1, shipping costs 36.0.\nIf I assign site 9 to hub F1, shipping costs 383.0.\nIf I assign site 10 to hub F1, shipping costs 46.0.\nIf I assign site 11 to hub F1, shipping costs 623.0.\nIf I assign site 12 to hub F1, shipping costs 335.0.\nIf I assign site 13 to hub F1, shipping costs 97.0.\nIf I assign site 14 to hub F1, shipping costs 475.0.\nIf I assign site 15 to hub F1, shipping costs 606.0.\nIf I assign site 0 to hub F2, shipping costs 634.0.\nIf I assign site 1 to hub F2, shipping costs 260.0.\nIf I assign site 2 to hub F2, shipping costs 478.0.\nIf I assign site 3 to hub F2, shipping costs 58.0.\nIf I assign site 4 to hub F2, shipping costs 660.0.\nIf I assign site 5 to hub F2, shipping costs 463.0.\nIf I assign site 6 to hub F2, shipping costs 391.0.\nIf I assign site 7 to hub F2, shipping costs 1374.0.\nIf I assign site 8 to hub F2, shipping costs 38.0.\nIf I assign site 9 to hub F2, shipping costs 1045.0.\nIf I assign site 10 to hub F2, shipping costs 352.0.\nIf I assign site 11 to hub F2, shipping costs 1057.0.\nIf I assign site 12 to hub F2, shipping costs 656.0.\nIf I assign site 13 to hub F2, shipping costs 201.0.\nIf I assign site 14 to hub F2, shipping costs 817.0.\nIf I assign site 15 to hub F2, shipping costs 1112.0.\nIf I assign site 0 to hub F3, shipping costs 517.0.\nIf I assign site 1 to hub F3, shipping costs 364.0.\nIf I assign site 2 to hub F3, shipping costs 515.0.\nIf I assign site 3 to hub F3, shipping costs 161.0.\nIf I assign site 4 to hub F3, shipping costs 691.0.\nIf I assign site 5 to hub F3, shipping costs 142.0.\nIf I assign site 6 to hub F3, shipping costs 495.0.\nIf I assign site 7 to hub F3, shipping costs 729.0.\nIf I assign site 8 to hub F3, shipping costs 50.0.\nIf I assign site 9 to hub F3, shipping costs 781.0.\nIf I assign site 10 to hub F3, shipping costs 342.0.\nIf I assign site 11 to hub F3, shipping costs 374.0.\nIf I assign site 12 to hub F3, shipping costs 720.0.\nIf I assign site 13 to hub F3, shipping costs 303.0.\nIf I assign site 14 to hub F3, shipping costs 875.0.\nIf I assign site 15 to hub F3, shipping costs 501.0.\nIf I assign site 0 to hub F4, shipping costs 213.0.\nIf I assign site 1 to hub F4, shipping costs 193.0.\nIf I assign site 2 to hub F4, shipping costs 257.0.\nIf I assign site 3 to hub F4, shipping costs 44.0.\nIf I assign site 4 to hub F4, shipping costs 412.0.\nIf I assign site 5 to hub F4, shipping costs 340.0.\nIf I assign site 6 to hub F4, shipping costs 315.0.\nIf I assign site 7 to hub F4, shipping costs 611.0.\nIf I assign site 8 to hub F4, shipping costs 38.0.\nIf I assign site 9 to hub F4, shipping costs 447.0.\nIf I assign site 10 to hub F4, shipping costs 105.0.\nIf I assign site 11 to hub F4, shipping costs 347.0.\nIf I assign site 12 to hub F4, shipping costs 459.0.\nIf I assign site 13 to hub F4, shipping costs 158.0.\nIf I assign site 14 to hub F4, shipping costs 604.0.\nIf I assign site 15 to hub F4, shipping costs 356.0.\nIf I assign site 0 to hub F5, shipping costs 389.0.\nIf I assign site 1 to hub F5, shipping costs 46.0.\nIf I assign site 2 to hub F5, shipping costs 102.0.\nIf I assign site 3 to hub F5, shipping costs 208.0.\nIf I assign site 4 to hub F5, shipping costs 33.0.\nIf I assign site 5 to hub F5, shipping costs 750.0.\nIf I assign site 6 to hub F5, shipping costs 91.0.\nIf I assign site 7 to hub F5, shipping costs 1286.0.\nIf I assign site 8 to hub F5, shipping costs 43.0.\nIf I assign site 9 to hub F5, shipping costs 691.0.\nIf I assign site 10 to hub F5, shipping costs 288.0.\nIf I assign site 11 to hub F5, shipping costs 1098.0.\nIf I assign site 12 to hub F5, shipping costs 86.0.\nIf I assign site 13 to hub F5, shipping costs 24.0.\nIf I assign site 14 to hub F5, shipping costs 200.0.\nIf I assign site 15 to hub F5, shipping costs 1077.0.\nIf I assign site 0 to hub F6, shipping costs 730.0.\nIf I assign site 1 to hub F6, shipping costs 76.0.\nIf I assign site 2 to hub F6, shipping costs 341.0.\nIf I assign site 3 to hub F6, shipping costs 382.0.\nIf I assign site 4 to hub F6, shipping costs 232.0.\nIf I assign site 5 to hub F6, shipping costs 909.0.\nIf I assign site 6 to hub F6, shipping costs 61.0.\nIf I assign site 7 to hub F6, shipping costs 1653.0.\nIf I assign site 8 to hub F6, shipping costs 52.0.\nIf I assign site 9 to hub F6, shipping costs 1078.0.\nIf I assign site 10 to hub F6, shipping costs 562.0.\nIf I assign site 11 to hub F6, shipping costs 1434.0.\nIf I assign site 12 to hub F6, shipping costs 22.0.\nIf I assign site 13 to hub F6, shipping costs 29.0.\nIf I assign site 14 to hub F6, shipping costs 185.0.\nIf I assign site 15 to hub F6, shipping costs 1429.0.\nIf I assign site 0 to hub F7, shipping costs 84.0.\nIf I assign site 1 to hub F7, shipping costs 70.0.\nIf I assign site 2 to hub F7, shipping costs 66.0.\nIf I assign site 3 to hub F7, shipping costs 78.0.\nIf I assign site 4 to hub F7, shipping costs 131.0.\nIf I assign site 5 to hub F7, shipping costs 561.0.\nIf I assign site 6 to hub F7, shipping costs 155.0.\nIf I assign site 7 to hub F7, shipping costs 829.0.\nIf I assign site 8 to hub F7, shipping costs 37.0.\nIf I assign site 9 to hub F7, shipping costs 220.0.\nIf I assign site 10 to hub F7, shipping costs 79.0.\nIf I assign site 11 to hub F7, shipping costs 683.0.\nIf I assign site 12 to hub F7, shipping costs 191.0.\nIf I assign site 13 to hub F7, shipping costs 53.0.\nIf I assign site 14 to hub F7, shipping costs 311.0.\nIf I assign site 15 to hub F7, shipping costs 640.0.\nIf I assign site 0 to hub F8, shipping costs 672.0.\nIf I assign site 1 to hub F8, shipping costs 370.0.\nIf I assign site 2 to hub F8, shipping costs 586.0.\nIf I assign site 3 to hub F8, shipping costs 165.0.\nIf I assign site 4 to hub F8, shipping costs 770.0.\nIf I assign site 5 to hub F8, shipping costs 254.0.\nIf I assign site 6 to hub F8, shipping costs 500.0.\nIf I assign site 7 to hub F8, shipping costs 1206.0.\nIf I assign site 8 to hub F8, shipping costs 46.0.\nIf I assign site 9 to hub F8, shipping costs 1034.0.\nIf I assign site 10 to hub F8, shipping costs 429.0.\nIf I assign site 11 to hub F8, shipping costs 849.0.\nIf I assign site 12 to hub F8, shipping costs 774.0.\nIf I assign site 13 to hub F8, shipping costs 298.0.\nIf I assign site 14 to hub F8, shipping costs 935.0.\nIf I assign site 15 to hub F8, shipping costs 943.0.\nI'll use this information to decide which hubs to open and how to assign every site.\n\nAlso, for the answer please use this simple JSON shape so it's easy to plug into my planner:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is the list of hubs you decide to open. \"assignments\" lists, for each relief site (in the same order the instance gives them), which open hub that site is assigned to. Think of it like a short form: which hubs to set up, and which hub each site will get supplies from.\n\nThis is just the expected shape of the reply — a sketch, not the actual filled-in solution. Please make sure to use the exact identifiers from the instance input; do not rename or invent new labels.\n\nValid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 83.0, 120.0, 145.0, 42.0, 282.0, 477.0, 231.0, 832.0, 36.0, 383.0, 46.0, 623.0, 335.0, 97.0, 475.0, 606.0 ], [ 634.0, 260.0, 478.0, 58.0, 660.0, 463.0, 391.0, 1374.0, 38.0, 1045.0, 352.0, 1057.0, 656.0, 201.0, 817.0, 1112.0 ], [ 517.0, 364.0, 515.0, 161.0, 691.0, 142.0, 495.0, 729.0, 50.0, 781.0, 342.0, 374.0, 720.0, 303.0, 875.0, 501.0 ], [ 213.0, 193.0, 257.0, 44.0, 412.0, 340.0, 315.0, 611.0, 38.0, 447.0, 105.0, 347.0, 459.0, 158.0, 604.0, 356.0 ], [ 389.0, 46.0, 102.0, 208.0, 33.0, 750.0, 91.0, 1286.0, 43.0, 691.0, 288.0, 1098.0, 86.0, 24.0, 200.0, 1077.0 ], [ 730.0, 76.0, 341.0, 382.0, 232.0, 909.0, 61.0, 1653.0, 52.0, 1078.0, 562.0, 1434.0, 22.0, 29.0, 185.0, 1429.0 ], [ 84.0, 70.0, 66.0, 78.0, 131.0, 561.0, 155.0, 829.0, 37.0, 220.0, 79.0, 683.0, 191.0, 53.0, 311.0, 640.0 ], [ 672.0, 370.0, 586.0, 165.0, 770.0, 254.0, 500.0, 1206.0, 46.0, 1034.0, 429.0, 849.0, 774.0, 298.0, 935.0, 943.0 ] ], "demands": [ 28.0, 23.0, 28.0, 18.0, 12.0, 20.0, 29.0, 22.0, 18.0, 27.0, 23.0, 21.0, 11.0, 11.0, 29.0, 11.0 ], "objective": 4283.0 }, "solution": { "open_facilities": [ 3, 4 ], "assignments": [ 3, 4, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 4, 4, 3 ] }, "obj": 4283.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 16, "facilities": [ { "id": "F1", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F2", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F3", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F4", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F5", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F6", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F7", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F8", "opening_cost": 600.0, "capacity": 700.0 } ], "customers": [ { "id": 0, "demand": 28.0 }, { "id": 1, "demand": 23.0 }, { "id": 2, "demand": 28.0 }, { "id": 3, "demand": 18.0 }, { "id": 4, "demand": 12.0 }, { "id": 5, "demand": 20.0 }, { "id": 6, "demand": 29.0 }, { "id": 7, "demand": 22.0 }, { "id": 8, "demand": 18.0 }, { "id": 9, "demand": 27.0 }, { "id": 10, "demand": 23.0 }, { "id": 11, "demand": 21.0 }, { "id": 12, "demand": 11.0 }, { "id": 13, "demand": 11.0 }, { "id": 14, "demand": 29.0 }, { "id": 15, "demand": 11.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 83.0 }, { "facility": "F1", "customer": 1, "cost": 120.0 }, { "facility": "F1", "customer": 2, "cost": 145.0 }, { "facility": "F1", "customer": 3, "cost": 42.0 }, { "facility": "F1", "customer": 4, "cost": 282.0 }, { "facility": "F1", "customer": 5, "cost": 477.0 }, { "facility": "F1", "customer": 6, "cost": 231.0 }, { "facility": "F1", "customer": 7, "cost": 832.0 }, { "facility": "F1", "customer": 8, "cost": 36.0 }, { "facility": "F1", "customer": 9, "cost": 383.0 }, { "facility": "F1", "customer": 10, "cost": 46.0 }, { "facility": "F1", "customer": 11, "cost": 623.0 }, { "facility": "F1", "customer": 12, "cost": 335.0 }, { "facility": "F1", "customer": 13, "cost": 97.0 }, { "facility": "F1", "customer": 14, "cost": 475.0 }, { "facility": "F1", "customer": 15, "cost": 606.0 }, { "facility": "F2", "customer": 0, "cost": 634.0 }, { "facility": "F2", "customer": 1, "cost": 260.0 }, { "facility": "F2", "customer": 2, "cost": 478.0 }, { "facility": "F2", "customer": 3, "cost": 58.0 }, { "facility": "F2", "customer": 4, "cost": 660.0 }, { "facility": "F2", "customer": 5, "cost": 463.0 }, { "facility": "F2", "customer": 6, "cost": 391.0 }, { "facility": "F2", "customer": 7, "cost": 1374.0 }, { "facility": "F2", "customer": 8, "cost": 38.0 }, { "facility": "F2", "customer": 9, "cost": 1045.0 }, { "facility": "F2", "customer": 10, "cost": 352.0 }, { "facility": "F2", "customer": 11, "cost": 1057.0 }, { "facility": "F2", "customer": 12, "cost": 656.0 }, { "facility": "F2", "customer": 13, "cost": 201.0 }, { "facility": "F2", "customer": 14, "cost": 817.0 }, { "facility": "F2", "customer": 15, "cost": 1112.0 }, { "facility": "F3", "customer": 0, "cost": 517.0 }, { "facility": "F3", "customer": 1, "cost": 364.0 }, { "facility": "F3", "customer": 2, "cost": 515.0 }, { "facility": "F3", "customer": 3, "cost": 161.0 }, { "facility": "F3", "customer": 4, "cost": 691.0 }, { "facility": "F3", "customer": 5, "cost": 142.0 }, { "facility": "F3", "customer": 6, "cost": 495.0 }, { "facility": "F3", "customer": 7, "cost": 729.0 }, { "facility": "F3", "customer": 8, "cost": 50.0 }, { "facility": "F3", "customer": 9, "cost": 781.0 }, { "facility": "F3", "customer": 10, "cost": 342.0 }, { "facility": "F3", "customer": 11, "cost": 374.0 }, { "facility": "F3", "customer": 12, "cost": 720.0 }, { "facility": "F3", "customer": 13, "cost": 303.0 }, { "facility": "F3", "customer": 14, "cost": 875.0 }, { "facility": "F3", "customer": 15, "cost": 501.0 }, { "facility": "F4", "customer": 0, "cost": 213.0 }, { "facility": "F4", "customer": 1, "cost": 193.0 }, { "facility": "F4", "customer": 2, "cost": 257.0 }, { "facility": "F4", "customer": 3, "cost": 44.0 }, { "facility": "F4", "customer": 4, "cost": 412.0 }, { "facility": "F4", "customer": 5, "cost": 340.0 }, { "facility": "F4", "customer": 6, "cost": 315.0 }, { "facility": "F4", "customer": 7, "cost": 611.0 }, { "facility": "F4", "customer": 8, "cost": 38.0 }, { "facility": "F4", "customer": 9, "cost": 447.0 }, { "facility": "F4", "customer": 10, "cost": 105.0 }, { "facility": "F4", "customer": 11, "cost": 347.0 }, { "facility": "F4", "customer": 12, "cost": 459.0 }, { "facility": "F4", "customer": 13, "cost": 158.0 }, { "facility": "F4", "customer": 14, "cost": 604.0 }, { "facility": "F4", "customer": 15, "cost": 356.0 }, { "facility": "F5", "customer": 0, "cost": 389.0 }, { "facility": "F5", "customer": 1, "cost": 46.0 }, { "facility": "F5", "customer": 2, "cost": 102.0 }, { "facility": "F5", "customer": 3, "cost": 208.0 }, { "facility": "F5", "customer": 4, "cost": 33.0 }, { "facility": "F5", "customer": 5, "cost": 750.0 }, { "facility": "F5", "customer": 6, "cost": 91.0 }, { "facility": "F5", "customer": 7, "cost": 1286.0 }, { "facility": "F5", "customer": 8, "cost": 43.0 }, { "facility": "F5", "customer": 9, "cost": 691.0 }, { "facility": "F5", "customer": 10, "cost": 288.0 }, { "facility": "F5", "customer": 11, "cost": 1098.0 }, { "facility": "F5", "customer": 12, "cost": 86.0 }, { "facility": "F5", "customer": 13, "cost": 24.0 }, { "facility": "F5", "customer": 14, "cost": 200.0 }, { "facility": "F5", "customer": 15, "cost": 1077.0 }, { "facility": "F6", "customer": 0, "cost": 730.0 }, { "facility": "F6", "customer": 1, "cost": 76.0 }, { "facility": "F6", "customer": 2, "cost": 341.0 }, { "facility": "F6", "customer": 3, "cost": 382.0 }, { "facility": "F6", "customer": 4, "cost": 232.0 }, { "facility": "F6", "customer": 5, "cost": 909.0 }, { "facility": "F6", "customer": 6, "cost": 61.0 }, { "facility": "F6", "customer": 7, "cost": 1653.0 }, { "facility": "F6", "customer": 8, "cost": 52.0 }, { "facility": "F6", "customer": 9, "cost": 1078.0 }, { "facility": "F6", "customer": 10, "cost": 562.0 }, { "facility": "F6", "customer": 11, "cost": 1434.0 }, { "facility": "F6", "customer": 12, "cost": 22.0 }, { "facility": "F6", "customer": 13, "cost": 29.0 }, { "facility": "F6", "customer": 14, "cost": 185.0 }, { "facility": "F6", "customer": 15, "cost": 1429.0 }, { "facility": "F7", "customer": 0, "cost": 84.0 }, { "facility": "F7", "customer": 1, "cost": 70.0 }, { "facility": "F7", "customer": 2, "cost": 66.0 }, { "facility": "F7", "customer": 3, "cost": 78.0 }, { "facility": "F7", "customer": 4, "cost": 131.0 }, { "facility": "F7", "customer": 5, "cost": 561.0 }, { "facility": "F7", "customer": 6, "cost": 155.0 }, { "facility": "F7", "customer": 7, "cost": 829.0 }, { "facility": "F7", "customer": 8, "cost": 37.0 }, { "facility": "F7", "customer": 9, "cost": 220.0 }, { "facility": "F7", "customer": 10, "cost": 79.0 }, { "facility": "F7", "customer": 11, "cost": 683.0 }, { "facility": "F7", "customer": 12, "cost": 191.0 }, { "facility": "F7", "customer": 13, "cost": 53.0 }, { "facility": "F7", "customer": 14, "cost": 311.0 }, { "facility": "F7", "customer": 15, "cost": 640.0 }, { "facility": "F8", "customer": 0, "cost": 672.0 }, { "facility": "F8", "customer": 1, "cost": 370.0 }, { "facility": "F8", "customer": 2, "cost": 586.0 }, { "facility": "F8", "customer": 3, "cost": 165.0 }, { "facility": "F8", "customer": 4, "cost": 770.0 }, { "facility": "F8", "customer": 5, "cost": 254.0 }, { "facility": "F8", "customer": 6, "cost": 500.0 }, { "facility": "F8", "customer": 7, "cost": 1206.0 }, { "facility": "F8", "customer": 8, "cost": 46.0 }, { "facility": "F8", "customer": 9, "cost": 1034.0 }, { "facility": "F8", "customer": 10, "cost": 429.0 }, { "facility": "F8", "customer": 11, "cost": 849.0 }, { "facility": "F8", "customer": 12, "cost": 774.0 }, { "facility": "F8", "customer": 13, "cost": 298.0 }, { "facility": "F8", "customer": 14, "cost": 935.0 }, { "facility": "F8", "customer": 15, "cost": 943.0 } ], "objective": 4283.0 }, "solution_variant": { "selected": [ "F4", "F5" ], "assignments": [ "F4", "F5", "F5", "F4", "F5", "F4", "F5", "F4", "F4", "F4", "F4", "F4", "F5", "F5", "F5", "F4" ] }, "context_index": 8, "input_format": "nl", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "We manage local solar install crews and need to figure out which teams to switch on and which team will do each installation. Each team you turn on charges an activation fee and can only take on a certain amount of work; sending a team to a customer also costs travel and the actual service time. What makes one plan better than another is the final tab: add up the charges for every team we activated plus every travel and service cost for each assigned customer, and choose the assignment that produces the lowest total, while making sure every customer is assigned to one active team and no team’s workload goes over its limit. The exact team fees, capacities, and customer requests are shown below.\n\n{\n \"num_teams\": 9,\n \"num_customers\": 19,\n \"teams\": [\n {\n \"team_id\": \"F1\",\n \"activation_fee\": 600.0,\n \"workload_capacity\": 500.0\n },\n {\n \"team_id\": \"F2\",\n \"activation_fee\": 600.0,\n \"workload_capacity\": 500.0\n },\n {\n \"team_id\": \"F3\",\n \"activation_fee\": 600.0,\n \"workload_capacity\": 500.0\n },\n {\n \"team_id\": \"F4\",\n \"activation_fee\": 600.0,\n \"workload_capacity\": 500.0\n },\n {\n \"team_id\": \"F5\",\n \"activation_fee\": 600.0,\n \"workload_capacity\": 500.0\n },\n {\n \"team_id\": \"F6\",\n \"activation_fee\": 600.0,\n \"workload_capacity\": 500.0\n },\n {\n \"team_id\": \"F7\",\n \"activation_fee\": 600.0,\n \"workload_capacity\": 500.0\n },\n {\n \"team_id\": \"F8\",\n \"activation_fee\": 600.0,\n \"workload_capacity\": 500.0\n },\n {\n \"team_id\": \"F9\",\n \"activation_fee\": 600.0,\n \"workload_capacity\": 500.0\n }\n ],\n \"requests\": [\n {\n \"request_id\": 1,\n \"installation_demand\": 18.0\n },\n {\n \"request_id\": 2,\n \"installation_demand\": 20.0\n },\n {\n \"request_id\": 3,\n \"installation_demand\": 15.0\n },\n {\n \"request_id\": 4,\n \"installation_demand\": 23.0\n },\n {\n \"request_id\": 5,\n \"installation_demand\": 18.0\n },\n {\n \"request_id\": 6,\n \"installation_demand\": 19.0\n },\n {\n \"request_id\": 7,\n \"installation_demand\": 19.0\n },\n {\n \"request_id\": 8,\n \"installation_demand\": 22.0\n },\n {\n \"request_id\": 9,\n \"installation_demand\": 19.0\n },\n {\n \"request_id\": 10,\n \"installation_demand\": 17.0\n },\n {\n \"request_id\": 11,\n \"installation_demand\": 23.0\n },\n {\n \"request_id\": 12,\n \"installation_demand\": 16.0\n },\n {\n \"request_id\": 13,\n \"installation_demand\": 18.0\n },\n {\n \"request_id\": 14,\n \"installation_demand\": 20.0\n },\n {\n \"request_id\": 15,\n \"installation_demand\": 29.0\n },\n {\n \"request_id\": 16,\n \"installation_demand\": 27.0\n },\n {\n \"request_id\": 17,\n \"installation_demand\": 13.0\n },\n {\n \"request_id\": 18,\n \"installation_demand\": 27.0\n },\n {\n \"request_id\": 19,\n \"installation_demand\": 22.0\n }\n ],\n \"travel_and_services\": [\n {\n \"team_id\": \"F1\",\n \"request_id\": 1,\n \"travel_and_service_cost\": 113.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 2,\n \"travel_and_service_cost\": 43.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 3,\n \"travel_and_service_cost\": 140.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 4,\n \"travel_and_service_cost\": 243.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 5,\n \"travel_and_service_cost\": 205.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 6,\n \"travel_and_service_cost\": 595.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 7,\n \"travel_and_service_cost\": 182.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 8,\n \"travel_and_service_cost\": 310.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 9,\n \"travel_and_service_cost\": 755.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 10,\n \"travel_and_service_cost\": 173.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 11,\n \"travel_and_service_cost\": 360.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 12,\n \"travel_and_service_cost\": 56.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 13,\n \"travel_and_service_cost\": 242.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 14,\n \"travel_and_service_cost\": 546.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 15,\n \"travel_and_service_cost\": 91.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 16,\n \"travel_and_service_cost\": 350.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 17,\n \"travel_and_service_cost\": 156.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 18,\n \"travel_and_service_cost\": 55.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 19,\n \"travel_and_service_cost\": 602.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 1,\n \"travel_and_service_cost\": 39.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 2,\n \"travel_and_service_cost\": 255.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 3,\n \"travel_and_service_cost\": 31.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 4,\n \"travel_and_service_cost\": 71.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 5,\n \"travel_and_service_cost\": 663.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 6,\n \"travel_and_service_cost\": 72.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 7,\n \"travel_and_service_cost\": 95.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 8,\n \"travel_and_service_cost\": 64.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 9,\n \"travel_and_service_cost\": 646.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 10,\n \"travel_and_service_cost\": 48.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 11,\n \"travel_and_service_cost\": 709.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 12,\n \"travel_and_service_cost\": 235.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 13,\n \"travel_and_service_cost\": 131.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 14,\n \"travel_and_service_cost\": 186.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 15,\n \"travel_and_service_cost\": 58.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 16,\n \"travel_and_service_cost\": 788.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 17,\n \"travel_and_service_cost\": 50.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 18,\n \"travel_and_service_cost\": 461.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 19,\n \"travel_and_service_cost\": 68.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 1,\n \"travel_and_service_cost\": 76.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 2,\n \"travel_and_service_cost\": 87.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 3,\n \"travel_and_service_cost\": 72.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 4,\n \"travel_and_service_cost\": 103.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 5,\n \"travel_and_service_cost\": 342.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 6,\n \"travel_and_service_cost\": 376.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 7,\n \"travel_and_service_cost\": 63.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 8,\n \"travel_and_service_cost\": 196.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 9,\n \"travel_and_service_cost\": 524.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 10,\n \"travel_and_service_cost\": 116.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 11,\n \"travel_and_service_cost\": 474.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 12,\n \"travel_and_service_cost\": 43.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 13,\n \"travel_and_service_cost\": 72.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 14,\n \"travel_and_service_cost\": 403.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 15,\n \"travel_and_service_cost\": 72.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 16,\n \"travel_and_service_cost\": 486.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 17,\n \"travel_and_service_cost\": 58.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 18,\n \"travel_and_service_cost\": 156.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 19,\n \"travel_and_service_cost\": 378.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 1,\n \"travel_and_service_cost\": 147.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 2,\n \"travel_and_service_cost\": 1048.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 3,\n \"travel_and_service_cost\": 684.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 4,\n \"travel_and_service_cost\": 1337.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 5,\n \"travel_and_service_cost\": 1825.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 6,\n \"travel_and_service_cost\": 1639.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 7,\n \"travel_and_service_cost\": 1338.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 8,\n \"travel_and_service_cost\": 889.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 9,\n \"travel_and_service_cost\": 2409.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 10,\n \"travel_and_service_cost\": 337.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 11,\n \"travel_and_service_cost\": 1262.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 12,\n \"travel_and_service_cost\": 1396.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 13,\n \"travel_and_service_cost\": 1562.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 14,\n \"travel_and_service_cost\": 1048.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 15,\n \"travel_and_service_cost\": 64.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 16,\n \"travel_and_service_cost\": 1717.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 17,\n \"travel_and_service_cost\": 1120.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 18,\n \"travel_and_service_cost\": 1738.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 19,\n \"travel_and_service_cost\": 1689.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 1,\n \"travel_and_service_cost\": 113.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 2,\n \"travel_and_service_cost\": 48.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 3,\n \"travel_and_service_cost\": 147.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 4,\n \"travel_and_service_cost\": 298.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 5,\n \"travel_and_service_cost\": 418.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 6,\n \"travel_and_service_cost\": 690.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 7,\n \"travel_and_service_cost\": 233.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 8,\n \"travel_and_service_cost\": 333.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 9,\n \"travel_and_service_cost\": 1017.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 10,\n \"travel_and_service_cost\": 176.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 11,\n \"travel_and_service_cost\": 425.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 12,\n \"travel_and_service_cost\": 75.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 13,\n \"travel_and_service_cost\": 342.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 14,\n \"travel_and_service_cost\": 578.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 15,\n \"travel_and_service_cost\": 89.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 16,\n \"travel_and_service_cost\": 491.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 17,\n \"travel_and_service_cost\": 185.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 18,\n \"travel_and_service_cost\": 273.0\n },\n {\n \"team_id\": \"F5\",\n \"request_id\": 19,\n \"travel_and_service_cost\": 704.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 1,\n \"travel_and_service_cost\": 53.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 2,\n \"travel_and_service_cost\": 395.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 3,\n \"travel_and_service_cost\": 40.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 4,\n \"travel_and_service_cost\": 459.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 5,\n \"travel_and_service_cost\": 1095.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 6,\n \"travel_and_service_cost\": 799.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 7,\n \"travel_and_service_cost\": 467.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 8,\n \"travel_and_service_cost\": 216.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 9,\n \"travel_and_service_cost\": 1542.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 10,\n \"travel_and_service_cost\": 84.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 11,\n \"travel_and_service_cost\": 839.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 12,\n \"travel_and_service_cost\": 589.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 13,\n \"travel_and_service_cost\": 690.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 14,\n \"travel_and_service_cost\": 471.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 15,\n \"travel_and_service_cost\": 61.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 16,\n \"travel_and_service_cost\": 1094.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 17,\n \"travel_and_service_cost\": 244.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 18,\n \"travel_and_service_cost\": 944.0\n },\n {\n \"team_id\": \"F6\",\n \"request_id\": 19,\n \"travel_and_service_cost\": 841.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 1,\n \"travel_and_service_cost\": 42.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 2,\n \"travel_and_service_cost\": 941.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 3,\n \"travel_and_service_cost\": 463.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 4,\n \"travel_and_service_cost\": 1120.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 5,\n \"travel_and_service_cost\": 1709.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 6,\n \"travel_and_service_cost\": 1376.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 7,\n \"travel_and_service_cost\": 1136.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 8,\n \"travel_and_service_cost\": 613.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 9,\n \"travel_and_service_cost\": 2210.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 10,\n \"travel_and_service_cost\": 34.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 11,\n \"travel_and_service_cost\": 1246.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 12,\n \"travel_and_service_cost\": 1237.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 13,\n \"travel_and_service_cost\": 1358.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 14,\n \"travel_and_service_cost\": 745.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 15,\n \"travel_and_service_cost\": 68.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 16,\n \"travel_and_service_cost\": 1643.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 17,\n \"travel_and_service_cost\": 912.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 18,\n \"travel_and_service_cost\": 1590.0\n },\n {\n \"team_id\": \"F7\",\n \"request_id\": 19,\n \"travel_and_service_cost\": 1430.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 1,\n \"travel_and_service_cost\": 56.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 2,\n \"travel_and_service_cost\": 196.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 3,\n \"travel_and_service_cost\": 42.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 4,\n \"travel_and_service_cost\": 55.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 5,\n \"travel_and_service_cost\": 682.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 6,\n \"travel_and_service_cost\": 388.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 7,\n \"travel_and_service_cost\": 42.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 8,\n \"travel_and_service_cost\": 145.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 9,\n \"travel_and_service_cost\": 960.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 10,\n \"travel_and_service_cost\": 83.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 11,\n \"travel_and_service_cost\": 654.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 12,\n \"travel_and_service_cost\": 192.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 13,\n \"travel_and_service_cost\": 116.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 14,\n \"travel_and_service_cost\": 353.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 15,\n \"travel_and_service_cost\": 63.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 16,\n \"travel_and_service_cost\": 770.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 17,\n \"travel_and_service_cost\": 27.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 18,\n \"travel_and_service_cost\": 483.0\n },\n {\n \"team_id\": \"F8\",\n \"request_id\": 19,\n \"travel_and_service_cost\": 402.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 1,\n \"travel_and_service_cost\": 47.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 2,\n \"travel_and_service_cost\": 274.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 3,\n \"travel_and_service_cost\": 32.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 4,\n \"travel_and_service_cost\": 67.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 5,\n \"travel_and_service_cost\": 828.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 6,\n \"travel_and_service_cost\": 398.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 7,\n \"travel_and_service_cost\": 121.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 8,\n \"travel_and_service_cost\": 114.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 9,\n \"travel_and_service_cost\": 1115.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 10,\n \"travel_and_service_cost\": 67.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 11,\n \"travel_and_service_cost\": 741.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 12,\n \"travel_and_service_cost\": 317.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 13,\n \"travel_and_service_cost\": 282.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 14,\n \"travel_and_service_cost\": 318.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 15,\n \"travel_and_service_cost\": 59.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 16,\n \"travel_and_service_cost\": 896.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 17,\n \"travel_and_service_cost\": 37.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 18,\n \"travel_and_service_cost\": 636.0\n },\n {\n \"team_id\": \"F9\",\n \"request_id\": 19,\n \"travel_and_service_cost\": 425.0\n }\n ]\n}\n\nWhen you send the plan back, please use this simple JSON layout so it's easy to read and plug into our system:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of crews/teams you switched on (the ones we'll pay an activation fee for), and \"assignments\" as which switched-on crew will handle each customer in the same order the customers were given. This is just the shape I expect — a sketch, not the final numbers.\n\nPlease use the exact identifiers from the instance input — do not rename them or invent new ones. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 113.0, 43.0, 140.0, 243.0, 205.0, 595.0, 182.0, 310.0, 755.0, 173.0, 360.0, 56.0, 242.0, 546.0, 91.0, 350.0, 156.0, 55.0, 602.0 ], [ 39.0, 255.0, 31.0, 71.0, 663.0, 72.0, 95.0, 64.0, 646.0, 48.0, 709.0, 235.0, 131.0, 186.0, 58.0, 788.0, 50.0, 461.0, 68.0 ], [ 76.0, 87.0, 72.0, 103.0, 342.0, 376.0, 63.0, 196.0, 524.0, 116.0, 474.0, 43.0, 72.0, 403.0, 72.0, 486.0, 58.0, 156.0, 378.0 ], [ 147.0, 1048.0, 684.0, 1337.0, 1825.0, 1639.0, 1338.0, 889.0, 2409.0, 337.0, 1262.0, 1396.0, 1562.0, 1048.0, 64.0, 1717.0, 1120.0, 1738.0, 1689.0 ], [ 113.0, 48.0, 147.0, 298.0, 418.0, 690.0, 233.0, 333.0, 1017.0, 176.0, 425.0, 75.0, 342.0, 578.0, 89.0, 491.0, 185.0, 273.0, 704.0 ], [ 53.0, 395.0, 40.0, 459.0, 1095.0, 799.0, 467.0, 216.0, 1542.0, 84.0, 839.0, 589.0, 690.0, 471.0, 61.0, 1094.0, 244.0, 944.0, 841.0 ], [ 42.0, 941.0, 463.0, 1120.0, 1709.0, 1376.0, 1136.0, 613.0, 2210.0, 34.0, 1246.0, 1237.0, 1358.0, 745.0, 68.0, 1643.0, 912.0, 1590.0, 1430.0 ], [ 56.0, 196.0, 42.0, 55.0, 682.0, 388.0, 42.0, 145.0, 960.0, 83.0, 654.0, 192.0, 116.0, 353.0, 63.0, 770.0, 27.0, 483.0, 402.0 ], [ 47.0, 274.0, 32.0, 67.0, 828.0, 398.0, 121.0, 114.0, 1115.0, 67.0, 741.0, 317.0, 282.0, 318.0, 59.0, 896.0, 37.0, 636.0, 425.0 ] ], "demands": [ 18.0, 20.0, 15.0, 23.0, 18.0, 19.0, 19.0, 22.0, 19.0, 17.0, 23.0, 16.0, 18.0, 20.0, 29.0, 27.0, 13.0, 27.0, 22.0 ], "objective": 3828.0 }, "solution": { "open_facilities": [ 0, 1 ], "assignments": [ 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1 ] }, "obj": 3828.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 9, "num_customers": 19, "facilities": [ { "id": "F1", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F2", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F3", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F4", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F5", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F6", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F7", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F8", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F9", "opening_cost": 600.0, "capacity": 500.0 } ], "customers": [ { "id": 1, "demand": 18.0 }, { "id": 2, "demand": 20.0 }, { "id": 3, "demand": 15.0 }, { "id": 4, "demand": 23.0 }, { "id": 5, "demand": 18.0 }, { "id": 6, "demand": 19.0 }, { "id": 7, "demand": 19.0 }, { "id": 8, "demand": 22.0 }, { "id": 9, "demand": 19.0 }, { "id": 10, "demand": 17.0 }, { "id": 11, "demand": 23.0 }, { "id": 12, "demand": 16.0 }, { "id": 13, "demand": 18.0 }, { "id": 14, "demand": 20.0 }, { "id": 15, "demand": 29.0 }, { "id": 16, "demand": 27.0 }, { "id": 17, "demand": 13.0 }, { "id": 18, "demand": 27.0 }, { "id": 19, "demand": 22.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 113.0 }, { "facility": "F1", "customer": 2, "cost": 43.0 }, { "facility": "F1", "customer": 3, "cost": 140.0 }, { "facility": "F1", "customer": 4, "cost": 243.0 }, { "facility": "F1", "customer": 5, "cost": 205.0 }, { "facility": "F1", "customer": 6, "cost": 595.0 }, { "facility": "F1", "customer": 7, "cost": 182.0 }, { "facility": "F1", "customer": 8, "cost": 310.0 }, { "facility": "F1", "customer": 9, "cost": 755.0 }, { "facility": "F1", "customer": 10, "cost": 173.0 }, { "facility": "F1", "customer": 11, "cost": 360.0 }, { "facility": "F1", "customer": 12, "cost": 56.0 }, { "facility": "F1", "customer": 13, "cost": 242.0 }, { "facility": "F1", "customer": 14, "cost": 546.0 }, { "facility": "F1", "customer": 15, "cost": 91.0 }, { "facility": "F1", "customer": 16, "cost": 350.0 }, { "facility": "F1", "customer": 17, "cost": 156.0 }, { "facility": "F1", "customer": 18, "cost": 55.0 }, { "facility": "F1", "customer": 19, "cost": 602.0 }, { "facility": "F2", "customer": 1, "cost": 39.0 }, { "facility": "F2", "customer": 2, "cost": 255.0 }, { "facility": "F2", "customer": 3, "cost": 31.0 }, { "facility": "F2", "customer": 4, "cost": 71.0 }, { "facility": "F2", "customer": 5, "cost": 663.0 }, { "facility": "F2", "customer": 6, "cost": 72.0 }, { "facility": "F2", "customer": 7, "cost": 95.0 }, { "facility": "F2", "customer": 8, "cost": 64.0 }, { "facility": "F2", "customer": 9, "cost": 646.0 }, { "facility": "F2", "customer": 10, "cost": 48.0 }, { "facility": "F2", "customer": 11, "cost": 709.0 }, { "facility": "F2", "customer": 12, "cost": 235.0 }, { "facility": "F2", "customer": 13, "cost": 131.0 }, { "facility": "F2", "customer": 14, "cost": 186.0 }, { "facility": "F2", "customer": 15, "cost": 58.0 }, { "facility": "F2", "customer": 16, "cost": 788.0 }, { "facility": "F2", "customer": 17, "cost": 50.0 }, { "facility": "F2", "customer": 18, "cost": 461.0 }, { "facility": "F2", "customer": 19, "cost": 68.0 }, { "facility": "F3", "customer": 1, "cost": 76.0 }, { "facility": "F3", "customer": 2, "cost": 87.0 }, { "facility": "F3", "customer": 3, "cost": 72.0 }, { "facility": "F3", "customer": 4, "cost": 103.0 }, { "facility": "F3", "customer": 5, "cost": 342.0 }, { "facility": "F3", "customer": 6, "cost": 376.0 }, { "facility": "F3", "customer": 7, "cost": 63.0 }, { "facility": "F3", "customer": 8, "cost": 196.0 }, { "facility": "F3", "customer": 9, "cost": 524.0 }, { "facility": "F3", "customer": 10, "cost": 116.0 }, { "facility": "F3", "customer": 11, "cost": 474.0 }, { "facility": "F3", "customer": 12, "cost": 43.0 }, { "facility": "F3", "customer": 13, "cost": 72.0 }, { "facility": "F3", "customer": 14, "cost": 403.0 }, { "facility": "F3", "customer": 15, "cost": 72.0 }, { "facility": "F3", "customer": 16, "cost": 486.0 }, { "facility": "F3", "customer": 17, "cost": 58.0 }, { "facility": "F3", "customer": 18, "cost": 156.0 }, { "facility": "F3", "customer": 19, "cost": 378.0 }, { "facility": "F4", "customer": 1, "cost": 147.0 }, { "facility": "F4", "customer": 2, "cost": 1048.0 }, { "facility": "F4", "customer": 3, "cost": 684.0 }, { "facility": "F4", "customer": 4, "cost": 1337.0 }, { "facility": "F4", "customer": 5, "cost": 1825.0 }, { "facility": "F4", "customer": 6, "cost": 1639.0 }, { "facility": "F4", "customer": 7, "cost": 1338.0 }, { "facility": "F4", "customer": 8, "cost": 889.0 }, { "facility": "F4", "customer": 9, "cost": 2409.0 }, { "facility": "F4", "customer": 10, "cost": 337.0 }, { "facility": "F4", "customer": 11, "cost": 1262.0 }, { "facility": "F4", "customer": 12, "cost": 1396.0 }, { "facility": "F4", "customer": 13, "cost": 1562.0 }, { "facility": "F4", "customer": 14, "cost": 1048.0 }, { "facility": "F4", "customer": 15, "cost": 64.0 }, { "facility": "F4", "customer": 16, "cost": 1717.0 }, { "facility": "F4", "customer": 17, "cost": 1120.0 }, { "facility": "F4", "customer": 18, "cost": 1738.0 }, { "facility": "F4", "customer": 19, "cost": 1689.0 }, { "facility": "F5", "customer": 1, "cost": 113.0 }, { "facility": "F5", "customer": 2, "cost": 48.0 }, { "facility": "F5", "customer": 3, "cost": 147.0 }, { "facility": "F5", "customer": 4, "cost": 298.0 }, { "facility": "F5", "customer": 5, "cost": 418.0 }, { "facility": "F5", "customer": 6, "cost": 690.0 }, { "facility": "F5", "customer": 7, "cost": 233.0 }, { "facility": "F5", "customer": 8, "cost": 333.0 }, { "facility": "F5", "customer": 9, "cost": 1017.0 }, { "facility": "F5", "customer": 10, "cost": 176.0 }, { "facility": "F5", "customer": 11, "cost": 425.0 }, { "facility": "F5", "customer": 12, "cost": 75.0 }, { "facility": "F5", "customer": 13, "cost": 342.0 }, { "facility": "F5", "customer": 14, "cost": 578.0 }, { "facility": "F5", "customer": 15, "cost": 89.0 }, { "facility": "F5", "customer": 16, "cost": 491.0 }, { "facility": "F5", "customer": 17, "cost": 185.0 }, { "facility": "F5", "customer": 18, "cost": 273.0 }, { "facility": "F5", "customer": 19, "cost": 704.0 }, { "facility": "F6", "customer": 1, "cost": 53.0 }, { "facility": "F6", "customer": 2, "cost": 395.0 }, { "facility": "F6", "customer": 3, "cost": 40.0 }, { "facility": "F6", "customer": 4, "cost": 459.0 }, { "facility": "F6", "customer": 5, "cost": 1095.0 }, { "facility": "F6", "customer": 6, "cost": 799.0 }, { "facility": "F6", "customer": 7, "cost": 467.0 }, { "facility": "F6", "customer": 8, "cost": 216.0 }, { "facility": "F6", "customer": 9, "cost": 1542.0 }, { "facility": "F6", "customer": 10, "cost": 84.0 }, { "facility": "F6", "customer": 11, "cost": 839.0 }, { "facility": "F6", "customer": 12, "cost": 589.0 }, { "facility": "F6", "customer": 13, "cost": 690.0 }, { "facility": "F6", "customer": 14, "cost": 471.0 }, { "facility": "F6", "customer": 15, "cost": 61.0 }, { "facility": "F6", "customer": 16, "cost": 1094.0 }, { "facility": "F6", "customer": 17, "cost": 244.0 }, { "facility": "F6", "customer": 18, "cost": 944.0 }, { "facility": "F6", "customer": 19, "cost": 841.0 }, { "facility": "F7", "customer": 1, "cost": 42.0 }, { "facility": "F7", "customer": 2, "cost": 941.0 }, { "facility": "F7", "customer": 3, "cost": 463.0 }, { "facility": "F7", "customer": 4, "cost": 1120.0 }, { "facility": "F7", "customer": 5, "cost": 1709.0 }, { "facility": "F7", "customer": 6, "cost": 1376.0 }, { "facility": "F7", "customer": 7, "cost": 1136.0 }, { "facility": "F7", "customer": 8, "cost": 613.0 }, { "facility": "F7", "customer": 9, "cost": 2210.0 }, { "facility": "F7", "customer": 10, "cost": 34.0 }, { "facility": "F7", "customer": 11, "cost": 1246.0 }, { "facility": "F7", "customer": 12, "cost": 1237.0 }, { "facility": "F7", "customer": 13, "cost": 1358.0 }, { "facility": "F7", "customer": 14, "cost": 745.0 }, { "facility": "F7", "customer": 15, "cost": 68.0 }, { "facility": "F7", "customer": 16, "cost": 1643.0 }, { "facility": "F7", "customer": 17, "cost": 912.0 }, { "facility": "F7", "customer": 18, "cost": 1590.0 }, { "facility": "F7", "customer": 19, "cost": 1430.0 }, { "facility": "F8", "customer": 1, "cost": 56.0 }, { "facility": "F8", "customer": 2, "cost": 196.0 }, { "facility": "F8", "customer": 3, "cost": 42.0 }, { "facility": "F8", "customer": 4, "cost": 55.0 }, { "facility": "F8", "customer": 5, "cost": 682.0 }, { "facility": "F8", "customer": 6, "cost": 388.0 }, { "facility": "F8", "customer": 7, "cost": 42.0 }, { "facility": "F8", "customer": 8, "cost": 145.0 }, { "facility": "F8", "customer": 9, "cost": 960.0 }, { "facility": "F8", "customer": 10, "cost": 83.0 }, { "facility": "F8", "customer": 11, "cost": 654.0 }, { "facility": "F8", "customer": 12, "cost": 192.0 }, { "facility": "F8", "customer": 13, "cost": 116.0 }, { "facility": "F8", "customer": 14, "cost": 353.0 }, { "facility": "F8", "customer": 15, "cost": 63.0 }, { "facility": "F8", "customer": 16, "cost": 770.0 }, { "facility": "F8", "customer": 17, "cost": 27.0 }, { "facility": "F8", "customer": 18, "cost": 483.0 }, { "facility": "F8", "customer": 19, "cost": 402.0 }, { "facility": "F9", "customer": 1, "cost": 47.0 }, { "facility": "F9", "customer": 2, "cost": 274.0 }, { "facility": "F9", "customer": 3, "cost": 32.0 }, { "facility": "F9", "customer": 4, "cost": 67.0 }, { "facility": "F9", "customer": 5, "cost": 828.0 }, { "facility": "F9", "customer": 6, "cost": 398.0 }, { "facility": "F9", "customer": 7, "cost": 121.0 }, { "facility": "F9", "customer": 8, "cost": 114.0 }, { "facility": "F9", "customer": 9, "cost": 1115.0 }, { "facility": "F9", "customer": 10, "cost": 67.0 }, { "facility": "F9", "customer": 11, "cost": 741.0 }, { "facility": "F9", "customer": 12, "cost": 317.0 }, { "facility": "F9", "customer": 13, "cost": 282.0 }, { "facility": "F9", "customer": 14, "cost": 318.0 }, { "facility": "F9", "customer": 15, "cost": 59.0 }, { "facility": "F9", "customer": 16, "cost": 896.0 }, { "facility": "F9", "customer": 17, "cost": 37.0 }, { "facility": "F9", "customer": 18, "cost": 636.0 }, { "facility": "F9", "customer": 19, "cost": 425.0 } ], "objective": 3828.0 }, "solution_variant": { "selected": [ "F1", "F2" ], "assignments": [ "F2", "F1", "F2", "F2", "F1", "F2", "F2", "F2", "F2", "F2", "F1", "F1", "F2", "F2", "F2", "F1", "F2", "F1", "F2" ] }, "context_index": 9, "input_format": "json", "input_index_base": 1 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Picture a rollout where each potential tower has a startup cost and a limit on how many users it can serve, and each service area has a certain number of users. The job is to decide which towers to commission and to assign each service area to exactly one of the commissioned towers — no area is left unassigned or assigned twice, and no tower is overloaded. The best plan is the one with the smallest overall bill: add together the commissioning costs for all commissioned towers and the connection penalties for each area’s assignment, and keep that sum as low as possible. The actual numbers for costs, capacities, and connection penalties are shown below.\n\nThere are 7 towers and 15 areas in this instance.\n\n**Towers**\n| tower_id | commissioning_cost | user_capacity |\n|---|---|---|\n| F1 | 372.0 | 436.0 |\n| F2 | 372.0 | 436.0 |\n| F3 | 253.0 | 377.0 |\n| F4 | 308.0 | 404.0 |\n| F5 | 114.0 | 307.0 |\n| F6 | 336.0 | 418.0 |\n| F7 | 472.0 | 486.0 |\n\n**Areas**\n| area_id | area_users |\n|---|---|\n| 0 | 30.0 |\n| 1 | 30.0 |\n| 2 | 20.0 |\n| 3 | 20.0 |\n| 4 | 10.0 |\n| 5 | 20.0 |\n| 6 | 10.0 |\n| 7 | 30.0 |\n| 8 | 20.0 |\n| 9 | 10.0 |\n| 10 | 23.0 |\n| 11 | 8.0 |\n| 12 | 2.0 |\n| 13 | 13.0 |\n| 14 | 6.0 |\n\n**Connection Penalty**\n| tower_id | area_id | connection_penalty |\n|---|---|---|\n| F1 | 0 | 289.0 |\n| F1 | 1 | 184.0 |\n| F1 | 2 | 213.0 |\n| F1 | 3 | 226.0 |\n| F1 | 4 | 41.0 |\n| F1 | 5 | 20.0 |\n| F1 | 6 | 324.0 |\n| F1 | 7 | 330.0 |\n| F1 | 8 | 326.0 |\n| F1 | 9 | 318.0 |\n| F1 | 10 | 89.0 |\n| F1 | 11 | 257.0 |\n| F1 | 12 | 117.0 |\n| F1 | 13 | 135.0 |\n| F1 | 14 | 168.0 |\n| F2 | 0 | 251.0 |\n| F2 | 1 | 156.0 |\n| F2 | 2 | 189.0 |\n| F2 | 3 | 200.0 |\n| F2 | 4 | 8.0 |\n| F2 | 5 | 45.0 |\n| F2 | 6 | 286.0 |\n| F2 | 7 | 291.0 |\n| F2 | 8 | 286.0 |\n| F2 | 9 | 280.0 |\n| F2 | 10 | 57.0 |\n| F2 | 11 | 220.0 |\n| F2 | 12 | 97.0 |\n| F2 | 13 | 118.0 |\n| F2 | 14 | 129.0 |\n| F3 | 0 | 153.0 |\n| F3 | 1 | 256.0 |\n| F3 | 2 | 288.0 |\n| F3 | 3 | 278.0 |\n| F3 | 4 | 270.0 |\n| F3 | 5 | 316.0 |\n| F3 | 6 | 22.0 |\n| F3 | 7 | 20.0 |\n| F3 | 8 | 28.0 |\n| F3 | 9 | 160.0 |\n| F3 | 10 | 251.0 |\n| F3 | 11 | 61.0 |\n| F3 | 12 | 228.0 |\n| F3 | 13 | 295.0 |\n| F3 | 14 | 161.0 |\n| F4 | 0 | 144.0 |\n| F4 | 1 | 38.0 |\n| F4 | 2 | 22.0 |\n| F4 | 3 | 8.0 |\n| F4 | 4 | 200.0 |\n| F4 | 5 | 207.0 |\n| F4 | 6 | 292.0 |\n| F4 | 7 | 282.0 |\n| F4 | 8 | 266.0 |\n| F4 | 9 | 165.0 |\n| F4 | 10 | 138.0 |\n| F4 | 11 | 257.0 |\n| F4 | 12 | 259.0 |\n| F4 | 13 | 93.0 |\n| F4 | 14 | 140.0 |\n| F5 | 0 | 195.0 |\n| F5 | 1 | 161.0 |\n| F5 | 2 | 201.0 |\n| F5 | 3 | 204.0 |\n| F5 | 4 | 86.0 |\n| F5 | 5 | 134.0 |\n| F5 | 6 | 197.0 |\n| F5 | 7 | 204.0 |\n| F5 | 8 | 201.0 |\n| F5 | 9 | 223.0 |\n| F5 | 10 | 89.0 |\n| F5 | 11 | 131.0 |\n| F5 | 12 | 71.0 |\n| F5 | 13 | 158.0 |\n| F5 | 14 | 71.0 |\n| F6 | 0 | 178.0 |\n| F6 | 1 | 172.0 |\n| F6 | 2 | 212.0 |\n| F6 | 3 | 212.0 |\n| F6 | 4 | 120.0 |\n| F6 | 5 | 168.0 |\n| F6 | 6 | 163.0 |\n| F6 | 7 | 170.0 |\n| F6 | 8 | 168.0 |\n| F6 | 9 | 204.0 |\n| F6 | 10 | 117.0 |\n| F6 | 11 | 97.0 |\n| F6 | 12 | 89.0 |\n| F6 | 13 | 181.0 |\n| F6 | 14 | 66.0 |\n| F7 | 0 | 93.0 |\n| F7 | 1 | 80.0 |\n| F7 | 2 | 115.0 |\n| F7 | 3 | 108.0 |\n| F7 | 4 | 161.0 |\n| F7 | 5 | 191.0 |\n| F7 | 6 | 197.0 |\n| F7 | 7 | 190.0 |\n| F7 | 8 | 176.0 |\n| F7 | 9 | 122.0 |\n| F7 | 10 | 109.0 |\n| F7 | 11 | 157.0 |\n| F7 | 12 | 188.0 |\n| F7 | 13 | 125.0 |\n| F7 | 14 | 48.0 |\n\nWhen you give the plan, just use a simple JSON layout like this so it's easy to read and parse — nothing fancy, just which sites you open and where each area gets assigned:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is the list of towers you decide to commission, and \"assignments\" says, for each service area in the order given by the instance, which commissioned tower it will use. Think of it like filling out a short form: a list of opened towers, and a list that points each area to one of those towers.\n\nThis JSON is just a sketch of the shape I expect — not the final answer itself. Please make sure to use the exact identifiers from the instance input (do not rename or invent IDs). \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 372.0, 372.0, 253.0, 308.0, 114.0, 336.0, 472.0 ], "capacities": [ 436.0, 436.0, 377.0, 404.0, 307.0, 418.0, 486.0 ], "connection_costs": [ [ 289.0, 184.0, 213.0, 226.0, 41.0, 20.0, 324.0, 330.0, 326.0, 318.0, 89.0, 257.0, 117.0, 135.0, 168.0 ], [ 251.0, 156.0, 189.0, 200.0, 8.0, 45.0, 286.0, 291.0, 286.0, 280.0, 57.0, 220.0, 97.0, 118.0, 129.0 ], [ 153.0, 256.0, 288.0, 278.0, 270.0, 316.0, 22.0, 20.0, 28.0, 160.0, 251.0, 61.0, 228.0, 295.0, 161.0 ], [ 144.0, 38.0, 22.0, 8.0, 200.0, 207.0, 292.0, 282.0, 266.0, 165.0, 138.0, 257.0, 259.0, 93.0, 140.0 ], [ 195.0, 161.0, 201.0, 204.0, 86.0, 134.0, 197.0, 204.0, 201.0, 223.0, 89.0, 131.0, 71.0, 158.0, 71.0 ], [ 178.0, 172.0, 212.0, 212.0, 120.0, 168.0, 163.0, 170.0, 168.0, 204.0, 117.0, 97.0, 89.0, 181.0, 66.0 ], [ 93.0, 80.0, 115.0, 108.0, 161.0, 191.0, 197.0, 190.0, 176.0, 122.0, 109.0, 157.0, 188.0, 125.0, 48.0 ] ], "demands": [ 30.0, 30.0, 20.0, 20.0, 10.0, 20.0, 10.0, 30.0, 20.0, 10.0, 23.0, 8.0, 2.0, 13.0, 6.0 ], "objective": 1722.0 }, "solution": { "open_facilities": [ 2, 3, 4 ], "assignments": [ 3, 3, 3, 3, 4, 4, 2, 2, 2, 2, 4, 2, 4, 3, 4 ] }, "obj": 1722.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 15, "facilities": [ { "id": "F1", "opening_cost": 372.0, "capacity": 436.0 }, { "id": "F2", "opening_cost": 372.0, "capacity": 436.0 }, { "id": "F3", "opening_cost": 253.0, "capacity": 377.0 }, { "id": "F4", "opening_cost": 308.0, "capacity": 404.0 }, { "id": "F5", "opening_cost": 114.0, "capacity": 307.0 }, { "id": "F6", "opening_cost": 336.0, "capacity": 418.0 }, { "id": "F7", "opening_cost": 472.0, "capacity": 486.0 } ], "customers": [ { "id": 0, "demand": 30.0 }, { "id": 1, "demand": 30.0 }, { "id": 2, "demand": 20.0 }, { "id": 3, "demand": 20.0 }, { "id": 4, "demand": 10.0 }, { "id": 5, "demand": 20.0 }, { "id": 6, "demand": 10.0 }, { "id": 7, "demand": 30.0 }, { "id": 8, "demand": 20.0 }, { "id": 9, "demand": 10.0 }, { "id": 10, "demand": 23.0 }, { "id": 11, "demand": 8.0 }, { "id": 12, "demand": 2.0 }, { "id": 13, "demand": 13.0 }, { "id": 14, "demand": 6.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 289.0 }, { "facility": "F1", "customer": 1, "cost": 184.0 }, { "facility": "F1", "customer": 2, "cost": 213.0 }, { "facility": "F1", "customer": 3, "cost": 226.0 }, { "facility": "F1", "customer": 4, "cost": 41.0 }, { "facility": "F1", "customer": 5, "cost": 20.0 }, { "facility": "F1", "customer": 6, "cost": 324.0 }, { "facility": "F1", "customer": 7, "cost": 330.0 }, { "facility": "F1", "customer": 8, "cost": 326.0 }, { "facility": "F1", "customer": 9, "cost": 318.0 }, { "facility": "F1", "customer": 10, "cost": 89.0 }, { "facility": "F1", "customer": 11, "cost": 257.0 }, { "facility": "F1", "customer": 12, "cost": 117.0 }, { "facility": "F1", "customer": 13, "cost": 135.0 }, { "facility": "F1", "customer": 14, "cost": 168.0 }, { "facility": "F2", "customer": 0, "cost": 251.0 }, { "facility": "F2", "customer": 1, "cost": 156.0 }, { "facility": "F2", "customer": 2, "cost": 189.0 }, { "facility": "F2", "customer": 3, "cost": 200.0 }, { "facility": "F2", "customer": 4, "cost": 8.0 }, { "facility": "F2", "customer": 5, "cost": 45.0 }, { "facility": "F2", "customer": 6, "cost": 286.0 }, { "facility": "F2", "customer": 7, "cost": 291.0 }, { "facility": "F2", "customer": 8, "cost": 286.0 }, { "facility": "F2", "customer": 9, "cost": 280.0 }, { "facility": "F2", "customer": 10, "cost": 57.0 }, { "facility": "F2", "customer": 11, "cost": 220.0 }, { "facility": "F2", "customer": 12, "cost": 97.0 }, { "facility": "F2", "customer": 13, "cost": 118.0 }, { "facility": "F2", "customer": 14, "cost": 129.0 }, { "facility": "F3", "customer": 0, "cost": 153.0 }, { "facility": "F3", "customer": 1, "cost": 256.0 }, { "facility": "F3", "customer": 2, "cost": 288.0 }, { "facility": "F3", "customer": 3, "cost": 278.0 }, { "facility": "F3", "customer": 4, "cost": 270.0 }, { "facility": "F3", "customer": 5, "cost": 316.0 }, { "facility": "F3", "customer": 6, "cost": 22.0 }, { "facility": "F3", "customer": 7, "cost": 20.0 }, { "facility": "F3", "customer": 8, "cost": 28.0 }, { "facility": "F3", "customer": 9, "cost": 160.0 }, { "facility": "F3", "customer": 10, "cost": 251.0 }, { "facility": "F3", "customer": 11, "cost": 61.0 }, { "facility": "F3", "customer": 12, "cost": 228.0 }, { "facility": "F3", "customer": 13, "cost": 295.0 }, { "facility": "F3", "customer": 14, "cost": 161.0 }, { "facility": "F4", "customer": 0, "cost": 144.0 }, { "facility": "F4", "customer": 1, "cost": 38.0 }, { "facility": "F4", "customer": 2, "cost": 22.0 }, { "facility": "F4", "customer": 3, "cost": 8.0 }, { "facility": "F4", "customer": 4, "cost": 200.0 }, { "facility": "F4", "customer": 5, "cost": 207.0 }, { "facility": "F4", "customer": 6, "cost": 292.0 }, { "facility": "F4", "customer": 7, "cost": 282.0 }, { "facility": "F4", "customer": 8, "cost": 266.0 }, { "facility": "F4", "customer": 9, "cost": 165.0 }, { "facility": "F4", "customer": 10, "cost": 138.0 }, { "facility": "F4", "customer": 11, "cost": 257.0 }, { "facility": "F4", "customer": 12, "cost": 259.0 }, { "facility": "F4", "customer": 13, "cost": 93.0 }, { "facility": "F4", "customer": 14, "cost": 140.0 }, { "facility": "F5", "customer": 0, "cost": 195.0 }, { "facility": "F5", "customer": 1, "cost": 161.0 }, { "facility": "F5", "customer": 2, "cost": 201.0 }, { "facility": "F5", "customer": 3, "cost": 204.0 }, { "facility": "F5", "customer": 4, "cost": 86.0 }, { "facility": "F5", "customer": 5, "cost": 134.0 }, { "facility": "F5", "customer": 6, "cost": 197.0 }, { "facility": "F5", "customer": 7, "cost": 204.0 }, { "facility": "F5", "customer": 8, "cost": 201.0 }, { "facility": "F5", "customer": 9, "cost": 223.0 }, { "facility": "F5", "customer": 10, "cost": 89.0 }, { "facility": "F5", "customer": 11, "cost": 131.0 }, { "facility": "F5", "customer": 12, "cost": 71.0 }, { "facility": "F5", "customer": 13, "cost": 158.0 }, { "facility": "F5", "customer": 14, "cost": 71.0 }, { "facility": "F6", "customer": 0, "cost": 178.0 }, { "facility": "F6", "customer": 1, "cost": 172.0 }, { "facility": "F6", "customer": 2, "cost": 212.0 }, { "facility": "F6", "customer": 3, "cost": 212.0 }, { "facility": "F6", "customer": 4, "cost": 120.0 }, { "facility": "F6", "customer": 5, "cost": 168.0 }, { "facility": "F6", "customer": 6, "cost": 163.0 }, { "facility": "F6", "customer": 7, "cost": 170.0 }, { "facility": "F6", "customer": 8, "cost": 168.0 }, { "facility": "F6", "customer": 9, "cost": 204.0 }, { "facility": "F6", "customer": 10, "cost": 117.0 }, { "facility": "F6", "customer": 11, "cost": 97.0 }, { "facility": "F6", "customer": 12, "cost": 89.0 }, { "facility": "F6", "customer": 13, "cost": 181.0 }, { "facility": "F6", "customer": 14, "cost": 66.0 }, { "facility": "F7", "customer": 0, "cost": 93.0 }, { "facility": "F7", "customer": 1, "cost": 80.0 }, { "facility": "F7", "customer": 2, "cost": 115.0 }, { "facility": "F7", "customer": 3, "cost": 108.0 }, { "facility": "F7", "customer": 4, "cost": 161.0 }, { "facility": "F7", "customer": 5, "cost": 191.0 }, { "facility": "F7", "customer": 6, "cost": 197.0 }, { "facility": "F7", "customer": 7, "cost": 190.0 }, { "facility": "F7", "customer": 8, "cost": 176.0 }, { "facility": "F7", "customer": 9, "cost": 122.0 }, { "facility": "F7", "customer": 10, "cost": 109.0 }, { "facility": "F7", "customer": 11, "cost": 157.0 }, { "facility": "F7", "customer": 12, "cost": 188.0 }, { "facility": "F7", "customer": 13, "cost": 125.0 }, { "facility": "F7", "customer": 14, "cost": 48.0 } ], "objective": 1722.0 }, "solution_variant": { "selected": [ "F3", "F4", "F5" ], "assignments": [ "F4", "F4", "F4", "F4", "F5", "F5", "F3", "F3", "F3", "F3", "F5", "F3", "F5", "F4", "F5" ] }, "context_index": 10, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Recently the health team put together a list of possible pop-up clinics and all the neighborhoods that need coverage; the task now is choosing which clinics to run and which single clinic each neighborhood will use. Each clinic has a daily throughput cap and an opening cost, and each neighborhood-to-clinic pairing carries a transport cost. The best setup keeps the combined expense down — sum the opening costs for clinics that get opened plus every neighborhood’s travel cost — and it must assign every neighborhood to one open clinic without exceeding any clinic’s daily capacity. Full details are shown below.\n\n{\n \"num_clinics\": 8,\n \"num_neighborhoods\": 20,\n \"clinics\": [\n {\n \"clinic_id\": \"F1\",\n \"clinic_opening_cost\": 600.0,\n \"clinic_daily_throughput\": 500.0\n },\n {\n \"clinic_id\": \"F2\",\n \"clinic_opening_cost\": 600.0,\n \"clinic_daily_throughput\": 500.0\n },\n {\n \"clinic_id\": \"F3\",\n \"clinic_opening_cost\": 600.0,\n \"clinic_daily_throughput\": 500.0\n },\n {\n \"clinic_id\": \"F4\",\n \"clinic_opening_cost\": 600.0,\n \"clinic_daily_throughput\": 500.0\n },\n {\n \"clinic_id\": \"F5\",\n \"clinic_opening_cost\": 600.0,\n \"clinic_daily_throughput\": 500.0\n },\n {\n \"clinic_id\": \"F6\",\n \"clinic_opening_cost\": 600.0,\n \"clinic_daily_throughput\": 500.0\n },\n {\n \"clinic_id\": \"F7\",\n \"clinic_opening_cost\": 600.0,\n \"clinic_daily_throughput\": 500.0\n },\n {\n \"clinic_id\": \"F8\",\n \"clinic_opening_cost\": 600.0,\n \"clinic_daily_throughput\": 500.0\n }\n ],\n \"neighborhoods\": [\n {\n \"neighborhood_id\": 1,\n \"neighborhood_demand\": 14.0\n },\n {\n \"neighborhood_id\": 2,\n \"neighborhood_demand\": 24.0\n },\n {\n \"neighborhood_id\": 3,\n \"neighborhood_demand\": 13.0\n },\n {\n \"neighborhood_id\": 4,\n \"neighborhood_demand\": 12.0\n },\n {\n \"neighborhood_id\": 5,\n \"neighborhood_demand\": 28.0\n },\n {\n \"neighborhood_id\": 6,\n \"neighborhood_demand\": 20.0\n },\n {\n \"neighborhood_id\": 7,\n \"neighborhood_demand\": 23.0\n },\n {\n \"neighborhood_id\": 8,\n \"neighborhood_demand\": 27.0\n },\n {\n \"neighborhood_id\": 9,\n \"neighborhood_demand\": 26.0\n },\n {\n \"neighborhood_id\": 10,\n \"neighborhood_demand\": 20.0\n },\n {\n \"neighborhood_id\": 11,\n \"neighborhood_demand\": 19.0\n },\n {\n \"neighborhood_id\": 12,\n \"neighborhood_demand\": 18.0\n },\n {\n \"neighborhood_id\": 13,\n \"neighborhood_demand\": 22.0\n },\n {\n \"neighborhood_id\": 14,\n \"neighborhood_demand\": 25.0\n },\n {\n \"neighborhood_id\": 15,\n \"neighborhood_demand\": 23.0\n },\n {\n \"neighborhood_id\": 16,\n \"neighborhood_demand\": 21.0\n },\n {\n \"neighborhood_id\": 17,\n \"neighborhood_demand\": 18.0\n },\n {\n \"neighborhood_id\": 18,\n \"neighborhood_demand\": 19.0\n },\n {\n \"neighborhood_id\": 19,\n \"neighborhood_demand\": 25.0\n },\n {\n \"neighborhood_id\": 20,\n \"neighborhood_demand\": 22.0\n }\n ],\n \"transports\": [\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 1,\n \"transport_cost\": 479.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 2,\n \"transport_cost\": 214.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 3,\n \"transport_cost\": 2081.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 4,\n \"transport_cost\": 279.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 5,\n \"transport_cost\": 1640.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 6,\n \"transport_cost\": 943.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 7,\n \"transport_cost\": 910.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 8,\n \"transport_cost\": 792.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 9,\n \"transport_cost\": 222.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 10,\n \"transport_cost\": 960.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 11,\n \"transport_cost\": 1889.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 12,\n \"transport_cost\": 1833.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 13,\n \"transport_cost\": 889.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 14,\n \"transport_cost\": 714.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 15,\n \"transport_cost\": 1443.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 16,\n \"transport_cost\": 1676.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 17,\n \"transport_cost\": 1944.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 18,\n \"transport_cost\": 373.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 19,\n \"transport_cost\": 1284.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 20,\n \"transport_cost\": 1335.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 1,\n \"transport_cost\": 268.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 2,\n \"transport_cost\": 154.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 3,\n \"transport_cost\": 902.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 4,\n \"transport_cost\": 127.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 5,\n \"transport_cost\": 648.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 6,\n \"transport_cost\": 391.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 7,\n \"transport_cost\": 243.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 8,\n \"transport_cost\": 441.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 9,\n \"transport_cost\": 76.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 10,\n \"transport_cost\": 212.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 11,\n \"transport_cost\": 755.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 12,\n \"transport_cost\": 649.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 13,\n \"transport_cost\": 82.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 14,\n \"transport_cost\": 162.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 15,\n \"transport_cost\": 349.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 16,\n \"transport_cost\": 623.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 17,\n \"transport_cost\": 769.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 18,\n \"transport_cost\": 133.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 19,\n \"transport_cost\": 203.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 20,\n \"transport_cost\": 602.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 1,\n \"transport_cost\": 89.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 2,\n \"transport_cost\": 60.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 3,\n \"transport_cost\": 1319.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 4,\n \"transport_cost\": 27.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 5,\n \"transport_cost\": 1118.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 6,\n \"transport_cost\": 728.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 7,\n \"transport_cost\": 595.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 8,\n \"transport_cost\": 707.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 9,\n \"transport_cost\": 202.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 10,\n \"transport_cost\": 92.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 11,\n \"transport_cost\": 1216.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 12,\n \"transport_cost\": 1070.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 13,\n \"transport_cost\": 418.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 14,\n \"transport_cost\": 64.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 15,\n \"transport_cost\": 549.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 16,\n \"transport_cost\": 1098.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 17,\n \"transport_cost\": 1198.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 18,\n \"transport_cost\": 38.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 19,\n \"transport_cost\": 449.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 20,\n \"transport_cost\": 1013.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 1,\n \"transport_cost\": 42.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 2,\n \"transport_cost\": 48.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 3,\n \"transport_cost\": 1700.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 4,\n \"transport_cost\": 36.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 5,\n \"transport_cost\": 1439.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 6,\n \"transport_cost\": 939.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 7,\n \"transport_cost\": 834.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 8,\n \"transport_cost\": 862.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 9,\n \"transport_cost\": 309.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 10,\n \"transport_cost\": 422.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 11,\n \"transport_cost\": 1578.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 12,\n \"transport_cost\": 1448.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 13,\n \"transport_cost\": 689.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 14,\n \"transport_cost\": 250.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 15,\n \"transport_cost\": 940.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 16,\n \"transport_cost\": 1434.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 17,\n \"transport_cost\": 1574.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 18,\n \"transport_cost\": 76.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 19,\n \"transport_cost\": 824.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 20,\n \"transport_cost\": 1270.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 1,\n \"transport_cost\": 936.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 2,\n \"transport_cost\": 643.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 3,\n \"transport_cost\": 1996.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 4,\n \"transport_cost\": 736.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 5,\n \"transport_cost\": 1367.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 6,\n \"transport_cost\": 461.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 7,\n \"transport_cost\": 681.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 8,\n \"transport_cost\": 66.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 9,\n \"transport_cost\": 295.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 10,\n \"transport_cost\": 1269.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 11,\n \"transport_cost\": 1740.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 12,\n \"transport_cost\": 1796.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 13,\n \"transport_cost\": 912.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 14,\n \"transport_cost\": 1069.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 15,\n \"transport_cost\": 1616.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 16,\n \"transport_cost\": 1463.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 17,\n \"transport_cost\": 1867.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 18,\n \"transport_cost\": 815.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 19,\n \"transport_cost\": 1452.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 20,\n \"transport_cost\": 857.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 1,\n \"transport_cost\": 39.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 2,\n \"transport_cost\": 48.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 3,\n \"transport_cost\": 1357.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 4,\n \"transport_cost\": 29.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 5,\n \"transport_cost\": 1203.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 6,\n \"transport_cost\": 820.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 7,\n \"transport_cost\": 689.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 8,\n \"transport_cost\": 788.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 9,\n \"transport_cost\": 263.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 10,\n \"transport_cost\": 187.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 11,\n \"transport_cost\": 1278.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 12,\n \"transport_cost\": 1116.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 13,\n \"transport_cost\": 514.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 14,\n \"transport_cost\": 130.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 15,\n \"transport_cost\": 587.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 16,\n \"transport_cost\": 1177.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 17,\n \"transport_cost\": 1244.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 18,\n \"transport_cost\": 56.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 19,\n \"transport_cost\": 516.0\n },\n {\n \"clinic_id\": \"F6\",\n \"neighborhood_id\": 20,\n \"transport_cost\": 1108.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 1,\n \"transport_cost\": 511.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 2,\n \"transport_cost\": 313.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 3,\n \"transport_cost\": 1203.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 4,\n \"transport_cost\": 323.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 5,\n \"transport_cost\": 644.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 6,\n \"transport_cost\": 182.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 7,\n \"transport_cost\": 55.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 8,\n \"transport_cost\": 261.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 9,\n \"transport_cost\": 57.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 10,\n \"transport_cost\": 610.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 11,\n \"transport_cost\": 960.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 12,\n \"transport_cost\": 992.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 13,\n \"transport_cost\": 190.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 14,\n \"transport_cost\": 477.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 15,\n \"transport_cost\": 850.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 16,\n \"transport_cost\": 704.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 17,\n \"transport_cost\": 1070.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 18,\n \"transport_cost\": 353.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 19,\n \"transport_cost\": 697.0\n },\n {\n \"clinic_id\": \"F7\",\n \"neighborhood_id\": 20,\n \"transport_cost\": 402.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 1,\n \"transport_cost\": 158.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 2,\n \"transport_cost\": 80.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 3,\n \"transport_cost\": 1543.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 4,\n \"transport_cost\": 43.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 5,\n \"transport_cost\": 1242.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 6,\n \"transport_cost\": 755.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 7,\n \"transport_cost\": 639.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 8,\n \"transport_cost\": 709.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 9,\n \"transport_cost\": 189.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 10,\n \"transport_cost\": 301.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 11,\n \"transport_cost\": 1400.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 12,\n \"transport_cost\": 1289.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 13,\n \"transport_cost\": 488.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 14,\n \"transport_cost\": 50.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 15,\n \"transport_cost\": 820.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 16,\n \"transport_cost\": 1242.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 17,\n \"transport_cost\": 1412.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 18,\n \"transport_cost\": 48.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 19,\n \"transport_cost\": 678.0\n },\n {\n \"clinic_id\": \"F8\",\n \"neighborhood_id\": 20,\n \"transport_cost\": 1073.0\n }\n ]\n}\n\nAlso, when you’re ready to hand over a proposed setup, just use a tiny JSON snippet like this so it’s easy to parse:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nPretty simple: \"selected\" is the list of clinic sites you plan to open, and \"assignments\" lists, in the same order as the neighborhoods in the instance, which open clinic each neighborhood will use. Think of it like filling out a form — which clinics are on, and for each neighborhood which clinic they go to.\n\nThis JSON is just the expected shape (a sketch), not the final answer.\n\nPlease be sure to use the exact identifiers from the input files — don’t rename or invent new labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 479.0, 214.0, 2081.0, 279.0, 1640.0, 943.0, 910.0, 792.0, 222.0, 960.0, 1889.0, 1833.0, 889.0, 714.0, 1443.0, 1676.0, 1944.0, 373.0, 1284.0, 1335.0 ], [ 268.0, 154.0, 902.0, 127.0, 648.0, 391.0, 243.0, 441.0, 76.0, 212.0, 755.0, 649.0, 82.0, 162.0, 349.0, 623.0, 769.0, 133.0, 203.0, 602.0 ], [ 89.0, 60.0, 1319.0, 27.0, 1118.0, 728.0, 595.0, 707.0, 202.0, 92.0, 1216.0, 1070.0, 418.0, 64.0, 549.0, 1098.0, 1198.0, 38.0, 449.0, 1013.0 ], [ 42.0, 48.0, 1700.0, 36.0, 1439.0, 939.0, 834.0, 862.0, 309.0, 422.0, 1578.0, 1448.0, 689.0, 250.0, 940.0, 1434.0, 1574.0, 76.0, 824.0, 1270.0 ], [ 936.0, 643.0, 1996.0, 736.0, 1367.0, 461.0, 681.0, 66.0, 295.0, 1269.0, 1740.0, 1796.0, 912.0, 1069.0, 1616.0, 1463.0, 1867.0, 815.0, 1452.0, 857.0 ], [ 39.0, 48.0, 1357.0, 29.0, 1203.0, 820.0, 689.0, 788.0, 263.0, 187.0, 1278.0, 1116.0, 514.0, 130.0, 587.0, 1177.0, 1244.0, 56.0, 516.0, 1108.0 ], [ 511.0, 313.0, 1203.0, 323.0, 644.0, 182.0, 55.0, 261.0, 57.0, 610.0, 960.0, 992.0, 190.0, 477.0, 850.0, 704.0, 1070.0, 353.0, 697.0, 402.0 ], [ 158.0, 80.0, 1543.0, 43.0, 1242.0, 755.0, 639.0, 709.0, 189.0, 301.0, 1400.0, 1289.0, 488.0, 50.0, 820.0, 1242.0, 1412.0, 48.0, 678.0, 1073.0 ] ], "demands": [ 14.0, 24.0, 13.0, 12.0, 28.0, 20.0, 23.0, 27.0, 26.0, 20.0, 19.0, 18.0, 22.0, 25.0, 23.0, 21.0, 18.0, 19.0, 25.0, 22.0 ], "objective": 8103.0 }, "solution": { "open_facilities": [ 1, 2, 6 ], "assignments": [ 2, 2, 1, 2, 6, 6, 6, 6, 6, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 6 ] }, "obj": 8103.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 20, "facilities": [ { "id": "F1", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F2", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F3", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F4", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F5", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F6", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F7", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F8", "opening_cost": 600.0, "capacity": 500.0 } ], "customers": [ { "id": 1, "demand": 14.0 }, { "id": 2, "demand": 24.0 }, { "id": 3, "demand": 13.0 }, { "id": 4, "demand": 12.0 }, { "id": 5, "demand": 28.0 }, { "id": 6, "demand": 20.0 }, { "id": 7, "demand": 23.0 }, { "id": 8, "demand": 27.0 }, { "id": 9, "demand": 26.0 }, { "id": 10, "demand": 20.0 }, { "id": 11, "demand": 19.0 }, { "id": 12, "demand": 18.0 }, { "id": 13, "demand": 22.0 }, { "id": 14, "demand": 25.0 }, { "id": 15, "demand": 23.0 }, { "id": 16, "demand": 21.0 }, { "id": 17, "demand": 18.0 }, { "id": 18, "demand": 19.0 }, { "id": 19, "demand": 25.0 }, { "id": 20, "demand": 22.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 479.0 }, { "facility": "F1", "customer": 2, "cost": 214.0 }, { "facility": "F1", "customer": 3, "cost": 2081.0 }, { "facility": "F1", "customer": 4, "cost": 279.0 }, { "facility": "F1", "customer": 5, "cost": 1640.0 }, { "facility": "F1", "customer": 6, "cost": 943.0 }, { "facility": "F1", "customer": 7, "cost": 910.0 }, { "facility": "F1", "customer": 8, "cost": 792.0 }, { "facility": "F1", "customer": 9, "cost": 222.0 }, { "facility": "F1", "customer": 10, "cost": 960.0 }, { "facility": "F1", "customer": 11, "cost": 1889.0 }, { "facility": "F1", "customer": 12, "cost": 1833.0 }, { "facility": "F1", "customer": 13, "cost": 889.0 }, { "facility": "F1", "customer": 14, "cost": 714.0 }, { "facility": "F1", "customer": 15, "cost": 1443.0 }, { "facility": "F1", "customer": 16, "cost": 1676.0 }, { "facility": "F1", "customer": 17, "cost": 1944.0 }, { "facility": "F1", "customer": 18, "cost": 373.0 }, { "facility": "F1", "customer": 19, "cost": 1284.0 }, { "facility": "F1", "customer": 20, "cost": 1335.0 }, { "facility": "F2", "customer": 1, "cost": 268.0 }, { "facility": "F2", "customer": 2, "cost": 154.0 }, { "facility": "F2", "customer": 3, "cost": 902.0 }, { "facility": "F2", "customer": 4, "cost": 127.0 }, { "facility": "F2", "customer": 5, "cost": 648.0 }, { "facility": "F2", "customer": 6, "cost": 391.0 }, { "facility": "F2", "customer": 7, "cost": 243.0 }, { "facility": "F2", "customer": 8, "cost": 441.0 }, { "facility": "F2", "customer": 9, "cost": 76.0 }, { "facility": "F2", "customer": 10, "cost": 212.0 }, { "facility": "F2", "customer": 11, "cost": 755.0 }, { "facility": "F2", "customer": 12, "cost": 649.0 }, { "facility": "F2", "customer": 13, "cost": 82.0 }, { "facility": "F2", "customer": 14, "cost": 162.0 }, { "facility": "F2", "customer": 15, "cost": 349.0 }, { "facility": "F2", "customer": 16, "cost": 623.0 }, { "facility": "F2", "customer": 17, "cost": 769.0 }, { "facility": "F2", "customer": 18, "cost": 133.0 }, { "facility": "F2", "customer": 19, "cost": 203.0 }, { "facility": "F2", "customer": 20, "cost": 602.0 }, { "facility": "F3", "customer": 1, "cost": 89.0 }, { "facility": "F3", "customer": 2, "cost": 60.0 }, { "facility": "F3", "customer": 3, "cost": 1319.0 }, { "facility": "F3", "customer": 4, "cost": 27.0 }, { "facility": "F3", "customer": 5, "cost": 1118.0 }, { "facility": "F3", "customer": 6, "cost": 728.0 }, { "facility": "F3", "customer": 7, "cost": 595.0 }, { "facility": "F3", "customer": 8, "cost": 707.0 }, { "facility": "F3", "customer": 9, "cost": 202.0 }, { "facility": "F3", "customer": 10, "cost": 92.0 }, { "facility": "F3", "customer": 11, "cost": 1216.0 }, { "facility": "F3", "customer": 12, "cost": 1070.0 }, { "facility": "F3", "customer": 13, "cost": 418.0 }, { "facility": "F3", "customer": 14, "cost": 64.0 }, { "facility": "F3", "customer": 15, "cost": 549.0 }, { "facility": "F3", "customer": 16, "cost": 1098.0 }, { "facility": "F3", "customer": 17, "cost": 1198.0 }, { "facility": "F3", "customer": 18, "cost": 38.0 }, { "facility": "F3", "customer": 19, "cost": 449.0 }, { "facility": "F3", "customer": 20, "cost": 1013.0 }, { "facility": "F4", "customer": 1, "cost": 42.0 }, { "facility": "F4", "customer": 2, "cost": 48.0 }, { "facility": "F4", "customer": 3, "cost": 1700.0 }, { "facility": "F4", "customer": 4, "cost": 36.0 }, { "facility": "F4", "customer": 5, "cost": 1439.0 }, { "facility": "F4", "customer": 6, "cost": 939.0 }, { "facility": "F4", "customer": 7, "cost": 834.0 }, { "facility": "F4", "customer": 8, "cost": 862.0 }, { "facility": "F4", "customer": 9, "cost": 309.0 }, { "facility": "F4", "customer": 10, "cost": 422.0 }, { "facility": "F4", "customer": 11, "cost": 1578.0 }, { "facility": "F4", "customer": 12, "cost": 1448.0 }, { "facility": "F4", "customer": 13, "cost": 689.0 }, { "facility": "F4", "customer": 14, "cost": 250.0 }, { "facility": "F4", "customer": 15, "cost": 940.0 }, { "facility": "F4", "customer": 16, "cost": 1434.0 }, { "facility": "F4", "customer": 17, "cost": 1574.0 }, { "facility": "F4", "customer": 18, "cost": 76.0 }, { "facility": "F4", "customer": 19, "cost": 824.0 }, { "facility": "F4", "customer": 20, "cost": 1270.0 }, { "facility": "F5", "customer": 1, "cost": 936.0 }, { "facility": "F5", "customer": 2, "cost": 643.0 }, { "facility": "F5", "customer": 3, "cost": 1996.0 }, { "facility": "F5", "customer": 4, "cost": 736.0 }, { "facility": "F5", "customer": 5, "cost": 1367.0 }, { "facility": "F5", "customer": 6, "cost": 461.0 }, { "facility": "F5", "customer": 7, "cost": 681.0 }, { "facility": "F5", "customer": 8, "cost": 66.0 }, { "facility": "F5", "customer": 9, "cost": 295.0 }, { "facility": "F5", "customer": 10, "cost": 1269.0 }, { "facility": "F5", "customer": 11, "cost": 1740.0 }, { "facility": "F5", "customer": 12, "cost": 1796.0 }, { "facility": "F5", "customer": 13, "cost": 912.0 }, { "facility": "F5", "customer": 14, "cost": 1069.0 }, { "facility": "F5", "customer": 15, "cost": 1616.0 }, { "facility": "F5", "customer": 16, "cost": 1463.0 }, { "facility": "F5", "customer": 17, "cost": 1867.0 }, { "facility": "F5", "customer": 18, "cost": 815.0 }, { "facility": "F5", "customer": 19, "cost": 1452.0 }, { "facility": "F5", "customer": 20, "cost": 857.0 }, { "facility": "F6", "customer": 1, "cost": 39.0 }, { "facility": "F6", "customer": 2, "cost": 48.0 }, { "facility": "F6", "customer": 3, "cost": 1357.0 }, { "facility": "F6", "customer": 4, "cost": 29.0 }, { "facility": "F6", "customer": 5, "cost": 1203.0 }, { "facility": "F6", "customer": 6, "cost": 820.0 }, { "facility": "F6", "customer": 7, "cost": 689.0 }, { "facility": "F6", "customer": 8, "cost": 788.0 }, { "facility": "F6", "customer": 9, "cost": 263.0 }, { "facility": "F6", "customer": 10, "cost": 187.0 }, { "facility": "F6", "customer": 11, "cost": 1278.0 }, { "facility": "F6", "customer": 12, "cost": 1116.0 }, { "facility": "F6", "customer": 13, "cost": 514.0 }, { "facility": "F6", "customer": 14, "cost": 130.0 }, { "facility": "F6", "customer": 15, "cost": 587.0 }, { "facility": "F6", "customer": 16, "cost": 1177.0 }, { "facility": "F6", "customer": 17, "cost": 1244.0 }, { "facility": "F6", "customer": 18, "cost": 56.0 }, { "facility": "F6", "customer": 19, "cost": 516.0 }, { "facility": "F6", "customer": 20, "cost": 1108.0 }, { "facility": "F7", "customer": 1, "cost": 511.0 }, { "facility": "F7", "customer": 2, "cost": 313.0 }, { "facility": "F7", "customer": 3, "cost": 1203.0 }, { "facility": "F7", "customer": 4, "cost": 323.0 }, { "facility": "F7", "customer": 5, "cost": 644.0 }, { "facility": "F7", "customer": 6, "cost": 182.0 }, { "facility": "F7", "customer": 7, "cost": 55.0 }, { "facility": "F7", "customer": 8, "cost": 261.0 }, { "facility": "F7", "customer": 9, "cost": 57.0 }, { "facility": "F7", "customer": 10, "cost": 610.0 }, { "facility": "F7", "customer": 11, "cost": 960.0 }, { "facility": "F7", "customer": 12, "cost": 992.0 }, { "facility": "F7", "customer": 13, "cost": 190.0 }, { "facility": "F7", "customer": 14, "cost": 477.0 }, { "facility": "F7", "customer": 15, "cost": 850.0 }, { "facility": "F7", "customer": 16, "cost": 704.0 }, { "facility": "F7", "customer": 17, "cost": 1070.0 }, { "facility": "F7", "customer": 18, "cost": 353.0 }, { "facility": "F7", "customer": 19, "cost": 697.0 }, { "facility": "F7", "customer": 20, "cost": 402.0 }, { "facility": "F8", "customer": 1, "cost": 158.0 }, { "facility": "F8", "customer": 2, "cost": 80.0 }, { "facility": "F8", "customer": 3, "cost": 1543.0 }, { "facility": "F8", "customer": 4, "cost": 43.0 }, { "facility": "F8", "customer": 5, "cost": 1242.0 }, { "facility": "F8", "customer": 6, "cost": 755.0 }, { "facility": "F8", "customer": 7, "cost": 639.0 }, { "facility": "F8", "customer": 8, "cost": 709.0 }, { "facility": "F8", "customer": 9, "cost": 189.0 }, { "facility": "F8", "customer": 10, "cost": 301.0 }, { "facility": "F8", "customer": 11, "cost": 1400.0 }, { "facility": "F8", "customer": 12, "cost": 1289.0 }, { "facility": "F8", "customer": 13, "cost": 488.0 }, { "facility": "F8", "customer": 14, "cost": 50.0 }, { "facility": "F8", "customer": 15, "cost": 820.0 }, { "facility": "F8", "customer": 16, "cost": 1242.0 }, { "facility": "F8", "customer": 17, "cost": 1412.0 }, { "facility": "F8", "customer": 18, "cost": 48.0 }, { "facility": "F8", "customer": 19, "cost": 678.0 }, { "facility": "F8", "customer": 20, "cost": 1073.0 } ], "objective": 8103.0 }, "solution_variant": { "selected": [ "F2", "F3", "F7" ], "assignments": [ "F3", "F3", "F2", "F3", "F7", "F7", "F7", "F7", "F7", "F3", "F2", "F2", "F2", "F3", "F2", "F2", "F2", "F3", "F2", "F7" ] }, "context_index": 11, "input_format": "json", "input_index_base": 1 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Many event planners know the drill: pick which mobile kitchens to bring and decide which kitchen will handle each event. Every kitchen has a rental price and a maximum number of meals it can do; every event needs all its meals from one kitchen only. The decision that works is the one where all events are assigned (no splits), no kitchen is overloaded, and the total expense — the sum of trailer deployment costs plus each event’s delivery fee — is kept as low as possible. The full set of trailer capacities, deployment fees, and event meal counts appears below.\n\nThere are 8 trailers and 16 events in this instance.\n\n**Trailers**\n| trailer_id | deployment_cost | meal_capacity |\n|---|---|---|\n| F1 | 300.0 | 300.0 |\n| F2 | 300.0 | 300.0 |\n| F3 | 300.0 | 300.0 |\n| F4 | 300.0 | 300.0 |\n| F5 | 300.0 | 300.0 |\n| F6 | 300.0 | 300.0 |\n| F7 | 300.0 | 300.0 |\n| F8 | 300.0 | 300.0 |\n\n**Events**\n| event_id | meals_required |\n|---|---|\n| 0 | 28.0 |\n| 1 | 12.0 |\n| 2 | 13.0 |\n| 3 | 19.0 |\n| 4 | 11.0 |\n| 5 | 20.0 |\n| 6 | 25.0 |\n| 7 | 22.0 |\n| 8 | 19.0 |\n| 9 | 13.0 |\n| 10 | 18.0 |\n| 11 | 23.0 |\n| 12 | 18.0 |\n| 13 | 23.0 |\n| 14 | 11.0 |\n| 15 | 25.0 |\n\n**Delivery Fee**\n| trailer_id | event_id | delivery_fee |\n|---|---|---|\n| F1 | 0 | 260.0 |\n| F1 | 1 | 913.0 |\n| F1 | 2 | 1263.0 |\n| F1 | 3 | 1185.0 |\n| F1 | 4 | 1542.0 |\n| F1 | 5 | 960.0 |\n| F1 | 6 | 1414.0 |\n| F1 | 7 | 1976.0 |\n| F1 | 8 | 878.0 |\n| F1 | 9 | 98.0 |\n| F1 | 10 | 1833.0 |\n| F1 | 11 | 993.0 |\n| F1 | 12 | 37.0 |\n| F1 | 13 | 841.0 |\n| F1 | 14 | 942.0 |\n| F1 | 15 | 1284.0 |\n| F2 | 0 | 439.0 |\n| F2 | 1 | 974.0 |\n| F2 | 2 | 1463.0 |\n| F2 | 3 | 1167.0 |\n| F2 | 4 | 1631.0 |\n| F2 | 5 | 862.0 |\n| F2 | 6 | 1362.0 |\n| F2 | 7 | 2045.0 |\n| F2 | 8 | 1042.0 |\n| F2 | 9 | 192.0 |\n| F2 | 10 | 1864.0 |\n| F2 | 11 | 1040.0 |\n| F2 | 12 | 59.0 |\n| F2 | 13 | 900.0 |\n| F2 | 14 | 1122.0 |\n| F2 | 15 | 1255.0 |\n| F3 | 0 | 78.0 |\n| F3 | 1 | 78.0 |\n| F3 | 2 | 404.0 |\n| F3 | 3 | 269.0 |\n| F3 | 4 | 180.0 |\n| F3 | 5 | 343.0 |\n| F3 | 6 | 445.0 |\n| F3 | 7 | 611.0 |\n| F3 | 8 | 63.0 |\n| F3 | 9 | 46.0 |\n| F3 | 10 | 516.0 |\n| F3 | 11 | 122.0 |\n| F3 | 12 | 38.0 |\n| F3 | 13 | 105.0 |\n| F3 | 14 | 109.0 |\n| F3 | 15 | 334.0 |\n| F4 | 0 | 109.0 |\n| F4 | 1 | 139.0 |\n| F4 | 2 | 242.0 |\n| F4 | 3 | 335.0 |\n| F4 | 4 | 90.0 |\n| F4 | 5 | 413.0 |\n| F4 | 6 | 497.0 |\n| F4 | 7 | 411.0 |\n| F4 | 8 | 38.0 |\n| F4 | 9 | 36.0 |\n| F4 | 10 | 441.0 |\n| F4 | 11 | 188.0 |\n| F4 | 12 | 41.0 |\n| F4 | 13 | 165.0 |\n| F4 | 14 | 39.0 |\n| F4 | 15 | 396.0 |\n| F5 | 0 | 255.0 |\n| F5 | 1 | 708.0 |\n| F5 | 2 | 756.0 |\n| F5 | 3 | 1037.0 |\n| F5 | 4 | 1194.0 |\n| F5 | 5 | 938.0 |\n| F5 | 6 | 1278.0 |\n| F5 | 7 | 1633.0 |\n| F5 | 8 | 467.0 |\n| F5 | 9 | 32.0 |\n| F5 | 10 | 1550.0 |\n| F5 | 11 | 797.0 |\n| F5 | 12 | 45.0 |\n| F5 | 13 | 667.0 |\n| F5 | 14 | 475.0 |\n| F5 | 15 | 1137.0 |\n| F6 | 0 | 145.0 |\n| F6 | 1 | 262.0 |\n| F6 | 2 | 270.0 |\n| F6 | 3 | 535.0 |\n| F6 | 4 | 426.0 |\n| F6 | 5 | 569.0 |\n| F6 | 6 | 740.0 |\n| F6 | 7 | 840.0 |\n| F6 | 8 | 48.0 |\n| F6 | 9 | 32.0 |\n| F6 | 10 | 817.0 |\n| F6 | 11 | 329.0 |\n| F6 | 12 | 44.0 |\n| F6 | 13 | 274.0 |\n| F6 | 14 | 27.0 |\n| F6 | 15 | 615.0 |\n| F7 | 0 | 141.0 |\n| F7 | 1 | 304.0 |\n| F7 | 2 | 399.0 |\n| F7 | 3 | 609.0 |\n| F7 | 4 | 617.0 |\n| F7 | 5 | 610.0 |\n| F7 | 6 | 831.0 |\n| F7 | 7 | 1051.0 |\n| F7 | 8 | 42.0 |\n| F7 | 9 | 35.0 |\n| F7 | 10 | 992.0 |\n| F7 | 11 | 381.0 |\n| F7 | 12 | 42.0 |\n| F7 | 13 | 305.0 |\n| F7 | 14 | 58.0 |\n| F7 | 15 | 697.0 |\n| F8 | 0 | 128.0 |\n| F8 | 1 | 429.0 |\n| F8 | 2 | 1045.0 |\n| F8 | 3 | 590.0 |\n| F8 | 4 | 1077.0 |\n| F8 | 5 | 301.0 |\n| F8 | 6 | 790.0 |\n| F8 | 7 | 1478.0 |\n| F8 | 8 | 579.0 |\n| F8 | 9 | 114.0 |\n| F8 | 10 | 1289.0 |\n| F8 | 11 | 483.0 |\n| F8 | 12 | 40.0 |\n| F8 | 13 | 362.0 |\n| F8 | 14 | 676.0 |\n| F8 | 15 | 678.0 |\n\nOne more thing — to keep things machine-friendly, please lay out the final decision in a tiny JSON sketch like this:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of mobile kitchens you'll rent, and \"assignments\" as, for each event (in the same order the events were given), which rented kitchen will handle it. Super casual form: which kitchens you bring, and who feeds which event.\n\nThis JSON is just the shape I expect — a sketch, not the actual values. Also, please use the exact identifiers from the instance input when filling those placeholders: do not rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "connection_costs": [ [ 260.0, 913.0, 1263.0, 1185.0, 1542.0, 960.0, 1414.0, 1976.0, 878.0, 98.0, 1833.0, 993.0, 37.0, 841.0, 942.0, 1284.0 ], [ 439.0, 974.0, 1463.0, 1167.0, 1631.0, 862.0, 1362.0, 2045.0, 1042.0, 192.0, 1864.0, 1040.0, 59.0, 900.0, 1122.0, 1255.0 ], [ 78.0, 78.0, 404.0, 269.0, 180.0, 343.0, 445.0, 611.0, 63.0, 46.0, 516.0, 122.0, 38.0, 105.0, 109.0, 334.0 ], [ 109.0, 139.0, 242.0, 335.0, 90.0, 413.0, 497.0, 411.0, 38.0, 36.0, 441.0, 188.0, 41.0, 165.0, 39.0, 396.0 ], [ 255.0, 708.0, 756.0, 1037.0, 1194.0, 938.0, 1278.0, 1633.0, 467.0, 32.0, 1550.0, 797.0, 45.0, 667.0, 475.0, 1137.0 ], [ 145.0, 262.0, 270.0, 535.0, 426.0, 569.0, 740.0, 840.0, 48.0, 32.0, 817.0, 329.0, 44.0, 274.0, 27.0, 615.0 ], [ 141.0, 304.0, 399.0, 609.0, 617.0, 610.0, 831.0, 1051.0, 42.0, 35.0, 992.0, 381.0, 42.0, 305.0, 58.0, 697.0 ], [ 128.0, 429.0, 1045.0, 590.0, 1077.0, 301.0, 790.0, 1478.0, 579.0, 114.0, 1289.0, 483.0, 40.0, 362.0, 676.0, 678.0 ] ], "demands": [ 28.0, 12.0, 13.0, 19.0, 11.0, 20.0, 25.0, 22.0, 19.0, 13.0, 18.0, 23.0, 18.0, 23.0, 11.0, 25.0 ], "objective": 3709.0 }, "solution": { "open_facilities": [ 2, 3 ], "assignments": [ 2, 2, 3, 2, 3, 2, 2, 3, 3, 3, 3, 2, 2, 2, 3, 2 ] }, "obj": 3709.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 16, "facilities": [ { "id": "F1", "opening_cost": 300.0, "capacity": 300.0 }, { "id": "F2", "opening_cost": 300.0, "capacity": 300.0 }, { "id": "F3", "opening_cost": 300.0, "capacity": 300.0 }, { "id": "F4", "opening_cost": 300.0, "capacity": 300.0 }, { "id": "F5", "opening_cost": 300.0, "capacity": 300.0 }, { "id": "F6", "opening_cost": 300.0, "capacity": 300.0 }, { "id": "F7", "opening_cost": 300.0, "capacity": 300.0 }, { "id": "F8", "opening_cost": 300.0, "capacity": 300.0 } ], "customers": [ { "id": 0, "demand": 28.0 }, { "id": 1, "demand": 12.0 }, { "id": 2, "demand": 13.0 }, { "id": 3, "demand": 19.0 }, { "id": 4, "demand": 11.0 }, { "id": 5, "demand": 20.0 }, { "id": 6, "demand": 25.0 }, { "id": 7, "demand": 22.0 }, { "id": 8, "demand": 19.0 }, { "id": 9, "demand": 13.0 }, { "id": 10, "demand": 18.0 }, { "id": 11, "demand": 23.0 }, { "id": 12, "demand": 18.0 }, { "id": 13, "demand": 23.0 }, { "id": 14, "demand": 11.0 }, { "id": 15, "demand": 25.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 260.0 }, { "facility": "F1", "customer": 1, "cost": 913.0 }, { "facility": "F1", "customer": 2, "cost": 1263.0 }, { "facility": "F1", "customer": 3, "cost": 1185.0 }, { "facility": "F1", "customer": 4, "cost": 1542.0 }, { "facility": "F1", "customer": 5, "cost": 960.0 }, { "facility": "F1", "customer": 6, "cost": 1414.0 }, { "facility": "F1", "customer": 7, "cost": 1976.0 }, { "facility": "F1", "customer": 8, "cost": 878.0 }, { "facility": "F1", "customer": 9, "cost": 98.0 }, { "facility": "F1", "customer": 10, "cost": 1833.0 }, { "facility": "F1", "customer": 11, "cost": 993.0 }, { "facility": "F1", "customer": 12, "cost": 37.0 }, { "facility": "F1", "customer": 13, "cost": 841.0 }, { "facility": "F1", "customer": 14, "cost": 942.0 }, { "facility": "F1", "customer": 15, "cost": 1284.0 }, { "facility": "F2", "customer": 0, "cost": 439.0 }, { "facility": "F2", "customer": 1, "cost": 974.0 }, { "facility": "F2", "customer": 2, "cost": 1463.0 }, { "facility": "F2", "customer": 3, "cost": 1167.0 }, { "facility": "F2", "customer": 4, "cost": 1631.0 }, { "facility": "F2", "customer": 5, "cost": 862.0 }, { "facility": "F2", "customer": 6, "cost": 1362.0 }, { "facility": "F2", "customer": 7, "cost": 2045.0 }, { "facility": "F2", "customer": 8, "cost": 1042.0 }, { "facility": "F2", "customer": 9, "cost": 192.0 }, { "facility": "F2", "customer": 10, "cost": 1864.0 }, { "facility": "F2", "customer": 11, "cost": 1040.0 }, { "facility": "F2", "customer": 12, "cost": 59.0 }, { "facility": "F2", "customer": 13, "cost": 900.0 }, { "facility": "F2", "customer": 14, "cost": 1122.0 }, { "facility": "F2", "customer": 15, "cost": 1255.0 }, { "facility": "F3", "customer": 0, "cost": 78.0 }, { "facility": "F3", "customer": 1, "cost": 78.0 }, { "facility": "F3", "customer": 2, "cost": 404.0 }, { "facility": "F3", "customer": 3, "cost": 269.0 }, { "facility": "F3", "customer": 4, "cost": 180.0 }, { "facility": "F3", "customer": 5, "cost": 343.0 }, { "facility": "F3", "customer": 6, "cost": 445.0 }, { "facility": "F3", "customer": 7, "cost": 611.0 }, { "facility": "F3", "customer": 8, "cost": 63.0 }, { "facility": "F3", "customer": 9, "cost": 46.0 }, { "facility": "F3", "customer": 10, "cost": 516.0 }, { "facility": "F3", "customer": 11, "cost": 122.0 }, { "facility": "F3", "customer": 12, "cost": 38.0 }, { "facility": "F3", "customer": 13, "cost": 105.0 }, { "facility": "F3", "customer": 14, "cost": 109.0 }, { "facility": "F3", "customer": 15, "cost": 334.0 }, { "facility": "F4", "customer": 0, "cost": 109.0 }, { "facility": "F4", "customer": 1, "cost": 139.0 }, { "facility": "F4", "customer": 2, "cost": 242.0 }, { "facility": "F4", "customer": 3, "cost": 335.0 }, { "facility": "F4", "customer": 4, "cost": 90.0 }, { "facility": "F4", "customer": 5, "cost": 413.0 }, { "facility": "F4", "customer": 6, "cost": 497.0 }, { "facility": "F4", "customer": 7, "cost": 411.0 }, { "facility": "F4", "customer": 8, "cost": 38.0 }, { "facility": "F4", "customer": 9, "cost": 36.0 }, { "facility": "F4", "customer": 10, "cost": 441.0 }, { "facility": "F4", "customer": 11, "cost": 188.0 }, { "facility": "F4", "customer": 12, "cost": 41.0 }, { "facility": "F4", "customer": 13, "cost": 165.0 }, { "facility": "F4", "customer": 14, "cost": 39.0 }, { "facility": "F4", "customer": 15, "cost": 396.0 }, { "facility": "F5", "customer": 0, "cost": 255.0 }, { "facility": "F5", "customer": 1, "cost": 708.0 }, { "facility": "F5", "customer": 2, "cost": 756.0 }, { "facility": "F5", "customer": 3, "cost": 1037.0 }, { "facility": "F5", "customer": 4, "cost": 1194.0 }, { "facility": "F5", "customer": 5, "cost": 938.0 }, { "facility": "F5", "customer": 6, "cost": 1278.0 }, { "facility": "F5", "customer": 7, "cost": 1633.0 }, { "facility": "F5", "customer": 8, "cost": 467.0 }, { "facility": "F5", "customer": 9, "cost": 32.0 }, { "facility": "F5", "customer": 10, "cost": 1550.0 }, { "facility": "F5", "customer": 11, "cost": 797.0 }, { "facility": "F5", "customer": 12, "cost": 45.0 }, { "facility": "F5", "customer": 13, "cost": 667.0 }, { "facility": "F5", "customer": 14, "cost": 475.0 }, { "facility": "F5", "customer": 15, "cost": 1137.0 }, { "facility": "F6", "customer": 0, "cost": 145.0 }, { "facility": "F6", "customer": 1, "cost": 262.0 }, { "facility": "F6", "customer": 2, "cost": 270.0 }, { "facility": "F6", "customer": 3, "cost": 535.0 }, { "facility": "F6", "customer": 4, "cost": 426.0 }, { "facility": "F6", "customer": 5, "cost": 569.0 }, { "facility": "F6", "customer": 6, "cost": 740.0 }, { "facility": "F6", "customer": 7, "cost": 840.0 }, { "facility": "F6", "customer": 8, "cost": 48.0 }, { "facility": "F6", "customer": 9, "cost": 32.0 }, { "facility": "F6", "customer": 10, "cost": 817.0 }, { "facility": "F6", "customer": 11, "cost": 329.0 }, { "facility": "F6", "customer": 12, "cost": 44.0 }, { "facility": "F6", "customer": 13, "cost": 274.0 }, { "facility": "F6", "customer": 14, "cost": 27.0 }, { "facility": "F6", "customer": 15, "cost": 615.0 }, { "facility": "F7", "customer": 0, "cost": 141.0 }, { "facility": "F7", "customer": 1, "cost": 304.0 }, { "facility": "F7", "customer": 2, "cost": 399.0 }, { "facility": "F7", "customer": 3, "cost": 609.0 }, { "facility": "F7", "customer": 4, "cost": 617.0 }, { "facility": "F7", "customer": 5, "cost": 610.0 }, { "facility": "F7", "customer": 6, "cost": 831.0 }, { "facility": "F7", "customer": 7, "cost": 1051.0 }, { "facility": "F7", "customer": 8, "cost": 42.0 }, { "facility": "F7", "customer": 9, "cost": 35.0 }, { "facility": "F7", "customer": 10, "cost": 992.0 }, { "facility": "F7", "customer": 11, "cost": 381.0 }, { "facility": "F7", "customer": 12, "cost": 42.0 }, { "facility": "F7", "customer": 13, "cost": 305.0 }, { "facility": "F7", "customer": 14, "cost": 58.0 }, { "facility": "F7", "customer": 15, "cost": 697.0 }, { "facility": "F8", "customer": 0, "cost": 128.0 }, { "facility": "F8", "customer": 1, "cost": 429.0 }, { "facility": "F8", "customer": 2, "cost": 1045.0 }, { "facility": "F8", "customer": 3, "cost": 590.0 }, { "facility": "F8", "customer": 4, "cost": 1077.0 }, { "facility": "F8", "customer": 5, "cost": 301.0 }, { "facility": "F8", "customer": 6, "cost": 790.0 }, { "facility": "F8", "customer": 7, "cost": 1478.0 }, { "facility": "F8", "customer": 8, "cost": 579.0 }, { "facility": "F8", "customer": 9, "cost": 114.0 }, { "facility": "F8", "customer": 10, "cost": 1289.0 }, { "facility": "F8", "customer": 11, "cost": 483.0 }, { "facility": "F8", "customer": 12, "cost": 40.0 }, { "facility": "F8", "customer": 13, "cost": 362.0 }, { "facility": "F8", "customer": 14, "cost": 676.0 }, { "facility": "F8", "customer": 15, "cost": 678.0 } ], "objective": 3709.0 }, "solution_variant": { "selected": [ "F3", "F4" ], "assignments": [ "F3", "F3", "F4", "F3", "F4", "F3", "F3", "F4", "F4", "F4", "F4", "F3", "F3", "F3", "F4", "F3" ] }, "context_index": 12, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "The planning team has to decide which candidate docking stations to activate and then assign each commuter zone to exactly one activated station, taking care that stations aren’t asked to serve more riders than their dock counts allow. Activating a station charges a cost, and each assignment carries a redistribution or travel cost; the total cost of any configuration is simply the sum of the activation costs for chosen stations plus all assignment costs, and the aim is to keep that combined total as low as possible. Every commuter zone needs a single assigned station (no omissions or duplicates), and station capacities must not be exceeded. The detailed instance information is provided below.\n\n# num_candidate_hubs=6\n# num_commuter_zones=16\n# HUBS\nhub_id,activation_cost,dock_capacity\nF1,400.0,700.0\nF2,400.0,700.0\nF3,400.0,700.0\nF4,400.0,700.0\nF5,400.0,700.0\nF6,400.0,700.0\n# ZONES\nzone_id,rider_demand\n1,28.0\n2,17.0\n3,13.0\n4,23.0\n5,24.0\n6,25.0\n7,12.0\n8,22.0\n9,19.0\n10,24.0\n11,17.0\n12,16.0\n13,27.0\n14,16.0\n15,23.0\n16,27.0\n# REDISTRIBUTIONS\nhub_id,zone_id,redistribution_cost\nF1,1,78.0\nF1,2,301.0\nF1,3,738.0\nF1,4,290.0\nF1,5,139.0\nF1,6,445.0\nF1,7,266.0\nF1,8,196.0\nF1,9,524.0\nF1,10,353.0\nF1,11,47.0\nF1,12,112.0\nF1,13,447.0\nF1,14,638.0\nF1,15,156.0\nF1,16,156.0\nF2,1,364.0\nF2,2,34.0\nF2,3,1609.0\nF2,4,1199.0\nF2,5,49.0\nF2,6,1268.0\nF2,7,817.0\nF2,8,44.0\nF2,9,1349.0\nF2,10,732.0\nF2,11,419.0\nF2,12,88.0\nF2,13,1316.0\nF2,14,1465.0\nF2,15,147.0\nF2,16,918.0\nF3,1,109.0\nF3,2,183.0\nF3,3,590.0\nF3,4,288.0\nF3,5,102.0\nF3,6,497.0\nF3,7,333.0\nF3,8,127.0\nF3,9,323.0\nF3,10,411.0\nF3,11,80.0\nF3,12,61.0\nF3,13,482.0\nF3,14,437.0\nF3,15,86.0\nF3,16,225.0\nF4,1,145.0\nF4,2,181.0\nF4,3,1006.0\nF4,4,608.0\nF4,5,91.0\nF4,6,740.0\nF4,7,451.0\nF4,8,114.0\nF4,9,749.0\nF4,10,485.0\nF4,11,128.0\nF4,12,49.0\nF4,13,759.0\nF4,14,867.0\nF4,15,72.0\nF4,16,406.0\nF5,1,738.0\nF5,2,1017.0\nF5,3,2444.0\nF5,4,1975.0\nF5,5,141.0\nF5,6,1904.0\nF5,7,1253.0\nF5,8,613.0\nF5,9,2210.0\nF5,10,976.0\nF5,11,929.0\nF5,12,729.0\nF5,13,2003.0\nF5,14,2328.0\nF5,15,933.0\nF5,16,1590.0\nF6,1,141.0\nF6,2,260.0\nF6,3,1203.0\nF6,4,763.0\nF6,5,104.0\nF6,6,831.0\nF6,7,473.0\nF6,8,145.0\nF6,9,960.0\nF6,10,487.0\nF6,11,127.0\nF6,12,67.0\nF6,13,873.0\nF6,14,1079.0\nF6,15,105.0\nF6,16,483.0\n\nYou can just reply with the results in a simple JSON shape — nothing fancy. Here's the layout to follow:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list the station identifiers you choose to activate, and \"assignments\" is a list that (in the same order as the commuter zones were given in the instance) names the single activated station each zone is assigned to. Think of it like filling out a short form: which stations are turned on, and which station each zone uses.\n\nThis JSON is just a sketch of the shape I expect — not the actual solution values.\n\nPlease use the exact identifiers from the instance input — do not rename them or invent new labels.\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 78.0, 301.0, 738.0, 290.0, 139.0, 445.0, 266.0, 196.0, 524.0, 353.0, 47.0, 112.0, 447.0, 638.0, 156.0, 156.0 ], [ 364.0, 34.0, 1609.0, 1199.0, 49.0, 1268.0, 817.0, 44.0, 1349.0, 732.0, 419.0, 88.0, 1316.0, 1465.0, 147.0, 918.0 ], [ 109.0, 183.0, 590.0, 288.0, 102.0, 497.0, 333.0, 127.0, 323.0, 411.0, 80.0, 61.0, 482.0, 437.0, 86.0, 225.0 ], [ 145.0, 181.0, 1006.0, 608.0, 91.0, 740.0, 451.0, 114.0, 749.0, 485.0, 128.0, 49.0, 759.0, 867.0, 72.0, 406.0 ], [ 738.0, 1017.0, 2444.0, 1975.0, 141.0, 1904.0, 1253.0, 613.0, 2210.0, 976.0, 929.0, 729.0, 2003.0, 2328.0, 933.0, 1590.0 ], [ 141.0, 260.0, 1203.0, 763.0, 104.0, 831.0, 473.0, 145.0, 960.0, 487.0, 127.0, 67.0, 873.0, 1079.0, 105.0, 483.0 ] ], "demands": [ 28.0, 17.0, 13.0, 23.0, 24.0, 25.0, 12.0, 22.0, 19.0, 24.0, 17.0, 16.0, 27.0, 16.0, 23.0, 27.0 ], "objective": 4734.0 }, "solution": { "open_facilities": [ 2 ], "assignments": [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ] }, "obj": 4734.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 6, "num_customers": 16, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 700.0 } ], "customers": [ { "id": 1, "demand": 28.0 }, { "id": 2, "demand": 17.0 }, { "id": 3, "demand": 13.0 }, { "id": 4, "demand": 23.0 }, { "id": 5, "demand": 24.0 }, { "id": 6, "demand": 25.0 }, { "id": 7, "demand": 12.0 }, { "id": 8, "demand": 22.0 }, { "id": 9, "demand": 19.0 }, { "id": 10, "demand": 24.0 }, { "id": 11, "demand": 17.0 }, { "id": 12, "demand": 16.0 }, { "id": 13, "demand": 27.0 }, { "id": 14, "demand": 16.0 }, { "id": 15, "demand": 23.0 }, { "id": 16, "demand": 27.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 78.0 }, { "facility": "F1", "customer": 2, "cost": 301.0 }, { "facility": "F1", "customer": 3, "cost": 738.0 }, { "facility": "F1", "customer": 4, "cost": 290.0 }, { "facility": "F1", "customer": 5, "cost": 139.0 }, { "facility": "F1", "customer": 6, "cost": 445.0 }, { "facility": "F1", "customer": 7, "cost": 266.0 }, { "facility": "F1", "customer": 8, "cost": 196.0 }, { "facility": "F1", "customer": 9, "cost": 524.0 }, { "facility": "F1", "customer": 10, "cost": 353.0 }, { "facility": "F1", "customer": 11, "cost": 47.0 }, { "facility": "F1", "customer": 12, "cost": 112.0 }, { "facility": "F1", "customer": 13, "cost": 447.0 }, { "facility": "F1", "customer": 14, "cost": 638.0 }, { "facility": "F1", "customer": 15, "cost": 156.0 }, { "facility": "F1", "customer": 16, "cost": 156.0 }, { "facility": "F2", "customer": 1, "cost": 364.0 }, { "facility": "F2", "customer": 2, "cost": 34.0 }, { "facility": "F2", "customer": 3, "cost": 1609.0 }, { "facility": "F2", "customer": 4, "cost": 1199.0 }, { "facility": "F2", "customer": 5, "cost": 49.0 }, { "facility": "F2", "customer": 6, "cost": 1268.0 }, { "facility": "F2", "customer": 7, "cost": 817.0 }, { "facility": "F2", "customer": 8, "cost": 44.0 }, { "facility": "F2", "customer": 9, "cost": 1349.0 }, { "facility": "F2", "customer": 10, "cost": 732.0 }, { "facility": "F2", "customer": 11, "cost": 419.0 }, { "facility": "F2", "customer": 12, "cost": 88.0 }, { "facility": "F2", "customer": 13, "cost": 1316.0 }, { "facility": "F2", "customer": 14, "cost": 1465.0 }, { "facility": "F2", "customer": 15, "cost": 147.0 }, { "facility": "F2", "customer": 16, "cost": 918.0 }, { "facility": "F3", "customer": 1, "cost": 109.0 }, { "facility": "F3", "customer": 2, "cost": 183.0 }, { "facility": "F3", "customer": 3, "cost": 590.0 }, { "facility": "F3", "customer": 4, "cost": 288.0 }, { "facility": "F3", "customer": 5, "cost": 102.0 }, { "facility": "F3", "customer": 6, "cost": 497.0 }, { "facility": "F3", "customer": 7, "cost": 333.0 }, { "facility": "F3", "customer": 8, "cost": 127.0 }, { "facility": "F3", "customer": 9, "cost": 323.0 }, { "facility": "F3", "customer": 10, "cost": 411.0 }, { "facility": "F3", "customer": 11, "cost": 80.0 }, { "facility": "F3", "customer": 12, "cost": 61.0 }, { "facility": "F3", "customer": 13, "cost": 482.0 }, { "facility": "F3", "customer": 14, "cost": 437.0 }, { "facility": "F3", "customer": 15, "cost": 86.0 }, { "facility": "F3", "customer": 16, "cost": 225.0 }, { "facility": "F4", "customer": 1, "cost": 145.0 }, { "facility": "F4", "customer": 2, "cost": 181.0 }, { "facility": "F4", "customer": 3, "cost": 1006.0 }, { "facility": "F4", "customer": 4, "cost": 608.0 }, { "facility": "F4", "customer": 5, "cost": 91.0 }, { "facility": "F4", "customer": 6, "cost": 740.0 }, { "facility": "F4", "customer": 7, "cost": 451.0 }, { "facility": "F4", "customer": 8, "cost": 114.0 }, { "facility": "F4", "customer": 9, "cost": 749.0 }, { "facility": "F4", "customer": 10, "cost": 485.0 }, { "facility": "F4", "customer": 11, "cost": 128.0 }, { "facility": "F4", "customer": 12, "cost": 49.0 }, { "facility": "F4", "customer": 13, "cost": 759.0 }, { "facility": "F4", "customer": 14, "cost": 867.0 }, { "facility": "F4", "customer": 15, "cost": 72.0 }, { "facility": "F4", "customer": 16, "cost": 406.0 }, { "facility": "F5", "customer": 1, "cost": 738.0 }, { "facility": "F5", "customer": 2, "cost": 1017.0 }, { "facility": "F5", "customer": 3, "cost": 2444.0 }, { "facility": "F5", "customer": 4, "cost": 1975.0 }, { "facility": "F5", "customer": 5, "cost": 141.0 }, { "facility": "F5", "customer": 6, "cost": 1904.0 }, { "facility": "F5", "customer": 7, "cost": 1253.0 }, { "facility": "F5", "customer": 8, "cost": 613.0 }, { "facility": "F5", "customer": 9, "cost": 2210.0 }, { "facility": "F5", "customer": 10, "cost": 976.0 }, { "facility": "F5", "customer": 11, "cost": 929.0 }, { "facility": "F5", "customer": 12, "cost": 729.0 }, { "facility": "F5", "customer": 13, "cost": 2003.0 }, { "facility": "F5", "customer": 14, "cost": 2328.0 }, { "facility": "F5", "customer": 15, "cost": 933.0 }, { "facility": "F5", "customer": 16, "cost": 1590.0 }, { "facility": "F6", "customer": 1, "cost": 141.0 }, { "facility": "F6", "customer": 2, "cost": 260.0 }, { "facility": "F6", "customer": 3, "cost": 1203.0 }, { "facility": "F6", "customer": 4, "cost": 763.0 }, { "facility": "F6", "customer": 5, "cost": 104.0 }, { "facility": "F6", "customer": 6, "cost": 831.0 }, { "facility": "F6", "customer": 7, "cost": 473.0 }, { "facility": "F6", "customer": 8, "cost": 145.0 }, { "facility": "F6", "customer": 9, "cost": 960.0 }, { "facility": "F6", "customer": 10, "cost": 487.0 }, { "facility": "F6", "customer": 11, "cost": 127.0 }, { "facility": "F6", "customer": 12, "cost": 67.0 }, { "facility": "F6", "customer": 13, "cost": 873.0 }, { "facility": "F6", "customer": 14, "cost": 1079.0 }, { "facility": "F6", "customer": 15, "cost": 105.0 }, { "facility": "F6", "customer": 16, "cost": 483.0 } ], "objective": 4734.0 }, "solution_variant": { "selected": [ "F3" ], "assignments": [ "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3" ] }, "context_index": 13, "input_format": "csv", "input_index_base": 1 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "We’ve got a bunch of farms and a shortlist of packing facilities; the job is to pick which facilities to operate and route each farm’s harvest to one of the open ones. Each facility has a running cost and a hard limit on how much it can process, and moving produce from farm to facility incurs transport charges. The winning plan is the one with the smallest overall cost — that’s just the sum of all facility opening costs plus all transport charges. Every farm’s output has to go to exactly one operating facility, and no facility can be overloaded beyond its limit. The exact facilities, capacities, and costs are listed below.\n\n# num_packing_facilities=8\n# num_farms=20\n# PACKING_FACILITYS\npacking_facility_id,facility_opening_cost,throughput_capacity\nF1,400.0,300.0\nF2,400.0,300.0\nF3,400.0,300.0\nF4,400.0,300.0\nF5,400.0,300.0\nF6,400.0,300.0\nF7,400.0,300.0\nF8,400.0,300.0\n# FARMS\nfarm_id,farm_production\n0,14.0\n1,23.0\n2,18.0\n3,30.0\n4,12.0\n5,26.0\n6,17.0\n7,23.0\n8,23.0\n9,18.0\n10,17.0\n11,13.0\n12,12.0\n13,23.0\n14,23.0\n15,10.0\n16,27.0\n17,29.0\n18,23.0\n19,19.0\n# TRANSPORTS\npacking_facility_id,farm_id,transport_cost\nF1,0,479.0\nF1,1,1589.0\nF1,2,1227.0\nF1,3,123.0\nF1,4,269.0\nF1,5,611.0\nF1,6,306.0\nF1,7,694.0\nF1,8,683.0\nF1,9,2008.0\nF1,10,508.0\nF1,11,955.0\nF1,12,1184.0\nF1,13,841.0\nF1,14,1443.0\nF1,15,20.0\nF1,16,123.0\nF1,17,122.0\nF1,18,828.0\nF1,19,373.0\nF2,0,457.0\nF2,1,1201.0\nF2,2,822.0\nF2,3,161.0\nF2,4,105.0\nF2,5,475.0\nF2,6,179.0\nF2,7,414.0\nF2,8,620.0\nF2,9,1614.0\nF2,10,114.0\nF2,11,547.0\nF2,12,776.0\nF2,13,476.0\nF2,14,1116.0\nF2,15,63.0\nF2,16,75.0\nF2,17,85.0\nF2,18,474.0\nF2,19,302.0\nF3,0,100.0\nF3,1,1633.0\nF3,2,1385.0\nF3,3,60.0\nF3,4,472.0\nF3,5,456.0\nF3,6,482.0\nF3,7,908.0\nF3,8,342.0\nF3,9,2051.0\nF3,10,648.0\nF3,11,1109.0\nF3,12,1334.0\nF3,13,900.0\nF3,14,1391.0\nF3,15,233.0\nF3,16,246.0\nF3,17,217.0\nF3,18,1030.0\nF3,19,263.0\nF4,0,89.0\nF4,1,867.0\nF4,2,815.0\nF4,3,71.0\nF4,4,253.0\nF4,5,53.0\nF4,6,316.0\nF4,7,584.0\nF4,8,136.0\nF4,9,1262.0\nF4,10,211.0\nF4,11,568.0\nF4,12,756.0\nF4,13,288.0\nF4,14,549.0\nF4,15,48.0\nF4,16,151.0\nF4,17,148.0\nF4,18,611.0\nF4,19,38.0\nF5,0,1030.0\nF5,1,2147.0\nF5,2,1665.0\nF5,3,377.0\nF5,4,478.0\nF5,5,1236.0\nF5,6,337.0\nF5,7,927.0\nF5,8,1262.0\nF5,9,2553.0\nF5,10,1064.0\nF5,11,1422.0\nF5,12,1637.0\nF5,13,1425.0\nF5,14,2054.0\nF5,15,651.0\nF5,16,54.0\nF5,17,64.0\nF5,18,1176.0\nF5,19,990.0\nF6,0,226.0\nF6,1,1556.0\nF6,2,1279.0\nF6,3,68.0\nF6,4,380.0\nF6,5,422.0\nF6,6,406.0\nF6,7,805.0\nF6,8,430.0\nF6,9,1976.0\nF6,10,542.0\nF6,11,1004.0\nF6,12,1230.0\nF6,13,812.0\nF6,14,1344.0\nF6,15,133.0\nF6,16,190.0\nF6,17,175.0\nF6,18,921.0\nF6,19,181.0\nF7,0,385.0\nF7,1,1732.0\nF7,2,1412.0\nF7,3,70.0\nF7,4,430.0\nF7,5,629.0\nF7,6,436.0\nF7,7,877.0\nF7,8,615.0\nF7,9,2153.0\nF7,10,680.0\nF7,11,1138.0\nF7,12,1367.0\nF7,13,982.0\nF7,14,1540.0\nF7,15,212.0\nF7,16,204.0\nF7,17,182.0\nF7,18,1020.0\nF7,19,382.0\nF8,0,312.0\nF8,1,701.0\nF8,2,506.0\nF8,3,134.0\nF8,4,102.0\nF8,5,257.0\nF8,6,176.0\nF8,7,343.0\nF8,8,425.0\nF8,9,1121.0\nF8,10,37.0\nF8,11,263.0\nF8,12,447.0\nF8,13,53.0\nF8,14,618.0\nF8,15,33.0\nF8,16,80.0\nF8,17,89.0\nF8,18,335.0\nF8,19,164.0\n\nOh, and when you send the plan back, keep it in a tiny, predictable JSON shape so it's easy to read. Something like this:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is just the list of packing sites you decide to run, and \"assignments\" is a list (in the same order as the farms were given) saying which open site each farm ships to. Super casual — think of it like filling out a short form, not a technical report.\n\nThis JSON is only a sketch of the expected shape, not the actual answer. Please use the exact identifiers from the instance input — do not rename or invent labels. \n\nValid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "connection_costs": [ [ 479.0, 1589.0, 1227.0, 123.0, 269.0, 611.0, 306.0, 694.0, 683.0, 2008.0, 508.0, 955.0, 1184.0, 841.0, 1443.0, 20.0, 123.0, 122.0, 828.0, 373.0 ], [ 457.0, 1201.0, 822.0, 161.0, 105.0, 475.0, 179.0, 414.0, 620.0, 1614.0, 114.0, 547.0, 776.0, 476.0, 1116.0, 63.0, 75.0, 85.0, 474.0, 302.0 ], [ 100.0, 1633.0, 1385.0, 60.0, 472.0, 456.0, 482.0, 908.0, 342.0, 2051.0, 648.0, 1109.0, 1334.0, 900.0, 1391.0, 233.0, 246.0, 217.0, 1030.0, 263.0 ], [ 89.0, 867.0, 815.0, 71.0, 253.0, 53.0, 316.0, 584.0, 136.0, 1262.0, 211.0, 568.0, 756.0, 288.0, 549.0, 48.0, 151.0, 148.0, 611.0, 38.0 ], [ 1030.0, 2147.0, 1665.0, 377.0, 478.0, 1236.0, 337.0, 927.0, 1262.0, 2553.0, 1064.0, 1422.0, 1637.0, 1425.0, 2054.0, 651.0, 54.0, 64.0, 1176.0, 990.0 ], [ 226.0, 1556.0, 1279.0, 68.0, 380.0, 422.0, 406.0, 805.0, 430.0, 1976.0, 542.0, 1004.0, 1230.0, 812.0, 1344.0, 133.0, 190.0, 175.0, 921.0, 181.0 ], [ 385.0, 1732.0, 1412.0, 70.0, 430.0, 629.0, 436.0, 877.0, 615.0, 2153.0, 680.0, 1138.0, 1367.0, 982.0, 1540.0, 212.0, 204.0, 182.0, 1020.0, 382.0 ], [ 312.0, 701.0, 506.0, 134.0, 102.0, 257.0, 176.0, 343.0, 425.0, 1121.0, 37.0, 263.0, 447.0, 53.0, 618.0, 33.0, 80.0, 89.0, 335.0, 164.0 ] ], "demands": [ 14.0, 23.0, 18.0, 30.0, 12.0, 26.0, 17.0, 23.0, 23.0, 18.0, 17.0, 13.0, 12.0, 23.0, 23.0, 10.0, 27.0, 29.0, 23.0, 19.0 ], "objective": 6022.0 }, "solution": { "open_facilities": [ 3, 7 ], "assignments": [ 3, 7, 7, 3, 7, 3, 7, 7, 3, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 3 ] }, "obj": 6022.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 20, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 300.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 300.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 300.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 300.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 300.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 300.0 }, { "id": "F7", "opening_cost": 400.0, "capacity": 300.0 }, { "id": "F8", "opening_cost": 400.0, "capacity": 300.0 } ], "customers": [ { "id": 0, "demand": 14.0 }, { "id": 1, "demand": 23.0 }, { "id": 2, "demand": 18.0 }, { "id": 3, "demand": 30.0 }, { "id": 4, "demand": 12.0 }, { "id": 5, "demand": 26.0 }, { "id": 6, "demand": 17.0 }, { "id": 7, "demand": 23.0 }, { "id": 8, "demand": 23.0 }, { "id": 9, "demand": 18.0 }, { "id": 10, "demand": 17.0 }, { "id": 11, "demand": 13.0 }, { "id": 12, "demand": 12.0 }, { "id": 13, "demand": 23.0 }, { "id": 14, "demand": 23.0 }, { "id": 15, "demand": 10.0 }, { "id": 16, "demand": 27.0 }, { "id": 17, "demand": 29.0 }, { "id": 18, "demand": 23.0 }, { "id": 19, "demand": 19.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 479.0 }, { "facility": "F1", "customer": 1, "cost": 1589.0 }, { "facility": "F1", "customer": 2, "cost": 1227.0 }, { "facility": "F1", "customer": 3, "cost": 123.0 }, { "facility": "F1", "customer": 4, "cost": 269.0 }, { "facility": "F1", "customer": 5, "cost": 611.0 }, { "facility": "F1", "customer": 6, "cost": 306.0 }, { "facility": "F1", "customer": 7, "cost": 694.0 }, { "facility": "F1", "customer": 8, "cost": 683.0 }, { "facility": "F1", "customer": 9, "cost": 2008.0 }, { "facility": "F1", "customer": 10, "cost": 508.0 }, { "facility": "F1", "customer": 11, "cost": 955.0 }, { "facility": "F1", "customer": 12, "cost": 1184.0 }, { "facility": "F1", "customer": 13, "cost": 841.0 }, { "facility": "F1", "customer": 14, "cost": 1443.0 }, { "facility": "F1", "customer": 15, "cost": 20.0 }, { "facility": "F1", "customer": 16, "cost": 123.0 }, { "facility": "F1", "customer": 17, "cost": 122.0 }, { "facility": "F1", "customer": 18, "cost": 828.0 }, { "facility": "F1", "customer": 19, "cost": 373.0 }, { "facility": "F2", "customer": 0, "cost": 457.0 }, { "facility": "F2", "customer": 1, "cost": 1201.0 }, { "facility": "F2", "customer": 2, "cost": 822.0 }, { "facility": "F2", "customer": 3, "cost": 161.0 }, { "facility": "F2", "customer": 4, "cost": 105.0 }, { "facility": "F2", "customer": 5, "cost": 475.0 }, { "facility": "F2", "customer": 6, "cost": 179.0 }, { "facility": "F2", "customer": 7, "cost": 414.0 }, { "facility": "F2", "customer": 8, "cost": 620.0 }, { "facility": "F2", "customer": 9, "cost": 1614.0 }, { "facility": "F2", "customer": 10, "cost": 114.0 }, { "facility": "F2", "customer": 11, "cost": 547.0 }, { "facility": "F2", "customer": 12, "cost": 776.0 }, { "facility": "F2", "customer": 13, "cost": 476.0 }, { "facility": "F2", "customer": 14, "cost": 1116.0 }, { "facility": "F2", "customer": 15, "cost": 63.0 }, { "facility": "F2", "customer": 16, "cost": 75.0 }, { "facility": "F2", "customer": 17, "cost": 85.0 }, { "facility": "F2", "customer": 18, "cost": 474.0 }, { "facility": "F2", "customer": 19, "cost": 302.0 }, { "facility": "F3", "customer": 0, "cost": 100.0 }, { "facility": "F3", "customer": 1, "cost": 1633.0 }, { "facility": "F3", "customer": 2, "cost": 1385.0 }, { "facility": "F3", "customer": 3, "cost": 60.0 }, { "facility": "F3", "customer": 4, "cost": 472.0 }, { "facility": "F3", "customer": 5, "cost": 456.0 }, { "facility": "F3", "customer": 6, "cost": 482.0 }, { "facility": "F3", "customer": 7, "cost": 908.0 }, { "facility": "F3", "customer": 8, "cost": 342.0 }, { "facility": "F3", "customer": 9, "cost": 2051.0 }, { "facility": "F3", "customer": 10, "cost": 648.0 }, { "facility": "F3", "customer": 11, "cost": 1109.0 }, { "facility": "F3", "customer": 12, "cost": 1334.0 }, { "facility": "F3", "customer": 13, "cost": 900.0 }, { "facility": "F3", "customer": 14, "cost": 1391.0 }, { "facility": "F3", "customer": 15, "cost": 233.0 }, { "facility": "F3", "customer": 16, "cost": 246.0 }, { "facility": "F3", "customer": 17, "cost": 217.0 }, { "facility": "F3", "customer": 18, "cost": 1030.0 }, { "facility": "F3", "customer": 19, "cost": 263.0 }, { "facility": "F4", "customer": 0, "cost": 89.0 }, { "facility": "F4", "customer": 1, "cost": 867.0 }, { "facility": "F4", "customer": 2, "cost": 815.0 }, { "facility": "F4", "customer": 3, "cost": 71.0 }, { "facility": "F4", "customer": 4, "cost": 253.0 }, { "facility": "F4", "customer": 5, "cost": 53.0 }, { "facility": "F4", "customer": 6, "cost": 316.0 }, { "facility": "F4", "customer": 7, "cost": 584.0 }, { "facility": "F4", "customer": 8, "cost": 136.0 }, { "facility": "F4", "customer": 9, "cost": 1262.0 }, { "facility": "F4", "customer": 10, "cost": 211.0 }, { "facility": "F4", "customer": 11, "cost": 568.0 }, { "facility": "F4", "customer": 12, "cost": 756.0 }, { "facility": "F4", "customer": 13, "cost": 288.0 }, { "facility": "F4", "customer": 14, "cost": 549.0 }, { "facility": "F4", "customer": 15, "cost": 48.0 }, { "facility": "F4", "customer": 16, "cost": 151.0 }, { "facility": "F4", "customer": 17, "cost": 148.0 }, { "facility": "F4", "customer": 18, "cost": 611.0 }, { "facility": "F4", "customer": 19, "cost": 38.0 }, { "facility": "F5", "customer": 0, "cost": 1030.0 }, { "facility": "F5", "customer": 1, "cost": 2147.0 }, { "facility": "F5", "customer": 2, "cost": 1665.0 }, { "facility": "F5", "customer": 3, "cost": 377.0 }, { "facility": "F5", "customer": 4, "cost": 478.0 }, { "facility": "F5", "customer": 5, "cost": 1236.0 }, { "facility": "F5", "customer": 6, "cost": 337.0 }, { "facility": "F5", "customer": 7, "cost": 927.0 }, { "facility": "F5", "customer": 8, "cost": 1262.0 }, { "facility": "F5", "customer": 9, "cost": 2553.0 }, { "facility": "F5", "customer": 10, "cost": 1064.0 }, { "facility": "F5", "customer": 11, "cost": 1422.0 }, { "facility": "F5", "customer": 12, "cost": 1637.0 }, { "facility": "F5", "customer": 13, "cost": 1425.0 }, { "facility": "F5", "customer": 14, "cost": 2054.0 }, { "facility": "F5", "customer": 15, "cost": 651.0 }, { "facility": "F5", "customer": 16, "cost": 54.0 }, { "facility": "F5", "customer": 17, "cost": 64.0 }, { "facility": "F5", "customer": 18, "cost": 1176.0 }, { "facility": "F5", "customer": 19, "cost": 990.0 }, { "facility": "F6", "customer": 0, "cost": 226.0 }, { "facility": "F6", "customer": 1, "cost": 1556.0 }, { "facility": "F6", "customer": 2, "cost": 1279.0 }, { "facility": "F6", "customer": 3, "cost": 68.0 }, { "facility": "F6", "customer": 4, "cost": 380.0 }, { "facility": "F6", "customer": 5, "cost": 422.0 }, { "facility": "F6", "customer": 6, "cost": 406.0 }, { "facility": "F6", "customer": 7, "cost": 805.0 }, { "facility": "F6", "customer": 8, "cost": 430.0 }, { "facility": "F6", "customer": 9, "cost": 1976.0 }, { "facility": "F6", "customer": 10, "cost": 542.0 }, { "facility": "F6", "customer": 11, "cost": 1004.0 }, { "facility": "F6", "customer": 12, "cost": 1230.0 }, { "facility": "F6", "customer": 13, "cost": 812.0 }, { "facility": "F6", "customer": 14, "cost": 1344.0 }, { "facility": "F6", "customer": 15, "cost": 133.0 }, { "facility": "F6", "customer": 16, "cost": 190.0 }, { "facility": "F6", "customer": 17, "cost": 175.0 }, { "facility": "F6", "customer": 18, "cost": 921.0 }, { "facility": "F6", "customer": 19, "cost": 181.0 }, { "facility": "F7", "customer": 0, "cost": 385.0 }, { "facility": "F7", "customer": 1, "cost": 1732.0 }, { "facility": "F7", "customer": 2, "cost": 1412.0 }, { "facility": "F7", "customer": 3, "cost": 70.0 }, { "facility": "F7", "customer": 4, "cost": 430.0 }, { "facility": "F7", "customer": 5, "cost": 629.0 }, { "facility": "F7", "customer": 6, "cost": 436.0 }, { "facility": "F7", "customer": 7, "cost": 877.0 }, { "facility": "F7", "customer": 8, "cost": 615.0 }, { "facility": "F7", "customer": 9, "cost": 2153.0 }, { "facility": "F7", "customer": 10, "cost": 680.0 }, { "facility": "F7", "customer": 11, "cost": 1138.0 }, { "facility": "F7", "customer": 12, "cost": 1367.0 }, { "facility": "F7", "customer": 13, "cost": 982.0 }, { "facility": "F7", "customer": 14, "cost": 1540.0 }, { "facility": "F7", "customer": 15, "cost": 212.0 }, { "facility": "F7", "customer": 16, "cost": 204.0 }, { "facility": "F7", "customer": 17, "cost": 182.0 }, { "facility": "F7", "customer": 18, "cost": 1020.0 }, { "facility": "F7", "customer": 19, "cost": 382.0 }, { "facility": "F8", "customer": 0, "cost": 312.0 }, { "facility": "F8", "customer": 1, "cost": 701.0 }, { "facility": "F8", "customer": 2, "cost": 506.0 }, { "facility": "F8", "customer": 3, "cost": 134.0 }, { "facility": "F8", "customer": 4, "cost": 102.0 }, { "facility": "F8", "customer": 5, "cost": 257.0 }, { "facility": "F8", "customer": 6, "cost": 176.0 }, { "facility": "F8", "customer": 7, "cost": 343.0 }, { "facility": "F8", "customer": 8, "cost": 425.0 }, { "facility": "F8", "customer": 9, "cost": 1121.0 }, { "facility": "F8", "customer": 10, "cost": 37.0 }, { "facility": "F8", "customer": 11, "cost": 263.0 }, { "facility": "F8", "customer": 12, "cost": 447.0 }, { "facility": "F8", "customer": 13, "cost": 53.0 }, { "facility": "F8", "customer": 14, "cost": 618.0 }, { "facility": "F8", "customer": 15, "cost": 33.0 }, { "facility": "F8", "customer": 16, "cost": 80.0 }, { "facility": "F8", "customer": 17, "cost": 89.0 }, { "facility": "F8", "customer": 18, "cost": 335.0 }, { "facility": "F8", "customer": 19, "cost": 164.0 } ], "objective": 6022.0 }, "solution_variant": { "selected": [ "F4", "F8" ], "assignments": [ "F4", "F8", "F8", "F4", "F8", "F4", "F8", "F8", "F4", "F8", "F8", "F8", "F8", "F8", "F4", "F8", "F8", "F8", "F8", "F4" ] }, "context_index": 14, "input_format": "csv", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Many people organizing artisan fairs face this: deciding which vendor booths to rent and how to assign each maker to a single rented spot. Booths cost money and have limited display space, and assigning a maker to a booth usually incurs a setup/transfer charge. A smarter layout is the one that costs the least overall — add together the booth rents and all assignment/setup charges to get the final cost — while making sure every maker gets one rented booth and no booth’s space limit is broken. The specific booth fees, capacities, and maker requirements come next below.\n\nThere are 7 booths and 16 makers in this instance.\n\n**Booths**\n| booth_id | booth_rental_fee | booth_space_capacity |\n|---|---|---|\n| F1 | 300.0 | 500.0 |\n| F2 | 300.0 | 500.0 |\n| F3 | 300.0 | 500.0 |\n| F4 | 300.0 | 500.0 |\n| F5 | 300.0 | 500.0 |\n| F6 | 300.0 | 500.0 |\n| F7 | 300.0 | 500.0 |\n\n**Makers**\n| maker_id | maker_space_requirement |\n|---|---|\n| 0 | 14.0 |\n| 1 | 12.0 |\n| 2 | 19.0 |\n| 3 | 15.0 |\n| 4 | 29.0 |\n| 5 | 18.0 |\n| 6 | 27.0 |\n| 7 | 10.0 |\n| 8 | 26.0 |\n| 9 | 23.0 |\n| 10 | 21.0 |\n| 11 | 27.0 |\n| 12 | 19.0 |\n| 13 | 16.0 |\n| 14 | 11.0 |\n| 15 | 27.0 |\n\n**Setup Transfer Cost**\n| booth_id | maker_id | setup_transfer_cost |\n|---|---|---|\n| F1 | 0 | 570.0 |\n| F1 | 1 | 83.0 |\n| F1 | 2 | 107.0 |\n| F1 | 3 | 46.0 |\n| F1 | 4 | 495.0 |\n| F1 | 5 | 92.0 |\n| F1 | 6 | 429.0 |\n| F1 | 7 | 938.0 |\n| F1 | 8 | 531.0 |\n| F1 | 9 | 791.0 |\n| F1 | 10 | 374.0 |\n| F1 | 11 | 101.0 |\n| F1 | 12 | 274.0 |\n| F1 | 13 | 752.0 |\n| F1 | 14 | 501.0 |\n| F1 | 15 | 461.0 |\n| F2 | 0 | 768.0 |\n| F2 | 1 | 241.0 |\n| F2 | 2 | 143.0 |\n| F2 | 3 | 766.0 |\n| F2 | 4 | 667.0 |\n| F2 | 5 | 686.0 |\n| F2 | 6 | 946.0 |\n| F2 | 7 | 1284.0 |\n| F2 | 8 | 735.0 |\n| F2 | 9 | 1288.0 |\n| F2 | 10 | 1070.0 |\n| F2 | 11 | 362.0 |\n| F2 | 12 | 407.0 |\n| F2 | 13 | 1465.0 |\n| F2 | 14 | 1182.0 |\n| F2 | 15 | 918.0 |\n| F3 | 0 | 1030.0 |\n| F3 | 1 | 900.0 |\n| F3 | 2 | 139.0 |\n| F3 | 3 | 1977.0 |\n| F3 | 4 | 900.0 |\n| F3 | 5 | 1814.0 |\n| F3 | 6 | 1854.0 |\n| F3 | 7 | 1760.0 |\n| F3 | 8 | 1034.0 |\n| F3 | 9 | 2054.0 |\n| F3 | 10 | 2164.0 |\n| F3 | 11 | 1611.0 |\n| F3 | 12 | 632.0 |\n| F3 | 13 | 2527.0 |\n| F3 | 14 | 2236.0 |\n| F3 | 15 | 1738.0 |\n| F4 | 0 | 385.0 |\n| F4 | 1 | 625.0 |\n| F4 | 2 | 40.0 |\n| F4 | 3 | 1770.0 |\n| F4 | 4 | 260.0 |\n| F4 | 5 | 1557.0 |\n| F4 | 6 | 1449.0 |\n| F4 | 7 | 1131.0 |\n| F4 | 8 | 388.0 |\n| F4 | 9 | 1540.0 |\n| F4 | 10 | 1846.0 |\n| F4 | 11 | 1478.0 |\n| F4 | 12 | 59.0 |\n| F4 | 13 | 2157.0 |\n| F4 | 14 | 1881.0 |\n| F4 | 15 | 1294.0 |\n| F5 | 0 | 312.0 |\n| F5 | 1 | 62.0 |\n| F5 | 2 | 50.0 |\n| F5 | 3 | 864.0 |\n| F5 | 4 | 263.0 |\n| F5 | 5 | 625.0 |\n| F5 | 6 | 416.0 |\n| F5 | 7 | 637.0 |\n| F5 | 8 | 275.0 |\n| F5 | 9 | 618.0 |\n| F5 | 10 | 839.0 |\n| F5 | 11 | 701.0 |\n| F5 | 12 | 100.0 |\n| F5 | 13 | 1125.0 |\n| F5 | 14 | 854.0 |\n| F5 | 15 | 273.0 |\n| F6 | 0 | 658.0 |\n| F6 | 1 | 138.0 |\n| F6 | 2 | 96.0 |\n| F6 | 3 | 1110.0 |\n| F6 | 4 | 558.0 |\n| F6 | 5 | 936.0 |\n| F6 | 6 | 1023.0 |\n| F6 | 7 | 1206.0 |\n| F6 | 8 | 626.0 |\n| F6 | 9 | 1302.0 |\n| F6 | 10 | 1289.0 |\n| F6 | 11 | 783.0 |\n| F6 | 12 | 302.0 |\n| F6 | 13 | 1661.0 |\n| F6 | 14 | 1368.0 |\n| F6 | 15 | 944.0 |\n| F7 | 0 | 692.0 |\n| F7 | 1 | 374.0 |\n| F7 | 2 | 79.0 |\n| F7 | 3 | 1492.0 |\n| F7 | 4 | 579.0 |\n| F7 | 5 | 1309.0 |\n| F7 | 6 | 1328.0 |\n| F7 | 7 | 1329.0 |\n| F7 | 8 | 670.0 |\n| F7 | 9 | 1544.0 |\n| F7 | 10 | 1646.0 |\n| F7 | 11 | 1160.0 |\n| F7 | 12 | 306.0 |\n| F7 | 13 | 2002.0 |\n| F7 | 14 | 1712.0 |\n| F7 | 15 | 1216.0 |\n\nOh, and when you send the solution back, just use this little JSON layout so it's easy to check:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list the booths you're renting. \"assignments\" is one entry per maker, saying which rented booth that maker gets (use the same order the instance lists the makers). This is just a sketch of the shape I expect, not the actual answer — fill in the real identifiers from the instance.\n\nPlease make sure you use each identifier exactly as it appears in the instance input — no renaming and no new labels. \n\n- For example: \"Valid identifiers look like plain numbers such as \"1\" or \"23\", single capital letters like \"A\" or \"B\", or a capital letter followed by digits like \"A1\" or \"X7\".\"", "instance": { "opening_costs": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 570.0, 83.0, 107.0, 46.0, 495.0, 92.0, 429.0, 938.0, 531.0, 791.0, 374.0, 101.0, 274.0, 752.0, 501.0, 461.0 ], [ 768.0, 241.0, 143.0, 766.0, 667.0, 686.0, 946.0, 1284.0, 735.0, 1288.0, 1070.0, 362.0, 407.0, 1465.0, 1182.0, 918.0 ], [ 1030.0, 900.0, 139.0, 1977.0, 900.0, 1814.0, 1854.0, 1760.0, 1034.0, 2054.0, 2164.0, 1611.0, 632.0, 2527.0, 2236.0, 1738.0 ], [ 385.0, 625.0, 40.0, 1770.0, 260.0, 1557.0, 1449.0, 1131.0, 388.0, 1540.0, 1846.0, 1478.0, 59.0, 2157.0, 1881.0, 1294.0 ], [ 312.0, 62.0, 50.0, 864.0, 263.0, 625.0, 416.0, 637.0, 275.0, 618.0, 839.0, 701.0, 100.0, 1125.0, 854.0, 273.0 ], [ 658.0, 138.0, 96.0, 1110.0, 558.0, 936.0, 1023.0, 1206.0, 626.0, 1302.0, 1289.0, 783.0, 302.0, 1661.0, 1368.0, 944.0 ], [ 692.0, 374.0, 79.0, 1492.0, 579.0, 1309.0, 1328.0, 1329.0, 670.0, 1544.0, 1646.0, 1160.0, 306.0, 2002.0, 1712.0, 1216.0 ] ], "demands": [ 14.0, 12.0, 19.0, 15.0, 29.0, 18.0, 27.0, 10.0, 26.0, 23.0, 21.0, 27.0, 19.0, 16.0, 11.0, 27.0 ], "objective": 5472.0 }, "solution": { "open_facilities": [ 0, 4 ], "assignments": [ 4, 4, 4, 0, 4, 0, 4, 4, 4, 4, 0, 0, 4, 0, 0, 4 ] }, "obj": 5472.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 16, "facilities": [ { "id": "F1", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F2", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F3", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F4", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F5", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F6", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F7", "opening_cost": 300.0, "capacity": 500.0 } ], "customers": [ { "id": 0, "demand": 14.0 }, { "id": 1, "demand": 12.0 }, { "id": 2, "demand": 19.0 }, { "id": 3, "demand": 15.0 }, { "id": 4, "demand": 29.0 }, { "id": 5, "demand": 18.0 }, { "id": 6, "demand": 27.0 }, { "id": 7, "demand": 10.0 }, { "id": 8, "demand": 26.0 }, { "id": 9, "demand": 23.0 }, { "id": 10, "demand": 21.0 }, { "id": 11, "demand": 27.0 }, { "id": 12, "demand": 19.0 }, { "id": 13, "demand": 16.0 }, { "id": 14, "demand": 11.0 }, { "id": 15, "demand": 27.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 570.0 }, { "facility": "F1", "customer": 1, "cost": 83.0 }, { "facility": "F1", "customer": 2, "cost": 107.0 }, { "facility": "F1", "customer": 3, "cost": 46.0 }, { "facility": "F1", "customer": 4, "cost": 495.0 }, { "facility": "F1", "customer": 5, "cost": 92.0 }, { "facility": "F1", "customer": 6, "cost": 429.0 }, { "facility": "F1", "customer": 7, "cost": 938.0 }, { "facility": "F1", "customer": 8, "cost": 531.0 }, { "facility": "F1", "customer": 9, "cost": 791.0 }, { "facility": "F1", "customer": 10, "cost": 374.0 }, { "facility": "F1", "customer": 11, "cost": 101.0 }, { "facility": "F1", "customer": 12, "cost": 274.0 }, { "facility": "F1", "customer": 13, "cost": 752.0 }, { "facility": "F1", "customer": 14, "cost": 501.0 }, { "facility": "F1", "customer": 15, "cost": 461.0 }, { "facility": "F2", "customer": 0, "cost": 768.0 }, { "facility": "F2", "customer": 1, "cost": 241.0 }, { "facility": "F2", "customer": 2, "cost": 143.0 }, { "facility": "F2", "customer": 3, "cost": 766.0 }, { "facility": "F2", "customer": 4, "cost": 667.0 }, { "facility": "F2", "customer": 5, "cost": 686.0 }, { "facility": "F2", "customer": 6, "cost": 946.0 }, { "facility": "F2", "customer": 7, "cost": 1284.0 }, { "facility": "F2", "customer": 8, "cost": 735.0 }, { "facility": "F2", "customer": 9, "cost": 1288.0 }, { "facility": "F2", "customer": 10, "cost": 1070.0 }, { "facility": "F2", "customer": 11, "cost": 362.0 }, { "facility": "F2", "customer": 12, "cost": 407.0 }, { "facility": "F2", "customer": 13, "cost": 1465.0 }, { "facility": "F2", "customer": 14, "cost": 1182.0 }, { "facility": "F2", "customer": 15, "cost": 918.0 }, { "facility": "F3", "customer": 0, "cost": 1030.0 }, { "facility": "F3", "customer": 1, "cost": 900.0 }, { "facility": "F3", "customer": 2, "cost": 139.0 }, { "facility": "F3", "customer": 3, "cost": 1977.0 }, { "facility": "F3", "customer": 4, "cost": 900.0 }, { "facility": "F3", "customer": 5, "cost": 1814.0 }, { "facility": "F3", "customer": 6, "cost": 1854.0 }, { "facility": "F3", "customer": 7, "cost": 1760.0 }, { "facility": "F3", "customer": 8, "cost": 1034.0 }, { "facility": "F3", "customer": 9, "cost": 2054.0 }, { "facility": "F3", "customer": 10, "cost": 2164.0 }, { "facility": "F3", "customer": 11, "cost": 1611.0 }, { "facility": "F3", "customer": 12, "cost": 632.0 }, { "facility": "F3", "customer": 13, "cost": 2527.0 }, { "facility": "F3", "customer": 14, "cost": 2236.0 }, { "facility": "F3", "customer": 15, "cost": 1738.0 }, { "facility": "F4", "customer": 0, "cost": 385.0 }, { "facility": "F4", "customer": 1, "cost": 625.0 }, { "facility": "F4", "customer": 2, "cost": 40.0 }, { "facility": "F4", "customer": 3, "cost": 1770.0 }, { "facility": "F4", "customer": 4, "cost": 260.0 }, { "facility": "F4", "customer": 5, "cost": 1557.0 }, { "facility": "F4", "customer": 6, "cost": 1449.0 }, { "facility": "F4", "customer": 7, "cost": 1131.0 }, { "facility": "F4", "customer": 8, "cost": 388.0 }, { "facility": "F4", "customer": 9, "cost": 1540.0 }, { "facility": "F4", "customer": 10, "cost": 1846.0 }, { "facility": "F4", "customer": 11, "cost": 1478.0 }, { "facility": "F4", "customer": 12, "cost": 59.0 }, { "facility": "F4", "customer": 13, "cost": 2157.0 }, { "facility": "F4", "customer": 14, "cost": 1881.0 }, { "facility": "F4", "customer": 15, "cost": 1294.0 }, { "facility": "F5", "customer": 0, "cost": 312.0 }, { "facility": "F5", "customer": 1, "cost": 62.0 }, { "facility": "F5", "customer": 2, "cost": 50.0 }, { "facility": "F5", "customer": 3, "cost": 864.0 }, { "facility": "F5", "customer": 4, "cost": 263.0 }, { "facility": "F5", "customer": 5, "cost": 625.0 }, { "facility": "F5", "customer": 6, "cost": 416.0 }, { "facility": "F5", "customer": 7, "cost": 637.0 }, { "facility": "F5", "customer": 8, "cost": 275.0 }, { "facility": "F5", "customer": 9, "cost": 618.0 }, { "facility": "F5", "customer": 10, "cost": 839.0 }, { "facility": "F5", "customer": 11, "cost": 701.0 }, { "facility": "F5", "customer": 12, "cost": 100.0 }, { "facility": "F5", "customer": 13, "cost": 1125.0 }, { "facility": "F5", "customer": 14, "cost": 854.0 }, { "facility": "F5", "customer": 15, "cost": 273.0 }, { "facility": "F6", "customer": 0, "cost": 658.0 }, { "facility": "F6", "customer": 1, "cost": 138.0 }, { "facility": "F6", "customer": 2, "cost": 96.0 }, { "facility": "F6", "customer": 3, "cost": 1110.0 }, { "facility": "F6", "customer": 4, "cost": 558.0 }, { "facility": "F6", "customer": 5, "cost": 936.0 }, { "facility": "F6", "customer": 6, "cost": 1023.0 }, { "facility": "F6", "customer": 7, "cost": 1206.0 }, { "facility": "F6", "customer": 8, "cost": 626.0 }, { "facility": "F6", "customer": 9, "cost": 1302.0 }, { "facility": "F6", "customer": 10, "cost": 1289.0 }, { "facility": "F6", "customer": 11, "cost": 783.0 }, { "facility": "F6", "customer": 12, "cost": 302.0 }, { "facility": "F6", "customer": 13, "cost": 1661.0 }, { "facility": "F6", "customer": 14, "cost": 1368.0 }, { "facility": "F6", "customer": 15, "cost": 944.0 }, { "facility": "F7", "customer": 0, "cost": 692.0 }, { "facility": "F7", "customer": 1, "cost": 374.0 }, { "facility": "F7", "customer": 2, "cost": 79.0 }, { "facility": "F7", "customer": 3, "cost": 1492.0 }, { "facility": "F7", "customer": 4, "cost": 579.0 }, { "facility": "F7", "customer": 5, "cost": 1309.0 }, { "facility": "F7", "customer": 6, "cost": 1328.0 }, { "facility": "F7", "customer": 7, "cost": 1329.0 }, { "facility": "F7", "customer": 8, "cost": 670.0 }, { "facility": "F7", "customer": 9, "cost": 1544.0 }, { "facility": "F7", "customer": 10, "cost": 1646.0 }, { "facility": "F7", "customer": 11, "cost": 1160.0 }, { "facility": "F7", "customer": 12, "cost": 306.0 }, { "facility": "F7", "customer": 13, "cost": 2002.0 }, { "facility": "F7", "customer": 14, "cost": 1712.0 }, { "facility": "F7", "customer": 15, "cost": 1216.0 } ], "objective": 5472.0 }, "solution_variant": { "selected": [ "F1", "F5" ], "assignments": [ "F5", "F5", "F5", "F1", "F5", "F1", "F5", "F5", "F5", "F5", "F1", "F1", "F5", "F1", "F1", "F5" ] }, "context_index": 15, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "At the coordination office the question is straightforward: which staging areas should be staffed, and which staffed area should handle each beneficiary community? Staffing each area costs money and comes with a limit on how many people it can serve; moving aid from a staffed area to a community also costs something. Each community must be assigned to one staffed area only, and no staffed area can be assigned more demand than it can support. The plan that’s “better” is the one with the lowest total expense — add together the staffing costs for all staffed areas used and the distribution costs for every community assignment — and choose the arrangement with the smallest sum. The concrete details are given below.\n\n# num_staging_areas=8\n# num_communities=19\n# STAGING_AREAS\nstaging_area_id,staffing_cost,staging_capacity\nF1,372.0,436.0\nF2,372.0,436.0\nF3,432.0,466.0\nF4,121.0,311.0\nF5,312.0,406.0\nF6,103.0,302.0\nF7,336.0,418.0\nF8,472.0,486.0\n# COMMUNITYS\ncommunity_id,beneficiary_demand\n0,20.0\n1,20.0\n2,20.0\n3,20.0\n4,10.0\n5,20.0\n6,30.0\n7,10.0\n8,30.0\n9,10.0\n10,9.0\n11,16.0\n12,21.0\n13,27.0\n14,8.0\n15,31.0\n16,13.0\n17,13.0\n18,26.0\n# DISTRIBUTIONS\nstaging_area_id,community_id,distribution_cost\nF1,0,326.0\nF1,1,330.0\nF1,2,297.0\nF1,3,205.0\nF1,4,213.0\nF1,5,213.0\nF1,6,8.0\nF1,7,233.0\nF1,8,216.0\nF1,9,324.0\nF1,10,241.0\nF1,11,128.0\nF1,12,220.0\nF1,13,191.0\nF1,14,100.0\nF1,15,85.0\nF1,16,170.0\nF1,17,135.0\nF1,18,205.0\nF2,0,286.0\nF2,1,291.0\nF2,2,260.0\nF2,3,175.0\nF2,4,184.0\nF2,5,189.0\nF2,6,41.0\nF2,7,215.0\nF2,8,197.0\nF2,9,286.0\nF2,10,201.0\nF2,11,88.0\nF2,12,180.0\nF2,13,152.0\nF2,14,82.0\nF2,15,81.0\nF2,16,131.0\nF2,17,118.0\nF2,18,167.0\nF3,0,220.0\nF3,1,221.0\nF3,2,184.0\nF3,3,91.0\nF3,4,100.0\nF3,5,108.0\nF3,6,113.0\nF3,7,261.0\nF3,8,241.0\nF3,9,262.0\nF3,10,161.0\nF3,11,70.0\nF3,12,134.0\nF3,13,91.0\nF3,14,45.0\nF3,15,157.0\nF3,16,111.0\nF3,17,57.0\nF3,18,154.0\nF4,0,303.0\nF4,1,301.0\nF4,2,260.0\nF4,3,143.0\nF4,4,146.0\nF4,5,134.0\nF4,6,94.0\nF4,7,316.0\nF4,8,297.0\nF4,9,351.0\nF4,10,251.0\nF4,11,150.0\nF4,12,224.0\nF4,13,180.0\nF4,14,45.0\nF4,15,180.0\nF4,16,196.0\nF4,17,57.0\nF4,18,238.0\nF5,0,267.0\nF5,1,263.0\nF5,2,221.0\nF5,3,100.0\nF5,4,102.0\nF5,5,89.0\nF5,6,127.0\nF5,7,326.0\nF5,8,306.0\nF5,9,332.0\nF5,10,228.0\nF5,11,141.0\nF5,12,200.0\nF5,13,153.0\nF5,14,40.0\nF5,15,203.0\nF5,16,183.0\nF5,17,18.0\nF5,18,226.0\nF6,0,305.0\nF6,1,316.0\nF6,2,297.0\nF6,3,249.0\nF6,4,260.0\nF6,5,272.0\nF6,6,124.0\nF6,7,117.0\nF6,8,100.0\nF6,9,248.0\nF6,10,197.0\nF6,11,118.0\nF6,12,189.0\nF6,13,187.0\nF6,14,180.0\nF6,15,38.0\nF6,16,130.0\nF6,17,213.0\nF6,18,142.0\nF7,0,202.0\nF7,1,214.0\nF7,2,199.0\nF7,3,180.0\nF7,4,192.0\nF7,5,212.0\nF7,6,163.0\nF7,7,151.0\nF7,8,132.0\nF7,9,163.0\nF7,10,94.0\nF7,11,54.0\nF7,12,86.0\nF7,13,95.0\nF7,14,161.0\nF7,15,127.0\nF7,16,29.0\nF7,17,181.0\nF7,18,45.0\nF8,0,132.0\nF8,1,134.0\nF8,2,102.0\nF8,3,77.0\nF8,4,89.0\nF8,5,115.0\nF8,6,194.0\nF8,7,265.0\nF8,8,246.0\nF8,9,197.0\nF8,10,92.0\nF8,11,85.0\nF8,12,64.0\nF8,13,20.0\nF8,14,130.0\nF8,15,210.0\nF8,16,86.0\nF8,17,125.0\nF8,18,116.0\n\nAlso, when you send the plan back, please follow this simple JSON layout so it's easy to parse and check:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of staging areas you'll staff, and \"assignments\" as which staffed area handles each beneficiary community (listed in the same order as the communities in the instance). This JSON is just a sketch of the shape I need — not the final answer itself.\n\nPlease make sure you use the exact identifiers from the instance input, without renaming or inventing new labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 372.0, 372.0, 432.0, 121.0, 312.0, 103.0, 336.0, 472.0 ], "capacities": [ 436.0, 436.0, 466.0, 311.0, 406.0, 302.0, 418.0, 486.0 ], "connection_costs": [ [ 326.0, 330.0, 297.0, 205.0, 213.0, 213.0, 8.0, 233.0, 216.0, 324.0, 241.0, 128.0, 220.0, 191.0, 100.0, 85.0, 170.0, 135.0, 205.0 ], [ 286.0, 291.0, 260.0, 175.0, 184.0, 189.0, 41.0, 215.0, 197.0, 286.0, 201.0, 88.0, 180.0, 152.0, 82.0, 81.0, 131.0, 118.0, 167.0 ], [ 220.0, 221.0, 184.0, 91.0, 100.0, 108.0, 113.0, 261.0, 241.0, 262.0, 161.0, 70.0, 134.0, 91.0, 45.0, 157.0, 111.0, 57.0, 154.0 ], [ 303.0, 301.0, 260.0, 143.0, 146.0, 134.0, 94.0, 316.0, 297.0, 351.0, 251.0, 150.0, 224.0, 180.0, 45.0, 180.0, 196.0, 57.0, 238.0 ], [ 267.0, 263.0, 221.0, 100.0, 102.0, 89.0, 127.0, 326.0, 306.0, 332.0, 228.0, 141.0, 200.0, 153.0, 40.0, 203.0, 183.0, 18.0, 226.0 ], [ 305.0, 316.0, 297.0, 249.0, 260.0, 272.0, 124.0, 117.0, 100.0, 248.0, 197.0, 118.0, 189.0, 187.0, 180.0, 38.0, 130.0, 213.0, 142.0 ], [ 202.0, 214.0, 199.0, 180.0, 192.0, 212.0, 163.0, 151.0, 132.0, 163.0, 94.0, 54.0, 86.0, 95.0, 161.0, 127.0, 29.0, 181.0, 45.0 ], [ 132.0, 134.0, 102.0, 77.0, 89.0, 115.0, 194.0, 265.0, 246.0, 197.0, 92.0, 85.0, 64.0, 20.0, 130.0, 210.0, 86.0, 125.0, 116.0 ] ], "demands": [ 20.0, 20.0, 20.0, 20.0, 10.0, 20.0, 30.0, 10.0, 30.0, 10.0, 9.0, 16.0, 21.0, 27.0, 8.0, 31.0, 13.0, 13.0, 26.0 ], "objective": 2456.0 }, "solution": { "open_facilities": [ 3, 5, 7 ], "assignments": [ 7, 7, 7, 7, 7, 7, 3, 5, 5, 7, 7, 7, 7, 7, 3, 5, 7, 3, 7 ] }, "obj": 2456.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 19, "facilities": [ { "id": "F1", "opening_cost": 372.0, "capacity": 436.0 }, { "id": "F2", "opening_cost": 372.0, "capacity": 436.0 }, { "id": "F3", "opening_cost": 432.0, "capacity": 466.0 }, { "id": "F4", "opening_cost": 121.0, "capacity": 311.0 }, { "id": "F5", "opening_cost": 312.0, "capacity": 406.0 }, { "id": "F6", "opening_cost": 103.0, "capacity": 302.0 }, { "id": "F7", "opening_cost": 336.0, "capacity": 418.0 }, { "id": "F8", "opening_cost": 472.0, "capacity": 486.0 } ], "customers": [ { "id": 0, "demand": 20.0 }, { "id": 1, "demand": 20.0 }, { "id": 2, "demand": 20.0 }, { "id": 3, "demand": 20.0 }, { "id": 4, "demand": 10.0 }, { "id": 5, "demand": 20.0 }, { "id": 6, "demand": 30.0 }, { "id": 7, "demand": 10.0 }, { "id": 8, "demand": 30.0 }, { "id": 9, "demand": 10.0 }, { "id": 10, "demand": 9.0 }, { "id": 11, "demand": 16.0 }, { "id": 12, "demand": 21.0 }, { "id": 13, "demand": 27.0 }, { "id": 14, "demand": 8.0 }, { "id": 15, "demand": 31.0 }, { "id": 16, "demand": 13.0 }, { "id": 17, "demand": 13.0 }, { "id": 18, "demand": 26.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 326.0 }, { "facility": "F1", "customer": 1, "cost": 330.0 }, { "facility": "F1", "customer": 2, "cost": 297.0 }, { "facility": "F1", "customer": 3, "cost": 205.0 }, { "facility": "F1", "customer": 4, "cost": 213.0 }, { "facility": "F1", "customer": 5, "cost": 213.0 }, { "facility": "F1", "customer": 6, "cost": 8.0 }, { "facility": "F1", "customer": 7, "cost": 233.0 }, { "facility": "F1", "customer": 8, "cost": 216.0 }, { "facility": "F1", "customer": 9, "cost": 324.0 }, { "facility": "F1", "customer": 10, "cost": 241.0 }, { "facility": "F1", "customer": 11, "cost": 128.0 }, { "facility": "F1", "customer": 12, "cost": 220.0 }, { "facility": "F1", "customer": 13, "cost": 191.0 }, { "facility": "F1", "customer": 14, "cost": 100.0 }, { "facility": "F1", "customer": 15, "cost": 85.0 }, { "facility": "F1", "customer": 16, "cost": 170.0 }, { "facility": "F1", "customer": 17, "cost": 135.0 }, { "facility": "F1", "customer": 18, "cost": 205.0 }, { "facility": "F2", "customer": 0, "cost": 286.0 }, { "facility": "F2", "customer": 1, "cost": 291.0 }, { "facility": "F2", "customer": 2, "cost": 260.0 }, { "facility": "F2", "customer": 3, "cost": 175.0 }, { "facility": "F2", "customer": 4, "cost": 184.0 }, { "facility": "F2", "customer": 5, "cost": 189.0 }, { "facility": "F2", "customer": 6, "cost": 41.0 }, { "facility": "F2", "customer": 7, "cost": 215.0 }, { "facility": "F2", "customer": 8, "cost": 197.0 }, { "facility": "F2", "customer": 9, "cost": 286.0 }, { "facility": "F2", "customer": 10, "cost": 201.0 }, { "facility": "F2", "customer": 11, "cost": 88.0 }, { "facility": "F2", "customer": 12, "cost": 180.0 }, { "facility": "F2", "customer": 13, "cost": 152.0 }, { "facility": "F2", "customer": 14, "cost": 82.0 }, { "facility": "F2", "customer": 15, "cost": 81.0 }, { "facility": "F2", "customer": 16, "cost": 131.0 }, { "facility": "F2", "customer": 17, "cost": 118.0 }, { "facility": "F2", "customer": 18, "cost": 167.0 }, { "facility": "F3", "customer": 0, "cost": 220.0 }, { "facility": "F3", "customer": 1, "cost": 221.0 }, { "facility": "F3", "customer": 2, "cost": 184.0 }, { "facility": "F3", "customer": 3, "cost": 91.0 }, { "facility": "F3", "customer": 4, "cost": 100.0 }, { "facility": "F3", "customer": 5, "cost": 108.0 }, { "facility": "F3", "customer": 6, "cost": 113.0 }, { "facility": "F3", "customer": 7, "cost": 261.0 }, { "facility": "F3", "customer": 8, "cost": 241.0 }, { "facility": "F3", "customer": 9, "cost": 262.0 }, { "facility": "F3", "customer": 10, "cost": 161.0 }, { "facility": "F3", "customer": 11, "cost": 70.0 }, { "facility": "F3", "customer": 12, "cost": 134.0 }, { "facility": "F3", "customer": 13, "cost": 91.0 }, { "facility": "F3", "customer": 14, "cost": 45.0 }, { "facility": "F3", "customer": 15, "cost": 157.0 }, { "facility": "F3", "customer": 16, "cost": 111.0 }, { "facility": "F3", "customer": 17, "cost": 57.0 }, { "facility": "F3", "customer": 18, "cost": 154.0 }, { "facility": "F4", "customer": 0, "cost": 303.0 }, { "facility": "F4", "customer": 1, "cost": 301.0 }, { "facility": "F4", "customer": 2, "cost": 260.0 }, { "facility": "F4", "customer": 3, "cost": 143.0 }, { "facility": "F4", "customer": 4, "cost": 146.0 }, { "facility": "F4", "customer": 5, "cost": 134.0 }, { "facility": "F4", "customer": 6, "cost": 94.0 }, { "facility": "F4", "customer": 7, "cost": 316.0 }, { "facility": "F4", "customer": 8, "cost": 297.0 }, { "facility": "F4", "customer": 9, "cost": 351.0 }, { "facility": "F4", "customer": 10, "cost": 251.0 }, { "facility": "F4", "customer": 11, "cost": 150.0 }, { "facility": "F4", "customer": 12, "cost": 224.0 }, { "facility": "F4", "customer": 13, "cost": 180.0 }, { "facility": "F4", "customer": 14, "cost": 45.0 }, { "facility": "F4", "customer": 15, "cost": 180.0 }, { "facility": "F4", "customer": 16, "cost": 196.0 }, { "facility": "F4", "customer": 17, "cost": 57.0 }, { "facility": "F4", "customer": 18, "cost": 238.0 }, { "facility": "F5", "customer": 0, "cost": 267.0 }, { "facility": "F5", "customer": 1, "cost": 263.0 }, { "facility": "F5", "customer": 2, "cost": 221.0 }, { "facility": "F5", "customer": 3, "cost": 100.0 }, { "facility": "F5", "customer": 4, "cost": 102.0 }, { "facility": "F5", "customer": 5, "cost": 89.0 }, { "facility": "F5", "customer": 6, "cost": 127.0 }, { "facility": "F5", "customer": 7, "cost": 326.0 }, { "facility": "F5", "customer": 8, "cost": 306.0 }, { "facility": "F5", "customer": 9, "cost": 332.0 }, { "facility": "F5", "customer": 10, "cost": 228.0 }, { "facility": "F5", "customer": 11, "cost": 141.0 }, { "facility": "F5", "customer": 12, "cost": 200.0 }, { "facility": "F5", "customer": 13, "cost": 153.0 }, { "facility": "F5", "customer": 14, "cost": 40.0 }, { "facility": "F5", "customer": 15, "cost": 203.0 }, { "facility": "F5", "customer": 16, "cost": 183.0 }, { "facility": "F5", "customer": 17, "cost": 18.0 }, { "facility": "F5", "customer": 18, "cost": 226.0 }, { "facility": "F6", "customer": 0, "cost": 305.0 }, { "facility": "F6", "customer": 1, "cost": 316.0 }, { "facility": "F6", "customer": 2, "cost": 297.0 }, { "facility": "F6", "customer": 3, "cost": 249.0 }, { "facility": "F6", "customer": 4, "cost": 260.0 }, { "facility": "F6", "customer": 5, "cost": 272.0 }, { "facility": "F6", "customer": 6, "cost": 124.0 }, { "facility": "F6", "customer": 7, "cost": 117.0 }, { "facility": "F6", "customer": 8, "cost": 100.0 }, { "facility": "F6", "customer": 9, "cost": 248.0 }, { "facility": "F6", "customer": 10, "cost": 197.0 }, { "facility": "F6", "customer": 11, "cost": 118.0 }, { "facility": "F6", "customer": 12, "cost": 189.0 }, { "facility": "F6", "customer": 13, "cost": 187.0 }, { "facility": "F6", "customer": 14, "cost": 180.0 }, { "facility": "F6", "customer": 15, "cost": 38.0 }, { "facility": "F6", "customer": 16, "cost": 130.0 }, { "facility": "F6", "customer": 17, "cost": 213.0 }, { "facility": "F6", "customer": 18, "cost": 142.0 }, { "facility": "F7", "customer": 0, "cost": 202.0 }, { "facility": "F7", "customer": 1, "cost": 214.0 }, { "facility": "F7", "customer": 2, "cost": 199.0 }, { "facility": "F7", "customer": 3, "cost": 180.0 }, { "facility": "F7", "customer": 4, "cost": 192.0 }, { "facility": "F7", "customer": 5, "cost": 212.0 }, { "facility": "F7", "customer": 6, "cost": 163.0 }, { "facility": "F7", "customer": 7, "cost": 151.0 }, { "facility": "F7", "customer": 8, "cost": 132.0 }, { "facility": "F7", "customer": 9, "cost": 163.0 }, { "facility": "F7", "customer": 10, "cost": 94.0 }, { "facility": "F7", "customer": 11, "cost": 54.0 }, { "facility": "F7", "customer": 12, "cost": 86.0 }, { "facility": "F7", "customer": 13, "cost": 95.0 }, { "facility": "F7", "customer": 14, "cost": 161.0 }, { "facility": "F7", "customer": 15, "cost": 127.0 }, { "facility": "F7", "customer": 16, "cost": 29.0 }, { "facility": "F7", "customer": 17, "cost": 181.0 }, { "facility": "F7", "customer": 18, "cost": 45.0 }, { "facility": "F8", "customer": 0, "cost": 132.0 }, { "facility": "F8", "customer": 1, "cost": 134.0 }, { "facility": "F8", "customer": 2, "cost": 102.0 }, { "facility": "F8", "customer": 3, "cost": 77.0 }, { "facility": "F8", "customer": 4, "cost": 89.0 }, { "facility": "F8", "customer": 5, "cost": 115.0 }, { "facility": "F8", "customer": 6, "cost": 194.0 }, { "facility": "F8", "customer": 7, "cost": 265.0 }, { "facility": "F8", "customer": 8, "cost": 246.0 }, { "facility": "F8", "customer": 9, "cost": 197.0 }, { "facility": "F8", "customer": 10, "cost": 92.0 }, { "facility": "F8", "customer": 11, "cost": 85.0 }, { "facility": "F8", "customer": 12, "cost": 64.0 }, { "facility": "F8", "customer": 13, "cost": 20.0 }, { "facility": "F8", "customer": 14, "cost": 130.0 }, { "facility": "F8", "customer": 15, "cost": 210.0 }, { "facility": "F8", "customer": 16, "cost": 86.0 }, { "facility": "F8", "customer": 17, "cost": 125.0 }, { "facility": "F8", "customer": 18, "cost": 116.0 } ], "objective": 2456.0 }, "solution_variant": { "selected": [ "F4", "F6", "F8" ], "assignments": [ "F8", "F8", "F8", "F8", "F8", "F8", "F4", "F6", "F6", "F8", "F8", "F8", "F8", "F8", "F4", "F6", "F8", "F4", "F8" ] }, "context_index": 16, "input_format": "csv", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "There’s a juggling act in the warehouse world: a bookstore chain has several candidate warehouses, each with a set capacity and a fixed fee to open, and a bunch of shops that all need restocking. The job is to pick which warehouses to open and assign every shop to one of the opened warehouses. Better choices are the ones that save money overall — add up the opened warehouses’ fixed fees and all the shipping charges to see the total — but a warehouse can’t be given more orders than its capacity, and every shop must be assigned to exactly one opened warehouse. The detailed figures are shown below.\n\nThey list 9 candidate warehouses and 19 shops.\nCandidate warehouse F1 has opening cost 400.0 and capacity 1382.0.\nCandidate warehouse F2 has opening cost 400.0 and capacity 567.0.\nCandidate warehouse F3 has opening cost 400.0 and capacity 898.0.\nCandidate warehouse F4 has opening cost 400.0 and capacity 975.0.\nCandidate warehouse F5 has opening cost 400.0 and capacity 588.0.\nCandidate warehouse F6 has opening cost 400.0 and capacity 972.0.\nCandidate warehouse F7 has opening cost 400.0 and capacity 1388.0.\nCandidate warehouse F8 has opening cost 400.0 and capacity 782.0.\nCandidate warehouse F9 has opening cost 400.0 and capacity 506.0.\nShop 0 requires 24.0.\nShop 1 requires 11.0.\nShop 2 requires 49.0.\nShop 3 requires 44.0.\nShop 4 requires 18.0.\nShop 5 requires 12.0.\nShop 6 requires 26.0.\nShop 7 requires 27.0.\nShop 8 requires 22.0.\nShop 9 requires 18.0.\nShop 10 requires 35.0.\nShop 11 requires 36.0.\nShop 12 requires 14.0.\nShop 13 requires 49.0.\nShop 14 requires 44.0.\nShop 15 requires 12.0.\nShop 16 requires 29.0.\nShop 17 requires 16.0.\nShop 18 requires 22.0.\nShipping from warehouse F1 to shop 0 costs 744.0.\nShipping from warehouse F1 to shop 1 costs 198.0.\nShipping from warehouse F1 to shop 2 costs 301.0.\nShipping from warehouse F1 to shop 3 costs 802.0.\nShipping from warehouse F1 to shop 4 costs 342.0.\nShipping from warehouse F1 to shop 5 costs 14.0.\nShipping from warehouse F1 to shop 6 costs 622.0.\nShipping from warehouse F1 to shop 7 costs 623.0.\nShipping from warehouse F1 to shop 8 costs 184.0.\nShipping from warehouse F1 to shop 9 costs 653.0.\nShipping from warehouse F1 to shop 10 costs 373.0.\nShipping from warehouse F1 to shop 11 costs 635.0.\nShipping from warehouse F1 to shop 12 costs 372.0.\nShipping from warehouse F1 to shop 13 costs 470.0.\nShipping from warehouse F1 to shop 14 costs 626.0.\nShipping from warehouse F1 to shop 15 costs 411.0.\nShipping from warehouse F1 to shop 16 costs 548.0.\nShipping from warehouse F1 to shop 17 costs 577.0.\nShipping from warehouse F1 to shop 18 costs 868.0.\nShipping from warehouse F2 to shop 0 costs 537.0.\nShipping from warehouse F2 to shop 1 costs 319.0.\nShipping from warehouse F2 to shop 2 costs 494.0.\nShipping from warehouse F2 to shop 3 costs 595.0.\nShipping from warehouse F2 to shop 4 costs 445.0.\nShipping from warehouse F2 to shop 5 costs 526.0.\nShipping from warehouse F2 to shop 6 costs 249.0.\nShipping from warehouse F2 to shop 7 costs 292.0.\nShipping from warehouse F2 to shop 8 costs 337.0.\nShipping from warehouse F2 to shop 9 costs 395.0.\nShipping from warehouse F2 to shop 10 costs 393.0.\nShipping from warehouse F2 to shop 11 costs 284.0.\nShipping from warehouse F2 to shop 12 costs 589.0.\nShipping from warehouse F2 to shop 13 costs 557.0.\nShipping from warehouse F2 to shop 14 costs 292.0.\nShipping from warehouse F2 to shop 15 costs 575.0.\nShipping from warehouse F2 to shop 16 costs 148.0.\nShipping from warehouse F2 to shop 17 costs 74.0.\nShipping from warehouse F2 to shop 18 costs 591.0.\nShipping from warehouse F3 to shop 0 costs 465.0.\nShipping from warehouse F3 to shop 1 costs 157.0.\nShipping from warehouse F3 to shop 2 costs 232.0.\nShipping from warehouse F3 to shop 3 costs 527.0.\nShipping from warehouse F3 to shop 4 costs 193.0.\nShipping from warehouse F3 to shop 5 costs 330.0.\nShipping from warehouse F3 to shop 6 costs 306.0.\nShipping from warehouse F3 to shop 7 costs 307.0.\nShipping from warehouse F3 to shop 8 costs 195.0.\nShipping from warehouse F3 to shop 9 costs 352.0.\nShipping from warehouse F3 to shop 10 costs 158.0.\nShipping from warehouse F3 to shop 11 costs 319.0.\nShipping from warehouse F3 to shop 12 costs 330.0.\nShipping from warehouse F3 to shop 13 costs 328.0.\nShipping from warehouse F3 to shop 14 costs 310.0.\nShipping from warehouse F3 to shop 15 costs 326.0.\nShipping from warehouse F3 to shop 16 costs 241.0.\nShipping from warehouse F3 to shop 17 costs 300.0.\nShipping from warehouse F3 to shop 18 costs 573.0.\nShipping from warehouse F4 to shop 0 costs 384.0.\nShipping from warehouse F4 to shop 1 costs 593.0.\nShipping from warehouse F4 to shop 2 costs 312.0.\nShipping from warehouse F4 to shop 3 costs 404.0.\nShipping from warehouse F4 to shop 4 costs 304.0.\nShipping from warehouse F4 to shop 5 costs 619.0.\nShipping from warehouse F4 to shop 6 costs 560.0.\nShipping from warehouse F4 to shop 7 costs 514.0.\nShipping from warehouse F4 to shop 8 costs 625.0.\nShipping from warehouse F4 to shop 9 costs 433.0.\nShipping from warehouse F4 to shop 10 costs 327.0.\nShipping from warehouse F4 to shop 11 costs 535.0.\nShipping from warehouse F4 to shop 12 costs 237.0.\nShipping from warehouse F4 to shop 13 costs 158.0.\nShipping from warehouse F4 to shop 14 costs 517.0.\nShipping from warehouse F4 to shop 15 costs 196.0.\nShipping from warehouse F4 to shop 16 costs 593.0.\nShipping from warehouse F4 to shop 17 costs 702.0.\nShipping from warehouse F4 to shop 18 costs 515.0.\nShipping from warehouse F5 to shop 0 costs 362.0.\nShipping from warehouse F5 to shop 1 costs 272.0.\nShipping from warehouse F5 to shop 2 costs 172.0.\nShipping from warehouse F5 to shop 3 costs 421.0.\nShipping from warehouse F5 to shop 4 costs 105.0.\nShipping from warehouse F5 to shop 5 costs 398.0.\nShipping from warehouse F5 to shop 6 costs 293.0.\nShipping from warehouse F5 to shop 7 costs 272.0.\nShipping from warehouse F5 to shop 8 costs 310.0.\nShipping from warehouse F5 to shop 9 costs 274.0.\nShipping from warehouse F5 to shop 10 costs 43.0.\nShipping from warehouse F5 to shop 11 costs 289.0.\nShipping from warehouse F5 to shop 12 costs 248.0.\nShipping from warehouse F5 to shop 13 costs 207.0.\nShipping from warehouse F5 to shop 14 costs 276.0.\nShipping from warehouse F5 to shop 15 costs 226.0.\nShipping from warehouse F5 to shop 16 costs 272.0.\nShipping from warehouse F5 to shop 17 costs 365.0.\nShipping from warehouse F5 to shop 18 costs 484.0.\nShipping from warehouse F6 to shop 0 costs 409.0.\nShipping from warehouse F6 to shop 1 costs 268.0.\nShipping from warehouse F6 to shop 2 costs 351.0.\nShipping from warehouse F6 to shop 3 costs 470.0.\nShipping from warehouse F6 to shop 4 costs 294.0.\nShipping from warehouse F6 to shop 5 costs 463.0.\nShipping from warehouse F6 to shop 6 costs 178.0.\nShipping from warehouse F6 to shop 7 costs 196.0.\nShipping from warehouse F6 to shop 8 costs 300.0.\nShipping from warehouse F6 to shop 9 costs 274.0.\nShipping from warehouse F6 to shop 10 costs 237.0.\nShipping from warehouse F6 to shop 11 costs 200.0.\nShipping from warehouse F6 to shop 12 costs 439.0.\nShipping from warehouse F6 to shop 13 costs 397.0.\nShipping from warehouse F6 to shop 14 costs 198.0.\nShipping from warehouse F6 to shop 15 costs 420.0.\nShipping from warehouse F6 to shop 16 costs 99.0.\nShipping from warehouse F6 to shop 17 costs 172.0.\nShipping from warehouse F6 to shop 18 costs 491.0.\nShipping from warehouse F7 to shop 0 costs 439.0.\nShipping from warehouse F7 to shop 1 costs 510.0.\nShipping from warehouse F7 to shop 2 costs 220.0.\nShipping from warehouse F7 to shop 3 costs 471.0.\nShipping from warehouse F7 to shop 4 costs 231.0.\nShipping from warehouse F7 to shop 5 costs 516.0.\nShipping from warehouse F7 to shop 6 costs 557.0.\nShipping from warehouse F7 to shop 7 costs 516.0.\nShipping from warehouse F7 to shop 8 costs 540.0.\nShipping from warehouse F7 to shop 9 costs 454.0.\nShipping from warehouse F7 to shop 10 costs 272.0.\nShipping from warehouse F7 to shop 11 costs 538.0.\nShipping from warehouse F7 to shop 12 costs 132.0.\nShipping from warehouse F7 to shop 13 costs 111.0.\nShipping from warehouse F7 to shop 14 costs 520.0.\nShipping from warehouse F7 to shop 15 costs 103.0.\nShipping from warehouse F7 to shop 16 costs 570.0.\nShipping from warehouse F7 to shop 17 costs 672.0.\nShipping from warehouse F7 to shop 18 costs 576.0.\nShipping from warehouse F8 to shop 0 costs 173.0.\nShipping from warehouse F8 to shop 1 costs 583.0.\nShipping from warehouse F8 to shop 2 costs 527.0.\nShipping from warehouse F8 to shop 3 costs 210.0.\nShipping from warehouse F8 to shop 4 costs 456.0.\nShipping from warehouse F8 to shop 5 costs 754.0.\nShipping from warehouse F8 to shop 6 costs 166.0.\nShipping from warehouse F8 to shop 7 costs 132.0.\nShipping from warehouse F8 to shop 8 costs 619.0.\nShipping from warehouse F8 to shop 9 costs 102.0.\nShipping from warehouse F8 to shop 10 costs 397.0.\nShipping from warehouse F8 to shop 11 costs 133.0.\nShipping from warehouse F8 to shop 12 costs 566.0.\nShipping from warehouse F8 to shop 13 costs 453.0.\nShipping from warehouse F8 to shop 14 costs 131.0.\nShipping from warehouse F8 to shop 15 costs 521.0.\nShipping from warehouse F8 to shop 16 costs 271.0.\nShipping from warehouse F8 to shop 17 costs 360.0.\nShipping from warehouse F8 to shop 18 costs 176.0.\nShipping from warehouse F9 to shop 0 costs 278.0.\nShipping from warehouse F9 to shop 1 costs 345.0.\nShipping from warehouse F9 to shop 2 costs 283.0.\nShipping from warehouse F9 to shop 3 costs 340.0.\nShipping from warehouse F9 to shop 4 costs 213.0.\nShipping from warehouse F9 to shop 5 costs 501.0.\nShipping from warehouse F9 to shop 6 costs 185.0.\nShipping from warehouse F9 to shop 7 costs 158.0.\nShipping from warehouse F9 to shop 8 costs 383.0.\nShipping from warehouse F9 to shop 9 costs 167.0.\nShipping from warehouse F9 to shop 10 costs 150.0.\nShipping from warehouse F9 to shop 11 costs 177.0.\nShipping from warehouse F9 to shop 12 costs 346.0.\nShipping from warehouse F9 to shop 13 costs 268.0.\nShipping from warehouse F9 to shop 14 costs 162.0.\nShipping from warehouse F9 to shop 15 costs 312.0.\nShipping from warehouse F9 to shop 16 costs 194.0.\nShipping from warehouse F9 to shop 17 costs 303.0.\nShipping from warehouse F9 to shop 18 costs 386.0.\nUse these figures to pick which warehouses to open and assign every shop while respecting capacities and minimizing total opening plus shipping costs.\n\nAlso, when you send back your choice, please use a little JSON sketch like the one below so it's easy to read and plug in:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of warehouse sites you decide to open, and \"assignments\" as the list (in the same order as the shops were given) of which opened warehouse each shop gets linked to. This is just the shape I want your answer in — a template, not the final numbers.\n\nPlease make sure to use the exact identifiers from the instance input when you fill this in — do not rename them or invent new ones. For example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 1382.0, 567.0, 898.0, 975.0, 588.0, 972.0, 1388.0, 782.0, 506.0 ], "connection_costs": [ [ 744.0, 198.0, 301.0, 802.0, 342.0, 14.0, 622.0, 623.0, 184.0, 653.0, 373.0, 635.0, 372.0, 470.0, 626.0, 411.0, 548.0, 577.0, 868.0 ], [ 537.0, 319.0, 494.0, 595.0, 445.0, 526.0, 249.0, 292.0, 337.0, 395.0, 393.0, 284.0, 589.0, 557.0, 292.0, 575.0, 148.0, 74.0, 591.0 ], [ 465.0, 157.0, 232.0, 527.0, 193.0, 330.0, 306.0, 307.0, 195.0, 352.0, 158.0, 319.0, 330.0, 328.0, 310.0, 326.0, 241.0, 300.0, 573.0 ], [ 384.0, 593.0, 312.0, 404.0, 304.0, 619.0, 560.0, 514.0, 625.0, 433.0, 327.0, 535.0, 237.0, 158.0, 517.0, 196.0, 593.0, 702.0, 515.0 ], [ 362.0, 272.0, 172.0, 421.0, 105.0, 398.0, 293.0, 272.0, 310.0, 274.0, 43.0, 289.0, 248.0, 207.0, 276.0, 226.0, 272.0, 365.0, 484.0 ], [ 409.0, 268.0, 351.0, 470.0, 294.0, 463.0, 178.0, 196.0, 300.0, 274.0, 237.0, 200.0, 439.0, 397.0, 198.0, 420.0, 99.0, 172.0, 491.0 ], [ 439.0, 510.0, 220.0, 471.0, 231.0, 516.0, 557.0, 516.0, 540.0, 454.0, 272.0, 538.0, 132.0, 111.0, 520.0, 103.0, 570.0, 672.0, 576.0 ], [ 173.0, 583.0, 527.0, 210.0, 456.0, 754.0, 166.0, 132.0, 619.0, 102.0, 397.0, 133.0, 566.0, 453.0, 131.0, 521.0, 271.0, 360.0, 176.0 ], [ 278.0, 345.0, 283.0, 340.0, 213.0, 501.0, 185.0, 158.0, 383.0, 167.0, 150.0, 177.0, 346.0, 268.0, 162.0, 312.0, 194.0, 303.0, 386.0 ] ], "demands": [ 24.0, 11.0, 49.0, 44.0, 18.0, 12.0, 26.0, 27.0, 22.0, 18.0, 35.0, 36.0, 14.0, 49.0, 44.0, 12.0, 29.0, 16.0, 22.0 ], "objective": 4442.0 }, "solution": { "open_facilities": [ 0, 1, 4, 7 ], "assignments": [ 7, 0, 4, 7, 4, 0, 7, 7, 0, 7, 4, 7, 4, 4, 7, 4, 1, 1, 7 ] }, "obj": 4442.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 9, "num_customers": 19, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 1382.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 567.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 898.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 975.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 588.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 972.0 }, { "id": "F7", "opening_cost": 400.0, "capacity": 1388.0 }, { "id": "F8", "opening_cost": 400.0, "capacity": 782.0 }, { "id": "F9", "opening_cost": 400.0, "capacity": 506.0 } ], "customers": [ { "id": 0, "demand": 24.0 }, { "id": 1, "demand": 11.0 }, { "id": 2, "demand": 49.0 }, { "id": 3, "demand": 44.0 }, { "id": 4, "demand": 18.0 }, { "id": 5, "demand": 12.0 }, { "id": 6, "demand": 26.0 }, { "id": 7, "demand": 27.0 }, { "id": 8, "demand": 22.0 }, { "id": 9, "demand": 18.0 }, { "id": 10, "demand": 35.0 }, { "id": 11, "demand": 36.0 }, { "id": 12, "demand": 14.0 }, { "id": 13, "demand": 49.0 }, { "id": 14, "demand": 44.0 }, { "id": 15, "demand": 12.0 }, { "id": 16, "demand": 29.0 }, { "id": 17, "demand": 16.0 }, { "id": 18, "demand": 22.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 744.0 }, { "facility": "F1", "customer": 1, "cost": 198.0 }, { "facility": "F1", "customer": 2, "cost": 301.0 }, { "facility": "F1", "customer": 3, "cost": 802.0 }, { "facility": "F1", "customer": 4, "cost": 342.0 }, { "facility": "F1", "customer": 5, "cost": 14.0 }, { "facility": "F1", "customer": 6, "cost": 622.0 }, { "facility": "F1", "customer": 7, "cost": 623.0 }, { "facility": "F1", "customer": 8, "cost": 184.0 }, { "facility": "F1", "customer": 9, "cost": 653.0 }, { "facility": "F1", "customer": 10, "cost": 373.0 }, { "facility": "F1", "customer": 11, "cost": 635.0 }, { "facility": "F1", "customer": 12, "cost": 372.0 }, { "facility": "F1", "customer": 13, "cost": 470.0 }, { "facility": "F1", "customer": 14, "cost": 626.0 }, { "facility": "F1", "customer": 15, "cost": 411.0 }, { "facility": "F1", "customer": 16, "cost": 548.0 }, { "facility": "F1", "customer": 17, "cost": 577.0 }, { "facility": "F1", "customer": 18, "cost": 868.0 }, { "facility": "F2", "customer": 0, "cost": 537.0 }, { "facility": "F2", "customer": 1, "cost": 319.0 }, { "facility": "F2", "customer": 2, "cost": 494.0 }, { "facility": "F2", "customer": 3, "cost": 595.0 }, { "facility": "F2", "customer": 4, "cost": 445.0 }, { "facility": "F2", "customer": 5, "cost": 526.0 }, { "facility": "F2", "customer": 6, "cost": 249.0 }, { "facility": "F2", "customer": 7, "cost": 292.0 }, { "facility": "F2", "customer": 8, "cost": 337.0 }, { "facility": "F2", "customer": 9, "cost": 395.0 }, { "facility": "F2", "customer": 10, "cost": 393.0 }, { "facility": "F2", "customer": 11, "cost": 284.0 }, { "facility": "F2", "customer": 12, "cost": 589.0 }, { "facility": "F2", "customer": 13, "cost": 557.0 }, { "facility": "F2", "customer": 14, "cost": 292.0 }, { "facility": "F2", "customer": 15, "cost": 575.0 }, { "facility": "F2", "customer": 16, "cost": 148.0 }, { "facility": "F2", "customer": 17, "cost": 74.0 }, { "facility": "F2", "customer": 18, "cost": 591.0 }, { "facility": "F3", "customer": 0, "cost": 465.0 }, { "facility": "F3", "customer": 1, "cost": 157.0 }, { "facility": "F3", "customer": 2, "cost": 232.0 }, { "facility": "F3", "customer": 3, "cost": 527.0 }, { "facility": "F3", "customer": 4, "cost": 193.0 }, { "facility": "F3", "customer": 5, "cost": 330.0 }, { "facility": "F3", "customer": 6, "cost": 306.0 }, { "facility": "F3", "customer": 7, "cost": 307.0 }, { "facility": "F3", "customer": 8, "cost": 195.0 }, { "facility": "F3", "customer": 9, "cost": 352.0 }, { "facility": "F3", "customer": 10, "cost": 158.0 }, { "facility": "F3", "customer": 11, "cost": 319.0 }, { "facility": "F3", "customer": 12, "cost": 330.0 }, { "facility": "F3", "customer": 13, "cost": 328.0 }, { "facility": "F3", "customer": 14, "cost": 310.0 }, { "facility": "F3", "customer": 15, "cost": 326.0 }, { "facility": "F3", "customer": 16, "cost": 241.0 }, { "facility": "F3", "customer": 17, "cost": 300.0 }, { "facility": "F3", "customer": 18, "cost": 573.0 }, { "facility": "F4", "customer": 0, "cost": 384.0 }, { "facility": "F4", "customer": 1, "cost": 593.0 }, { "facility": "F4", "customer": 2, "cost": 312.0 }, { "facility": "F4", "customer": 3, "cost": 404.0 }, { "facility": "F4", "customer": 4, "cost": 304.0 }, { "facility": "F4", "customer": 5, "cost": 619.0 }, { "facility": "F4", "customer": 6, "cost": 560.0 }, { "facility": "F4", "customer": 7, "cost": 514.0 }, { "facility": "F4", "customer": 8, "cost": 625.0 }, { "facility": "F4", "customer": 9, "cost": 433.0 }, { "facility": "F4", "customer": 10, "cost": 327.0 }, { "facility": "F4", "customer": 11, "cost": 535.0 }, { "facility": "F4", "customer": 12, "cost": 237.0 }, { "facility": "F4", "customer": 13, "cost": 158.0 }, { "facility": "F4", "customer": 14, "cost": 517.0 }, { "facility": "F4", "customer": 15, "cost": 196.0 }, { "facility": "F4", "customer": 16, "cost": 593.0 }, { "facility": "F4", "customer": 17, "cost": 702.0 }, { "facility": "F4", "customer": 18, "cost": 515.0 }, { "facility": "F5", "customer": 0, "cost": 362.0 }, { "facility": "F5", "customer": 1, "cost": 272.0 }, { "facility": "F5", "customer": 2, "cost": 172.0 }, { "facility": "F5", "customer": 3, "cost": 421.0 }, { "facility": "F5", "customer": 4, "cost": 105.0 }, { "facility": "F5", "customer": 5, "cost": 398.0 }, { "facility": "F5", "customer": 6, "cost": 293.0 }, { "facility": "F5", "customer": 7, "cost": 272.0 }, { "facility": "F5", "customer": 8, "cost": 310.0 }, { "facility": "F5", "customer": 9, "cost": 274.0 }, { "facility": "F5", "customer": 10, "cost": 43.0 }, { "facility": "F5", "customer": 11, "cost": 289.0 }, { "facility": "F5", "customer": 12, "cost": 248.0 }, { "facility": "F5", "customer": 13, "cost": 207.0 }, { "facility": "F5", "customer": 14, "cost": 276.0 }, { "facility": "F5", "customer": 15, "cost": 226.0 }, { "facility": "F5", "customer": 16, "cost": 272.0 }, { "facility": "F5", "customer": 17, "cost": 365.0 }, { "facility": "F5", "customer": 18, "cost": 484.0 }, { "facility": "F6", "customer": 0, "cost": 409.0 }, { "facility": "F6", "customer": 1, "cost": 268.0 }, { "facility": "F6", "customer": 2, "cost": 351.0 }, { "facility": "F6", "customer": 3, "cost": 470.0 }, { "facility": "F6", "customer": 4, "cost": 294.0 }, { "facility": "F6", "customer": 5, "cost": 463.0 }, { "facility": "F6", "customer": 6, "cost": 178.0 }, { "facility": "F6", "customer": 7, "cost": 196.0 }, { "facility": "F6", "customer": 8, "cost": 300.0 }, { "facility": "F6", "customer": 9, "cost": 274.0 }, { "facility": "F6", "customer": 10, "cost": 237.0 }, { "facility": "F6", "customer": 11, "cost": 200.0 }, { "facility": "F6", "customer": 12, "cost": 439.0 }, { "facility": "F6", "customer": 13, "cost": 397.0 }, { "facility": "F6", "customer": 14, "cost": 198.0 }, { "facility": "F6", "customer": 15, "cost": 420.0 }, { "facility": "F6", "customer": 16, "cost": 99.0 }, { "facility": "F6", "customer": 17, "cost": 172.0 }, { "facility": "F6", "customer": 18, "cost": 491.0 }, { "facility": "F7", "customer": 0, "cost": 439.0 }, { "facility": "F7", "customer": 1, "cost": 510.0 }, { "facility": "F7", "customer": 2, "cost": 220.0 }, { "facility": "F7", "customer": 3, "cost": 471.0 }, { "facility": "F7", "customer": 4, "cost": 231.0 }, { "facility": "F7", "customer": 5, "cost": 516.0 }, { "facility": "F7", "customer": 6, "cost": 557.0 }, { "facility": "F7", "customer": 7, "cost": 516.0 }, { "facility": "F7", "customer": 8, "cost": 540.0 }, { "facility": "F7", "customer": 9, "cost": 454.0 }, { "facility": "F7", "customer": 10, "cost": 272.0 }, { "facility": "F7", "customer": 11, "cost": 538.0 }, { "facility": "F7", "customer": 12, "cost": 132.0 }, { "facility": "F7", "customer": 13, "cost": 111.0 }, { "facility": "F7", "customer": 14, "cost": 520.0 }, { "facility": "F7", "customer": 15, "cost": 103.0 }, { "facility": "F7", "customer": 16, "cost": 570.0 }, { "facility": "F7", "customer": 17, "cost": 672.0 }, { "facility": "F7", "customer": 18, "cost": 576.0 }, { "facility": "F8", "customer": 0, "cost": 173.0 }, { "facility": "F8", "customer": 1, "cost": 583.0 }, { "facility": "F8", "customer": 2, "cost": 527.0 }, { "facility": "F8", "customer": 3, "cost": 210.0 }, { "facility": "F8", "customer": 4, "cost": 456.0 }, { "facility": "F8", "customer": 5, "cost": 754.0 }, { "facility": "F8", "customer": 6, "cost": 166.0 }, { "facility": "F8", "customer": 7, "cost": 132.0 }, { "facility": "F8", "customer": 8, "cost": 619.0 }, { "facility": "F8", "customer": 9, "cost": 102.0 }, { "facility": "F8", "customer": 10, "cost": 397.0 }, { "facility": "F8", "customer": 11, "cost": 133.0 }, { "facility": "F8", "customer": 12, "cost": 566.0 }, { "facility": "F8", "customer": 13, "cost": 453.0 }, { "facility": "F8", "customer": 14, "cost": 131.0 }, { "facility": "F8", "customer": 15, "cost": 521.0 }, { "facility": "F8", "customer": 16, "cost": 271.0 }, { "facility": "F8", "customer": 17, "cost": 360.0 }, { "facility": "F8", "customer": 18, "cost": 176.0 }, { "facility": "F9", "customer": 0, "cost": 278.0 }, { "facility": "F9", "customer": 1, "cost": 345.0 }, { "facility": "F9", "customer": 2, "cost": 283.0 }, { "facility": "F9", "customer": 3, "cost": 340.0 }, { "facility": "F9", "customer": 4, "cost": 213.0 }, { "facility": "F9", "customer": 5, "cost": 501.0 }, { "facility": "F9", "customer": 6, "cost": 185.0 }, { "facility": "F9", "customer": 7, "cost": 158.0 }, { "facility": "F9", "customer": 8, "cost": 383.0 }, { "facility": "F9", "customer": 9, "cost": 167.0 }, { "facility": "F9", "customer": 10, "cost": 150.0 }, { "facility": "F9", "customer": 11, "cost": 177.0 }, { "facility": "F9", "customer": 12, "cost": 346.0 }, { "facility": "F9", "customer": 13, "cost": 268.0 }, { "facility": "F9", "customer": 14, "cost": 162.0 }, { "facility": "F9", "customer": 15, "cost": 312.0 }, { "facility": "F9", "customer": 16, "cost": 194.0 }, { "facility": "F9", "customer": 17, "cost": 303.0 }, { "facility": "F9", "customer": 18, "cost": 386.0 } ], "objective": 4442.0 }, "solution_variant": { "selected": [ "F1", "F2", "F5", "F8" ], "assignments": [ "F8", "F1", "F5", "F8", "F5", "F1", "F8", "F8", "F1", "F8", "F5", "F8", "F5", "F5", "F8", "F5", "F2", "F2", "F8" ] }, "context_index": 17, "input_format": "nl", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "I run the city's bike repair program and need to pick which repair hubs to keep running, then send every reported fault to exactly one of the hubs that are open. Each hub has a startup price and can only handle a certain number of fixes, and getting a mechanic out to a fault costs something based on distance — so a better plan is the one that keeps the total bill as small as possible by adding up the opening fees for the hubs we choose and the travel cost for every repair. Nothing can be left unassigned or sent to two places, and no hub can be asked to do more than its limit. The concrete details — locations, opening costs, capacities and reported faults — are shown below.\n\nHere are the details for the 8 candidate hubs and the 17 reported faults:\nHub F1 would cost 300.0 to open and can handle up to 384.0 fixes.\nHub F2 would cost 300.0 to open and can handle up to 256.0 fixes.\nHub F3 would cost 300.0 to open and can handle up to 376.0 fixes.\nHub F4 would cost 300.0 to open and can handle up to 425.0 fixes.\nHub F5 would cost 300.0 to open and can handle up to 430.0 fixes.\nHub F6 would cost 300.0 to open and can handle up to 378.0 fixes.\nHub F7 would cost 300.0 to open and can handle up to 435.0 fixes.\nHub F8 would cost 300.0 to open and can handle up to 503.0 fixes.\nFault 1 requires 24.0 repair-units that I must assign to an open hub.\nFault 2 requires 28.0 repair-units that I must assign to an open hub.\nFault 3 requires 25.0 repair-units that I must assign to an open hub.\nFault 4 requires 19.0 repair-units that I must assign to an open hub.\nFault 5 requires 18.0 repair-units that I must assign to an open hub.\nFault 6 requires 29.0 repair-units that I must assign to an open hub.\nFault 7 requires 17.0 repair-units that I must assign to an open hub.\nFault 8 requires 18.0 repair-units that I must assign to an open hub.\nFault 9 requires 17.0 repair-units that I must assign to an open hub.\nFault 10 requires 23.0 repair-units that I must assign to an open hub.\nFault 11 requires 19.0 repair-units that I must assign to an open hub.\nFault 12 requires 18.0 repair-units that I must assign to an open hub.\nFault 13 requires 27.0 repair-units that I must assign to an open hub.\nFault 14 requires 17.0 repair-units that I must assign to an open hub.\nFault 15 requires 29.0 repair-units that I must assign to an open hub.\nFault 16 requires 23.0 repair-units that I must assign to an open hub.\nFault 17 requires 22.0 repair-units that I must assign to an open hub.\nAssigning fault 1 to hub F1 would incur a travel service cost of 731.0.\nAssigning fault 2 to hub F1 would incur a travel service cost of 145.0.\nAssigning fault 3 to hub F1 would incur a travel service cost of 227.0.\nAssigning fault 4 to hub F1 would incur a travel service cost of 131.0.\nAssigning fault 5 to hub F1 would incur a travel service cost of 205.0.\nAssigning fault 6 to hub F1 would incur a travel service cost of 231.0.\nAssigning fault 7 to hub F1 would incur a travel service cost of 38.0.\nAssigning fault 8 to hub F1 would incur a travel service cost of 36.0.\nAssigning fault 9 to hub F1 would incur a travel service cost of 72.0.\nAssigning fault 10 to hub F1 would incur a travel service cost of 46.0.\nAssigning fault 11 to hub F1 would incur a travel service cost of 63.0.\nAssigning fault 12 to hub F1 would incur a travel service cost of 242.0.\nAssigning fault 13 to hub F1 would incur a travel service cost of 613.0.\nAssigning fault 14 to hub F1 would incur a travel service cost of 271.0.\nAssigning fault 15 to hub F1 would incur a travel service cost of 475.0.\nAssigning fault 16 to hub F1 would incur a travel service cost of 677.0.\nAssigning fault 17 to hub F1 would incur a travel service cost of 602.0.\nAssigning fault 1 to hub F2 would incur a travel service cost of 1000.0.\nAssigning fault 2 to hub F2 would incur a travel service cost of 478.0.\nAssigning fault 3 to hub F2 would incur a travel service cost of 881.0.\nAssigning fault 4 to hub F2 would incur a travel service cost of 720.0.\nAssigning fault 5 to hub F2 would incur a travel service cost of 779.0.\nAssigning fault 6 to hub F2 would incur a travel service cost of 391.0.\nAssigning fault 7 to hub F2 would incur a travel service cost of 82.0.\nAssigning fault 8 to hub F2 would incur a travel service cost of 38.0.\nAssigning fault 9 to hub F2 would incur a travel service cost of 114.0.\nAssigning fault 10 to hub F2 would incur a travel service cost of 352.0.\nAssigning fault 11 to hub F2 would incur a travel service cost of 43.0.\nAssigning fault 12 to hub F2 would incur a travel service cost of 464.0.\nAssigning fault 13 to hub F2 would incur a travel service cost of 728.0.\nAssigning fault 14 to hub F2 would incur a travel service cost of 385.0.\nAssigning fault 15 to hub F2 would incur a travel service cost of 817.0.\nAssigning fault 16 to hub F2 would incur a travel service cost of 904.0.\nAssigning fault 17 to hub F2 would incur a travel service cost of 755.0.\nAssigning fault 1 to hub F3 would incur a travel service cost of 467.0.\nAssigning fault 2 to hub F3 would incur a travel service cost of 257.0.\nAssigning fault 3 to hub F3 would incur a travel service cost of 334.0.\nAssigning fault 4 to hub F3 would incur a travel service cost of 269.0.\nAssigning fault 5 to hub F3 would incur a travel service cost of 342.0.\nAssigning fault 6 to hub F3 would incur a travel service cost of 315.0.\nAssigning fault 7 to hub F3 would incur a travel service cost of 47.0.\nAssigning fault 8 to hub F3 would incur a travel service cost of 38.0.\nAssigning fault 9 to hub F3 would incur a travel service cost of 104.0.\nAssigning fault 10 to hub F3 would incur a travel service cost of 105.0.\nAssigning fault 11 to hub F3 would incur a travel service cost of 39.0.\nAssigning fault 12 to hub F3 would incur a travel service cost of 72.0.\nAssigning fault 13 to hub F3 would incur a travel service cost of 401.0.\nAssigning fault 14 to hub F3 would incur a travel service cost of 110.0.\nAssigning fault 15 to hub F3 would incur a travel service cost of 604.0.\nAssigning fault 16 to hub F3 would incur a travel service cost of 426.0.\nAssigning fault 17 to hub F3 would incur a travel service cost of 378.0.\nAssigning fault 1 to hub F4 would incur a travel service cost of 2269.0.\nAssigning fault 2 to hub F4 would incur a travel service cost of 1519.0.\nAssigning fault 3 to hub F4 would incur a travel service cost of 2126.0.\nAssigning fault 4 to hub F4 would incur a travel service cost of 1935.0.\nAssigning fault 5 to hub F4 would incur a travel service cost of 1957.0.\nAssigning fault 6 to hub F4 would incur a travel service cost of 910.0.\nAssigning fault 7 to hub F4 would incur a travel service cost of 1241.0.\nAssigning fault 8 to hub F4 would incur a travel service cost of 45.0.\nAssigning fault 9 to hub F4 would incur a travel service cost of 243.0.\nAssigning fault 10 to hub F4 would incur a travel service cost of 1588.0.\nAssigning fault 11 to hub F4 would incur a travel service cost of 1294.0.\nAssigning fault 12 to hub F4 would incur a travel service cost of 1784.0.\nAssigning fault 13 to hub F4 would incur a travel service cost of 1878.0.\nAssigning fault 14 to hub F4 would incur a travel service cost of 1654.0.\nAssigning fault 15 to hub F4 would incur a travel service cost of 1583.0.\nAssigning fault 16 to hub F4 would incur a travel service cost of 2151.0.\nAssigning fault 17 to hub F4 would incur a travel service cost of 1951.0.\nAssigning fault 1 to hub F5 would incur a travel service cost of 2018.0.\nAssigning fault 2 to hub F5 would incur a travel service cost of 1406.0.\nAssigning fault 3 to hub F5 would incur a travel service cost of 1973.0.\nAssigning fault 4 to hub F5 would incur a travel service cost of 1790.0.\nAssigning fault 5 to hub F5 would incur a travel service cost of 1825.0.\nAssigning fault 6 to hub F5 would incur a travel service cost of 900.0.\nAssigning fault 7 to hub F5 would incur a travel service cost of 1064.0.\nAssigning fault 8 to hub F5 would incur a travel service cost of 49.0.\nAssigning fault 9 to hub F5 would incur a travel service cost of 291.0.\nAssigning fault 10 to hub F5 would incur a travel service cost of 1425.0.\nAssigning fault 11 to hub F5 would incur a travel service cost of 1097.0.\nAssigning fault 12 to hub F5 would incur a travel service cost of 1562.0.\nAssigning fault 13 to hub F5 would incur a travel service cost of 1611.0.\nAssigning fault 14 to hub F5 would incur a travel service cost of 1416.0.\nAssigning fault 15 to hub F5 would incur a travel service cost of 1552.0.\nAssigning fault 16 to hub F5 would incur a travel service cost of 1897.0.\nAssigning fault 17 to hub F5 would incur a travel service cost of 1689.0.\nAssigning fault 1 to hub F6 would incur a travel service cost of 342.0.\nAssigning fault 2 to hub F6 would incur a travel service cost of 175.0.\nAssigning fault 3 to hub F6 would incur a travel service cost of 147.0.\nAssigning fault 4 to hub F6 would incur a travel service cost of 132.0.\nAssigning fault 5 to hub F6 would incur a travel service cost of 182.0.\nAssigning fault 6 to hub F6 would incur a travel service cost of 264.0.\nAssigning fault 7 to hub F6 would incur a travel service cost of 37.0.\nAssigning fault 8 to hub F6 would incur a travel service cost of 37.0.\nAssigning fault 9 to hub F6 would incur a travel service cost of 91.0.\nAssigning fault 10 to hub F6 would incur a travel service cost of 67.0.\nAssigning fault 11 to hub F6 would incur a travel service cost of 38.0.\nAssigning fault 12 to hub F6 would incur a travel service cost of 73.0.\nAssigning fault 13 to hub F6 would incur a travel service cost of 350.0.\nAssigning fault 14 to hub F6 would incur a travel service cost of 106.0.\nAssigning fault 15 to hub F6 would incur a travel service cost of 481.0.\nAssigning fault 16 to hub F6 would incur a travel service cost of 330.0.\nAssigning fault 17 to hub F6 would incur a travel service cost of 318.0.\nAssigning fault 1 to hub F7 would incur a travel service cost of 385.0.\nAssigning fault 2 to hub F7 would incur a travel service cost of 447.0.\nAssigning fault 3 to hub F7 would incur a travel service cost of 630.0.\nAssigning fault 4 to hub F7 would incur a travel service cost of 535.0.\nAssigning fault 5 to hub F7 would incur a travel service cost of 611.0.\nAssigning fault 6 to hub F7 would incur a travel service cost of 436.0.\nAssigning fault 7 to hub F7 would incur a travel service cost of 128.0.\nAssigning fault 8 to hub F7 would incur a travel service cost of 44.0.\nAssigning fault 9 to hub F7 would incur a travel service cost of 149.0.\nAssigning fault 10 to hub F7 would incur a travel service cost of 274.0.\nAssigning fault 11 to hub F7 would incur a travel service cost of 91.0.\nAssigning fault 12 to hub F7 would incur a travel service cost of 65.0.\nAssigning fault 13 to hub F7 would incur a travel service cost of 267.0.\nAssigning fault 14 to hub F7 would incur a travel service cost of 35.0.\nAssigning fault 15 to hub F7 would incur a travel service cost of 808.0.\nAssigning fault 16 to hub F7 would incur a travel service cost of 314.0.\nAssigning fault 17 to hub F7 would incur a travel service cost of 244.0.\nAssigning fault 1 to hub F8 would incur a travel service cost of 1280.0.\nAssigning fault 2 to hub F8 would incur a travel service cost of 147.0.\nAssigning fault 3 to hub F8 would incur a travel service cost of 784.0.\nAssigning fault 4 to hub F8 would incur a travel service cost of 590.0.\nAssigning fault 5 to hub F8 would incur a travel service cost of 585.0.\nAssigning fault 6 to hub F8 would incur a travel service cost of 133.0.\nAssigning fault 7 to hub F8 would incur a travel service cost of 220.0.\nAssigning fault 8 to hub F8 would incur a travel service cost of 40.0.\nAssigning fault 9 to hub F8 would incur a travel service cost of 41.0.\nAssigning fault 10 to hub F8 would incur a travel service cost of 362.0.\nAssigning fault 11 to hub F8 would incur a travel service cost of 310.0.\nAssigning fault 12 to hub F8 would incur a travel service cost of 730.0.\nAssigning fault 13 to hub F8 would incur a travel service cost of 1055.0.\nAssigning fault 14 to hub F8 would incur a travel service cost of 701.0.\nAssigning fault 15 to hub F8 would incur a travel service cost of 404.0.\nAssigning fault 16 to hub F8 would incur a travel service cost of 1200.0.\nAssigning fault 17 to hub F8 would incur a travel service cost of 1073.0.\nI'll pick which hubs to open and assign every fault so all 17 are covered within capacities and the total of opening fees plus travel costs is minimized.\n\nAlso, when you send back the plan, please stick to this simple JSON shape so I can read it easily:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThis is just a sketch of the shape I expect, not the real answer — fill the arrays with the actual hub identifiers from the instance. \"selected\" is the list of hubs you choose to keep running; \"assignments\" is a list that, for each reported fault in the same order as the input, gives the single open hub that will handle it.\n\nPlease don't invent new labels or change the identifiers from the instance — use them exactly as given. \nFor example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 384.0, 256.0, 376.0, 425.0, 430.0, 378.0, 435.0, 503.0 ], "connection_costs": [ [ 731.0, 145.0, 227.0, 131.0, 205.0, 231.0, 38.0, 36.0, 72.0, 46.0, 63.0, 242.0, 613.0, 271.0, 475.0, 677.0, 602.0 ], [ 1000.0, 478.0, 881.0, 720.0, 779.0, 391.0, 82.0, 38.0, 114.0, 352.0, 43.0, 464.0, 728.0, 385.0, 817.0, 904.0, 755.0 ], [ 467.0, 257.0, 334.0, 269.0, 342.0, 315.0, 47.0, 38.0, 104.0, 105.0, 39.0, 72.0, 401.0, 110.0, 604.0, 426.0, 378.0 ], [ 2269.0, 1519.0, 2126.0, 1935.0, 1957.0, 910.0, 1241.0, 45.0, 243.0, 1588.0, 1294.0, 1784.0, 1878.0, 1654.0, 1583.0, 2151.0, 1951.0 ], [ 2018.0, 1406.0, 1973.0, 1790.0, 1825.0, 900.0, 1064.0, 49.0, 291.0, 1425.0, 1097.0, 1562.0, 1611.0, 1416.0, 1552.0, 1897.0, 1689.0 ], [ 342.0, 175.0, 147.0, 132.0, 182.0, 264.0, 37.0, 37.0, 91.0, 67.0, 38.0, 73.0, 350.0, 106.0, 481.0, 330.0, 318.0 ], [ 385.0, 447.0, 630.0, 535.0, 611.0, 436.0, 128.0, 44.0, 149.0, 274.0, 91.0, 65.0, 267.0, 35.0, 808.0, 314.0, 244.0 ], [ 1280.0, 147.0, 784.0, 590.0, 585.0, 133.0, 220.0, 40.0, 41.0, 362.0, 310.0, 730.0, 1055.0, 701.0, 404.0, 1200.0, 1073.0 ] ], "demands": [ 24.0, 28.0, 25.0, 19.0, 18.0, 29.0, 17.0, 18.0, 17.0, 23.0, 19.0, 18.0, 27.0, 17.0, 29.0, 23.0, 22.0 ], "objective": 3470.0 }, "solution": { "open_facilities": [ 5 ], "assignments": [ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 ] }, "obj": 3470.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 17, "facilities": [ { "id": "F1", "opening_cost": 300.0, "capacity": 384.0 }, { "id": "F2", "opening_cost": 300.0, "capacity": 256.0 }, { "id": "F3", "opening_cost": 300.0, "capacity": 376.0 }, { "id": "F4", "opening_cost": 300.0, "capacity": 425.0 }, { "id": "F5", "opening_cost": 300.0, "capacity": 430.0 }, { "id": "F6", "opening_cost": 300.0, "capacity": 378.0 }, { "id": "F7", "opening_cost": 300.0, "capacity": 435.0 }, { "id": "F8", "opening_cost": 300.0, "capacity": 503.0 } ], "customers": [ { "id": 1, "demand": 24.0 }, { "id": 2, "demand": 28.0 }, { "id": 3, "demand": 25.0 }, { "id": 4, "demand": 19.0 }, { "id": 5, "demand": 18.0 }, { "id": 6, "demand": 29.0 }, { "id": 7, "demand": 17.0 }, { "id": 8, "demand": 18.0 }, { "id": 9, "demand": 17.0 }, { "id": 10, "demand": 23.0 }, { "id": 11, "demand": 19.0 }, { "id": 12, "demand": 18.0 }, { "id": 13, "demand": 27.0 }, { "id": 14, "demand": 17.0 }, { "id": 15, "demand": 29.0 }, { "id": 16, "demand": 23.0 }, { "id": 17, "demand": 22.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 731.0 }, { "facility": "F1", "customer": 2, "cost": 145.0 }, { "facility": "F1", "customer": 3, "cost": 227.0 }, { "facility": "F1", "customer": 4, "cost": 131.0 }, { "facility": "F1", "customer": 5, "cost": 205.0 }, { "facility": "F1", "customer": 6, "cost": 231.0 }, { "facility": "F1", "customer": 7, "cost": 38.0 }, { "facility": "F1", "customer": 8, "cost": 36.0 }, { "facility": "F1", "customer": 9, "cost": 72.0 }, { "facility": "F1", "customer": 10, "cost": 46.0 }, { "facility": "F1", "customer": 11, "cost": 63.0 }, { "facility": "F1", "customer": 12, "cost": 242.0 }, { "facility": "F1", "customer": 13, "cost": 613.0 }, { "facility": "F1", "customer": 14, "cost": 271.0 }, { "facility": "F1", "customer": 15, "cost": 475.0 }, { "facility": "F1", "customer": 16, "cost": 677.0 }, { "facility": "F1", "customer": 17, "cost": 602.0 }, { "facility": "F2", "customer": 1, "cost": 1000.0 }, { "facility": "F2", "customer": 2, "cost": 478.0 }, { "facility": "F2", "customer": 3, "cost": 881.0 }, { "facility": "F2", "customer": 4, "cost": 720.0 }, { "facility": "F2", "customer": 5, "cost": 779.0 }, { "facility": "F2", "customer": 6, "cost": 391.0 }, { "facility": "F2", "customer": 7, "cost": 82.0 }, { "facility": "F2", "customer": 8, "cost": 38.0 }, { "facility": "F2", "customer": 9, "cost": 114.0 }, { "facility": "F2", "customer": 10, "cost": 352.0 }, { "facility": "F2", "customer": 11, "cost": 43.0 }, { "facility": "F2", "customer": 12, "cost": 464.0 }, { "facility": "F2", "customer": 13, "cost": 728.0 }, { "facility": "F2", "customer": 14, "cost": 385.0 }, { "facility": "F2", "customer": 15, "cost": 817.0 }, { "facility": "F2", "customer": 16, "cost": 904.0 }, { "facility": "F2", "customer": 17, "cost": 755.0 }, { "facility": "F3", "customer": 1, "cost": 467.0 }, { "facility": "F3", "customer": 2, "cost": 257.0 }, { "facility": "F3", "customer": 3, "cost": 334.0 }, { "facility": "F3", "customer": 4, "cost": 269.0 }, { "facility": "F3", "customer": 5, "cost": 342.0 }, { "facility": "F3", "customer": 6, "cost": 315.0 }, { "facility": "F3", "customer": 7, "cost": 47.0 }, { "facility": "F3", "customer": 8, "cost": 38.0 }, { "facility": "F3", "customer": 9, "cost": 104.0 }, { "facility": "F3", "customer": 10, "cost": 105.0 }, { "facility": "F3", "customer": 11, "cost": 39.0 }, { "facility": "F3", "customer": 12, "cost": 72.0 }, { "facility": "F3", "customer": 13, "cost": 401.0 }, { "facility": "F3", "customer": 14, "cost": 110.0 }, { "facility": "F3", "customer": 15, "cost": 604.0 }, { "facility": "F3", "customer": 16, "cost": 426.0 }, { "facility": "F3", "customer": 17, "cost": 378.0 }, { "facility": "F4", "customer": 1, "cost": 2269.0 }, { "facility": "F4", "customer": 2, "cost": 1519.0 }, { "facility": "F4", "customer": 3, "cost": 2126.0 }, { "facility": "F4", "customer": 4, "cost": 1935.0 }, { "facility": "F4", "customer": 5, "cost": 1957.0 }, { "facility": "F4", "customer": 6, "cost": 910.0 }, { "facility": "F4", "customer": 7, "cost": 1241.0 }, { "facility": "F4", "customer": 8, "cost": 45.0 }, { "facility": "F4", "customer": 9, "cost": 243.0 }, { "facility": "F4", "customer": 10, "cost": 1588.0 }, { "facility": "F4", "customer": 11, "cost": 1294.0 }, { "facility": "F4", "customer": 12, "cost": 1784.0 }, { "facility": "F4", "customer": 13, "cost": 1878.0 }, { "facility": "F4", "customer": 14, "cost": 1654.0 }, { "facility": "F4", "customer": 15, "cost": 1583.0 }, { "facility": "F4", "customer": 16, "cost": 2151.0 }, { "facility": "F4", "customer": 17, "cost": 1951.0 }, { "facility": "F5", "customer": 1, "cost": 2018.0 }, { "facility": "F5", "customer": 2, "cost": 1406.0 }, { "facility": "F5", "customer": 3, "cost": 1973.0 }, { "facility": "F5", "customer": 4, "cost": 1790.0 }, { "facility": "F5", "customer": 5, "cost": 1825.0 }, { "facility": "F5", "customer": 6, "cost": 900.0 }, { "facility": "F5", "customer": 7, "cost": 1064.0 }, { "facility": "F5", "customer": 8, "cost": 49.0 }, { "facility": "F5", "customer": 9, "cost": 291.0 }, { "facility": "F5", "customer": 10, "cost": 1425.0 }, { "facility": "F5", "customer": 11, "cost": 1097.0 }, { "facility": "F5", "customer": 12, "cost": 1562.0 }, { "facility": "F5", "customer": 13, "cost": 1611.0 }, { "facility": "F5", "customer": 14, "cost": 1416.0 }, { "facility": "F5", "customer": 15, "cost": 1552.0 }, { "facility": "F5", "customer": 16, "cost": 1897.0 }, { "facility": "F5", "customer": 17, "cost": 1689.0 }, { "facility": "F6", "customer": 1, "cost": 342.0 }, { "facility": "F6", "customer": 2, "cost": 175.0 }, { "facility": "F6", "customer": 3, "cost": 147.0 }, { "facility": "F6", "customer": 4, "cost": 132.0 }, { "facility": "F6", "customer": 5, "cost": 182.0 }, { "facility": "F6", "customer": 6, "cost": 264.0 }, { "facility": "F6", "customer": 7, "cost": 37.0 }, { "facility": "F6", "customer": 8, "cost": 37.0 }, { "facility": "F6", "customer": 9, "cost": 91.0 }, { "facility": "F6", "customer": 10, "cost": 67.0 }, { "facility": "F6", "customer": 11, "cost": 38.0 }, { "facility": "F6", "customer": 12, "cost": 73.0 }, { "facility": "F6", "customer": 13, "cost": 350.0 }, { "facility": "F6", "customer": 14, "cost": 106.0 }, { "facility": "F6", "customer": 15, "cost": 481.0 }, { "facility": "F6", "customer": 16, "cost": 330.0 }, { "facility": "F6", "customer": 17, "cost": 318.0 }, { "facility": "F7", "customer": 1, "cost": 385.0 }, { "facility": "F7", "customer": 2, "cost": 447.0 }, { "facility": "F7", "customer": 3, "cost": 630.0 }, { "facility": "F7", "customer": 4, "cost": 535.0 }, { "facility": "F7", "customer": 5, "cost": 611.0 }, { "facility": "F7", "customer": 6, "cost": 436.0 }, { "facility": "F7", "customer": 7, "cost": 128.0 }, { "facility": "F7", "customer": 8, "cost": 44.0 }, { "facility": "F7", "customer": 9, "cost": 149.0 }, { "facility": "F7", "customer": 10, "cost": 274.0 }, { "facility": "F7", "customer": 11, "cost": 91.0 }, { "facility": "F7", "customer": 12, "cost": 65.0 }, { "facility": "F7", "customer": 13, "cost": 267.0 }, { "facility": "F7", "customer": 14, "cost": 35.0 }, { "facility": "F7", "customer": 15, "cost": 808.0 }, { "facility": "F7", "customer": 16, "cost": 314.0 }, { "facility": "F7", "customer": 17, "cost": 244.0 }, { "facility": "F8", "customer": 1, "cost": 1280.0 }, { "facility": "F8", "customer": 2, "cost": 147.0 }, { "facility": "F8", "customer": 3, "cost": 784.0 }, { "facility": "F8", "customer": 4, "cost": 590.0 }, { "facility": "F8", "customer": 5, "cost": 585.0 }, { "facility": "F8", "customer": 6, "cost": 133.0 }, { "facility": "F8", "customer": 7, "cost": 220.0 }, { "facility": "F8", "customer": 8, "cost": 40.0 }, { "facility": "F8", "customer": 9, "cost": 41.0 }, { "facility": "F8", "customer": 10, "cost": 362.0 }, { "facility": "F8", "customer": 11, "cost": 310.0 }, { "facility": "F8", "customer": 12, "cost": 730.0 }, { "facility": "F8", "customer": 13, "cost": 1055.0 }, { "facility": "F8", "customer": 14, "cost": 701.0 }, { "facility": "F8", "customer": 15, "cost": 404.0 }, { "facility": "F8", "customer": 16, "cost": 1200.0 }, { "facility": "F8", "customer": 17, "cost": 1073.0 } ], "objective": 3470.0 }, "solution_variant": { "selected": [ "F6" ], "assignments": [ "F6", "F6", "F6", "F6", "F6", "F6", "F6", "F6", "F6", "F6", "F6", "F6", "F6", "F6", "F6", "F6", "F6" ] }, "context_index": 18, "input_format": "nl", "input_index_base": 1 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Out in the field, the food bank team must choose a handful of distribution points to staff and then direct every recipient area to exactly one of those staffed points. Each staffed point has a price tag to keep it open and each assignment from a point to an area has a delivery cost, so the best-looking plan is the one with the lowest total cost — add the staffing cost of each open point to all the delivery costs for the assignments. Each area must be covered once and only once, and each staffed point has a maximum amount it can serve, so assignments must stay within those limits. The concrete figures are provided below.\n\n{\n \"num_distribution_points\": 6,\n \"num_recipient_areas\": 15,\n \"distribution_points\": [\n {\n \"distribution_point_id\": \"F1\",\n \"staffing_cost\": 295.0,\n \"distribution_capacity\": 500.0\n },\n {\n \"distribution_point_id\": \"F2\",\n \"staffing_cost\": 487.0,\n \"distribution_capacity\": 500.0\n },\n {\n \"distribution_point_id\": \"F3\",\n \"staffing_cost\": 201.0,\n \"distribution_capacity\": 500.0\n },\n {\n \"distribution_point_id\": \"F4\",\n \"staffing_cost\": 544.0,\n \"distribution_capacity\": 500.0\n },\n {\n \"distribution_point_id\": \"F5\",\n \"staffing_cost\": 444.0,\n \"distribution_capacity\": 500.0\n },\n {\n \"distribution_point_id\": \"F6\",\n \"staffing_cost\": 333.0,\n \"distribution_capacity\": 500.0\n }\n ],\n \"recipient_areas\": [\n {\n \"recipient_area_id\": \"A\",\n \"area_demand\": 28.0\n },\n {\n \"recipient_area_id\": \"B\",\n \"area_demand\": 17.0\n },\n {\n \"recipient_area_id\": \"C\",\n \"area_demand\": 30.0\n },\n {\n \"recipient_area_id\": \"D\",\n \"area_demand\": 20.0\n },\n {\n \"recipient_area_id\": \"E\",\n \"area_demand\": 14.0\n },\n {\n \"recipient_area_id\": \"F\",\n \"area_demand\": 23.0\n },\n {\n \"recipient_area_id\": \"G\",\n \"area_demand\": 17.0\n },\n {\n \"recipient_area_id\": \"H\",\n \"area_demand\": 17.0\n },\n {\n \"recipient_area_id\": \"I\",\n \"area_demand\": 15.0\n },\n {\n \"recipient_area_id\": \"J\",\n \"area_demand\": 12.0\n },\n {\n \"recipient_area_id\": \"K\",\n \"area_demand\": 10.0\n },\n {\n \"recipient_area_id\": \"L\",\n \"area_demand\": 27.0\n },\n {\n \"recipient_area_id\": \"M\",\n \"area_demand\": 11.0\n },\n {\n \"recipient_area_id\": \"N\",\n \"area_demand\": 19.0\n },\n {\n \"recipient_area_id\": \"O\",\n \"area_demand\": 18.0\n }\n ],\n \"deliverys\": [\n {\n \"distribution_point_id\": \"F1\",\n \"recipient_area_id\": \"A\",\n \"delivery_cost\": 838.0\n },\n {\n \"distribution_point_id\": \"F1\",\n \"recipient_area_id\": \"B\",\n \"delivery_cost\": 1292.0\n },\n {\n \"distribution_point_id\": \"F1\",\n \"recipient_area_id\": \"C\",\n \"delivery_cost\": 377.0\n },\n {\n \"distribution_point_id\": \"F1\",\n \"recipient_area_id\": \"D\",\n \"delivery_cost\": 995.0\n },\n {\n \"distribution_point_id\": \"F1\",\n \"recipient_area_id\": \"E\",\n \"delivery_cost\": 1876.0\n },\n {\n \"distribution_point_id\": \"F1\",\n \"recipient_area_id\": \"F\",\n \"delivery_cost\": 356.0\n },\n {\n \"distribution_point_id\": \"F1\",\n \"recipient_area_id\": \"G\",\n \"delivery_cost\": 1700.0\n },\n {\n \"distribution_point_id\": \"F1\",\n \"recipient_area_id\": \"H\",\n \"delivery_cost\": 291.0\n },\n {\n \"distribution_point_id\": \"F1\",\n \"recipient_area_id\": \"I\",\n \"delivery_cost\": 547.0\n },\n {\n \"distribution_point_id\": \"F1\",\n \"recipient_area_id\": \"J\",\n \"delivery_cost\": 1637.0\n },\n {\n \"distribution_point_id\": \"F1\",\n \"recipient_area_id\": \"K\",\n \"delivery_cost\": 651.0\n },\n {\n \"distribution_point_id\": \"F1\",\n \"recipient_area_id\": \"L\",\n \"delivery_cost\": 1611.0\n },\n {\n \"distribution_point_id\": \"F1\",\n \"recipient_area_id\": \"M\",\n \"delivery_cost\": 669.0\n },\n {\n \"distribution_point_id\": \"F1\",\n \"recipient_area_id\": \"N\",\n \"delivery_cost\": 889.0\n },\n {\n \"distribution_point_id\": \"F1\",\n \"recipient_area_id\": \"O\",\n \"delivery_cost\": 2492.0\n },\n {\n \"distribution_point_id\": \"F2\",\n \"recipient_area_id\": \"A\",\n \"delivery_cost\": 262.0\n },\n {\n \"distribution_point_id\": \"F2\",\n \"recipient_area_id\": \"B\",\n \"delivery_cost\": 1022.0\n },\n {\n \"distribution_point_id\": \"F2\",\n \"recipient_area_id\": \"C\",\n \"delivery_cost\": 61.0\n },\n {\n \"distribution_point_id\": \"F2\",\n \"recipient_area_id\": \"D\",\n \"delivery_cost\": 909.0\n },\n {\n \"distribution_point_id\": \"F2\",\n \"recipient_area_id\": \"E\",\n \"delivery_cost\": 887.0\n },\n {\n \"distribution_point_id\": \"F2\",\n \"recipient_area_id\": \"F\",\n \"delivery_cost\": 383.0\n },\n {\n \"distribution_point_id\": \"F2\",\n \"recipient_area_id\": \"G\",\n \"delivery_cost\": 813.0\n },\n {\n \"distribution_point_id\": \"F2\",\n \"recipient_area_id\": \"H\",\n \"delivery_cost\": 35.0\n },\n {\n \"distribution_point_id\": \"F2\",\n \"recipient_area_id\": \"I\",\n \"delivery_cost\": 43.0\n },\n {\n \"distribution_point_id\": \"F2\",\n \"recipient_area_id\": \"J\",\n \"delivery_cost\": 1039.0\n },\n {\n \"distribution_point_id\": \"F2\",\n \"recipient_area_id\": \"K\",\n \"delivery_cost\": 118.0\n },\n {\n \"distribution_point_id\": \"F2\",\n \"recipient_area_id\": \"L\",\n \"delivery_cost\": 1248.0\n },\n {\n \"distribution_point_id\": \"F2\",\n \"recipient_area_id\": \"M\",\n \"delivery_cost\": 29.0\n },\n {\n \"distribution_point_id\": \"F2\",\n \"recipient_area_id\": \"N\",\n \"delivery_cost\": 389.0\n },\n {\n \"distribution_point_id\": \"F2\",\n \"recipient_area_id\": \"O\",\n \"delivery_cost\": 1574.0\n },\n {\n \"distribution_point_id\": \"F3\",\n \"recipient_area_id\": \"A\",\n \"delivery_cost\": 66.0\n },\n {\n \"distribution_point_id\": \"F3\",\n \"recipient_area_id\": \"B\",\n \"delivery_cost\": 280.0\n },\n {\n \"distribution_point_id\": \"F3\",\n \"recipient_area_id\": \"C\",\n \"delivery_cost\": 148.0\n },\n {\n \"distribution_point_id\": \"F3\",\n \"recipient_area_id\": \"D\",\n \"delivery_cost\": 332.0\n },\n {\n \"distribution_point_id\": \"F3\",\n \"recipient_area_id\": \"E\",\n \"delivery_cost\": 84.0\n },\n {\n \"distribution_point_id\": \"F3\",\n \"recipient_area_id\": \"F\",\n \"delivery_cost\": 107.0\n },\n {\n \"distribution_point_id\": \"F3\",\n \"recipient_area_id\": \"G\",\n \"delivery_cost\": 47.0\n },\n {\n \"distribution_point_id\": \"F3\",\n \"recipient_area_id\": \"H\",\n \"delivery_cost\": 91.0\n },\n {\n \"distribution_point_id\": \"F3\",\n \"recipient_area_id\": \"I\",\n \"delivery_cost\": 102.0\n },\n {\n \"distribution_point_id\": \"F3\",\n \"recipient_area_id\": \"J\",\n \"delivery_cost\": 102.0\n },\n {\n \"distribution_point_id\": \"F3\",\n \"recipient_area_id\": \"K\",\n \"delivery_cost\": 46.0\n },\n {\n \"distribution_point_id\": \"F3\",\n \"recipient_area_id\": \"L\",\n \"delivery_cost\": 350.0\n },\n {\n \"distribution_point_id\": \"F3\",\n \"recipient_area_id\": \"M\",\n \"delivery_cost\": 127.0\n },\n {\n \"distribution_point_id\": \"F3\",\n \"recipient_area_id\": \"N\",\n \"delivery_cost\": 38.0\n },\n {\n \"distribution_point_id\": \"F3\",\n \"recipient_area_id\": \"O\",\n \"delivery_cost\": 36.0\n },\n {\n \"distribution_point_id\": \"F4\",\n \"recipient_area_id\": \"A\",\n \"delivery_cost\": 320.0\n },\n {\n \"distribution_point_id\": \"F4\",\n \"recipient_area_id\": \"B\",\n \"delivery_cost\": 34.0\n },\n {\n \"distribution_point_id\": \"F4\",\n \"recipient_area_id\": \"C\",\n \"delivery_cost\": 317.0\n },\n {\n \"distribution_point_id\": \"F4\",\n \"recipient_area_id\": \"D\",\n \"delivery_cost\": 77.0\n },\n {\n \"distribution_point_id\": \"F4\",\n \"recipient_area_id\": \"E\",\n \"delivery_cost\": 881.0\n },\n {\n \"distribution_point_id\": \"F4\",\n \"recipient_area_id\": \"F\",\n \"delivery_cost\": 48.0\n },\n {\n \"distribution_point_id\": \"F4\",\n \"recipient_area_id\": \"G\",\n \"delivery_cost\": 697.0\n },\n {\n \"distribution_point_id\": \"F4\",\n \"recipient_area_id\": \"H\",\n \"delivery_cost\": 238.0\n },\n {\n \"distribution_point_id\": \"F4\",\n \"recipient_area_id\": \"I\",\n \"delivery_cost\": 340.0\n },\n {\n \"distribution_point_id\": \"F4\",\n \"recipient_area_id\": \"J\",\n \"delivery_cost\": 360.0\n },\n {\n \"distribution_point_id\": \"F4\",\n \"recipient_area_id\": \"K\",\n \"delivery_cost\": 287.0\n },\n {\n \"distribution_point_id\": \"F4\",\n \"recipient_area_id\": \"L\",\n \"delivery_cost\": 76.0\n },\n {\n \"distribution_point_id\": \"F4\",\n \"recipient_area_id\": \"M\",\n \"delivery_cost\": 416.0\n },\n {\n \"distribution_point_id\": \"F4\",\n \"recipient_area_id\": \"N\",\n \"delivery_cost\": 231.0\n },\n {\n \"distribution_point_id\": \"F4\",\n \"recipient_area_id\": \"O\",\n \"delivery_cost\": 1226.0\n },\n {\n \"distribution_point_id\": \"F5\",\n \"recipient_area_id\": \"A\",\n \"delivery_cost\": 738.0\n },\n {\n \"distribution_point_id\": \"F5\",\n \"recipient_area_id\": \"B\",\n \"delivery_cost\": 1017.0\n },\n {\n \"distribution_point_id\": \"F5\",\n \"recipient_area_id\": \"C\",\n \"delivery_cost\": 415.0\n },\n {\n \"distribution_point_id\": \"F5\",\n \"recipient_area_id\": \"D\",\n \"delivery_cost\": 695.0\n },\n {\n \"distribution_point_id\": \"F5\",\n \"recipient_area_id\": \"E\",\n \"delivery_cost\": 1733.0\n },\n {\n \"distribution_point_id\": \"F5\",\n \"recipient_area_id\": \"F\",\n \"delivery_cost\": 114.0\n },\n {\n \"distribution_point_id\": \"F5\",\n \"recipient_area_id\": \"G\",\n \"delivery_cost\": 1546.0\n },\n {\n \"distribution_point_id\": \"F5\",\n \"recipient_area_id\": \"H\",\n \"delivery_cost\": 328.0\n },\n {\n \"distribution_point_id\": \"F5\",\n \"recipient_area_id\": \"I\",\n \"delivery_cost\": 546.0\n },\n {\n \"distribution_point_id\": \"F5\",\n \"recipient_area_id\": \"J\",\n \"delivery_cost\": 1419.0\n },\n {\n \"distribution_point_id\": \"F5\",\n \"recipient_area_id\": \"K\",\n \"delivery_cost\": 595.0\n },\n {\n \"distribution_point_id\": \"F5\",\n \"recipient_area_id\": \"L\",\n \"delivery_cost\": 1343.0\n },\n {\n \"distribution_point_id\": \"F5\",\n \"recipient_area_id\": \"M\",\n \"delivery_cost\": 661.0\n },\n {\n \"distribution_point_id\": \"F5\",\n \"recipient_area_id\": \"N\",\n \"delivery_cost\": 741.0\n },\n {\n \"distribution_point_id\": \"F5\",\n \"recipient_area_id\": \"O\",\n \"delivery_cost\": 2309.0\n },\n {\n \"distribution_point_id\": \"F6\",\n \"recipient_area_id\": \"A\",\n \"delivery_cost\": 141.0\n },\n {\n \"distribution_point_id\": \"F6\",\n \"recipient_area_id\": \"B\",\n \"delivery_cost\": 260.0\n },\n {\n \"distribution_point_id\": \"F6\",\n \"recipient_area_id\": \"C\",\n \"delivery_cost\": 213.0\n },\n {\n \"distribution_point_id\": \"F6\",\n \"recipient_area_id\": \"D\",\n \"delivery_cost\": 289.0\n },\n {\n \"distribution_point_id\": \"F6\",\n \"recipient_area_id\": \"E\",\n \"delivery_cost\": 612.0\n },\n {\n \"distribution_point_id\": \"F6\",\n \"recipient_area_id\": \"F\",\n \"delivery_cost\": 73.0\n },\n {\n \"distribution_point_id\": \"F6\",\n \"recipient_area_id\": \"G\",\n \"delivery_cost\": 421.0\n },\n {\n \"distribution_point_id\": \"F6\",\n \"recipient_area_id\": \"H\",\n \"delivery_cost\": 144.0\n },\n {\n \"distribution_point_id\": \"F6\",\n \"recipient_area_id\": \"I\",\n \"delivery_cost\": 193.0\n },\n {\n \"distribution_point_id\": \"F6\",\n \"recipient_area_id\": \"J\",\n \"delivery_cost\": 180.0\n },\n {\n \"distribution_point_id\": \"F6\",\n \"recipient_area_id\": \"K\",\n \"delivery_cost\": 127.0\n },\n {\n \"distribution_point_id\": \"F6\",\n \"recipient_area_id\": \"L\",\n \"delivery_cost\": 401.0\n },\n {\n \"distribution_point_id\": \"F6\",\n \"recipient_area_id\": \"M\",\n \"delivery_cost\": 247.0\n },\n {\n \"distribution_point_id\": \"F6\",\n \"recipient_area_id\": \"N\",\n \"delivery_cost\": 67.0\n },\n {\n \"distribution_point_id\": \"F6\",\n \"recipient_area_id\": \"O\",\n \"delivery_cost\": 1070.0\n }\n ]\n}\n\nJust to keep things tidy, when you send the plan back please use this simple JSON layout so I can read it reliably:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list the distribution points you'll staff (one placeholder per open point). \"assignments\" is a list showing, for each recipient area (in the same order as the instance), which staffed point it gets assigned to. Think of it like filling out a short form — who we open, and who goes where.\n\nThis JSON is just the expected shape — a sketch, not the actual filled-in answer.\n\nPlease use the exact identifiers from the instance input when you fill this in — do not rename them or invent new labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 295.0, 487.0, 201.0, 544.0, 444.0, 333.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 838.0, 1292.0, 377.0, 995.0, 1876.0, 356.0, 1700.0, 291.0, 547.0, 1637.0, 651.0, 1611.0, 669.0, 889.0, 2492.0 ], [ 262.0, 1022.0, 61.0, 909.0, 887.0, 383.0, 813.0, 35.0, 43.0, 1039.0, 118.0, 1248.0, 29.0, 389.0, 1574.0 ], [ 66.0, 280.0, 148.0, 332.0, 84.0, 107.0, 47.0, 91.0, 102.0, 102.0, 46.0, 350.0, 127.0, 38.0, 36.0 ], [ 320.0, 34.0, 317.0, 77.0, 881.0, 48.0, 697.0, 238.0, 340.0, 360.0, 287.0, 76.0, 416.0, 231.0, 1226.0 ], [ 738.0, 1017.0, 415.0, 695.0, 1733.0, 114.0, 1546.0, 328.0, 546.0, 1419.0, 595.0, 1343.0, 661.0, 741.0, 2309.0 ], [ 141.0, 260.0, 213.0, 289.0, 612.0, 73.0, 421.0, 144.0, 193.0, 180.0, 127.0, 401.0, 247.0, 67.0, 1070.0 ] ], "demands": [ 28.0, 17.0, 30.0, 20.0, 14.0, 23.0, 17.0, 17.0, 15.0, 12.0, 10.0, 27.0, 11.0, 19.0, 18.0 ], "objective": 1867.0 }, "solution": { "open_facilities": [ 2, 3 ], "assignments": [ 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2 ] }, "obj": 1867.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 6, "num_customers": 15, "facilities": [ { "id": "F1", "opening_cost": 295.0, "capacity": 500.0 }, { "id": "F2", "opening_cost": 487.0, "capacity": 500.0 }, { "id": "F3", "opening_cost": 201.0, "capacity": 500.0 }, { "id": "F4", "opening_cost": 544.0, "capacity": 500.0 }, { "id": "F5", "opening_cost": 444.0, "capacity": 500.0 }, { "id": "F6", "opening_cost": 333.0, "capacity": 500.0 } ], "customers": [ { "id": "A", "demand": 28.0 }, { "id": "B", "demand": 17.0 }, { "id": "C", "demand": 30.0 }, { "id": "D", "demand": 20.0 }, { "id": "E", "demand": 14.0 }, { "id": "F", "demand": 23.0 }, { "id": "G", "demand": 17.0 }, { "id": "H", "demand": 17.0 }, { "id": "I", "demand": 15.0 }, { "id": "J", "demand": 12.0 }, { "id": "K", "demand": 10.0 }, { "id": "L", "demand": 27.0 }, { "id": "M", "demand": 11.0 }, { "id": "N", "demand": 19.0 }, { "id": "O", "demand": 18.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 838.0 }, { "facility": "F1", "customer": "B", "cost": 1292.0 }, { "facility": "F1", "customer": "C", "cost": 377.0 }, { "facility": "F1", "customer": "D", "cost": 995.0 }, { "facility": "F1", "customer": "E", "cost": 1876.0 }, { "facility": "F1", "customer": "F", "cost": 356.0 }, { "facility": "F1", "customer": "G", "cost": 1700.0 }, { "facility": "F1", "customer": "H", "cost": 291.0 }, { "facility": "F1", "customer": "I", "cost": 547.0 }, { "facility": "F1", "customer": "J", "cost": 1637.0 }, { "facility": "F1", "customer": "K", "cost": 651.0 }, { "facility": "F1", "customer": "L", "cost": 1611.0 }, { "facility": "F1", "customer": "M", "cost": 669.0 }, { "facility": "F1", "customer": "N", "cost": 889.0 }, { "facility": "F1", "customer": "O", "cost": 2492.0 }, { "facility": "F2", "customer": "A", "cost": 262.0 }, { "facility": "F2", "customer": "B", "cost": 1022.0 }, { "facility": "F2", "customer": "C", "cost": 61.0 }, { "facility": "F2", "customer": "D", "cost": 909.0 }, { "facility": "F2", "customer": "E", "cost": 887.0 }, { "facility": "F2", "customer": "F", "cost": 383.0 }, { "facility": "F2", "customer": "G", "cost": 813.0 }, { "facility": "F2", "customer": "H", "cost": 35.0 }, { "facility": "F2", "customer": "I", "cost": 43.0 }, { "facility": "F2", "customer": "J", "cost": 1039.0 }, { "facility": "F2", "customer": "K", "cost": 118.0 }, { "facility": "F2", "customer": "L", "cost": 1248.0 }, { "facility": "F2", "customer": "M", "cost": 29.0 }, { "facility": "F2", "customer": "N", "cost": 389.0 }, { "facility": "F2", "customer": "O", "cost": 1574.0 }, { "facility": "F3", "customer": "A", "cost": 66.0 }, { "facility": "F3", "customer": "B", "cost": 280.0 }, { "facility": "F3", "customer": "C", "cost": 148.0 }, { "facility": "F3", "customer": "D", "cost": 332.0 }, { "facility": "F3", "customer": "E", "cost": 84.0 }, { "facility": "F3", "customer": "F", "cost": 107.0 }, { "facility": "F3", "customer": "G", "cost": 47.0 }, { "facility": "F3", "customer": "H", "cost": 91.0 }, { "facility": "F3", "customer": "I", "cost": 102.0 }, { "facility": "F3", "customer": "J", "cost": 102.0 }, { "facility": "F3", "customer": "K", "cost": 46.0 }, { "facility": "F3", "customer": "L", "cost": 350.0 }, { "facility": "F3", "customer": "M", "cost": 127.0 }, { "facility": "F3", "customer": "N", "cost": 38.0 }, { "facility": "F3", "customer": "O", "cost": 36.0 }, { "facility": "F4", "customer": "A", "cost": 320.0 }, { "facility": "F4", "customer": "B", "cost": 34.0 }, { "facility": "F4", "customer": "C", "cost": 317.0 }, { "facility": "F4", "customer": "D", "cost": 77.0 }, { "facility": "F4", "customer": "E", "cost": 881.0 }, { "facility": "F4", "customer": "F", "cost": 48.0 }, { "facility": "F4", "customer": "G", "cost": 697.0 }, { "facility": "F4", "customer": "H", "cost": 238.0 }, { "facility": "F4", "customer": "I", "cost": 340.0 }, { "facility": "F4", "customer": "J", "cost": 360.0 }, { "facility": "F4", "customer": "K", "cost": 287.0 }, { "facility": "F4", "customer": "L", "cost": 76.0 }, { "facility": "F4", "customer": "M", "cost": 416.0 }, { "facility": "F4", "customer": "N", "cost": 231.0 }, { "facility": "F4", "customer": "O", "cost": 1226.0 }, { "facility": "F5", "customer": "A", "cost": 738.0 }, { "facility": "F5", "customer": "B", "cost": 1017.0 }, { "facility": "F5", "customer": "C", "cost": 415.0 }, { "facility": "F5", "customer": "D", "cost": 695.0 }, { "facility": "F5", "customer": "E", "cost": 1733.0 }, { "facility": "F5", "customer": "F", "cost": 114.0 }, { "facility": "F5", "customer": "G", "cost": 1546.0 }, { "facility": "F5", "customer": "H", "cost": 328.0 }, { "facility": "F5", "customer": "I", "cost": 546.0 }, { "facility": "F5", "customer": "J", "cost": 1419.0 }, { "facility": "F5", "customer": "K", "cost": 595.0 }, { "facility": "F5", "customer": "L", "cost": 1343.0 }, { "facility": "F5", "customer": "M", "cost": 661.0 }, { "facility": "F5", "customer": "N", "cost": 741.0 }, { "facility": "F5", "customer": "O", "cost": 2309.0 }, { "facility": "F6", "customer": "A", "cost": 141.0 }, { "facility": "F6", "customer": "B", "cost": 260.0 }, { "facility": "F6", "customer": "C", "cost": 213.0 }, { "facility": "F6", "customer": "D", "cost": 289.0 }, { "facility": "F6", "customer": "E", "cost": 612.0 }, { "facility": "F6", "customer": "F", "cost": 73.0 }, { "facility": "F6", "customer": "G", "cost": 421.0 }, { "facility": "F6", "customer": "H", "cost": 144.0 }, { "facility": "F6", "customer": "I", "cost": 193.0 }, { "facility": "F6", "customer": "J", "cost": 180.0 }, { "facility": "F6", "customer": "K", "cost": 127.0 }, { "facility": "F6", "customer": "L", "cost": 401.0 }, { "facility": "F6", "customer": "M", "cost": 247.0 }, { "facility": "F6", "customer": "N", "cost": 67.0 }, { "facility": "F6", "customer": "O", "cost": 1070.0 } ], "objective": 1867.0 }, "solution_variant": { "selected": [ "F3", "F4" ], "assignments": [ "F3", "F4", "F3", "F4", "F3", "F4", "F3", "F3", "F3", "F3", "F3", "F4", "F3", "F3", "F3" ] }, "context_index": 19, "input_format": "json", "input_index_base": "names" }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "There’s a bit of a balancing act at the returns desk: choose a subset of repair hubs to keep running, then route each incoming device to one of those hubs. Each hub charges a fixed amount to stay active and can only process a limited number of devices, and moving a device to a hub adds a per-item cost. The smart plan is the one that keeps the total expense (hub-running fees plus device-movement costs) as small as possible, with every returned device assigned once and no hub given more than it can handle. The exact details — what each hub costs and how many devices they can take — are shown below.\n\n{\n \"num_repair_hubs\": 8,\n \"num_returned_devices\": 18,\n \"hubs\": [\n {\n \"hub_id\": \"F1\",\n \"hub_running_cost\": 400.0,\n \"hub_capacity\": 700.0\n },\n {\n \"hub_id\": \"F2\",\n \"hub_running_cost\": 400.0,\n \"hub_capacity\": 700.0\n },\n {\n \"hub_id\": \"F3\",\n \"hub_running_cost\": 400.0,\n \"hub_capacity\": 700.0\n },\n {\n \"hub_id\": \"F4\",\n \"hub_running_cost\": 400.0,\n \"hub_capacity\": 700.0\n },\n {\n \"hub_id\": \"F5\",\n \"hub_running_cost\": 400.0,\n \"hub_capacity\": 700.0\n },\n {\n \"hub_id\": \"F6\",\n \"hub_running_cost\": 400.0,\n \"hub_capacity\": 700.0\n },\n {\n \"hub_id\": \"F7\",\n \"hub_running_cost\": 400.0,\n \"hub_capacity\": 700.0\n },\n {\n \"hub_id\": \"F8\",\n \"hub_running_cost\": 400.0,\n \"hub_capacity\": 700.0\n }\n ],\n \"devices\": [\n {\n \"device_id\": \"A\",\n \"device_demand\": 11.0\n },\n {\n \"device_id\": \"B\",\n \"device_demand\": 24.0\n },\n {\n \"device_id\": \"C\",\n \"device_demand\": 17.0\n },\n {\n \"device_id\": \"D\",\n \"device_demand\": 18.0\n },\n {\n \"device_id\": \"E\",\n \"device_demand\": 21.0\n },\n {\n \"device_id\": \"F\",\n \"device_demand\": 23.0\n },\n {\n \"device_id\": \"G\",\n \"device_demand\": 20.0\n },\n {\n \"device_id\": \"H\",\n \"device_demand\": 24.0\n },\n {\n \"device_id\": \"I\",\n \"device_demand\": 30.0\n },\n {\n \"device_id\": \"J\",\n \"device_demand\": 19.0\n },\n {\n \"device_id\": \"K\",\n \"device_demand\": 29.0\n },\n {\n \"device_id\": \"L\",\n \"device_demand\": 13.0\n },\n {\n \"device_id\": \"M\",\n \"device_demand\": 19.0\n },\n {\n \"device_id\": \"N\",\n \"device_demand\": 19.0\n },\n {\n \"device_id\": \"O\",\n \"device_demand\": 16.0\n },\n {\n \"device_id\": \"P\",\n \"device_demand\": 15.0\n },\n {\n \"device_id\": \"Q\",\n \"device_demand\": 19.0\n },\n {\n \"device_id\": \"R\",\n \"device_demand\": 29.0\n }\n ],\n \"device_transfers\": [\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"A\",\n \"device_transfer_cost\": 31.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"B\",\n \"device_transfer_cost\": 1185.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"C\",\n \"device_transfer_cost\": 813.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"D\",\n \"device_transfer_cost\": 213.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"E\",\n \"device_transfer_cost\": 162.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"F\",\n \"device_transfer_cost\": 867.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"G\",\n \"device_transfer_cost\": 136.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"H\",\n \"device_transfer_cost\": 366.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"I\",\n \"device_transfer_cost\": 71.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"J\",\n \"device_transfer_cost\": 386.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"K\",\n \"device_transfer_cost\": 82.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"L\",\n \"device_transfer_cost\": 185.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"M\",\n \"device_transfer_cost\": 997.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"N\",\n \"device_transfer_cost\": 530.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"O\",\n \"device_transfer_cost\": 491.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"P\",\n \"device_transfer_cost\": 1116.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"Q\",\n \"device_transfer_cost\": 38.0\n },\n {\n \"hub_id\": \"F1\",\n \"device_id\": \"R\",\n \"device_transfer_cost\": 200.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"A\",\n \"device_transfer_cost\": 690.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"B\",\n \"device_transfer_cost\": 2269.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"C\",\n \"device_transfer_cost\": 1566.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"D\",\n \"device_transfer_cost\": 425.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"E\",\n \"device_transfer_cost\": 1642.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"F\",\n \"device_transfer_cost\": 2332.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"G\",\n \"device_transfer_cost\": 1197.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"H\",\n \"device_transfer_cost\": 721.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"I\",\n \"device_transfer_cost\": 317.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"J\",\n \"device_transfer_cost\": 1935.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"K\",\n \"device_transfer_cost\": 845.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"L\",\n \"device_transfer_cost\": 665.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"M\",\n \"device_transfer_cost\": 1904.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"N\",\n \"device_transfer_cost\": 1563.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"O\",\n \"device_transfer_cost\": 1227.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"P\",\n \"device_transfer_cost\": 2235.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"Q\",\n \"device_transfer_cost\": 683.0\n },\n {\n \"hub_id\": \"F2\",\n \"device_id\": \"R\",\n \"device_transfer_cost\": 1583.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"A\",\n \"device_transfer_cost\": 673.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"B\",\n \"device_transfer_cost\": 2018.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"C\",\n \"device_transfer_cost\": 1292.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"D\",\n \"device_transfer_cost\": 147.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"E\",\n \"device_transfer_cost\": 1597.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"F\",\n \"device_transfer_cost\": 2147.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"G\",\n \"device_transfer_cost\": 1048.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"H\",\n \"device_transfer_cost\": 436.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"I\",\n \"device_transfer_cost\": 377.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"J\",\n \"device_transfer_cost\": 1790.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"K\",\n \"device_transfer_cost\": 731.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"L\",\n \"device_transfer_cost\": 426.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"M\",\n \"device_transfer_cost\": 1639.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"N\",\n \"device_transfer_cost\": 1338.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"O\",\n \"device_transfer_cost\": 969.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"P\",\n \"device_transfer_cost\": 1990.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"Q\",\n \"device_transfer_cost\": 632.0\n },\n {\n \"hub_id\": \"F3\",\n \"device_id\": \"R\",\n \"device_transfer_cost\": 1552.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"A\",\n \"device_transfer_cost\": 23.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"B\",\n \"device_transfer_cost\": 1480.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"C\",\n \"device_transfer_cost\": 1022.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"D\",\n \"device_transfer_cost\": 277.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"E\",\n \"device_transfer_cost\": 217.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"F\",\n \"device_transfer_cost\": 1232.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"G\",\n \"device_transfer_cost\": 302.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"H\",\n \"device_transfer_cost\": 465.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"I\",\n \"device_transfer_cost\": 61.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"J\",\n \"device_transfer_cost\": 748.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"K\",\n \"device_transfer_cost\": 151.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"L\",\n \"device_transfer_cost\": 280.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"M\",\n \"device_transfer_cost\": 1247.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"N\",\n \"device_transfer_cost\": 776.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"O\",\n \"device_transfer_cost\": 671.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"P\",\n \"device_transfer_cost\": 1418.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"Q\",\n \"device_transfer_cost\": 55.0\n },\n {\n \"hub_id\": \"F4\",\n \"device_id\": \"R\",\n \"device_transfer_cost\": 185.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"A\",\n \"device_transfer_cost\": 445.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"B\",\n \"device_transfer_cost\": 491.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"C\",\n \"device_transfer_cost\": 34.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"D\",\n \"device_transfer_cost\": 37.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"E\",\n \"device_transfer_cost\": 1084.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"F\",\n \"device_transfer_cost\": 979.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"G\",\n \"device_transfer_cost\": 421.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"H\",\n \"device_transfer_cost\": 48.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"I\",\n \"device_transfer_cost\": 317.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"J\",\n \"device_transfer_cost\": 887.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"K\",\n \"device_transfer_cost\": 354.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"L\",\n \"device_transfer_cost\": 77.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"M\",\n \"device_transfer_cost\": 103.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"N\",\n \"device_transfer_cost\": 274.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"O\",\n \"device_transfer_cost\": 68.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"P\",\n \"device_transfer_cost\": 503.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"Q\",\n \"device_transfer_cost\": 380.0\n },\n {\n \"hub_id\": \"F5\",\n \"device_id\": \"R\",\n \"device_transfer_cost\": 1088.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"A\",\n \"device_transfer_cost\": 281.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"B\",\n \"device_transfer_cost\": 385.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"C\",\n \"device_transfer_cost\": 181.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"D\",\n \"device_transfer_cost\": 51.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"E\",\n \"device_transfer_cost\": 791.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"F\",\n \"device_transfer_cost\": 608.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"G\",\n \"device_transfer_cost\": 193.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"H\",\n \"device_transfer_cost\": 91.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"I\",\n \"device_transfer_cost\": 219.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"J\",\n \"device_transfer_cost\": 535.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"K\",\n \"device_transfer_cost\": 188.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"L\",\n \"device_transfer_cost\": 27.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"M\",\n \"device_transfer_cost\": 242.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"N\",\n \"device_transfer_cost\": 48.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"O\",\n \"device_transfer_cost\": 49.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"P\",\n \"device_transfer_cost\": 325.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"Q\",\n \"device_transfer_cost\": 224.0\n },\n {\n \"hub_id\": \"F6\",\n \"device_id\": \"R\",\n \"device_transfer_cost\": 808.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"A\",\n \"device_transfer_cost\": 277.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"B\",\n \"device_transfer_cost\": 615.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"C\",\n \"device_transfer_cost\": 260.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"D\",\n \"device_transfer_cost\": 56.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"E\",\n \"device_transfer_cost\": 820.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"F\",\n \"device_transfer_cost\": 763.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"G\",\n \"device_transfer_cost\": 196.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"H\",\n \"device_transfer_cost\": 104.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"I\",\n \"device_transfer_cost\": 213.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"J\",\n \"device_transfer_cost\": 609.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"K\",\n \"device_transfer_cost\": 184.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"L\",\n \"device_transfer_cost\": 26.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"M\",\n \"device_transfer_cost\": 388.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"N\",\n \"device_transfer_cost\": 42.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"O\",\n \"device_transfer_cost\": 67.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"P\",\n \"device_transfer_cost\": 564.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"Q\",\n \"device_transfer_cost\": 220.0\n },\n {\n \"hub_id\": \"F7\",\n \"device_id\": \"R\",\n \"device_transfer_cost\": 831.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"A\",\n \"device_transfer_cost\": 329.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"B\",\n \"device_transfer_cost\": 699.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"C\",\n \"device_transfer_cost\": 228.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"D\",\n \"device_transfer_cost\": 47.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"E\",\n \"device_transfer_cost\": 930.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"F\",\n \"device_transfer_cost\": 928.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"G\",\n \"device_transfer_cost\": 274.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"H\",\n \"device_transfer_cost\": 85.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"I\",\n \"device_transfer_cost\": 241.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"J\",\n \"device_transfer_cost\": 757.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"K\",\n \"device_transfer_cost\": 234.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"L\",\n \"device_transfer_cost\": 30.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"M\",\n \"device_transfer_cost\": 398.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"N\",\n \"device_transfer_cost\": 121.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"O\",\n \"device_transfer_cost\": 43.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"P\",\n \"device_transfer_cost\": 662.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"Q\",\n \"device_transfer_cost\": 267.0\n },\n {\n \"hub_id\": \"F8\",\n \"device_id\": \"R\",\n \"device_transfer_cost\": 935.0\n }\n ]\n}\n\nOh, and when you send the plan back, please stick to this simple JSON shape so it's easy to read and check:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of repair hubs you decide to keep running, and \"assignments\" as, for each returned device in the order they were listed, which hub it gets routed to. It's just a sketch of the form I need, not the actual final answer.\n\nPlease use the exact identifiers from the instance input — do not rename them or invent new labels. Valid identifiers look like plain numbers such as \"1\" or \"23\", single capital letters like \"A\" or \"B\", or a capital letter followed by digits like \"A1\" or \"X7\".", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 31.0, 1185.0, 813.0, 213.0, 162.0, 867.0, 136.0, 366.0, 71.0, 386.0, 82.0, 185.0, 997.0, 530.0, 491.0, 1116.0, 38.0, 200.0 ], [ 690.0, 2269.0, 1566.0, 425.0, 1642.0, 2332.0, 1197.0, 721.0, 317.0, 1935.0, 845.0, 665.0, 1904.0, 1563.0, 1227.0, 2235.0, 683.0, 1583.0 ], [ 673.0, 2018.0, 1292.0, 147.0, 1597.0, 2147.0, 1048.0, 436.0, 377.0, 1790.0, 731.0, 426.0, 1639.0, 1338.0, 969.0, 1990.0, 632.0, 1552.0 ], [ 23.0, 1480.0, 1022.0, 277.0, 217.0, 1232.0, 302.0, 465.0, 61.0, 748.0, 151.0, 280.0, 1247.0, 776.0, 671.0, 1418.0, 55.0, 185.0 ], [ 445.0, 491.0, 34.0, 37.0, 1084.0, 979.0, 421.0, 48.0, 317.0, 887.0, 354.0, 77.0, 103.0, 274.0, 68.0, 503.0, 380.0, 1088.0 ], [ 281.0, 385.0, 181.0, 51.0, 791.0, 608.0, 193.0, 91.0, 219.0, 535.0, 188.0, 27.0, 242.0, 48.0, 49.0, 325.0, 224.0, 808.0 ], [ 277.0, 615.0, 260.0, 56.0, 820.0, 763.0, 196.0, 104.0, 213.0, 609.0, 184.0, 26.0, 388.0, 42.0, 67.0, 564.0, 220.0, 831.0 ], [ 329.0, 699.0, 228.0, 47.0, 930.0, 928.0, 274.0, 85.0, 241.0, 757.0, 234.0, 30.0, 398.0, 121.0, 43.0, 662.0, 267.0, 935.0 ] ], "demands": [ 11.0, 24.0, 17.0, 18.0, 21.0, 23.0, 20.0, 24.0, 30.0, 19.0, 29.0, 13.0, 19.0, 19.0, 16.0, 15.0, 19.0, 29.0 ], "objective": 3913.0 }, "solution": { "open_facilities": [ 0, 5 ], "assignments": [ 0, 5, 5, 5, 0, 5, 0, 5, 0, 0, 0, 5, 5, 5, 5, 5, 0, 0 ] }, "obj": 3913.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 18, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F7", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F8", "opening_cost": 400.0, "capacity": 700.0 } ], "customers": [ { "id": "A", "demand": 11.0 }, { "id": "B", "demand": 24.0 }, { "id": "C", "demand": 17.0 }, { "id": "D", "demand": 18.0 }, { "id": "E", "demand": 21.0 }, { "id": "F", "demand": 23.0 }, { "id": "G", "demand": 20.0 }, { "id": "H", "demand": 24.0 }, { "id": "I", "demand": 30.0 }, { "id": "J", "demand": 19.0 }, { "id": "K", "demand": 29.0 }, { "id": "L", "demand": 13.0 }, { "id": "M", "demand": 19.0 }, { "id": "N", "demand": 19.0 }, { "id": "O", "demand": 16.0 }, { "id": "P", "demand": 15.0 }, { "id": "Q", "demand": 19.0 }, { "id": "R", "demand": 29.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 31.0 }, { "facility": "F1", "customer": "B", "cost": 1185.0 }, { "facility": "F1", "customer": "C", "cost": 813.0 }, { "facility": "F1", "customer": "D", "cost": 213.0 }, { "facility": "F1", "customer": "E", "cost": 162.0 }, { "facility": "F1", "customer": "F", "cost": 867.0 }, { "facility": "F1", "customer": "G", "cost": 136.0 }, { "facility": "F1", "customer": "H", "cost": 366.0 }, { "facility": "F1", "customer": "I", "cost": 71.0 }, { "facility": "F1", "customer": "J", "cost": 386.0 }, { "facility": "F1", "customer": "K", "cost": 82.0 }, { "facility": "F1", "customer": "L", "cost": 185.0 }, { "facility": "F1", "customer": "M", "cost": 997.0 }, { "facility": "F1", "customer": "N", "cost": 530.0 }, { "facility": "F1", "customer": "O", "cost": 491.0 }, { "facility": "F1", "customer": "P", "cost": 1116.0 }, { "facility": "F1", "customer": "Q", "cost": 38.0 }, { "facility": "F1", "customer": "R", "cost": 200.0 }, { "facility": "F2", "customer": "A", "cost": 690.0 }, { "facility": "F2", "customer": "B", "cost": 2269.0 }, { "facility": "F2", "customer": "C", "cost": 1566.0 }, { "facility": "F2", "customer": "D", "cost": 425.0 }, { "facility": "F2", "customer": "E", "cost": 1642.0 }, { "facility": "F2", "customer": "F", "cost": 2332.0 }, { "facility": "F2", "customer": "G", "cost": 1197.0 }, { "facility": "F2", "customer": "H", "cost": 721.0 }, { "facility": "F2", "customer": "I", "cost": 317.0 }, { "facility": "F2", "customer": "J", "cost": 1935.0 }, { "facility": "F2", "customer": "K", "cost": 845.0 }, { "facility": "F2", "customer": "L", "cost": 665.0 }, { "facility": "F2", "customer": "M", "cost": 1904.0 }, { "facility": "F2", "customer": "N", "cost": 1563.0 }, { "facility": "F2", "customer": "O", "cost": 1227.0 }, { "facility": "F2", "customer": "P", "cost": 2235.0 }, { "facility": "F2", "customer": "Q", "cost": 683.0 }, { "facility": "F2", "customer": "R", "cost": 1583.0 }, { "facility": "F3", "customer": "A", "cost": 673.0 }, { "facility": "F3", "customer": "B", "cost": 2018.0 }, { "facility": "F3", "customer": "C", "cost": 1292.0 }, { "facility": "F3", "customer": "D", "cost": 147.0 }, { "facility": "F3", "customer": "E", "cost": 1597.0 }, { "facility": "F3", "customer": "F", "cost": 2147.0 }, { "facility": "F3", "customer": "G", "cost": 1048.0 }, { "facility": "F3", "customer": "H", "cost": 436.0 }, { "facility": "F3", "customer": "I", "cost": 377.0 }, { "facility": "F3", "customer": "J", "cost": 1790.0 }, { "facility": "F3", "customer": "K", "cost": 731.0 }, { "facility": "F3", "customer": "L", "cost": 426.0 }, { "facility": "F3", "customer": "M", "cost": 1639.0 }, { "facility": "F3", "customer": "N", "cost": 1338.0 }, { "facility": "F3", "customer": "O", "cost": 969.0 }, { "facility": "F3", "customer": "P", "cost": 1990.0 }, { "facility": "F3", "customer": "Q", "cost": 632.0 }, { "facility": "F3", "customer": "R", "cost": 1552.0 }, { "facility": "F4", "customer": "A", "cost": 23.0 }, { "facility": "F4", "customer": "B", "cost": 1480.0 }, { "facility": "F4", "customer": "C", "cost": 1022.0 }, { "facility": "F4", "customer": "D", "cost": 277.0 }, { "facility": "F4", "customer": "E", "cost": 217.0 }, { "facility": "F4", "customer": "F", "cost": 1232.0 }, { "facility": "F4", "customer": "G", "cost": 302.0 }, { "facility": "F4", "customer": "H", "cost": 465.0 }, { "facility": "F4", "customer": "I", "cost": 61.0 }, { "facility": "F4", "customer": "J", "cost": 748.0 }, { "facility": "F4", "customer": "K", "cost": 151.0 }, { "facility": "F4", "customer": "L", "cost": 280.0 }, { "facility": "F4", "customer": "M", "cost": 1247.0 }, { "facility": "F4", "customer": "N", "cost": 776.0 }, { "facility": "F4", "customer": "O", "cost": 671.0 }, { "facility": "F4", "customer": "P", "cost": 1418.0 }, { "facility": "F4", "customer": "Q", "cost": 55.0 }, { "facility": "F4", "customer": "R", "cost": 185.0 }, { "facility": "F5", "customer": "A", "cost": 445.0 }, { "facility": "F5", "customer": "B", "cost": 491.0 }, { "facility": "F5", "customer": "C", "cost": 34.0 }, { "facility": "F5", "customer": "D", "cost": 37.0 }, { "facility": "F5", "customer": "E", "cost": 1084.0 }, { "facility": "F5", "customer": "F", "cost": 979.0 }, { "facility": "F5", "customer": "G", "cost": 421.0 }, { "facility": "F5", "customer": "H", "cost": 48.0 }, { "facility": "F5", "customer": "I", "cost": 317.0 }, { "facility": "F5", "customer": "J", "cost": 887.0 }, { "facility": "F5", "customer": "K", "cost": 354.0 }, { "facility": "F5", "customer": "L", "cost": 77.0 }, { "facility": "F5", "customer": "M", "cost": 103.0 }, { "facility": "F5", "customer": "N", "cost": 274.0 }, { "facility": "F5", "customer": "O", "cost": 68.0 }, { "facility": "F5", "customer": "P", "cost": 503.0 }, { "facility": "F5", "customer": "Q", "cost": 380.0 }, { "facility": "F5", "customer": "R", "cost": 1088.0 }, { "facility": "F6", "customer": "A", "cost": 281.0 }, { "facility": "F6", "customer": "B", "cost": 385.0 }, { "facility": "F6", "customer": "C", "cost": 181.0 }, { "facility": "F6", "customer": "D", "cost": 51.0 }, { "facility": "F6", "customer": "E", "cost": 791.0 }, { "facility": "F6", "customer": "F", "cost": 608.0 }, { "facility": "F6", "customer": "G", "cost": 193.0 }, { "facility": "F6", "customer": "H", "cost": 91.0 }, { "facility": "F6", "customer": "I", "cost": 219.0 }, { "facility": "F6", "customer": "J", "cost": 535.0 }, { "facility": "F6", "customer": "K", "cost": 188.0 }, { "facility": "F6", "customer": "L", "cost": 27.0 }, { "facility": "F6", "customer": "M", "cost": 242.0 }, { "facility": "F6", "customer": "N", "cost": 48.0 }, { "facility": "F6", "customer": "O", "cost": 49.0 }, { "facility": "F6", "customer": "P", "cost": 325.0 }, { "facility": "F6", "customer": "Q", "cost": 224.0 }, { "facility": "F6", "customer": "R", "cost": 808.0 }, { "facility": "F7", "customer": "A", "cost": 277.0 }, { "facility": "F7", "customer": "B", "cost": 615.0 }, { "facility": "F7", "customer": "C", "cost": 260.0 }, { "facility": "F7", "customer": "D", "cost": 56.0 }, { "facility": "F7", "customer": "E", "cost": 820.0 }, { "facility": "F7", "customer": "F", "cost": 763.0 }, { "facility": "F7", "customer": "G", "cost": 196.0 }, { "facility": "F7", "customer": "H", "cost": 104.0 }, { "facility": "F7", "customer": "I", "cost": 213.0 }, { "facility": "F7", "customer": "J", "cost": 609.0 }, { "facility": "F7", "customer": "K", "cost": 184.0 }, { "facility": "F7", "customer": "L", "cost": 26.0 }, { "facility": "F7", "customer": "M", "cost": 388.0 }, { "facility": "F7", "customer": "N", "cost": 42.0 }, { "facility": "F7", "customer": "O", "cost": 67.0 }, { "facility": "F7", "customer": "P", "cost": 564.0 }, { "facility": "F7", "customer": "Q", "cost": 220.0 }, { "facility": "F7", "customer": "R", "cost": 831.0 }, { "facility": "F8", "customer": "A", "cost": 329.0 }, { "facility": "F8", "customer": "B", "cost": 699.0 }, { "facility": "F8", "customer": "C", "cost": 228.0 }, { "facility": "F8", "customer": "D", "cost": 47.0 }, { "facility": "F8", "customer": "E", "cost": 930.0 }, { "facility": "F8", "customer": "F", "cost": 928.0 }, { "facility": "F8", "customer": "G", "cost": 274.0 }, { "facility": "F8", "customer": "H", "cost": 85.0 }, { "facility": "F8", "customer": "I", "cost": 241.0 }, { "facility": "F8", "customer": "J", "cost": 757.0 }, { "facility": "F8", "customer": "K", "cost": 234.0 }, { "facility": "F8", "customer": "L", "cost": 30.0 }, { "facility": "F8", "customer": "M", "cost": 398.0 }, { "facility": "F8", "customer": "N", "cost": 121.0 }, { "facility": "F8", "customer": "O", "cost": 43.0 }, { "facility": "F8", "customer": "P", "cost": 662.0 }, { "facility": "F8", "customer": "Q", "cost": 267.0 }, { "facility": "F8", "customer": "R", "cost": 935.0 } ], "objective": 3913.0 }, "solution_variant": { "selected": [ "F1", "F6" ], "assignments": [ "F1", "F6", "F6", "F6", "F1", "F6", "F1", "F6", "F1", "F1", "F1", "F6", "F6", "F6", "F6", "F6", "F1", "F1" ] }, "context_index": 20, "input_format": "json", "input_index_base": "names" }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Recently the team mapped out options for neighborhood meal centers: which ones to bring online and which households each should handle. Bringing a center online requires paying its activation cost, and every center can only cover a fixed amount of demand. Serving a household from a particular center also costs something (distance, time, etc.). Every household must be assigned to exactly one active center—no splitting across centers—and no active center can exceed its service limit. The best plan keeps the total cost (activation costs plus all delivery costs) as low as possible; that total is just the sum of the centers’ activation fees that are used plus all the household delivery costs. The specific numbers appear below.\n\nThere are 7 centers and 19 households in this instance.\n\n**Centers**\n| center_id | activation_cost | center_capacity |\n|---|---|---|\n| F1 | 400.0 | 700.0 |\n| F2 | 400.0 | 700.0 |\n| F3 | 400.0 | 700.0 |\n| F4 | 400.0 | 700.0 |\n| F5 | 400.0 | 700.0 |\n| F6 | 400.0 | 700.0 |\n| F7 | 400.0 | 700.0 |\n\n**Households**\n| household_id | household_demand |\n|---|---|\n| 1 | 28.0 |\n| 2 | 18.0 |\n| 3 | 28.0 |\n| 4 | 12.0 |\n| 5 | 13.0 |\n| 6 | 24.0 |\n| 7 | 15.0 |\n| 8 | 20.0 |\n| 9 | 12.0 |\n| 10 | 22.0 |\n| 11 | 10.0 |\n| 12 | 23.0 |\n| 13 | 13.0 |\n| 14 | 28.0 |\n| 15 | 16.0 |\n| 16 | 19.0 |\n| 17 | 27.0 |\n| 18 | 23.0 |\n| 19 | 27.0 |\n\n**Delivery Cost**\n| center_id | household_id | delivery_cost |\n|---|---|---|\n| F1 | 1 | 196.0 |\n| F1 | 2 | 39.0 |\n| F1 | 3 | 262.0 |\n| F1 | 4 | 328.0 |\n| F1 | 5 | 97.0 |\n| F1 | 6 | 63.0 |\n| F1 | 7 | 31.0 |\n| F1 | 8 | 634.0 |\n| F1 | 9 | 25.0 |\n| F1 | 10 | 1088.0 |\n| F1 | 11 | 938.0 |\n| F1 | 12 | 65.0 |\n| F1 | 13 | 1023.0 |\n| F1 | 14 | 459.0 |\n| F1 | 15 | 235.0 |\n| F1 | 16 | 116.0 |\n| F1 | 17 | 788.0 |\n| F1 | 18 | 54.0 |\n| F1 | 19 | 461.0 |\n| F2 | 1 | 140.0 |\n| F2 | 2 | 213.0 |\n| F2 | 3 | 1118.0 |\n| F2 | 4 | 333.0 |\n| F2 | 5 | 1000.0 |\n| F2 | 6 | 366.0 |\n| F2 | 7 | 339.0 |\n| F2 | 8 | 92.0 |\n| F2 | 9 | 253.0 |\n| F2 | 10 | 360.0 |\n| F2 | 11 | 206.0 |\n| F2 | 12 | 584.0 |\n| F2 | 13 | 293.0 |\n| F2 | 14 | 342.0 |\n| F2 | 15 | 373.0 |\n| F2 | 16 | 229.0 |\n| F2 | 17 | 54.0 |\n| F2 | 18 | 1118.0 |\n| F2 | 19 | 479.0 |\n| F3 | 1 | 109.0 |\n| F3 | 2 | 57.0 |\n| F3 | 3 | 108.0 |\n| F3 | 4 | 139.0 |\n| F3 | 5 | 242.0 |\n| F3 | 6 | 102.0 |\n| F3 | 7 | 43.0 |\n| F3 | 8 | 413.0 |\n| F3 | 9 | 32.0 |\n| F3 | 10 | 840.0 |\n| F3 | 11 | 706.0 |\n| F3 | 12 | 129.0 |\n| F3 | 13 | 778.0 |\n| F3 | 14 | 243.0 |\n| F3 | 15 | 85.0 |\n| F3 | 16 | 51.0 |\n| F3 | 17 | 555.0 |\n| F3 | 18 | 214.0 |\n| F3 | 19 | 225.0 |\n| F4 | 1 | 57.0 |\n| F4 | 2 | 113.0 |\n| F4 | 3 | 837.0 |\n| F4 | 4 | 24.0 |\n| F4 | 5 | 697.0 |\n| F4 | 6 | 210.0 |\n| F4 | 7 | 147.0 |\n| F4 | 8 | 332.0 |\n| F4 | 9 | 102.0 |\n| F4 | 10 | 796.0 |\n| F4 | 11 | 637.0 |\n| F4 | 12 | 343.0 |\n| F4 | 13 | 729.0 |\n| F4 | 14 | 174.0 |\n| F4 | 15 | 75.0 |\n| F4 | 16 | 57.0 |\n| F4 | 17 | 491.0 |\n| F4 | 18 | 810.0 |\n| F4 | 19 | 273.0 |\n| F5 | 1 | 451.0 |\n| F5 | 2 | 36.0 |\n| F5 | 3 | 1334.0 |\n| F5 | 4 | 924.0 |\n| F5 | 5 | 727.0 |\n| F5 | 6 | 49.0 |\n| F5 | 7 | 101.0 |\n| F5 | 8 | 1160.0 |\n| F5 | 9 | 66.0 |\n| F5 | 10 | 1609.0 |\n| F5 | 11 | 1423.0 |\n| F5 | 12 | 85.0 |\n| F5 | 13 | 1542.0 |\n| F5 | 14 | 1071.0 |\n| F5 | 15 | 801.0 |\n| F5 | 16 | 385.0 |\n| F5 | 17 | 1316.0 |\n| F5 | 18 | 1081.0 |\n| F5 | 19 | 1153.0 |\n| F6 | 1 | 320.0 |\n| F6 | 2 | 37.0 |\n| F6 | 3 | 684.0 |\n| F6 | 4 | 584.0 |\n| F6 | 5 | 26.0 |\n| F6 | 6 | 48.0 |\n| F6 | 7 | 60.0 |\n| F6 | 8 | 886.0 |\n| F6 | 9 | 49.0 |\n| F6 | 10 | 1352.0 |\n| F6 | 11 | 1186.0 |\n| F6 | 12 | 46.0 |\n| F6 | 13 | 1286.0 |\n| F6 | 14 | 729.0 |\n| F6 | 15 | 466.0 |\n| F6 | 16 | 231.0 |\n| F6 | 17 | 1047.0 |\n| F6 | 18 | 363.0 |\n| F6 | 19 | 760.0 |\n| F7 | 1 | 141.0 |\n| F7 | 2 | 56.0 |\n| F7 | 3 | 644.0 |\n| F7 | 4 | 304.0 |\n| F7 | 5 | 399.0 |\n| F7 | 6 | 104.0 |\n| F7 | 7 | 42.0 |\n| F7 | 8 | 610.0 |\n| F7 | 9 | 30.0 |\n| F7 | 10 | 1075.0 |\n| F7 | 11 | 913.0 |\n| F7 | 12 | 149.0 |\n| F7 | 13 | 1009.0 |\n| F7 | 14 | 449.0 |\n| F7 | 15 | 192.0 |\n| F7 | 16 | 67.0 |\n| F7 | 17 | 770.0 |\n| F7 | 18 | 524.0 |\n| F7 | 19 | 483.0 |\n\nAlso, when you send back the actual plan, please use this JSON layout so everything lines up cleanly:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is the list of centers you decide to bring online (use the exact IDs from the instance). \"assignments\" is a list, one entry per household in the same order as the input, giving the open center that will serve that household. Think of it like a simple form — this block just shows the shape I need, not the final answers.\n\nPlease make sure to use the identifiers exactly as they appear in the instance input — do not rename them or invent new labels. For example:\n- Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 196.0, 39.0, 262.0, 328.0, 97.0, 63.0, 31.0, 634.0, 25.0, 1088.0, 938.0, 65.0, 1023.0, 459.0, 235.0, 116.0, 788.0, 54.0, 461.0 ], [ 140.0, 213.0, 1118.0, 333.0, 1000.0, 366.0, 339.0, 92.0, 253.0, 360.0, 206.0, 584.0, 293.0, 342.0, 373.0, 229.0, 54.0, 1118.0, 479.0 ], [ 109.0, 57.0, 108.0, 139.0, 242.0, 102.0, 43.0, 413.0, 32.0, 840.0, 706.0, 129.0, 778.0, 243.0, 85.0, 51.0, 555.0, 214.0, 225.0 ], [ 57.0, 113.0, 837.0, 24.0, 697.0, 210.0, 147.0, 332.0, 102.0, 796.0, 637.0, 343.0, 729.0, 174.0, 75.0, 57.0, 491.0, 810.0, 273.0 ], [ 451.0, 36.0, 1334.0, 924.0, 727.0, 49.0, 101.0, 1160.0, 66.0, 1609.0, 1423.0, 85.0, 1542.0, 1071.0, 801.0, 385.0, 1316.0, 1081.0, 1153.0 ], [ 320.0, 37.0, 684.0, 584.0, 26.0, 48.0, 60.0, 886.0, 49.0, 1352.0, 1186.0, 46.0, 1286.0, 729.0, 466.0, 231.0, 1047.0, 363.0, 760.0 ], [ 141.0, 56.0, 644.0, 304.0, 399.0, 104.0, 42.0, 610.0, 30.0, 1075.0, 913.0, 149.0, 1009.0, 449.0, 192.0, 67.0, 770.0, 524.0, 483.0 ] ], "demands": [ 28.0, 18.0, 28.0, 12.0, 13.0, 24.0, 15.0, 20.0, 12.0, 22.0, 10.0, 23.0, 13.0, 28.0, 16.0, 19.0, 27.0, 23.0, 27.0 ], "objective": 3501.0 }, "solution": { "open_facilities": [ 0, 1, 3 ], "assignments": [ 3, 0, 0, 3, 0, 0, 0, 1, 0, 1, 1, 0, 1, 3, 3, 3, 1, 0, 3 ] }, "obj": 3501.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 19, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 700.0 }, { "id": "F7", "opening_cost": 400.0, "capacity": 700.0 } ], "customers": [ { "id": 1, "demand": 28.0 }, { "id": 2, "demand": 18.0 }, { "id": 3, "demand": 28.0 }, { "id": 4, "demand": 12.0 }, { "id": 5, "demand": 13.0 }, { "id": 6, "demand": 24.0 }, { "id": 7, "demand": 15.0 }, { "id": 8, "demand": 20.0 }, { "id": 9, "demand": 12.0 }, { "id": 10, "demand": 22.0 }, { "id": 11, "demand": 10.0 }, { "id": 12, "demand": 23.0 }, { "id": 13, "demand": 13.0 }, { "id": 14, "demand": 28.0 }, { "id": 15, "demand": 16.0 }, { "id": 16, "demand": 19.0 }, { "id": 17, "demand": 27.0 }, { "id": 18, "demand": 23.0 }, { "id": 19, "demand": 27.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 196.0 }, { "facility": "F1", "customer": 2, "cost": 39.0 }, { "facility": "F1", "customer": 3, "cost": 262.0 }, { "facility": "F1", "customer": 4, "cost": 328.0 }, { "facility": "F1", "customer": 5, "cost": 97.0 }, { "facility": "F1", "customer": 6, "cost": 63.0 }, { "facility": "F1", "customer": 7, "cost": 31.0 }, { "facility": "F1", "customer": 8, "cost": 634.0 }, { "facility": "F1", "customer": 9, "cost": 25.0 }, { "facility": "F1", "customer": 10, "cost": 1088.0 }, { "facility": "F1", "customer": 11, "cost": 938.0 }, { "facility": "F1", "customer": 12, "cost": 65.0 }, { "facility": "F1", "customer": 13, "cost": 1023.0 }, { "facility": "F1", "customer": 14, "cost": 459.0 }, { "facility": "F1", "customer": 15, "cost": 235.0 }, { "facility": "F1", "customer": 16, "cost": 116.0 }, { "facility": "F1", "customer": 17, "cost": 788.0 }, { "facility": "F1", "customer": 18, "cost": 54.0 }, { "facility": "F1", "customer": 19, "cost": 461.0 }, { "facility": "F2", "customer": 1, "cost": 140.0 }, { "facility": "F2", "customer": 2, "cost": 213.0 }, { "facility": "F2", "customer": 3, "cost": 1118.0 }, { "facility": "F2", "customer": 4, "cost": 333.0 }, { "facility": "F2", "customer": 5, "cost": 1000.0 }, { "facility": "F2", "customer": 6, "cost": 366.0 }, { "facility": "F2", "customer": 7, "cost": 339.0 }, { "facility": "F2", "customer": 8, "cost": 92.0 }, { "facility": "F2", "customer": 9, "cost": 253.0 }, { "facility": "F2", "customer": 10, "cost": 360.0 }, { "facility": "F2", "customer": 11, "cost": 206.0 }, { "facility": "F2", "customer": 12, "cost": 584.0 }, { "facility": "F2", "customer": 13, "cost": 293.0 }, { "facility": "F2", "customer": 14, "cost": 342.0 }, { "facility": "F2", "customer": 15, "cost": 373.0 }, { "facility": "F2", "customer": 16, "cost": 229.0 }, { "facility": "F2", "customer": 17, "cost": 54.0 }, { "facility": "F2", "customer": 18, "cost": 1118.0 }, { "facility": "F2", "customer": 19, "cost": 479.0 }, { "facility": "F3", "customer": 1, "cost": 109.0 }, { "facility": "F3", "customer": 2, "cost": 57.0 }, { "facility": "F3", "customer": 3, "cost": 108.0 }, { "facility": "F3", "customer": 4, "cost": 139.0 }, { "facility": "F3", "customer": 5, "cost": 242.0 }, { "facility": "F3", "customer": 6, "cost": 102.0 }, { "facility": "F3", "customer": 7, "cost": 43.0 }, { "facility": "F3", "customer": 8, "cost": 413.0 }, { "facility": "F3", "customer": 9, "cost": 32.0 }, { "facility": "F3", "customer": 10, "cost": 840.0 }, { "facility": "F3", "customer": 11, "cost": 706.0 }, { "facility": "F3", "customer": 12, "cost": 129.0 }, { "facility": "F3", "customer": 13, "cost": 778.0 }, { "facility": "F3", "customer": 14, "cost": 243.0 }, { "facility": "F3", "customer": 15, "cost": 85.0 }, { "facility": "F3", "customer": 16, "cost": 51.0 }, { "facility": "F3", "customer": 17, "cost": 555.0 }, { "facility": "F3", "customer": 18, "cost": 214.0 }, { "facility": "F3", "customer": 19, "cost": 225.0 }, { "facility": "F4", "customer": 1, "cost": 57.0 }, { "facility": "F4", "customer": 2, "cost": 113.0 }, { "facility": "F4", "customer": 3, "cost": 837.0 }, { "facility": "F4", "customer": 4, "cost": 24.0 }, { "facility": "F4", "customer": 5, "cost": 697.0 }, { "facility": "F4", "customer": 6, "cost": 210.0 }, { "facility": "F4", "customer": 7, "cost": 147.0 }, { "facility": "F4", "customer": 8, "cost": 332.0 }, { "facility": "F4", "customer": 9, "cost": 102.0 }, { "facility": "F4", "customer": 10, "cost": 796.0 }, { "facility": "F4", "customer": 11, "cost": 637.0 }, { "facility": "F4", "customer": 12, "cost": 343.0 }, { "facility": "F4", "customer": 13, "cost": 729.0 }, { "facility": "F4", "customer": 14, "cost": 174.0 }, { "facility": "F4", "customer": 15, "cost": 75.0 }, { "facility": "F4", "customer": 16, "cost": 57.0 }, { "facility": "F4", "customer": 17, "cost": 491.0 }, { "facility": "F4", "customer": 18, "cost": 810.0 }, { "facility": "F4", "customer": 19, "cost": 273.0 }, { "facility": "F5", "customer": 1, "cost": 451.0 }, { "facility": "F5", "customer": 2, "cost": 36.0 }, { "facility": "F5", "customer": 3, "cost": 1334.0 }, { "facility": "F5", "customer": 4, "cost": 924.0 }, { "facility": "F5", "customer": 5, "cost": 727.0 }, { "facility": "F5", "customer": 6, "cost": 49.0 }, { "facility": "F5", "customer": 7, "cost": 101.0 }, { "facility": "F5", "customer": 8, "cost": 1160.0 }, { "facility": "F5", "customer": 9, "cost": 66.0 }, { "facility": "F5", "customer": 10, "cost": 1609.0 }, { "facility": "F5", "customer": 11, "cost": 1423.0 }, { "facility": "F5", "customer": 12, "cost": 85.0 }, { "facility": "F5", "customer": 13, "cost": 1542.0 }, { "facility": "F5", "customer": 14, "cost": 1071.0 }, { "facility": "F5", "customer": 15, "cost": 801.0 }, { "facility": "F5", "customer": 16, "cost": 385.0 }, { "facility": "F5", "customer": 17, "cost": 1316.0 }, { "facility": "F5", "customer": 18, "cost": 1081.0 }, { "facility": "F5", "customer": 19, "cost": 1153.0 }, { "facility": "F6", "customer": 1, "cost": 320.0 }, { "facility": "F6", "customer": 2, "cost": 37.0 }, { "facility": "F6", "customer": 3, "cost": 684.0 }, { "facility": "F6", "customer": 4, "cost": 584.0 }, { "facility": "F6", "customer": 5, "cost": 26.0 }, { "facility": "F6", "customer": 6, "cost": 48.0 }, { "facility": "F6", "customer": 7, "cost": 60.0 }, { "facility": "F6", "customer": 8, "cost": 886.0 }, { "facility": "F6", "customer": 9, "cost": 49.0 }, { "facility": "F6", "customer": 10, "cost": 1352.0 }, { "facility": "F6", "customer": 11, "cost": 1186.0 }, { "facility": "F6", "customer": 12, "cost": 46.0 }, { "facility": "F6", "customer": 13, "cost": 1286.0 }, { "facility": "F6", "customer": 14, "cost": 729.0 }, { "facility": "F6", "customer": 15, "cost": 466.0 }, { "facility": "F6", "customer": 16, "cost": 231.0 }, { "facility": "F6", "customer": 17, "cost": 1047.0 }, { "facility": "F6", "customer": 18, "cost": 363.0 }, { "facility": "F6", "customer": 19, "cost": 760.0 }, { "facility": "F7", "customer": 1, "cost": 141.0 }, { "facility": "F7", "customer": 2, "cost": 56.0 }, { "facility": "F7", "customer": 3, "cost": 644.0 }, { "facility": "F7", "customer": 4, "cost": 304.0 }, { "facility": "F7", "customer": 5, "cost": 399.0 }, { "facility": "F7", "customer": 6, "cost": 104.0 }, { "facility": "F7", "customer": 7, "cost": 42.0 }, { "facility": "F7", "customer": 8, "cost": 610.0 }, { "facility": "F7", "customer": 9, "cost": 30.0 }, { "facility": "F7", "customer": 10, "cost": 1075.0 }, { "facility": "F7", "customer": 11, "cost": 913.0 }, { "facility": "F7", "customer": 12, "cost": 149.0 }, { "facility": "F7", "customer": 13, "cost": 1009.0 }, { "facility": "F7", "customer": 14, "cost": 449.0 }, { "facility": "F7", "customer": 15, "cost": 192.0 }, { "facility": "F7", "customer": 16, "cost": 67.0 }, { "facility": "F7", "customer": 17, "cost": 770.0 }, { "facility": "F7", "customer": 18, "cost": 524.0 }, { "facility": "F7", "customer": 19, "cost": 483.0 } ], "objective": 3501.0 }, "solution_variant": { "selected": [ "F1", "F2", "F4" ], "assignments": [ "F4", "F1", "F1", "F4", "F1", "F1", "F1", "F2", "F1", "F2", "F2", "F1", "F2", "F4", "F4", "F4", "F2", "F1", "F4" ] }, "context_index": 21, "input_format": "markdown_table", "input_index_base": 1 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Recently the festival team was working out where to install temporary water stations and how to route attendees, with the rule that each attendee must go to one installed station and stations can’t handle more people than their limit. Each station has a fee to set up and people have different walking distances depending on where they’re sent. The idea is to pick stations and assignments so the combined cost — setup fees plus total walking distance — is as low as possible. The actual station choices, capacities, fees, and attendee numbers will be shown below.\n\nThere are 8 stations and 19 attendee groups in this instance.\n\n**Stations**\n| station_id | setup_fee | max_capacity |\n|---|---|---|\n| F1 | 128.0 | 314.0 |\n| F2 | 296.0 | 504.0 |\n| F3 | 225.0 | 504.0 |\n| F4 | 310.0 | 580.0 |\n| F5 | 329.0 | 456.0 |\n| F6 | 179.0 | 549.0 |\n| F7 | 114.0 | 310.0 |\n| F8 | 321.0 | 316.0 |\n\n**Attendee Groups**\n| attendee_group_id | group_size |\n|---|---|\n| 0 | 17.0 |\n| 1 | 31.0 |\n| 2 | 39.0 |\n| 3 | 45.0 |\n| 4 | 38.0 |\n| 5 | 26.0 |\n| 6 | 20.0 |\n| 7 | 13.0 |\n| 8 | 27.0 |\n| 9 | 42.0 |\n| 10 | 31.0 |\n| 11 | 45.0 |\n| 12 | 20.0 |\n| 13 | 38.0 |\n| 14 | 21.0 |\n| 15 | 13.0 |\n| 16 | 21.0 |\n| 17 | 37.0 |\n| 18 | 17.0 |\n\n**Walking Distance Cost**\n| station_id | attendee_group_id | walking_distance_cost |\n|---|---|---|\n| F1 | 0 | 522.0 |\n| F1 | 1 | 652.0 |\n| F1 | 2 | 242.0 |\n| F1 | 3 | 401.0 |\n| F1 | 4 | 155.0 |\n| F1 | 5 | 195.0 |\n| F1 | 6 | 426.0 |\n| F1 | 7 | 107.0 |\n| F1 | 8 | 387.0 |\n| F1 | 9 | 234.0 |\n| F1 | 10 | 495.0 |\n| F1 | 11 | 612.0 |\n| F1 | 12 | 239.0 |\n| F1 | 13 | 392.0 |\n| F1 | 14 | 507.0 |\n| F1 | 15 | 459.0 |\n| F1 | 16 | 463.0 |\n| F1 | 17 | 467.0 |\n| F1 | 18 | 574.0 |\n| F2 | 0 | 348.0 |\n| F2 | 1 | 504.0 |\n| F2 | 2 | 262.0 |\n| F2 | 3 | 310.0 |\n| F2 | 4 | 249.0 |\n| F2 | 5 | 337.0 |\n| F2 | 6 | 288.0 |\n| F2 | 7 | 284.0 |\n| F2 | 8 | 140.0 |\n| F2 | 9 | 215.0 |\n| F2 | 10 | 192.0 |\n| F2 | 11 | 267.0 |\n| F2 | 12 | 403.0 |\n| F2 | 13 | 244.0 |\n| F2 | 14 | 162.0 |\n| F2 | 15 | 270.0 |\n| F2 | 16 | 400.0 |\n| F2 | 17 | 156.0 |\n| F2 | 18 | 248.0 |\n| F3 | 0 | 336.0 |\n| F3 | 1 | 451.0 |\n| F3 | 2 | 59.0 |\n| F3 | 3 | 205.0 |\n| F3 | 4 | 84.0 |\n| F3 | 5 | 367.0 |\n| F3 | 6 | 241.0 |\n| F3 | 7 | 261.0 |\n| F3 | 8 | 414.0 |\n| F3 | 9 | 94.0 |\n| F3 | 10 | 496.0 |\n| F3 | 11 | 541.0 |\n| F3 | 12 | 97.0 |\n| F3 | 13 | 218.0 |\n| F3 | 14 | 456.0 |\n| F3 | 15 | 286.0 |\n| F3 | 16 | 258.0 |\n| F3 | 17 | 461.0 |\n| F3 | 18 | 466.0 |\n| F4 | 0 | 441.0 |\n| F4 | 1 | 576.0 |\n| F4 | 2 | 484.0 |\n| F4 | 3 | 474.0 |\n| F4 | 4 | 487.0 |\n| F4 | 5 | 532.0 |\n| F4 | 6 | 432.0 |\n| F4 | 7 | 508.0 |\n| F4 | 8 | 235.0 |\n| F4 | 9 | 442.0 |\n| F4 | 10 | 138.0 |\n| F4 | 11 | 72.0 |\n| F4 | 12 | 631.0 |\n| F4 | 13 | 402.0 |\n| F4 | 14 | 80.0 |\n| F4 | 15 | 385.0 |\n| F4 | 16 | 552.0 |\n| F4 | 17 | 141.0 |\n| F4 | 18 | 179.0 |\n| F5 | 0 | 691.0 |\n| F5 | 1 | 847.0 |\n| F5 | 2 | 523.0 |\n| F5 | 3 | 632.0 |\n| F5 | 4 | 451.0 |\n| F5 | 5 | 237.0 |\n| F5 | 6 | 622.0 |\n| F5 | 7 | 309.0 |\n| F5 | 8 | 222.0 |\n| F5 | 9 | 479.0 |\n| F5 | 10 | 293.0 |\n| F5 | 11 | 498.0 |\n| F5 | 12 | 614.0 |\n| F5 | 13 | 576.0 |\n| F5 | 14 | 401.0 |\n| F5 | 15 | 612.0 |\n| F5 | 16 | 720.0 |\n| F5 | 17 | 297.0 |\n| F5 | 18 | 551.0 |\n| F6 | 0 | 490.0 |\n| F6 | 1 | 587.0 |\n| F6 | 2 | 622.0 |\n| F6 | 3 | 567.0 |\n| F6 | 4 | 646.0 |\n| F6 | 5 | 724.0 |\n| F6 | 6 | 518.0 |\n| F6 | 7 | 693.0 |\n| F6 | 8 | 428.0 |\n| F6 | 9 | 586.0 |\n| F6 | 10 | 328.0 |\n| F6 | 11 | 147.0 |\n| F6 | 12 | 770.0 |\n| F6 | 13 | 501.0 |\n| F6 | 14 | 256.0 |\n| F6 | 15 | 460.0 |\n| F6 | 16 | 627.0 |\n| F6 | 17 | 334.0 |\n| F6 | 18 | 223.0 |\n| F7 | 0 | 14.0 |\n| F7 | 1 | 155.0 |\n| F7 | 2 | 296.0 |\n| F7 | 3 | 148.0 |\n| F7 | 4 | 378.0 |\n| F7 | 5 | 630.0 |\n| F7 | 6 | 108.0 |\n| F7 | 7 | 539.0 |\n| F7 | 8 | 485.0 |\n| F7 | 9 | 299.0 |\n| F7 | 10 | 492.0 |\n| F7 | 11 | 392.0 |\n| F7 | 12 | 401.0 |\n| F7 | 13 | 142.0 |\n| F7 | 14 | 380.0 |\n| F7 | 15 | 83.0 |\n| F7 | 16 | 161.0 |\n| F7 | 17 | 460.0 |\n| F7 | 18 | 269.0 |\n| F8 | 0 | 628.0 |\n| F8 | 1 | 774.0 |\n| F8 | 2 | 585.0 |\n| F8 | 3 | 626.0 |\n| F8 | 4 | 553.0 |\n| F8 | 5 | 474.0 |\n| F8 | 6 | 595.0 |\n| F8 | 7 | 496.0 |\n| F8 | 8 | 213.0 |\n| F8 | 9 | 537.0 |\n| F8 | 10 | 137.0 |\n| F8 | 11 | 289.0 |\n| F8 | 12 | 718.0 |\n| F8 | 13 | 555.0 |\n| F8 | 14 | 245.0 |\n| F8 | 15 | 559.0 |\n| F8 | 16 | 713.0 |\n| F8 | 17 | 172.0 |\n| F8 | 18 | 392.0 |\n\nIf you want to submit a candidate solution, just stick to this little JSON shape so it's easy to parse — here’s the informal template I’ll expect:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nPretty simple: \"selected\" is where you say which water stations you plan to set up, and \"assignments\" says, for each attendee in the input order, which opened station they should go to. This is just a sketch of the shape I need, not the actual answer.\n\nPlease make sure you use the exact identifiers from the instance input — do not rename them or invent new labels. Valid identifiers look like plain numbers such as \"1\" or \"23\", single capital letters like \"A\" or \"B\", or a capital letter followed by digits like \"A1\" or \"X7\".", "instance": { "opening_costs": [ 128.0, 296.0, 225.0, 310.0, 329.0, 179.0, 114.0, 321.0 ], "capacities": [ 314.0, 504.0, 504.0, 580.0, 456.0, 549.0, 310.0, 316.0 ], "connection_costs": [ [ 522.0, 652.0, 242.0, 401.0, 155.0, 195.0, 426.0, 107.0, 387.0, 234.0, 495.0, 612.0, 239.0, 392.0, 507.0, 459.0, 463.0, 467.0, 574.0 ], [ 348.0, 504.0, 262.0, 310.0, 249.0, 337.0, 288.0, 284.0, 140.0, 215.0, 192.0, 267.0, 403.0, 244.0, 162.0, 270.0, 400.0, 156.0, 248.0 ], [ 336.0, 451.0, 59.0, 205.0, 84.0, 367.0, 241.0, 261.0, 414.0, 94.0, 496.0, 541.0, 97.0, 218.0, 456.0, 286.0, 258.0, 461.0, 466.0 ], [ 441.0, 576.0, 484.0, 474.0, 487.0, 532.0, 432.0, 508.0, 235.0, 442.0, 138.0, 72.0, 631.0, 402.0, 80.0, 385.0, 552.0, 141.0, 179.0 ], [ 691.0, 847.0, 523.0, 632.0, 451.0, 237.0, 622.0, 309.0, 222.0, 479.0, 293.0, 498.0, 614.0, 576.0, 401.0, 612.0, 720.0, 297.0, 551.0 ], [ 490.0, 587.0, 622.0, 567.0, 646.0, 724.0, 518.0, 693.0, 428.0, 586.0, 328.0, 147.0, 770.0, 501.0, 256.0, 460.0, 627.0, 334.0, 223.0 ], [ 14.0, 155.0, 296.0, 148.0, 378.0, 630.0, 108.0, 539.0, 485.0, 299.0, 492.0, 392.0, 401.0, 142.0, 380.0, 83.0, 161.0, 460.0, 269.0 ], [ 628.0, 774.0, 585.0, 626.0, 553.0, 474.0, 595.0, 496.0, 213.0, 537.0, 137.0, 289.0, 718.0, 555.0, 245.0, 559.0, 713.0, 172.0, 392.0 ] ], "demands": [ 17.0, 31.0, 39.0, 45.0, 38.0, 26.0, 20.0, 13.0, 27.0, 42.0, 31.0, 45.0, 20.0, 38.0, 21.0, 13.0, 21.0, 37.0, 17.0 ], "objective": 3069.0 }, "solution": { "open_facilities": [ 0, 2, 3, 6 ], "assignments": [ 6, 6, 2, 6, 2, 0, 6, 0, 3, 2, 3, 3, 2, 6, 3, 6, 6, 3, 3 ] }, "obj": 3069.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 19, "facilities": [ { "id": "F1", "opening_cost": 128.0, "capacity": 314.0 }, { "id": "F2", "opening_cost": 296.0, "capacity": 504.0 }, { "id": "F3", "opening_cost": 225.0, "capacity": 504.0 }, { "id": "F4", "opening_cost": 310.0, "capacity": 580.0 }, { "id": "F5", "opening_cost": 329.0, "capacity": 456.0 }, { "id": "F6", "opening_cost": 179.0, "capacity": 549.0 }, { "id": "F7", "opening_cost": 114.0, "capacity": 310.0 }, { "id": "F8", "opening_cost": 321.0, "capacity": 316.0 } ], "customers": [ { "id": 0, "demand": 17.0 }, { "id": 1, "demand": 31.0 }, { "id": 2, "demand": 39.0 }, { "id": 3, "demand": 45.0 }, { "id": 4, "demand": 38.0 }, { "id": 5, "demand": 26.0 }, { "id": 6, "demand": 20.0 }, { "id": 7, "demand": 13.0 }, { "id": 8, "demand": 27.0 }, { "id": 9, "demand": 42.0 }, { "id": 10, "demand": 31.0 }, { "id": 11, "demand": 45.0 }, { "id": 12, "demand": 20.0 }, { "id": 13, "demand": 38.0 }, { "id": 14, "demand": 21.0 }, { "id": 15, "demand": 13.0 }, { "id": 16, "demand": 21.0 }, { "id": 17, "demand": 37.0 }, { "id": 18, "demand": 17.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 522.0 }, { "facility": "F1", "customer": 1, "cost": 652.0 }, { "facility": "F1", "customer": 2, "cost": 242.0 }, { "facility": "F1", "customer": 3, "cost": 401.0 }, { "facility": "F1", "customer": 4, "cost": 155.0 }, { "facility": "F1", "customer": 5, "cost": 195.0 }, { "facility": "F1", "customer": 6, "cost": 426.0 }, { "facility": "F1", "customer": 7, "cost": 107.0 }, { "facility": "F1", "customer": 8, "cost": 387.0 }, { "facility": "F1", "customer": 9, "cost": 234.0 }, { "facility": "F1", "customer": 10, "cost": 495.0 }, { "facility": "F1", "customer": 11, "cost": 612.0 }, { "facility": "F1", "customer": 12, "cost": 239.0 }, { "facility": "F1", "customer": 13, "cost": 392.0 }, { "facility": "F1", "customer": 14, "cost": 507.0 }, { "facility": "F1", "customer": 15, "cost": 459.0 }, { "facility": "F1", "customer": 16, "cost": 463.0 }, { "facility": "F1", "customer": 17, "cost": 467.0 }, { "facility": "F1", "customer": 18, "cost": 574.0 }, { "facility": "F2", "customer": 0, "cost": 348.0 }, { "facility": "F2", "customer": 1, "cost": 504.0 }, { "facility": "F2", "customer": 2, "cost": 262.0 }, { "facility": "F2", "customer": 3, "cost": 310.0 }, { "facility": "F2", "customer": 4, "cost": 249.0 }, { "facility": "F2", "customer": 5, "cost": 337.0 }, { "facility": "F2", "customer": 6, "cost": 288.0 }, { "facility": "F2", "customer": 7, "cost": 284.0 }, { "facility": "F2", "customer": 8, "cost": 140.0 }, { "facility": "F2", "customer": 9, "cost": 215.0 }, { "facility": "F2", "customer": 10, "cost": 192.0 }, { "facility": "F2", "customer": 11, "cost": 267.0 }, { "facility": "F2", "customer": 12, "cost": 403.0 }, { "facility": "F2", "customer": 13, "cost": 244.0 }, { "facility": "F2", "customer": 14, "cost": 162.0 }, { "facility": "F2", "customer": 15, "cost": 270.0 }, { "facility": "F2", "customer": 16, "cost": 400.0 }, { "facility": "F2", "customer": 17, "cost": 156.0 }, { "facility": "F2", "customer": 18, "cost": 248.0 }, { "facility": "F3", "customer": 0, "cost": 336.0 }, { "facility": "F3", "customer": 1, "cost": 451.0 }, { "facility": "F3", "customer": 2, "cost": 59.0 }, { "facility": "F3", "customer": 3, "cost": 205.0 }, { "facility": "F3", "customer": 4, "cost": 84.0 }, { "facility": "F3", "customer": 5, "cost": 367.0 }, { "facility": "F3", "customer": 6, "cost": 241.0 }, { "facility": "F3", "customer": 7, "cost": 261.0 }, { "facility": "F3", "customer": 8, "cost": 414.0 }, { "facility": "F3", "customer": 9, "cost": 94.0 }, { "facility": "F3", "customer": 10, "cost": 496.0 }, { "facility": "F3", "customer": 11, "cost": 541.0 }, { "facility": "F3", "customer": 12, "cost": 97.0 }, { "facility": "F3", "customer": 13, "cost": 218.0 }, { "facility": "F3", "customer": 14, "cost": 456.0 }, { "facility": "F3", "customer": 15, "cost": 286.0 }, { "facility": "F3", "customer": 16, "cost": 258.0 }, { "facility": "F3", "customer": 17, "cost": 461.0 }, { "facility": "F3", "customer": 18, "cost": 466.0 }, { "facility": "F4", "customer": 0, "cost": 441.0 }, { "facility": "F4", "customer": 1, "cost": 576.0 }, { "facility": "F4", "customer": 2, "cost": 484.0 }, { "facility": "F4", "customer": 3, "cost": 474.0 }, { "facility": "F4", "customer": 4, "cost": 487.0 }, { "facility": "F4", "customer": 5, "cost": 532.0 }, { "facility": "F4", "customer": 6, "cost": 432.0 }, { "facility": "F4", "customer": 7, "cost": 508.0 }, { "facility": "F4", "customer": 8, "cost": 235.0 }, { "facility": "F4", "customer": 9, "cost": 442.0 }, { "facility": "F4", "customer": 10, "cost": 138.0 }, { "facility": "F4", "customer": 11, "cost": 72.0 }, { "facility": "F4", "customer": 12, "cost": 631.0 }, { "facility": "F4", "customer": 13, "cost": 402.0 }, { "facility": "F4", "customer": 14, "cost": 80.0 }, { "facility": "F4", "customer": 15, "cost": 385.0 }, { "facility": "F4", "customer": 16, "cost": 552.0 }, { "facility": "F4", "customer": 17, "cost": 141.0 }, { "facility": "F4", "customer": 18, "cost": 179.0 }, { "facility": "F5", "customer": 0, "cost": 691.0 }, { "facility": "F5", "customer": 1, "cost": 847.0 }, { "facility": "F5", "customer": 2, "cost": 523.0 }, { "facility": "F5", "customer": 3, "cost": 632.0 }, { "facility": "F5", "customer": 4, "cost": 451.0 }, { "facility": "F5", "customer": 5, "cost": 237.0 }, { "facility": "F5", "customer": 6, "cost": 622.0 }, { "facility": "F5", "customer": 7, "cost": 309.0 }, { "facility": "F5", "customer": 8, "cost": 222.0 }, { "facility": "F5", "customer": 9, "cost": 479.0 }, { "facility": "F5", "customer": 10, "cost": 293.0 }, { "facility": "F5", "customer": 11, "cost": 498.0 }, { "facility": "F5", "customer": 12, "cost": 614.0 }, { "facility": "F5", "customer": 13, "cost": 576.0 }, { "facility": "F5", "customer": 14, "cost": 401.0 }, { "facility": "F5", "customer": 15, "cost": 612.0 }, { "facility": "F5", "customer": 16, "cost": 720.0 }, { "facility": "F5", "customer": 17, "cost": 297.0 }, { "facility": "F5", "customer": 18, "cost": 551.0 }, { "facility": "F6", "customer": 0, "cost": 490.0 }, { "facility": "F6", "customer": 1, "cost": 587.0 }, { "facility": "F6", "customer": 2, "cost": 622.0 }, { "facility": "F6", "customer": 3, "cost": 567.0 }, { "facility": "F6", "customer": 4, "cost": 646.0 }, { "facility": "F6", "customer": 5, "cost": 724.0 }, { "facility": "F6", "customer": 6, "cost": 518.0 }, { "facility": "F6", "customer": 7, "cost": 693.0 }, { "facility": "F6", "customer": 8, "cost": 428.0 }, { "facility": "F6", "customer": 9, "cost": 586.0 }, { "facility": "F6", "customer": 10, "cost": 328.0 }, { "facility": "F6", "customer": 11, "cost": 147.0 }, { "facility": "F6", "customer": 12, "cost": 770.0 }, { "facility": "F6", "customer": 13, "cost": 501.0 }, { "facility": "F6", "customer": 14, "cost": 256.0 }, { "facility": "F6", "customer": 15, "cost": 460.0 }, { "facility": "F6", "customer": 16, "cost": 627.0 }, { "facility": "F6", "customer": 17, "cost": 334.0 }, { "facility": "F6", "customer": 18, "cost": 223.0 }, { "facility": "F7", "customer": 0, "cost": 14.0 }, { "facility": "F7", "customer": 1, "cost": 155.0 }, { "facility": "F7", "customer": 2, "cost": 296.0 }, { "facility": "F7", "customer": 3, "cost": 148.0 }, { "facility": "F7", "customer": 4, "cost": 378.0 }, { "facility": "F7", "customer": 5, "cost": 630.0 }, { "facility": "F7", "customer": 6, "cost": 108.0 }, { "facility": "F7", "customer": 7, "cost": 539.0 }, { "facility": "F7", "customer": 8, "cost": 485.0 }, { "facility": "F7", "customer": 9, "cost": 299.0 }, { "facility": "F7", "customer": 10, "cost": 492.0 }, { "facility": "F7", "customer": 11, "cost": 392.0 }, { "facility": "F7", "customer": 12, "cost": 401.0 }, { "facility": "F7", "customer": 13, "cost": 142.0 }, { "facility": "F7", "customer": 14, "cost": 380.0 }, { "facility": "F7", "customer": 15, "cost": 83.0 }, { "facility": "F7", "customer": 16, "cost": 161.0 }, { "facility": "F7", "customer": 17, "cost": 460.0 }, { "facility": "F7", "customer": 18, "cost": 269.0 }, { "facility": "F8", "customer": 0, "cost": 628.0 }, { "facility": "F8", "customer": 1, "cost": 774.0 }, { "facility": "F8", "customer": 2, "cost": 585.0 }, { "facility": "F8", "customer": 3, "cost": 626.0 }, { "facility": "F8", "customer": 4, "cost": 553.0 }, { "facility": "F8", "customer": 5, "cost": 474.0 }, { "facility": "F8", "customer": 6, "cost": 595.0 }, { "facility": "F8", "customer": 7, "cost": 496.0 }, { "facility": "F8", "customer": 8, "cost": 213.0 }, { "facility": "F8", "customer": 9, "cost": 537.0 }, { "facility": "F8", "customer": 10, "cost": 137.0 }, { "facility": "F8", "customer": 11, "cost": 289.0 }, { "facility": "F8", "customer": 12, "cost": 718.0 }, { "facility": "F8", "customer": 13, "cost": 555.0 }, { "facility": "F8", "customer": 14, "cost": 245.0 }, { "facility": "F8", "customer": 15, "cost": 559.0 }, { "facility": "F8", "customer": 16, "cost": 713.0 }, { "facility": "F8", "customer": 17, "cost": 172.0 }, { "facility": "F8", "customer": 18, "cost": 392.0 } ], "objective": 3069.0 }, "solution_variant": { "selected": [ "F1", "F3", "F4", "F7" ], "assignments": [ "F7", "F7", "F3", "F7", "F3", "F1", "F7", "F1", "F4", "F3", "F4", "F4", "F3", "F7", "F4", "F7", "F7", "F4", "F4" ] }, "context_index": 22, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "We’re juggling dorm space for the upcoming semester and have to choose which wings to bring online and where each student should live. The task is to open some wings (each has an opening price and a fixed number of beds) and then assign every student to a single opened wing without exceeding those beds. Better choices are the ones that minimize what we pay overall: add up all wing-opening expenses and the distance or hassle cost for every student move — that total is what we want as small as possible. Concrete details will be shown below.\n\nThere are 8 wings and 19 students in this instance.\n\n**Wings**\n| wing_id | wing_opening_cost | wing_bed_capacity |\n|---|---|---|\n| F1 | 300.0 | 500.0 |\n| F2 | 300.0 | 500.0 |\n| F3 | 300.0 | 500.0 |\n| F4 | 300.0 | 500.0 |\n| F5 | 300.0 | 500.0 |\n| F6 | 300.0 | 500.0 |\n| F7 | 300.0 | 500.0 |\n| F8 | 300.0 | 500.0 |\n\n**Students**\n| student_id | student_bed_requirement |\n|---|---|\n| 0 | 24.0 |\n| 1 | 11.0 |\n| 2 | 12.0 |\n| 3 | 18.0 |\n| 4 | 13.0 |\n| 5 | 14.0 |\n| 6 | 19.0 |\n| 7 | 22.0 |\n| 8 | 30.0 |\n| 9 | 24.0 |\n| 10 | 26.0 |\n| 11 | 24.0 |\n| 12 | 12.0 |\n| 13 | 23.0 |\n| 14 | 16.0 |\n| 15 | 19.0 |\n| 16 | 14.0 |\n| 17 | 17.0 |\n| 18 | 22.0 |\n\n**Relocation Distance Cost**\n| wing_id | student_id | relocation_distance_cost |\n|---|---|---|\n| F1 | 0 | 218.0 |\n| F1 | 1 | 183.0 |\n| F1 | 2 | 24.0 |\n| F1 | 3 | 46.0 |\n| F1 | 4 | 44.0 |\n| F1 | 5 | 145.0 |\n| F1 | 6 | 248.0 |\n| F1 | 7 | 157.0 |\n| F1 | 8 | 248.0 |\n| F1 | 9 | 339.0 |\n| F1 | 10 | 283.0 |\n| F1 | 11 | 49.0 |\n| F1 | 12 | 57.0 |\n| F1 | 13 | 98.0 |\n| F1 | 14 | 81.0 |\n| F1 | 15 | 142.0 |\n| F1 | 16 | 28.0 |\n| F1 | 17 | 304.0 |\n| F1 | 18 | 554.0 |\n| F2 | 0 | 369.0 |\n| F2 | 1 | 333.0 |\n| F2 | 2 | 83.0 |\n| F2 | 3 | 161.0 |\n| F2 | 4 | 85.0 |\n| F2 | 5 | 558.0 |\n| F2 | 6 | 72.0 |\n| F2 | 7 | 64.0 |\n| F2 | 8 | 430.0 |\n| F2 | 9 | 547.0 |\n| F2 | 10 | 542.0 |\n| F2 | 11 | 153.0 |\n| F2 | 12 | 88.0 |\n| F2 | 13 | 342.0 |\n| F2 | 14 | 102.0 |\n| F2 | 15 | 274.0 |\n| F2 | 16 | 61.0 |\n| F2 | 17 | 131.0 |\n| F2 | 18 | 872.0 |\n| F3 | 0 | 60.0 |\n| F3 | 1 | 40.0 |\n| F3 | 2 | 626.0 |\n| F3 | 3 | 607.0 |\n| F3 | 4 | 1187.0 |\n| F3 | 5 | 1297.0 |\n| F3 | 6 | 1491.0 |\n| F3 | 7 | 881.0 |\n| F3 | 8 | 125.0 |\n| F3 | 9 | 48.0 |\n| F3 | 10 | 456.0 |\n| F3 | 11 | 825.0 |\n| F3 | 12 | 1334.0 |\n| F3 | 13 | 900.0 |\n| F3 | 14 | 1453.0 |\n| F3 | 15 | 105.0 |\n| F3 | 16 | 403.0 |\n| F3 | 17 | 1357.0 |\n| F3 | 18 | 604.0 |\n| F4 | 0 | 713.0 |\n| F4 | 1 | 690.0 |\n| F4 | 2 | 1110.0 |\n| F4 | 3 | 1169.0 |\n| F4 | 4 | 1716.0 |\n| F4 | 5 | 2037.0 |\n| F4 | 6 | 1904.0 |\n| F4 | 7 | 1166.0 |\n| F4 | 8 | 913.0 |\n| F4 | 9 | 986.0 |\n| F4 | 10 | 1309.0 |\n| F4 | 11 | 1381.0 |\n| F4 | 12 | 1869.0 |\n| F4 | 13 | 1588.0 |\n| F4 | 14 | 1989.0 |\n| F4 | 15 | 683.0 |\n| F4 | 16 | 769.0 |\n| F4 | 17 | 1683.0 |\n| F4 | 18 | 1542.0 |\n| F5 | 0 | 266.0 |\n| F5 | 1 | 231.0 |\n| F5 | 2 | 30.0 |\n| F5 | 3 | 70.0 |\n| F5 | 4 | 27.0 |\n| F5 | 5 | 290.0 |\n| F5 | 6 | 210.0 |\n| F5 | 7 | 127.0 |\n| F5 | 8 | 307.0 |\n| F5 | 9 | 411.0 |\n| F5 | 10 | 372.0 |\n| F5 | 11 | 63.0 |\n| F5 | 12 | 31.0 |\n| F5 | 13 | 165.0 |\n| F5 | 14 | 48.0 |\n| F5 | 15 | 182.0 |\n| F5 | 16 | 31.0 |\n| F5 | 17 | 266.0 |\n| F5 | 18 | 675.0 |\n| F6 | 0 | 643.0 |\n| F6 | 1 | 610.0 |\n| F6 | 2 | 466.0 |\n| F6 | 3 | 602.0 |\n| F6 | 4 | 831.0 |\n| F6 | 5 | 1389.0 |\n| F6 | 6 | 796.0 |\n| F6 | 7 | 154.0 |\n| F6 | 8 | 768.0 |\n| F6 | 9 | 894.0 |\n| F6 | 10 | 1024.0 |\n| F6 | 11 | 688.0 |\n| F6 | 12 | 946.0 |\n| F6 | 13 | 992.0 |\n| F6 | 14 | 1043.0 |\n| F6 | 15 | 546.0 |\n| F6 | 16 | 277.0 |\n| F6 | 17 | 497.0 |\n| F6 | 18 | 1363.0 |\n| F7 | 0 | 313.0 |\n| F7 | 1 | 277.0 |\n| F7 | 2 | 39.0 |\n| F7 | 3 | 104.0 |\n| F7 | 4 | 26.0 |\n| F7 | 5 | 612.0 |\n| F7 | 6 | 388.0 |\n| F7 | 7 | 145.0 |\n| F7 | 8 | 371.0 |\n| F7 | 9 | 487.0 |\n| F7 | 10 | 489.0 |\n| F7 | 11 | 94.0 |\n| F7 | 12 | 180.0 |\n| F7 | 13 | 305.0 |\n| F7 | 14 | 301.0 |\n| F7 | 15 | 220.0 |\n| F7 | 16 | 34.0 |\n| F7 | 17 | 377.0 |\n| F7 | 18 | 826.0 |\n| F8 | 0 | 364.0 |\n| F8 | 1 | 329.0 |\n| F8 | 2 | 73.0 |\n| F8 | 3 | 165.0 |\n| F8 | 4 | 192.0 |\n| F8 | 5 | 770.0 |\n| F8 | 6 | 398.0 |\n| F8 | 7 | 114.0 |\n| F8 | 8 | 435.0 |\n| F8 | 9 | 557.0 |\n| F8 | 10 | 583.0 |\n| F8 | 11 | 169.0 |\n| F8 | 12 | 317.0 |\n| F8 | 13 | 429.0 |\n| F8 | 14 | 429.0 |\n| F8 | 15 | 267.0 |\n| F8 | 16 | 49.0 |\n| F8 | 17 | 352.0 |\n| F8 | 18 | 927.0 |\n\nOne more small thing: when you send the solution back, please use this little JSON shape so I can read it automatically — just a list of the wings you open and a list that says, for each student in the input order, which opened wing they’ll live in.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you put the identifiers for the wings you decide to open. \"assignments\" lists, in the same order as the students showed up in the input, which opened wing each student gets assigned to. Super informal: think of \"selected\" as the checkboxes for which wings we flip on, and \"assignments\" like the roommate list showing everyone's wing.\n\nThis JSON is just a sketch of the shape I need — not the real answer itself. Please make sure to use the exact identifiers from the instance input (don’t rename them or invent new labels). Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 218.0, 183.0, 24.0, 46.0, 44.0, 145.0, 248.0, 157.0, 248.0, 339.0, 283.0, 49.0, 57.0, 98.0, 81.0, 142.0, 28.0, 304.0, 554.0 ], [ 369.0, 333.0, 83.0, 161.0, 85.0, 558.0, 72.0, 64.0, 430.0, 547.0, 542.0, 153.0, 88.0, 342.0, 102.0, 274.0, 61.0, 131.0, 872.0 ], [ 60.0, 40.0, 626.0, 607.0, 1187.0, 1297.0, 1491.0, 881.0, 125.0, 48.0, 456.0, 825.0, 1334.0, 900.0, 1453.0, 105.0, 403.0, 1357.0, 604.0 ], [ 713.0, 690.0, 1110.0, 1169.0, 1716.0, 2037.0, 1904.0, 1166.0, 913.0, 986.0, 1309.0, 1381.0, 1869.0, 1588.0, 1989.0, 683.0, 769.0, 1683.0, 1542.0 ], [ 266.0, 231.0, 30.0, 70.0, 27.0, 290.0, 210.0, 127.0, 307.0, 411.0, 372.0, 63.0, 31.0, 165.0, 48.0, 182.0, 31.0, 266.0, 675.0 ], [ 643.0, 610.0, 466.0, 602.0, 831.0, 1389.0, 796.0, 154.0, 768.0, 894.0, 1024.0, 688.0, 946.0, 992.0, 1043.0, 546.0, 277.0, 497.0, 1363.0 ], [ 313.0, 277.0, 39.0, 104.0, 26.0, 612.0, 388.0, 145.0, 371.0, 487.0, 489.0, 94.0, 180.0, 305.0, 301.0, 220.0, 34.0, 377.0, 826.0 ], [ 364.0, 329.0, 73.0, 165.0, 192.0, 770.0, 398.0, 114.0, 435.0, 557.0, 583.0, 169.0, 317.0, 429.0, 429.0, 267.0, 49.0, 352.0, 927.0 ] ], "demands": [ 24.0, 11.0, 12.0, 18.0, 13.0, 14.0, 19.0, 22.0, 30.0, 24.0, 26.0, 24.0, 12.0, 23.0, 16.0, 19.0, 14.0, 17.0, 22.0 ], "objective": 2954.0 }, "solution": { "open_facilities": [ 0, 1, 2 ], "assignments": [ 2, 2, 0, 0, 0, 0, 1, 1, 2, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0 ] }, "obj": 2954.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 19, "facilities": [ { "id": "F1", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F2", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F3", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F4", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F5", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F6", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F7", "opening_cost": 300.0, "capacity": 500.0 }, { "id": "F8", "opening_cost": 300.0, "capacity": 500.0 } ], "customers": [ { "id": 0, "demand": 24.0 }, { "id": 1, "demand": 11.0 }, { "id": 2, "demand": 12.0 }, { "id": 3, "demand": 18.0 }, { "id": 4, "demand": 13.0 }, { "id": 5, "demand": 14.0 }, { "id": 6, "demand": 19.0 }, { "id": 7, "demand": 22.0 }, { "id": 8, "demand": 30.0 }, { "id": 9, "demand": 24.0 }, { "id": 10, "demand": 26.0 }, { "id": 11, "demand": 24.0 }, { "id": 12, "demand": 12.0 }, { "id": 13, "demand": 23.0 }, { "id": 14, "demand": 16.0 }, { "id": 15, "demand": 19.0 }, { "id": 16, "demand": 14.0 }, { "id": 17, "demand": 17.0 }, { "id": 18, "demand": 22.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 218.0 }, { "facility": "F1", "customer": 1, "cost": 183.0 }, { "facility": "F1", "customer": 2, "cost": 24.0 }, { "facility": "F1", "customer": 3, "cost": 46.0 }, { "facility": "F1", "customer": 4, "cost": 44.0 }, { "facility": "F1", "customer": 5, "cost": 145.0 }, { "facility": "F1", "customer": 6, "cost": 248.0 }, { "facility": "F1", "customer": 7, "cost": 157.0 }, { "facility": "F1", "customer": 8, "cost": 248.0 }, { "facility": "F1", "customer": 9, "cost": 339.0 }, { "facility": "F1", "customer": 10, "cost": 283.0 }, { "facility": "F1", "customer": 11, "cost": 49.0 }, { "facility": "F1", "customer": 12, "cost": 57.0 }, { "facility": "F1", "customer": 13, "cost": 98.0 }, { "facility": "F1", "customer": 14, "cost": 81.0 }, { "facility": "F1", "customer": 15, "cost": 142.0 }, { "facility": "F1", "customer": 16, "cost": 28.0 }, { "facility": "F1", "customer": 17, "cost": 304.0 }, { "facility": "F1", "customer": 18, "cost": 554.0 }, { "facility": "F2", "customer": 0, "cost": 369.0 }, { "facility": "F2", "customer": 1, "cost": 333.0 }, { "facility": "F2", "customer": 2, "cost": 83.0 }, { "facility": "F2", "customer": 3, "cost": 161.0 }, { "facility": "F2", "customer": 4, "cost": 85.0 }, { "facility": "F2", "customer": 5, "cost": 558.0 }, { "facility": "F2", "customer": 6, "cost": 72.0 }, { "facility": "F2", "customer": 7, "cost": 64.0 }, { "facility": "F2", "customer": 8, "cost": 430.0 }, { "facility": "F2", "customer": 9, "cost": 547.0 }, { "facility": "F2", "customer": 10, "cost": 542.0 }, { "facility": "F2", "customer": 11, "cost": 153.0 }, { "facility": "F2", "customer": 12, "cost": 88.0 }, { "facility": "F2", "customer": 13, "cost": 342.0 }, { "facility": "F2", "customer": 14, "cost": 102.0 }, { "facility": "F2", "customer": 15, "cost": 274.0 }, { "facility": "F2", "customer": 16, "cost": 61.0 }, { "facility": "F2", "customer": 17, "cost": 131.0 }, { "facility": "F2", "customer": 18, "cost": 872.0 }, { "facility": "F3", "customer": 0, "cost": 60.0 }, { "facility": "F3", "customer": 1, "cost": 40.0 }, { "facility": "F3", "customer": 2, "cost": 626.0 }, { "facility": "F3", "customer": 3, "cost": 607.0 }, { "facility": "F3", "customer": 4, "cost": 1187.0 }, { "facility": "F3", "customer": 5, "cost": 1297.0 }, { "facility": "F3", "customer": 6, "cost": 1491.0 }, { "facility": "F3", "customer": 7, "cost": 881.0 }, { "facility": "F3", "customer": 8, "cost": 125.0 }, { "facility": "F3", "customer": 9, "cost": 48.0 }, { "facility": "F3", "customer": 10, "cost": 456.0 }, { "facility": "F3", "customer": 11, "cost": 825.0 }, { "facility": "F3", "customer": 12, "cost": 1334.0 }, { "facility": "F3", "customer": 13, "cost": 900.0 }, { "facility": "F3", "customer": 14, "cost": 1453.0 }, { "facility": "F3", "customer": 15, "cost": 105.0 }, { "facility": "F3", "customer": 16, "cost": 403.0 }, { "facility": "F3", "customer": 17, "cost": 1357.0 }, { "facility": "F3", "customer": 18, "cost": 604.0 }, { "facility": "F4", "customer": 0, "cost": 713.0 }, { "facility": "F4", "customer": 1, "cost": 690.0 }, { "facility": "F4", "customer": 2, "cost": 1110.0 }, { "facility": "F4", "customer": 3, "cost": 1169.0 }, { "facility": "F4", "customer": 4, "cost": 1716.0 }, { "facility": "F4", "customer": 5, "cost": 2037.0 }, { "facility": "F4", "customer": 6, "cost": 1904.0 }, { "facility": "F4", "customer": 7, "cost": 1166.0 }, { "facility": "F4", "customer": 8, "cost": 913.0 }, { "facility": "F4", "customer": 9, "cost": 986.0 }, { "facility": "F4", "customer": 10, "cost": 1309.0 }, { "facility": "F4", "customer": 11, "cost": 1381.0 }, { "facility": "F4", "customer": 12, "cost": 1869.0 }, { "facility": "F4", "customer": 13, "cost": 1588.0 }, { "facility": "F4", "customer": 14, "cost": 1989.0 }, { "facility": "F4", "customer": 15, "cost": 683.0 }, { "facility": "F4", "customer": 16, "cost": 769.0 }, { "facility": "F4", "customer": 17, "cost": 1683.0 }, { "facility": "F4", "customer": 18, "cost": 1542.0 }, { "facility": "F5", "customer": 0, "cost": 266.0 }, { "facility": "F5", "customer": 1, "cost": 231.0 }, { "facility": "F5", "customer": 2, "cost": 30.0 }, { "facility": "F5", "customer": 3, "cost": 70.0 }, { "facility": "F5", "customer": 4, "cost": 27.0 }, { "facility": "F5", "customer": 5, "cost": 290.0 }, { "facility": "F5", "customer": 6, "cost": 210.0 }, { "facility": "F5", "customer": 7, "cost": 127.0 }, { "facility": "F5", "customer": 8, "cost": 307.0 }, { "facility": "F5", "customer": 9, "cost": 411.0 }, { "facility": "F5", "customer": 10, "cost": 372.0 }, { "facility": "F5", "customer": 11, "cost": 63.0 }, { "facility": "F5", "customer": 12, "cost": 31.0 }, { "facility": "F5", "customer": 13, "cost": 165.0 }, { "facility": "F5", "customer": 14, "cost": 48.0 }, { "facility": "F5", "customer": 15, "cost": 182.0 }, { "facility": "F5", "customer": 16, "cost": 31.0 }, { "facility": "F5", "customer": 17, "cost": 266.0 }, { "facility": "F5", "customer": 18, "cost": 675.0 }, { "facility": "F6", "customer": 0, "cost": 643.0 }, { "facility": "F6", "customer": 1, "cost": 610.0 }, { "facility": "F6", "customer": 2, "cost": 466.0 }, { "facility": "F6", "customer": 3, "cost": 602.0 }, { "facility": "F6", "customer": 4, "cost": 831.0 }, { "facility": "F6", "customer": 5, "cost": 1389.0 }, { "facility": "F6", "customer": 6, "cost": 796.0 }, { "facility": "F6", "customer": 7, "cost": 154.0 }, { "facility": "F6", "customer": 8, "cost": 768.0 }, { "facility": "F6", "customer": 9, "cost": 894.0 }, { "facility": "F6", "customer": 10, "cost": 1024.0 }, { "facility": "F6", "customer": 11, "cost": 688.0 }, { "facility": "F6", "customer": 12, "cost": 946.0 }, { "facility": "F6", "customer": 13, "cost": 992.0 }, { "facility": "F6", "customer": 14, "cost": 1043.0 }, { "facility": "F6", "customer": 15, "cost": 546.0 }, { "facility": "F6", "customer": 16, "cost": 277.0 }, { "facility": "F6", "customer": 17, "cost": 497.0 }, { "facility": "F6", "customer": 18, "cost": 1363.0 }, { "facility": "F7", "customer": 0, "cost": 313.0 }, { "facility": "F7", "customer": 1, "cost": 277.0 }, { "facility": "F7", "customer": 2, "cost": 39.0 }, { "facility": "F7", "customer": 3, "cost": 104.0 }, { "facility": "F7", "customer": 4, "cost": 26.0 }, { "facility": "F7", "customer": 5, "cost": 612.0 }, { "facility": "F7", "customer": 6, "cost": 388.0 }, { "facility": "F7", "customer": 7, "cost": 145.0 }, { "facility": "F7", "customer": 8, "cost": 371.0 }, { "facility": "F7", "customer": 9, "cost": 487.0 }, { "facility": "F7", "customer": 10, "cost": 489.0 }, { "facility": "F7", "customer": 11, "cost": 94.0 }, { "facility": "F7", "customer": 12, "cost": 180.0 }, { "facility": "F7", "customer": 13, "cost": 305.0 }, { "facility": "F7", "customer": 14, "cost": 301.0 }, { "facility": "F7", "customer": 15, "cost": 220.0 }, { "facility": "F7", "customer": 16, "cost": 34.0 }, { "facility": "F7", "customer": 17, "cost": 377.0 }, { "facility": "F7", "customer": 18, "cost": 826.0 }, { "facility": "F8", "customer": 0, "cost": 364.0 }, { "facility": "F8", "customer": 1, "cost": 329.0 }, { "facility": "F8", "customer": 2, "cost": 73.0 }, { "facility": "F8", "customer": 3, "cost": 165.0 }, { "facility": "F8", "customer": 4, "cost": 192.0 }, { "facility": "F8", "customer": 5, "cost": 770.0 }, { "facility": "F8", "customer": 6, "cost": 398.0 }, { "facility": "F8", "customer": 7, "cost": 114.0 }, { "facility": "F8", "customer": 8, "cost": 435.0 }, { "facility": "F8", "customer": 9, "cost": 557.0 }, { "facility": "F8", "customer": 10, "cost": 583.0 }, { "facility": "F8", "customer": 11, "cost": 169.0 }, { "facility": "F8", "customer": 12, "cost": 317.0 }, { "facility": "F8", "customer": 13, "cost": 429.0 }, { "facility": "F8", "customer": 14, "cost": 429.0 }, { "facility": "F8", "customer": 15, "cost": 267.0 }, { "facility": "F8", "customer": 16, "cost": 49.0 }, { "facility": "F8", "customer": 17, "cost": 352.0 }, { "facility": "F8", "customer": 18, "cost": 927.0 } ], "objective": 2954.0 }, "solution_variant": { "selected": [ "F1", "F2", "F3" ], "assignments": [ "F3", "F3", "F1", "F1", "F1", "F1", "F2", "F2", "F3", "F3", "F1", "F1", "F1", "F1", "F1", "F3", "F1", "F2", "F1" ] }, "context_index": 23, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Recently the team had to map out which neighborhood lockers to activate and how to route customers: activating a locker incurs a fixed charge, each locker has a parcel limit, and customers can’t have their parcels split across multiple lockers — each customer goes to one active locker only. To pick the best setup, add up all activation charges for the lockers opened and all customer travel costs to their assigned lockers; the setup with the smallest total cost is preferable. The detailed list of lockers, capacities, costs and customers appears below.\n\n# num_lockers=8\n# num_customers=17\n# LOCKERS\nlocker_id,activation_cost,parcel_capacity\nF1,600.0,700.0\nF2,600.0,700.0\nF3,600.0,700.0\nF4,600.0,700.0\nF5,600.0,700.0\nF6,600.0,700.0\nF7,600.0,700.0\nF8,600.0,700.0\n# CUSTOMERS\ncustomer_id,parcels_needed\n0,28.0\n1,12.0\n2,21.0\n3,12.0\n4,30.0\n5,25.0\n6,12.0\n7,14.0\n8,30.0\n9,18.0\n10,26.0\n11,26.0\n12,10.0\n13,16.0\n14,22.0\n15,19.0\n16,19.0\n# TRAVELS\nlocker_id,customer_id,travel_cost\nF1,0,517.0\nF1,1,382.0\nF1,2,858.0\nF1,3,691.0\nF1,4,254.0\nF1,5,779.0\nF1,6,519.0\nF1,7,84.0\nF1,8,430.0\nF1,9,92.0\nF1,10,204.0\nF1,11,542.0\nF1,12,938.0\nF1,13,253.0\nF1,14,316.0\nF1,15,116.0\nF1,16,412.0\nF2,0,1126.0\nF2,1,133.0\nF2,2,715.0\nF2,3,705.0\nF2,4,60.0\nF2,5,1362.0\nF2,6,588.0\nF2,7,808.0\nF2,8,125.0\nF2,9,1525.0\nF2,10,1217.0\nF2,11,456.0\nF2,12,891.0\nF2,13,960.0\nF2,14,154.0\nF2,15,586.0\nF2,16,263.0\nF3,0,389.0\nF3,1,27.0\nF3,2,162.0\nF3,3,33.0\nF3,4,71.0\nF3,5,522.0\nF3,6,31.0\nF3,7,368.0\nF3,8,68.0\nF3,9,928.0\nF3,10,895.0\nF3,11,53.0\nF3,12,206.0\nF3,13,368.0\nF3,14,44.0\nF3,15,229.0\nF3,16,38.0\nF4,0,1268.0\nF4,1,736.0\nF4,2,1400.0\nF4,3,1264.0\nF4,4,405.0\nF4,5,1593.0\nF4,6,1059.0\nF4,7,567.0\nF4,8,768.0\nF4,9,1079.0\nF4,10,213.0\nF4,11,1024.0\nF4,12,1533.0\nF4,13,926.0\nF4,14,633.0\nF4,15,495.0\nF4,16,815.0\nF5,0,1168.0\nF5,1,636.0\nF5,2,1291.0\nF5,3,1154.0\nF5,4,344.0\nF5,5,1494.0\nF5,6,949.0\nF5,7,464.0\nF5,8,670.0\nF5,9,1041.0\nF5,10,383.0\nF5,11,915.0\nF5,12,1423.0\nF5,13,826.0\nF5,14,536.0\nF5,15,385.0\nF5,16,711.0\nF6,0,1199.0\nF6,1,493.0\nF6,2,1182.0\nF6,3,1066.0\nF6,4,228.0\nF6,5,1517.0\nF6,6,864.0\nF6,7,571.0\nF6,8,524.0\nF6,9,1309.0\nF6,10,836.0\nF6,11,804.0\nF6,12,1329.0\nF6,13,891.0\nF6,14,390.0\nF6,15,363.0\nF6,16,580.0\nF7,0,806.0\nF7,1,523.0\nF7,2,1084.0\nF7,3,923.0\nF7,4,317.0\nF7,5,1104.0\nF7,6,732.0\nF7,7,219.0\nF7,8,566.0\nF7,9,429.0\nF7,10,124.0\nF7,11,734.0\nF7,12,1186.0\nF7,13,489.0\nF7,14,439.0\nF7,15,231.0\nF7,16,570.0\nF8,0,1582.0\nF8,1,840.0\nF8,2,1557.0\nF8,3,1453.0\nF8,4,415.0\nF8,5,1904.0\nF8,6,1253.0\nF8,7,908.0\nF8,8,861.0\nF8,9,1586.0\nF8,10,866.0\nF8,11,1184.0\nF8,12,1711.0\nF8,13,1260.0\nF8,14,731.0\nF8,15,741.0\nF8,16,948.0\n\nIf you could, please return the final choice in this simple JSON shape so it's easy to parse — nothing fancy, just the two bits we need.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is the list of neighborhood lockers you activate (the ones you pay the fixed charge for). \"assignments\" is a customer-by-customer list (in the same order as the customers in the instance) saying which opened locker each customer will use. This is just the skeleton of the answer — fill in the actual identifiers from the instance when you submit the solution.\n\nPlease make sure to use the exact identifiers from the instance input — do not rename or invent labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 517.0, 382.0, 858.0, 691.0, 254.0, 779.0, 519.0, 84.0, 430.0, 92.0, 204.0, 542.0, 938.0, 253.0, 316.0, 116.0, 412.0 ], [ 1126.0, 133.0, 715.0, 705.0, 60.0, 1362.0, 588.0, 808.0, 125.0, 1525.0, 1217.0, 456.0, 891.0, 960.0, 154.0, 586.0, 263.0 ], [ 389.0, 27.0, 162.0, 33.0, 71.0, 522.0, 31.0, 368.0, 68.0, 928.0, 895.0, 53.0, 206.0, 368.0, 44.0, 229.0, 38.0 ], [ 1268.0, 736.0, 1400.0, 1264.0, 405.0, 1593.0, 1059.0, 567.0, 768.0, 1079.0, 213.0, 1024.0, 1533.0, 926.0, 633.0, 495.0, 815.0 ], [ 1168.0, 636.0, 1291.0, 1154.0, 344.0, 1494.0, 949.0, 464.0, 670.0, 1041.0, 383.0, 915.0, 1423.0, 826.0, 536.0, 385.0, 711.0 ], [ 1199.0, 493.0, 1182.0, 1066.0, 228.0, 1517.0, 864.0, 571.0, 524.0, 1309.0, 836.0, 804.0, 1329.0, 891.0, 390.0, 363.0, 580.0 ], [ 806.0, 523.0, 1084.0, 923.0, 317.0, 1104.0, 732.0, 219.0, 566.0, 429.0, 124.0, 734.0, 1186.0, 489.0, 439.0, 231.0, 570.0 ], [ 1582.0, 840.0, 1557.0, 1453.0, 415.0, 1904.0, 1253.0, 908.0, 861.0, 1586.0, 866.0, 1184.0, 1711.0, 1260.0, 731.0, 741.0, 948.0 ] ], "demands": [ 28.0, 12.0, 21.0, 12.0, 30.0, 25.0, 12.0, 14.0, 30.0, 18.0, 26.0, 26.0, 10.0, 16.0, 22.0, 19.0, 19.0 ], "objective": 3593.0 }, "solution": { "open_facilities": [ 0, 2 ], "assignments": [ 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2 ] }, "obj": 3593.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 17, "facilities": [ { "id": "F1", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F2", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F3", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F4", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F5", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F6", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F7", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F8", "opening_cost": 600.0, "capacity": 700.0 } ], "customers": [ { "id": 0, "demand": 28.0 }, { "id": 1, "demand": 12.0 }, { "id": 2, "demand": 21.0 }, { "id": 3, "demand": 12.0 }, { "id": 4, "demand": 30.0 }, { "id": 5, "demand": 25.0 }, { "id": 6, "demand": 12.0 }, { "id": 7, "demand": 14.0 }, { "id": 8, "demand": 30.0 }, { "id": 9, "demand": 18.0 }, { "id": 10, "demand": 26.0 }, { "id": 11, "demand": 26.0 }, { "id": 12, "demand": 10.0 }, { "id": 13, "demand": 16.0 }, { "id": 14, "demand": 22.0 }, { "id": 15, "demand": 19.0 }, { "id": 16, "demand": 19.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 517.0 }, { "facility": "F1", "customer": 1, "cost": 382.0 }, { "facility": "F1", "customer": 2, "cost": 858.0 }, { "facility": "F1", "customer": 3, "cost": 691.0 }, { "facility": "F1", "customer": 4, "cost": 254.0 }, { "facility": "F1", "customer": 5, "cost": 779.0 }, { "facility": "F1", "customer": 6, "cost": 519.0 }, { "facility": "F1", "customer": 7, "cost": 84.0 }, { "facility": "F1", "customer": 8, "cost": 430.0 }, { "facility": "F1", "customer": 9, "cost": 92.0 }, { "facility": "F1", "customer": 10, "cost": 204.0 }, { "facility": "F1", "customer": 11, "cost": 542.0 }, { "facility": "F1", "customer": 12, "cost": 938.0 }, { "facility": "F1", "customer": 13, "cost": 253.0 }, { "facility": "F1", "customer": 14, "cost": 316.0 }, { "facility": "F1", "customer": 15, "cost": 116.0 }, { "facility": "F1", "customer": 16, "cost": 412.0 }, { "facility": "F2", "customer": 0, "cost": 1126.0 }, { "facility": "F2", "customer": 1, "cost": 133.0 }, { "facility": "F2", "customer": 2, "cost": 715.0 }, { "facility": "F2", "customer": 3, "cost": 705.0 }, { "facility": "F2", "customer": 4, "cost": 60.0 }, { "facility": "F2", "customer": 5, "cost": 1362.0 }, { "facility": "F2", "customer": 6, "cost": 588.0 }, { "facility": "F2", "customer": 7, "cost": 808.0 }, { "facility": "F2", "customer": 8, "cost": 125.0 }, { "facility": "F2", "customer": 9, "cost": 1525.0 }, { "facility": "F2", "customer": 10, "cost": 1217.0 }, { "facility": "F2", "customer": 11, "cost": 456.0 }, { "facility": "F2", "customer": 12, "cost": 891.0 }, { "facility": "F2", "customer": 13, "cost": 960.0 }, { "facility": "F2", "customer": 14, "cost": 154.0 }, { "facility": "F2", "customer": 15, "cost": 586.0 }, { "facility": "F2", "customer": 16, "cost": 263.0 }, { "facility": "F3", "customer": 0, "cost": 389.0 }, { "facility": "F3", "customer": 1, "cost": 27.0 }, { "facility": "F3", "customer": 2, "cost": 162.0 }, { "facility": "F3", "customer": 3, "cost": 33.0 }, { "facility": "F3", "customer": 4, "cost": 71.0 }, { "facility": "F3", "customer": 5, "cost": 522.0 }, { "facility": "F3", "customer": 6, "cost": 31.0 }, { "facility": "F3", "customer": 7, "cost": 368.0 }, { "facility": "F3", "customer": 8, "cost": 68.0 }, { "facility": "F3", "customer": 9, "cost": 928.0 }, { "facility": "F3", "customer": 10, "cost": 895.0 }, { "facility": "F3", "customer": 11, "cost": 53.0 }, { "facility": "F3", "customer": 12, "cost": 206.0 }, { "facility": "F3", "customer": 13, "cost": 368.0 }, { "facility": "F3", "customer": 14, "cost": 44.0 }, { "facility": "F3", "customer": 15, "cost": 229.0 }, { "facility": "F3", "customer": 16, "cost": 38.0 }, { "facility": "F4", "customer": 0, "cost": 1268.0 }, { "facility": "F4", "customer": 1, "cost": 736.0 }, { "facility": "F4", "customer": 2, "cost": 1400.0 }, { "facility": "F4", "customer": 3, "cost": 1264.0 }, { "facility": "F4", "customer": 4, "cost": 405.0 }, { "facility": "F4", "customer": 5, "cost": 1593.0 }, { "facility": "F4", "customer": 6, "cost": 1059.0 }, { "facility": "F4", "customer": 7, "cost": 567.0 }, { "facility": "F4", "customer": 8, "cost": 768.0 }, { "facility": "F4", "customer": 9, "cost": 1079.0 }, { "facility": "F4", "customer": 10, "cost": 213.0 }, { "facility": "F4", "customer": 11, "cost": 1024.0 }, { "facility": "F4", "customer": 12, "cost": 1533.0 }, { "facility": "F4", "customer": 13, "cost": 926.0 }, { "facility": "F4", "customer": 14, "cost": 633.0 }, { "facility": "F4", "customer": 15, "cost": 495.0 }, { "facility": "F4", "customer": 16, "cost": 815.0 }, { "facility": "F5", "customer": 0, "cost": 1168.0 }, { "facility": "F5", "customer": 1, "cost": 636.0 }, { "facility": "F5", "customer": 2, "cost": 1291.0 }, { "facility": "F5", "customer": 3, "cost": 1154.0 }, { "facility": "F5", "customer": 4, "cost": 344.0 }, { "facility": "F5", "customer": 5, "cost": 1494.0 }, { "facility": "F5", "customer": 6, "cost": 949.0 }, { "facility": "F5", "customer": 7, "cost": 464.0 }, { "facility": "F5", "customer": 8, "cost": 670.0 }, { "facility": "F5", "customer": 9, "cost": 1041.0 }, { "facility": "F5", "customer": 10, "cost": 383.0 }, { "facility": "F5", "customer": 11, "cost": 915.0 }, { "facility": "F5", "customer": 12, "cost": 1423.0 }, { "facility": "F5", "customer": 13, "cost": 826.0 }, { "facility": "F5", "customer": 14, "cost": 536.0 }, { "facility": "F5", "customer": 15, "cost": 385.0 }, { "facility": "F5", "customer": 16, "cost": 711.0 }, { "facility": "F6", "customer": 0, "cost": 1199.0 }, { "facility": "F6", "customer": 1, "cost": 493.0 }, { "facility": "F6", "customer": 2, "cost": 1182.0 }, { "facility": "F6", "customer": 3, "cost": 1066.0 }, { "facility": "F6", "customer": 4, "cost": 228.0 }, { "facility": "F6", "customer": 5, "cost": 1517.0 }, { "facility": "F6", "customer": 6, "cost": 864.0 }, { "facility": "F6", "customer": 7, "cost": 571.0 }, { "facility": "F6", "customer": 8, "cost": 524.0 }, { "facility": "F6", "customer": 9, "cost": 1309.0 }, { "facility": "F6", "customer": 10, "cost": 836.0 }, { "facility": "F6", "customer": 11, "cost": 804.0 }, { "facility": "F6", "customer": 12, "cost": 1329.0 }, { "facility": "F6", "customer": 13, "cost": 891.0 }, { "facility": "F6", "customer": 14, "cost": 390.0 }, { "facility": "F6", "customer": 15, "cost": 363.0 }, { "facility": "F6", "customer": 16, "cost": 580.0 }, { "facility": "F7", "customer": 0, "cost": 806.0 }, { "facility": "F7", "customer": 1, "cost": 523.0 }, { "facility": "F7", "customer": 2, "cost": 1084.0 }, { "facility": "F7", "customer": 3, "cost": 923.0 }, { "facility": "F7", "customer": 4, "cost": 317.0 }, { "facility": "F7", "customer": 5, "cost": 1104.0 }, { "facility": "F7", "customer": 6, "cost": 732.0 }, { "facility": "F7", "customer": 7, "cost": 219.0 }, { "facility": "F7", "customer": 8, "cost": 566.0 }, { "facility": "F7", "customer": 9, "cost": 429.0 }, { "facility": "F7", "customer": 10, "cost": 124.0 }, { "facility": "F7", "customer": 11, "cost": 734.0 }, { "facility": "F7", "customer": 12, "cost": 1186.0 }, { "facility": "F7", "customer": 13, "cost": 489.0 }, { "facility": "F7", "customer": 14, "cost": 439.0 }, { "facility": "F7", "customer": 15, "cost": 231.0 }, { "facility": "F7", "customer": 16, "cost": 570.0 }, { "facility": "F8", "customer": 0, "cost": 1582.0 }, { "facility": "F8", "customer": 1, "cost": 840.0 }, { "facility": "F8", "customer": 2, "cost": 1557.0 }, { "facility": "F8", "customer": 3, "cost": 1453.0 }, { "facility": "F8", "customer": 4, "cost": 415.0 }, { "facility": "F8", "customer": 5, "cost": 1904.0 }, { "facility": "F8", "customer": 6, "cost": 1253.0 }, { "facility": "F8", "customer": 7, "cost": 908.0 }, { "facility": "F8", "customer": 8, "cost": 861.0 }, { "facility": "F8", "customer": 9, "cost": 1586.0 }, { "facility": "F8", "customer": 10, "cost": 866.0 }, { "facility": "F8", "customer": 11, "cost": 1184.0 }, { "facility": "F8", "customer": 12, "cost": 1711.0 }, { "facility": "F8", "customer": 13, "cost": 1260.0 }, { "facility": "F8", "customer": 14, "cost": 731.0 }, { "facility": "F8", "customer": 15, "cost": 741.0 }, { "facility": "F8", "customer": 16, "cost": 948.0 } ], "objective": 3593.0 }, "solution_variant": { "selected": [ "F1", "F3" ], "assignments": [ "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F1", "F3", "F1", "F1", "F3", "F3", "F1", "F3", "F1", "F3" ] }, "context_index": 24, "input_format": "csv", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "We’re coordinating post-disaster sheltering and have to decide which temporary shelters to stand up and which families go where, making sure no household gets split and no shelter has more people than it can handle. Each potential shelter has a price to get it running and a limit on how many people it can take, and every family must be assigned to one of the shelters we open. The goal is to keep the overall expense as low as possible — just tally the opening costs for the shelters we choose plus the transport cost for each family’s move, and aim for the lowest total. The specific numbers and options are listed below.\n\n# num_shelters=9\n# num_families=18\n# SHELTERS\nshelter_id,shelter_setup_cost,shelter_capacity_people\nF1,258.0,366.0\nF2,128.0,314.0\nF3,296.0,504.0\nF4,225.0,504.0\nF5,310.0,580.0\nF6,373.0,415.0\nF7,329.0,456.0\nF8,179.0,549.0\nF9,321.0,316.0\n# FAMILYS\nfamily_id,household_size\n0,40.0\n1,18.0\n2,17.0\n3,13.0\n4,31.0\n5,23.0\n6,39.0\n7,43.0\n8,32.0\n9,28.0\n10,27.0\n11,22.0\n12,45.0\n13,25.0\n14,19.0\n15,42.0\n16,27.0\n17,17.0\n# TRANSPORTS\nshelter_id,family_id,transport_cost\nF1,0,557.0\nF1,1,346.0\nF1,2,161.0\nF1,3,568.0\nF1,4,392.0\nF1,5,344.0\nF1,6,143.0\nF1,7,654.0\nF1,8,524.0\nF1,9,318.0\nF1,10,458.0\nF1,11,758.0\nF1,12,475.0\nF1,13,303.0\nF1,14,362.0\nF1,15,519.0\nF1,16,72.0\nF1,17,370.0\nF2,0,386.0\nF2,1,180.0\nF2,2,522.0\nF2,3,636.0\nF2,4,28.0\nF2,5,712.0\nF2,6,242.0\nF2,7,812.0\nF2,8,284.0\nF2,9,80.0\nF2,10,387.0\nF2,11,516.0\nF2,12,612.0\nF2,13,145.0\nF2,14,104.0\nF2,15,286.0\nF2,16,349.0\nF2,17,574.0\nF3,0,258.0\nF3,1,455.0\nF3,2,348.0\nF3,3,302.0\nF3,4,329.0\nF3,5,502.0\nF3,6,262.0\nF3,7,466.0\nF3,8,274.0\nF3,9,345.0\nF3,10,140.0\nF3,11,467.0\nF3,12,267.0\nF3,13,202.0\nF3,14,411.0\nF3,15,267.0\nF3,16,356.0\nF3,17,248.0\nF4,0,474.0\nF4,1,179.0\nF4,2,336.0\nF4,3,603.0\nF4,4,219.0\nF4,5,525.0\nF4,6,59.0\nF4,7,738.0\nF4,8,409.0\nF4,9,135.0\nF4,10,414.0\nF4,11,653.0\nF4,12,541.0\nF4,13,174.0\nF4,14,180.0\nF4,15,406.0\nF4,16,142.0\nF4,17,466.0\nF5,0,349.0\nF5,1,694.0\nF5,2,441.0\nF5,3,73.0\nF5,4,564.0\nF5,5,519.0\nF5,6,484.0\nF5,7,237.0\nF5,8,432.0\nF5,9,586.0\nF5,10,235.0\nF5,11,524.0\nF5,12,72.0\nF5,13,441.0\nF5,14,651.0\nF5,15,424.0\nF5,16,550.0\nF5,17,179.0\nF6,0,228.0\nF6,1,365.0\nF6,2,598.0\nF6,3,548.0\nF6,4,157.0\nF6,5,779.0\nF6,6,357.0\nF6,7,748.0\nF6,8,113.0\nF6,9,255.0\nF6,10,281.0\nF6,11,332.0\nF6,12,559.0\nF6,13,190.0\nF6,14,288.0\nF6,15,118.0\nF6,16,480.0\nF6,17,560.0\nF7,0,90.0\nF7,1,593.0\nF7,2,691.0\nF7,3,436.0\nF7,4,387.0\nF7,5,846.0\nF7,6,523.0\nF7,7,648.0\nF7,8,132.0\nF7,9,476.0\nF7,10,222.0\nF7,11,124.0\nF7,12,498.0\nF7,13,361.0\nF7,14,519.0\nF7,15,132.0\nF7,16,644.0\nF7,17,551.0\nF8,0,540.0\nF8,1,850.0\nF8,2,490.0\nF8,3,186.0\nF8,4,742.0\nF8,5,493.0\nF8,6,622.0\nF8,7,61.0\nF8,8,625.0\nF8,9,751.0\nF8,10,428.0\nF8,11,702.0\nF8,12,147.0\nF8,13,614.0\nF8,14,817.0\nF8,15,617.0\nF8,16,659.0\nF8,17,223.0\nF9,0,240.0\nF9,1,746.0\nF9,2,628.0\nF9,3,183.0\nF9,4,569.0\nF9,5,730.0\nF9,6,585.0\nF9,7,381.0\nF9,8,354.0\nF9,9,626.0\nF9,10,213.0\nF9,11,345.0\nF9,12,289.0\nF9,13,478.0\nF9,14,686.0\nF9,15,347.0\nF9,16,681.0\nF9,17,392.0\n\nAlso, when you send back your choice, please follow this simple JSON layout so it's easy to read and check:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThis just means: \"selected\" is the list of shelters we decide to open, and \"assignments\" is a list (in the same order as the families in the input) saying which opened shelter each family goes to. Think of it like filling out a quick form — which sites are active, and which site each family is sent to. The JSON above is only a sketch of the shape I need, not the actual solution.\n\nPlease make sure you use the exact identifiers from the instance input — do not rename them or invent new labels. To be clear: Valid identifiers look like plain numbers such as \"1\" or \"23\", single capital letters like \"A\" or \"B\", or a capital letter followed by digits like \"A1\" or \"X7\".", "instance": { "opening_costs": [ 258.0, 128.0, 296.0, 225.0, 310.0, 373.0, 329.0, 179.0, 321.0 ], "capacities": [ 366.0, 314.0, 504.0, 504.0, 580.0, 415.0, 456.0, 549.0, 316.0 ], "connection_costs": [ [ 557.0, 346.0, 161.0, 568.0, 392.0, 344.0, 143.0, 654.0, 524.0, 318.0, 458.0, 758.0, 475.0, 303.0, 362.0, 519.0, 72.0, 370.0 ], [ 386.0, 180.0, 522.0, 636.0, 28.0, 712.0, 242.0, 812.0, 284.0, 80.0, 387.0, 516.0, 612.0, 145.0, 104.0, 286.0, 349.0, 574.0 ], [ 258.0, 455.0, 348.0, 302.0, 329.0, 502.0, 262.0, 466.0, 274.0, 345.0, 140.0, 467.0, 267.0, 202.0, 411.0, 267.0, 356.0, 248.0 ], [ 474.0, 179.0, 336.0, 603.0, 219.0, 525.0, 59.0, 738.0, 409.0, 135.0, 414.0, 653.0, 541.0, 174.0, 180.0, 406.0, 142.0, 466.0 ], [ 349.0, 694.0, 441.0, 73.0, 564.0, 519.0, 484.0, 237.0, 432.0, 586.0, 235.0, 524.0, 72.0, 441.0, 651.0, 424.0, 550.0, 179.0 ], [ 228.0, 365.0, 598.0, 548.0, 157.0, 779.0, 357.0, 748.0, 113.0, 255.0, 281.0, 332.0, 559.0, 190.0, 288.0, 118.0, 480.0, 560.0 ], [ 90.0, 593.0, 691.0, 436.0, 387.0, 846.0, 523.0, 648.0, 132.0, 476.0, 222.0, 124.0, 498.0, 361.0, 519.0, 132.0, 644.0, 551.0 ], [ 540.0, 850.0, 490.0, 186.0, 742.0, 493.0, 622.0, 61.0, 625.0, 751.0, 428.0, 702.0, 147.0, 614.0, 817.0, 617.0, 659.0, 223.0 ], [ 240.0, 746.0, 628.0, 183.0, 569.0, 730.0, 585.0, 381.0, 354.0, 626.0, 213.0, 345.0, 289.0, 478.0, 686.0, 347.0, 681.0, 392.0 ] ], "demands": [ 40.0, 18.0, 17.0, 13.0, 31.0, 23.0, 39.0, 43.0, 32.0, 28.0, 27.0, 22.0, 45.0, 25.0, 19.0, 42.0, 27.0, 17.0 ], "objective": 3468.0 }, "solution": { "open_facilities": [ 0, 1, 6, 7 ], "assignments": [ 6, 1, 0, 7, 1, 0, 0, 7, 6, 1, 6, 6, 7, 1, 1, 6, 0, 7 ] }, "obj": 3468.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 9, "num_customers": 18, "facilities": [ { "id": "F1", "opening_cost": 258.0, "capacity": 366.0 }, { "id": "F2", "opening_cost": 128.0, "capacity": 314.0 }, { "id": "F3", "opening_cost": 296.0, "capacity": 504.0 }, { "id": "F4", "opening_cost": 225.0, "capacity": 504.0 }, { "id": "F5", "opening_cost": 310.0, "capacity": 580.0 }, { "id": "F6", "opening_cost": 373.0, "capacity": 415.0 }, { "id": "F7", "opening_cost": 329.0, "capacity": 456.0 }, { "id": "F8", "opening_cost": 179.0, "capacity": 549.0 }, { "id": "F9", "opening_cost": 321.0, "capacity": 316.0 } ], "customers": [ { "id": 0, "demand": 40.0 }, { "id": 1, "demand": 18.0 }, { "id": 2, "demand": 17.0 }, { "id": 3, "demand": 13.0 }, { "id": 4, "demand": 31.0 }, { "id": 5, "demand": 23.0 }, { "id": 6, "demand": 39.0 }, { "id": 7, "demand": 43.0 }, { "id": 8, "demand": 32.0 }, { "id": 9, "demand": 28.0 }, { "id": 10, "demand": 27.0 }, { "id": 11, "demand": 22.0 }, { "id": 12, "demand": 45.0 }, { "id": 13, "demand": 25.0 }, { "id": 14, "demand": 19.0 }, { "id": 15, "demand": 42.0 }, { "id": 16, "demand": 27.0 }, { "id": 17, "demand": 17.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 557.0 }, { "facility": "F1", "customer": 1, "cost": 346.0 }, { "facility": "F1", "customer": 2, "cost": 161.0 }, { "facility": "F1", "customer": 3, "cost": 568.0 }, { "facility": "F1", "customer": 4, "cost": 392.0 }, { "facility": "F1", "customer": 5, "cost": 344.0 }, { "facility": "F1", "customer": 6, "cost": 143.0 }, { "facility": "F1", "customer": 7, "cost": 654.0 }, { "facility": "F1", "customer": 8, "cost": 524.0 }, { "facility": "F1", "customer": 9, "cost": 318.0 }, { "facility": "F1", "customer": 10, "cost": 458.0 }, { "facility": "F1", "customer": 11, "cost": 758.0 }, { "facility": "F1", "customer": 12, "cost": 475.0 }, { "facility": "F1", "customer": 13, "cost": 303.0 }, { "facility": "F1", "customer": 14, "cost": 362.0 }, { "facility": "F1", "customer": 15, "cost": 519.0 }, { "facility": "F1", "customer": 16, "cost": 72.0 }, { "facility": "F1", "customer": 17, "cost": 370.0 }, { "facility": "F2", "customer": 0, "cost": 386.0 }, { "facility": "F2", "customer": 1, "cost": 180.0 }, { "facility": "F2", "customer": 2, "cost": 522.0 }, { "facility": "F2", "customer": 3, "cost": 636.0 }, { "facility": "F2", "customer": 4, "cost": 28.0 }, { "facility": "F2", "customer": 5, "cost": 712.0 }, { "facility": "F2", "customer": 6, "cost": 242.0 }, { "facility": "F2", "customer": 7, "cost": 812.0 }, { "facility": "F2", "customer": 8, "cost": 284.0 }, { "facility": "F2", "customer": 9, "cost": 80.0 }, { "facility": "F2", "customer": 10, "cost": 387.0 }, { "facility": "F2", "customer": 11, "cost": 516.0 }, { "facility": "F2", "customer": 12, "cost": 612.0 }, { "facility": "F2", "customer": 13, "cost": 145.0 }, { "facility": "F2", "customer": 14, "cost": 104.0 }, { "facility": "F2", "customer": 15, "cost": 286.0 }, { "facility": "F2", "customer": 16, "cost": 349.0 }, { "facility": "F2", "customer": 17, "cost": 574.0 }, { "facility": "F3", "customer": 0, "cost": 258.0 }, { "facility": "F3", "customer": 1, "cost": 455.0 }, { "facility": "F3", "customer": 2, "cost": 348.0 }, { "facility": "F3", "customer": 3, "cost": 302.0 }, { "facility": "F3", "customer": 4, "cost": 329.0 }, { "facility": "F3", "customer": 5, "cost": 502.0 }, { "facility": "F3", "customer": 6, "cost": 262.0 }, { "facility": "F3", "customer": 7, "cost": 466.0 }, { "facility": "F3", "customer": 8, "cost": 274.0 }, { "facility": "F3", "customer": 9, "cost": 345.0 }, { "facility": "F3", "customer": 10, "cost": 140.0 }, { "facility": "F3", "customer": 11, "cost": 467.0 }, { "facility": "F3", "customer": 12, "cost": 267.0 }, { "facility": "F3", "customer": 13, "cost": 202.0 }, { "facility": "F3", "customer": 14, "cost": 411.0 }, { "facility": "F3", "customer": 15, "cost": 267.0 }, { "facility": "F3", "customer": 16, "cost": 356.0 }, { "facility": "F3", "customer": 17, "cost": 248.0 }, { "facility": "F4", "customer": 0, "cost": 474.0 }, { "facility": "F4", "customer": 1, "cost": 179.0 }, { "facility": "F4", "customer": 2, "cost": 336.0 }, { "facility": "F4", "customer": 3, "cost": 603.0 }, { "facility": "F4", "customer": 4, "cost": 219.0 }, { "facility": "F4", "customer": 5, "cost": 525.0 }, { "facility": "F4", "customer": 6, "cost": 59.0 }, { "facility": "F4", "customer": 7, "cost": 738.0 }, { "facility": "F4", "customer": 8, "cost": 409.0 }, { "facility": "F4", "customer": 9, "cost": 135.0 }, { "facility": "F4", "customer": 10, "cost": 414.0 }, { "facility": "F4", "customer": 11, "cost": 653.0 }, { "facility": "F4", "customer": 12, "cost": 541.0 }, { "facility": "F4", "customer": 13, "cost": 174.0 }, { "facility": "F4", "customer": 14, "cost": 180.0 }, { "facility": "F4", "customer": 15, "cost": 406.0 }, { "facility": "F4", "customer": 16, "cost": 142.0 }, { "facility": "F4", "customer": 17, "cost": 466.0 }, { "facility": "F5", "customer": 0, "cost": 349.0 }, { "facility": "F5", "customer": 1, "cost": 694.0 }, { "facility": "F5", "customer": 2, "cost": 441.0 }, { "facility": "F5", "customer": 3, "cost": 73.0 }, { "facility": "F5", "customer": 4, "cost": 564.0 }, { "facility": "F5", "customer": 5, "cost": 519.0 }, { "facility": "F5", "customer": 6, "cost": 484.0 }, { "facility": "F5", "customer": 7, "cost": 237.0 }, { "facility": "F5", "customer": 8, "cost": 432.0 }, { "facility": "F5", "customer": 9, "cost": 586.0 }, { "facility": "F5", "customer": 10, "cost": 235.0 }, { "facility": "F5", "customer": 11, "cost": 524.0 }, { "facility": "F5", "customer": 12, "cost": 72.0 }, { "facility": "F5", "customer": 13, "cost": 441.0 }, { "facility": "F5", "customer": 14, "cost": 651.0 }, { "facility": "F5", "customer": 15, "cost": 424.0 }, { "facility": "F5", "customer": 16, "cost": 550.0 }, { "facility": "F5", "customer": 17, "cost": 179.0 }, { "facility": "F6", "customer": 0, "cost": 228.0 }, { "facility": "F6", "customer": 1, "cost": 365.0 }, { "facility": "F6", "customer": 2, "cost": 598.0 }, { "facility": "F6", "customer": 3, "cost": 548.0 }, { "facility": "F6", "customer": 4, "cost": 157.0 }, { "facility": "F6", "customer": 5, "cost": 779.0 }, { "facility": "F6", "customer": 6, "cost": 357.0 }, { "facility": "F6", "customer": 7, "cost": 748.0 }, { "facility": "F6", "customer": 8, "cost": 113.0 }, { "facility": "F6", "customer": 9, "cost": 255.0 }, { "facility": "F6", "customer": 10, "cost": 281.0 }, { "facility": "F6", "customer": 11, "cost": 332.0 }, { "facility": "F6", "customer": 12, "cost": 559.0 }, { "facility": "F6", "customer": 13, "cost": 190.0 }, { "facility": "F6", "customer": 14, "cost": 288.0 }, { "facility": "F6", "customer": 15, "cost": 118.0 }, { "facility": "F6", "customer": 16, "cost": 480.0 }, { "facility": "F6", "customer": 17, "cost": 560.0 }, { "facility": "F7", "customer": 0, "cost": 90.0 }, { "facility": "F7", "customer": 1, "cost": 593.0 }, { "facility": "F7", "customer": 2, "cost": 691.0 }, { "facility": "F7", "customer": 3, "cost": 436.0 }, { "facility": "F7", "customer": 4, "cost": 387.0 }, { "facility": "F7", "customer": 5, "cost": 846.0 }, { "facility": "F7", "customer": 6, "cost": 523.0 }, { "facility": "F7", "customer": 7, "cost": 648.0 }, { "facility": "F7", "customer": 8, "cost": 132.0 }, { "facility": "F7", "customer": 9, "cost": 476.0 }, { "facility": "F7", "customer": 10, "cost": 222.0 }, { "facility": "F7", "customer": 11, "cost": 124.0 }, { "facility": "F7", "customer": 12, "cost": 498.0 }, { "facility": "F7", "customer": 13, "cost": 361.0 }, { "facility": "F7", "customer": 14, "cost": 519.0 }, { "facility": "F7", "customer": 15, "cost": 132.0 }, { "facility": "F7", "customer": 16, "cost": 644.0 }, { "facility": "F7", "customer": 17, "cost": 551.0 }, { "facility": "F8", "customer": 0, "cost": 540.0 }, { "facility": "F8", "customer": 1, "cost": 850.0 }, { "facility": "F8", "customer": 2, "cost": 490.0 }, { "facility": "F8", "customer": 3, "cost": 186.0 }, { "facility": "F8", "customer": 4, "cost": 742.0 }, { "facility": "F8", "customer": 5, "cost": 493.0 }, { "facility": "F8", "customer": 6, "cost": 622.0 }, { "facility": "F8", "customer": 7, "cost": 61.0 }, { "facility": "F8", "customer": 8, "cost": 625.0 }, { "facility": "F8", "customer": 9, "cost": 751.0 }, { "facility": "F8", "customer": 10, "cost": 428.0 }, { "facility": "F8", "customer": 11, "cost": 702.0 }, { "facility": "F8", "customer": 12, "cost": 147.0 }, { "facility": "F8", "customer": 13, "cost": 614.0 }, { "facility": "F8", "customer": 14, "cost": 817.0 }, { "facility": "F8", "customer": 15, "cost": 617.0 }, { "facility": "F8", "customer": 16, "cost": 659.0 }, { "facility": "F8", "customer": 17, "cost": 223.0 }, { "facility": "F9", "customer": 0, "cost": 240.0 }, { "facility": "F9", "customer": 1, "cost": 746.0 }, { "facility": "F9", "customer": 2, "cost": 628.0 }, { "facility": "F9", "customer": 3, "cost": 183.0 }, { "facility": "F9", "customer": 4, "cost": 569.0 }, { "facility": "F9", "customer": 5, "cost": 730.0 }, { "facility": "F9", "customer": 6, "cost": 585.0 }, { "facility": "F9", "customer": 7, "cost": 381.0 }, { "facility": "F9", "customer": 8, "cost": 354.0 }, { "facility": "F9", "customer": 9, "cost": 626.0 }, { "facility": "F9", "customer": 10, "cost": 213.0 }, { "facility": "F9", "customer": 11, "cost": 345.0 }, { "facility": "F9", "customer": 12, "cost": 289.0 }, { "facility": "F9", "customer": 13, "cost": 478.0 }, { "facility": "F9", "customer": 14, "cost": 686.0 }, { "facility": "F9", "customer": 15, "cost": 347.0 }, { "facility": "F9", "customer": 16, "cost": 681.0 }, { "facility": "F9", "customer": 17, "cost": 392.0 } ], "objective": 3468.0 }, "solution_variant": { "selected": [ "F1", "F2", "F7", "F8" ], "assignments": [ "F7", "F2", "F1", "F8", "F2", "F1", "F1", "F8", "F7", "F2", "F7", "F7", "F8", "F2", "F2", "F7", "F1", "F8" ] }, "context_index": 25, "input_format": "csv", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Many operators face the same trade-off: turn on enough edge servers to serve everyone but not so many that setup costs blow up, and assign each device to a single server so no traffic is split and every server stays within its capacity. To pick the best arrangement, total up the cost of provisioning the chosen servers and the latency cost for each device’s connection; the arrangement with the lowest total is preferred. The full set of numbers and choices is shown below.\n\nThere are 8 candidate edge servers and 18 user devices in the scenario.\nEdge server F1 can be provisioned at cost 119.0 and offers capacity 309.0.\nEdge server F2 can be provisioned at cost 372.0 and offers capacity 436.0.\nEdge server F3 can be provisioned at cost 372.0 and offers capacity 436.0.\nEdge server F4 can be provisioned at cost 308.0 and offers capacity 404.0.\nEdge server F5 can be provisioned at cost 114.0 and offers capacity 307.0.\nEdge server F6 can be provisioned at cost 312.0 and offers capacity 406.0.\nEdge server F7 can be provisioned at cost 336.0 and offers capacity 418.0.\nEdge server F8 can be provisioned at cost 438.0 and offers capacity 469.0.\nDevice A has demand 20.0.\nDevice B has demand 20.0.\nDevice C has demand 20.0.\nDevice D has demand 20.0.\nDevice E has demand 20.0.\nDevice F has demand 20.0.\nDevice G has demand 40.0.\nDevice H has demand 20.0.\nDevice I has demand 10.0.\nDevice J has demand 9.0.\nDevice K has demand 5.0.\nDevice L has demand 8.0.\nDevice M has demand 16.0.\nDevice N has demand 31.0.\nDevice O has demand 2.0.\nDevice P has demand 28.0.\nDevice Q has demand 19.0.\nDevice R has demand 6.0.\nAssigning device A to edge server F1 incurs latency cost 192.0.\nAssigning device B to edge server F1 incurs latency cost 146.0.\nAssigning device C to edge server F1 incurs latency cost 20.0.\nAssigning device D to edge server F1 incurs latency cost 177.0.\nAssigning device E to edge server F1 incurs latency cost 349.0.\nAssigning device F to edge server F1 incurs latency cost 297.0.\nAssigning device G to edge server F1 incurs latency cost 290.0.\nAssigning device H to edge server F1 incurs latency cost 260.0.\nAssigning device I to edge server F1 incurs latency cost 252.0.\nAssigning device J to edge server F1 incurs latency cost 224.0.\nAssigning device K to edge server F1 incurs latency cost 84.0.\nAssigning device L to edge server F1 incurs latency cost 93.0.\nAssigning device M to edge server F1 incurs latency cost 141.0.\nAssigning device N to edge server F1 incurs latency cost 236.0.\nAssigning device O to edge server F1 incurs latency cost 230.0.\nAssigning device P to edge server F1 incurs latency cost 82.0.\nAssigning device Q to edge server F1 incurs latency cost 96.0.\nAssigning device R to edge server F1 incurs latency cost 192.0.\nAssigning device A to edge server F2 incurs latency cost 326.0.\nAssigning device B to edge server F2 incurs latency cost 294.0.\nAssigning device C to edge server F2 incurs latency cost 205.0.\nAssigning device D to edge server F2 incurs latency cost 20.0.\nAssigning device E to edge server F2 incurs latency cost 251.0.\nAssigning device F to edge server F2 incurs latency cost 338.0.\nAssigning device G to edge server F2 incurs latency cost 335.0.\nAssigning device H to edge server F2 incurs latency cost 326.0.\nAssigning device I to edge server F2 incurs latency cost 314.0.\nAssigning device J to edge server F2 incurs latency cost 176.0.\nAssigning device K to edge server F2 incurs latency cost 267.0.\nAssigning device L to edge server F2 incurs latency cost 100.0.\nAssigning device M to edge server F2 incurs latency cost 140.0.\nAssigning device N to edge server F2 incurs latency cost 85.0.\nAssigning device O to edge server F2 incurs latency cost 117.0.\nAssigning device P to edge server F2 incurs latency cost 107.0.\nAssigning device Q to edge server F2 incurs latency cost 221.0.\nAssigning device R to edge server F2 incurs latency cost 143.0.\nAssigning device A to edge server F3 incurs latency cost 286.0.\nAssigning device B to edge server F3 incurs latency cost 256.0.\nAssigning device C to edge server F3 incurs latency cost 175.0.\nAssigning device D to edge server F3 incurs latency cost 45.0.\nAssigning device E to edge server F3 incurs latency cost 234.0.\nAssigning device F to edge server F3 incurs latency cost 300.0.\nAssigning device G to edge server F3 incurs latency cost 297.0.\nAssigning device H to edge server F3 incurs latency cost 286.0.\nAssigning device I to edge server F3 incurs latency cost 275.0.\nAssigning device J to edge server F3 incurs latency cost 144.0.\nAssigning device K to edge server F3 incurs latency cost 236.0.\nAssigning device L to edge server F3 incurs latency cost 82.0.\nAssigning device M to edge server F3 incurs latency cost 146.0.\nAssigning device N to edge server F3 incurs latency cost 81.0.\nAssigning device O to edge server F3 incurs latency cost 97.0.\nAssigning device P to edge server F3 incurs latency cost 84.0.\nAssigning device Q to edge server F3 incurs latency cost 184.0.\nAssigning device R to edge server F3 incurs latency cost 109.0.\nAssigning device A to edge server F4 incurs latency cost 185.0.\nAssigning device B to edge server F4 incurs latency cost 136.0.\nAssigning device C to edge server F4 incurs latency cost 24.0.\nAssigning device D to edge server F4 incurs latency cost 207.0.\nAssigning device E to edge server F4 incurs latency cost 374.0.\nAssigning device F to edge server F4 incurs latency cost 305.0.\nAssigning device G to edge server F4 incurs latency cost 299.0.\nAssigning device H to edge server F4 incurs latency cost 266.0.\nAssigning device I to edge server F4 incurs latency cost 259.0.\nAssigning device J to edge server F4 incurs latency cost 248.0.\nAssigning device K to edge server F4 incurs latency cost 60.0.\nAssigning device L to edge server F4 incurs latency cost 123.0.\nAssigning device M to edge server F4 incurs latency cost 160.0.\nAssigning device N to edge server F4 incurs latency cost 267.0.\nAssigning device O to edge server F4 incurs latency cost 259.0.\nAssigning device P to edge server F4 incurs latency cost 113.0.\nAssigning device Q to edge server F4 incurs latency cost 102.0.\nAssigning device R to edge server F4 incurs latency cost 218.0.\nAssigning device A to edge server F5 incurs latency cost 224.0.\nAssigning device B to edge server F5 incurs latency cost 205.0.\nAssigning device C to edge server F5 incurs latency cost 173.0.\nAssigning device D to edge server F5 incurs latency cost 134.0.\nAssigning device E to edge server F5 incurs latency cost 180.0.\nAssigning device F to edge server F5 incurs latency cost 211.0.\nAssigning device G to edge server F5 incurs latency cost 209.0.\nAssigning device H to edge server F5 incurs latency cost 201.0.\nAssigning device I to edge server F5 incurs latency cost 189.0.\nAssigning device J to edge server F5 incurs latency cost 63.0.\nAssigning device K to edge server F5 incurs latency cost 216.0.\nAssigning device L to edge server F5 incurs latency cost 134.0.\nAssigning device M to edge server F5 incurs latency cost 216.0.\nAssigning device N to edge server F5 incurs latency cost 100.0.\nAssigning device O to edge server F5 incurs latency cost 71.0.\nAssigning device P to edge server F5 incurs latency cost 124.0.\nAssigning device Q to edge server F5 incurs latency cost 139.0.\nAssigning device R to edge server F5 incurs latency cost 25.0.\nAssigning device A to edge server F6 incurs latency cost 267.0.\nAssigning device B to edge server F6 incurs latency cost 222.0.\nAssigning device C to edge server F6 incurs latency cost 100.0.\nAssigning device D to edge server F6 incurs latency cost 117.0.\nAssigning device E to edge server F6 incurs latency cost 345.0.\nAssigning device F to edge server F6 incurs latency cost 346.0.\nAssigning device G to edge server F6 incurs latency cost 341.0.\nAssigning device H to edge server F6 incurs latency cost 316.0.\nAssigning device I to edge server F6 incurs latency cost 306.0.\nAssigning device J to edge server F6 incurs latency cost 233.0.\nAssigning device K to edge server F6 incurs latency cost 163.0.\nAssigning device L to edge server F6 incurs latency cost 40.0.\nAssigning device M to edge server F6 incurs latency cost 63.0.\nAssigning device N to edge server F6 incurs latency cost 203.0.\nAssigning device O to edge server F6 incurs latency cost 212.0.\nAssigning device P to edge server F6 incurs latency cost 47.0.\nAssigning device Q to edge server F6 incurs latency cost 162.0.\nAssigning device R to edge server F6 incurs latency cost 196.0.\nAssigning device A to edge server F7 incurs latency cost 202.0.\nAssigning device B to edge server F7 incurs latency cost 190.0.\nAssigning device C to edge server F7 incurs latency cost 180.0.\nAssigning device D to edge server F7 incurs latency cost 168.0.\nAssigning device E to edge server F7 incurs latency cost 171.0.\nAssigning device F to edge server F7 incurs latency cost 177.0.\nAssigning device G to edge server F7 incurs latency cost 175.0.\nAssigning device H to edge server F7 incurs latency cost 168.0.\nAssigning device I to edge server F7 incurs latency cost 156.0.\nAssigning device J to edge server F7 incurs latency cost 44.0.\nAssigning device K to edge server F7 incurs latency cost 215.0.\nAssigning device L to edge server F7 incurs latency cost 161.0.\nAssigning device M to edge server F7 incurs latency cost 245.0.\nAssigning device N to edge server F7 incurs latency cost 127.0.\nAssigning device O to edge server F7 incurs latency cost 89.0.\nAssigning device P to edge server F7 incurs latency cost 149.0.\nAssigning device Q to edge server F7 incurs latency cost 131.0.\nAssigning device R to edge server F7 incurs latency cost 27.0.\nAssigning device A to edge server F8 incurs latency cost 76.0.\nAssigning device B to edge server F8 incurs latency cost 61.0.\nAssigning device C to edge server F8 incurs latency cost 127.0.\nAssigning device D to edge server F8 incurs latency cost 249.0.\nAssigning device E to edge server F8 incurs latency cost 286.0.\nAssigning device F to edge server F8 incurs latency cost 161.0.\nAssigning device G to edge server F8 incurs latency cost 154.0.\nAssigning device H to edge server F8 incurs latency cost 120.0.\nAssigning device I to edge server F8 incurs latency cost 113.0.\nAssigning device J to edge server F8 incurs latency cost 166.0.\nAssigning device K to edge server F8 incurs latency cost 119.0.\nAssigning device L to edge server F8 incurs latency cost 193.0.\nAssigning device M to edge server F8 incurs latency cost 269.0.\nAssigning device N to edge server F8 incurs latency cost 249.0.\nAssigning device O to edge server F8 incurs latency cost 218.0.\nAssigning device P to edge server F8 incurs latency cost 177.0.\nAssigning device Q to edge server F8 incurs latency cost 46.0.\nAssigning device R to edge server F8 incurs latency cost 156.0.\nThe preferred arrangement minimizes the combined provisioning and latency costs.\n\nIf you want to send the answer back, just use this little JSON shape — nothing fancy, just a compact form I can read easily.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of servers you're switching on, and \"assignments\" as, in order, which server each device talks to. Super simple: one server per device, and the arrays should line up with the instance ordering.\n\nThis is just a sketch of the shape I need — not the actual answer yet. Please make sure to use the exact identifiers from the instance input, with no renaming and no new labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 119.0, 372.0, 372.0, 308.0, 114.0, 312.0, 336.0, 438.0 ], "capacities": [ 309.0, 436.0, 436.0, 404.0, 307.0, 406.0, 418.0, 469.0 ], "connection_costs": [ [ 192.0, 146.0, 20.0, 177.0, 349.0, 297.0, 290.0, 260.0, 252.0, 224.0, 84.0, 93.0, 141.0, 236.0, 230.0, 82.0, 96.0, 192.0 ], [ 326.0, 294.0, 205.0, 20.0, 251.0, 338.0, 335.0, 326.0, 314.0, 176.0, 267.0, 100.0, 140.0, 85.0, 117.0, 107.0, 221.0, 143.0 ], [ 286.0, 256.0, 175.0, 45.0, 234.0, 300.0, 297.0, 286.0, 275.0, 144.0, 236.0, 82.0, 146.0, 81.0, 97.0, 84.0, 184.0, 109.0 ], [ 185.0, 136.0, 24.0, 207.0, 374.0, 305.0, 299.0, 266.0, 259.0, 248.0, 60.0, 123.0, 160.0, 267.0, 259.0, 113.0, 102.0, 218.0 ], [ 224.0, 205.0, 173.0, 134.0, 180.0, 211.0, 209.0, 201.0, 189.0, 63.0, 216.0, 134.0, 216.0, 100.0, 71.0, 124.0, 139.0, 25.0 ], [ 267.0, 222.0, 100.0, 117.0, 345.0, 346.0, 341.0, 316.0, 306.0, 233.0, 163.0, 40.0, 63.0, 203.0, 212.0, 47.0, 162.0, 196.0 ], [ 202.0, 190.0, 180.0, 168.0, 171.0, 177.0, 175.0, 168.0, 156.0, 44.0, 215.0, 161.0, 245.0, 127.0, 89.0, 149.0, 131.0, 27.0 ], [ 76.0, 61.0, 127.0, 249.0, 286.0, 161.0, 154.0, 120.0, 113.0, 166.0, 119.0, 193.0, 269.0, 249.0, 218.0, 177.0, 46.0, 156.0 ] ], "demands": [ 20.0, 20.0, 20.0, 20.0, 20.0, 20.0, 40.0, 20.0, 10.0, 9.0, 5.0, 8.0, 16.0, 31.0, 2.0, 28.0, 19.0, 6.0 ], "objective": 2395.0 }, "solution": { "open_facilities": [ 0, 4, 7 ], "assignments": [ 7, 7, 0, 4, 4, 7, 7, 7, 7, 4, 0, 0, 0, 4, 4, 0, 7, 4 ] }, "obj": 2395.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 18, "facilities": [ { "id": "F1", "opening_cost": 119.0, "capacity": 309.0 }, { "id": "F2", "opening_cost": 372.0, "capacity": 436.0 }, { "id": "F3", "opening_cost": 372.0, "capacity": 436.0 }, { "id": "F4", "opening_cost": 308.0, "capacity": 404.0 }, { "id": "F5", "opening_cost": 114.0, "capacity": 307.0 }, { "id": "F6", "opening_cost": 312.0, "capacity": 406.0 }, { "id": "F7", "opening_cost": 336.0, "capacity": 418.0 }, { "id": "F8", "opening_cost": 438.0, "capacity": 469.0 } ], "customers": [ { "id": "A", "demand": 20.0 }, { "id": "B", "demand": 20.0 }, { "id": "C", "demand": 20.0 }, { "id": "D", "demand": 20.0 }, { "id": "E", "demand": 20.0 }, { "id": "F", "demand": 20.0 }, { "id": "G", "demand": 40.0 }, { "id": "H", "demand": 20.0 }, { "id": "I", "demand": 10.0 }, { "id": "J", "demand": 9.0 }, { "id": "K", "demand": 5.0 }, { "id": "L", "demand": 8.0 }, { "id": "M", "demand": 16.0 }, { "id": "N", "demand": 31.0 }, { "id": "O", "demand": 2.0 }, { "id": "P", "demand": 28.0 }, { "id": "Q", "demand": 19.0 }, { "id": "R", "demand": 6.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 192.0 }, { "facility": "F1", "customer": "B", "cost": 146.0 }, { "facility": "F1", "customer": "C", "cost": 20.0 }, { "facility": "F1", "customer": "D", "cost": 177.0 }, { "facility": "F1", "customer": "E", "cost": 349.0 }, { "facility": "F1", "customer": "F", "cost": 297.0 }, { "facility": "F1", "customer": "G", "cost": 290.0 }, { "facility": "F1", "customer": "H", "cost": 260.0 }, { "facility": "F1", "customer": "I", "cost": 252.0 }, { "facility": "F1", "customer": "J", "cost": 224.0 }, { "facility": "F1", "customer": "K", "cost": 84.0 }, { "facility": "F1", "customer": "L", "cost": 93.0 }, { "facility": "F1", "customer": "M", "cost": 141.0 }, { "facility": "F1", "customer": "N", "cost": 236.0 }, { "facility": "F1", "customer": "O", "cost": 230.0 }, { "facility": "F1", "customer": "P", "cost": 82.0 }, { "facility": "F1", "customer": "Q", "cost": 96.0 }, { "facility": "F1", "customer": "R", "cost": 192.0 }, { "facility": "F2", "customer": "A", "cost": 326.0 }, { "facility": "F2", "customer": "B", "cost": 294.0 }, { "facility": "F2", "customer": "C", "cost": 205.0 }, { "facility": "F2", "customer": "D", "cost": 20.0 }, { "facility": "F2", "customer": "E", "cost": 251.0 }, { "facility": "F2", "customer": "F", "cost": 338.0 }, { "facility": "F2", "customer": "G", "cost": 335.0 }, { "facility": "F2", "customer": "H", "cost": 326.0 }, { "facility": "F2", "customer": "I", "cost": 314.0 }, { "facility": "F2", "customer": "J", "cost": 176.0 }, { "facility": "F2", "customer": "K", "cost": 267.0 }, { "facility": "F2", "customer": "L", "cost": 100.0 }, { "facility": "F2", "customer": "M", "cost": 140.0 }, { "facility": "F2", "customer": "N", "cost": 85.0 }, { "facility": "F2", "customer": "O", "cost": 117.0 }, { "facility": "F2", "customer": "P", "cost": 107.0 }, { "facility": "F2", "customer": "Q", "cost": 221.0 }, { "facility": "F2", "customer": "R", "cost": 143.0 }, { "facility": "F3", "customer": "A", "cost": 286.0 }, { "facility": "F3", "customer": "B", "cost": 256.0 }, { "facility": "F3", "customer": "C", "cost": 175.0 }, { "facility": "F3", "customer": "D", "cost": 45.0 }, { "facility": "F3", "customer": "E", "cost": 234.0 }, { "facility": "F3", "customer": "F", "cost": 300.0 }, { "facility": "F3", "customer": "G", "cost": 297.0 }, { "facility": "F3", "customer": "H", "cost": 286.0 }, { "facility": "F3", "customer": "I", "cost": 275.0 }, { "facility": "F3", "customer": "J", "cost": 144.0 }, { "facility": "F3", "customer": "K", "cost": 236.0 }, { "facility": "F3", "customer": "L", "cost": 82.0 }, { "facility": "F3", "customer": "M", "cost": 146.0 }, { "facility": "F3", "customer": "N", "cost": 81.0 }, { "facility": "F3", "customer": "O", "cost": 97.0 }, { "facility": "F3", "customer": "P", "cost": 84.0 }, { "facility": "F3", "customer": "Q", "cost": 184.0 }, { "facility": "F3", "customer": "R", "cost": 109.0 }, { "facility": "F4", "customer": "A", "cost": 185.0 }, { "facility": "F4", "customer": "B", "cost": 136.0 }, { "facility": "F4", "customer": "C", "cost": 24.0 }, { "facility": "F4", "customer": "D", "cost": 207.0 }, { "facility": "F4", "customer": "E", "cost": 374.0 }, { "facility": "F4", "customer": "F", "cost": 305.0 }, { "facility": "F4", "customer": "G", "cost": 299.0 }, { "facility": "F4", "customer": "H", "cost": 266.0 }, { "facility": "F4", "customer": "I", "cost": 259.0 }, { "facility": "F4", "customer": "J", "cost": 248.0 }, { "facility": "F4", "customer": "K", "cost": 60.0 }, { "facility": "F4", "customer": "L", "cost": 123.0 }, { "facility": "F4", "customer": "M", "cost": 160.0 }, { "facility": "F4", "customer": "N", "cost": 267.0 }, { "facility": "F4", "customer": "O", "cost": 259.0 }, { "facility": "F4", "customer": "P", "cost": 113.0 }, { "facility": "F4", "customer": "Q", "cost": 102.0 }, { "facility": "F4", "customer": "R", "cost": 218.0 }, { "facility": "F5", "customer": "A", "cost": 224.0 }, { "facility": "F5", "customer": "B", "cost": 205.0 }, { "facility": "F5", "customer": "C", "cost": 173.0 }, { "facility": "F5", "customer": "D", "cost": 134.0 }, { "facility": "F5", "customer": "E", "cost": 180.0 }, { "facility": "F5", "customer": "F", "cost": 211.0 }, { "facility": "F5", "customer": "G", "cost": 209.0 }, { "facility": "F5", "customer": "H", "cost": 201.0 }, { "facility": "F5", "customer": "I", "cost": 189.0 }, { "facility": "F5", "customer": "J", "cost": 63.0 }, { "facility": "F5", "customer": "K", "cost": 216.0 }, { "facility": "F5", "customer": "L", "cost": 134.0 }, { "facility": "F5", "customer": "M", "cost": 216.0 }, { "facility": "F5", "customer": "N", "cost": 100.0 }, { "facility": "F5", "customer": "O", "cost": 71.0 }, { "facility": "F5", "customer": "P", "cost": 124.0 }, { "facility": "F5", "customer": "Q", "cost": 139.0 }, { "facility": "F5", "customer": "R", "cost": 25.0 }, { "facility": "F6", "customer": "A", "cost": 267.0 }, { "facility": "F6", "customer": "B", "cost": 222.0 }, { "facility": "F6", "customer": "C", "cost": 100.0 }, { "facility": "F6", "customer": "D", "cost": 117.0 }, { "facility": "F6", "customer": "E", "cost": 345.0 }, { "facility": "F6", "customer": "F", "cost": 346.0 }, { "facility": "F6", "customer": "G", "cost": 341.0 }, { "facility": "F6", "customer": "H", "cost": 316.0 }, { "facility": "F6", "customer": "I", "cost": 306.0 }, { "facility": "F6", "customer": "J", "cost": 233.0 }, { "facility": "F6", "customer": "K", "cost": 163.0 }, { "facility": "F6", "customer": "L", "cost": 40.0 }, { "facility": "F6", "customer": "M", "cost": 63.0 }, { "facility": "F6", "customer": "N", "cost": 203.0 }, { "facility": "F6", "customer": "O", "cost": 212.0 }, { "facility": "F6", "customer": "P", "cost": 47.0 }, { "facility": "F6", "customer": "Q", "cost": 162.0 }, { "facility": "F6", "customer": "R", "cost": 196.0 }, { "facility": "F7", "customer": "A", "cost": 202.0 }, { "facility": "F7", "customer": "B", "cost": 190.0 }, { "facility": "F7", "customer": "C", "cost": 180.0 }, { "facility": "F7", "customer": "D", "cost": 168.0 }, { "facility": "F7", "customer": "E", "cost": 171.0 }, { "facility": "F7", "customer": "F", "cost": 177.0 }, { "facility": "F7", "customer": "G", "cost": 175.0 }, { "facility": "F7", "customer": "H", "cost": 168.0 }, { "facility": "F7", "customer": "I", "cost": 156.0 }, { "facility": "F7", "customer": "J", "cost": 44.0 }, { "facility": "F7", "customer": "K", "cost": 215.0 }, { "facility": "F7", "customer": "L", "cost": 161.0 }, { "facility": "F7", "customer": "M", "cost": 245.0 }, { "facility": "F7", "customer": "N", "cost": 127.0 }, { "facility": "F7", "customer": "O", "cost": 89.0 }, { "facility": "F7", "customer": "P", "cost": 149.0 }, { "facility": "F7", "customer": "Q", "cost": 131.0 }, { "facility": "F7", "customer": "R", "cost": 27.0 }, { "facility": "F8", "customer": "A", "cost": 76.0 }, { "facility": "F8", "customer": "B", "cost": 61.0 }, { "facility": "F8", "customer": "C", "cost": 127.0 }, { "facility": "F8", "customer": "D", "cost": 249.0 }, { "facility": "F8", "customer": "E", "cost": 286.0 }, { "facility": "F8", "customer": "F", "cost": 161.0 }, { "facility": "F8", "customer": "G", "cost": 154.0 }, { "facility": "F8", "customer": "H", "cost": 120.0 }, { "facility": "F8", "customer": "I", "cost": 113.0 }, { "facility": "F8", "customer": "J", "cost": 166.0 }, { "facility": "F8", "customer": "K", "cost": 119.0 }, { "facility": "F8", "customer": "L", "cost": 193.0 }, { "facility": "F8", "customer": "M", "cost": 269.0 }, { "facility": "F8", "customer": "N", "cost": 249.0 }, { "facility": "F8", "customer": "O", "cost": 218.0 }, { "facility": "F8", "customer": "P", "cost": 177.0 }, { "facility": "F8", "customer": "Q", "cost": 46.0 }, { "facility": "F8", "customer": "R", "cost": 156.0 } ], "objective": 2395.0 }, "solution_variant": { "selected": [ "F1", "F5", "F8" ], "assignments": [ "F8", "F8", "F1", "F5", "F5", "F8", "F8", "F8", "F8", "F5", "F1", "F1", "F1", "F5", "F5", "F1", "F8", "F5" ] }, "context_index": 26, "input_format": "nl", "input_index_base": "names" }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "There’s a weekend market coming and someone has to choose which vendor stalls to rent and which sellers go into which rented stalls. Each stall has a rental fee and a maximum amount of space, while each seller needs a fixed amount of space and will incur a setup/travel cost to use a particular stall. Sellers can’t be split between stalls and every seller must have exactly one assigned stall; also a stall can’t hold more seller space than it allows. The goal is straightforward: pick stalls and assignments that keep the total bill — stall rentals plus sellers’ setup/travel costs — as small as possible. The concrete details follow below.\n\nThere are 7 candidate stalls and 16 sellers.\nStall F1 has a rental fee of 600.0 and a space limit of 700.0.\nStall F2 has a rental fee of 600.0 and a space limit of 700.0.\nStall F3 has a rental fee of 600.0 and a space limit of 700.0.\nStall F4 has a rental fee of 600.0 and a space limit of 700.0.\nStall F5 has a rental fee of 600.0 and a space limit of 700.0.\nStall F6 has a rental fee of 600.0 and a space limit of 700.0.\nStall F7 has a rental fee of 600.0 and a space limit of 700.0.\nSeller 1 requires 18.0 units of stall space.\nSeller 2 requires 20.0 units of stall space.\nSeller 3 requires 18.0 units of stall space.\nSeller 4 requires 20.0 units of stall space.\nSeller 5 requires 23.0 units of stall space.\nSeller 6 requires 27.0 units of stall space.\nSeller 7 requires 10.0 units of stall space.\nSeller 8 requires 20.0 units of stall space.\nSeller 9 requires 12.0 units of stall space.\nSeller 10 requires 23.0 units of stall space.\nSeller 11 requires 26.0 units of stall space.\nSeller 12 requires 27.0 units of stall space.\nSeller 13 requires 21.0 units of stall space.\nSeller 14 requires 18.0 units of stall space.\nSeller 15 requires 29.0 units of stall space.\nSeller 16 requires 13.0 units of stall space.\nIf seller 1 uses stall F1, the setup/travel cost is 187.0.\nIf seller 2 uses stall F1, the setup/travel cost is 448.0.\nIf seller 3 uses stall F1, the setup/travel cost is 1227.0.\nIf seller 4 uses stall F1, the setup/travel cost is 839.0.\nIf seller 5 uses stall F1, the setup/travel cost is 285.0.\nIf seller 6 uses stall F1, the setup/travel cost is 1300.0.\nIf seller 7 uses stall F1, the setup/travel cost is 1138.0.\nIf seller 8 uses stall F1, the setup/travel cost is 41.0.\nIf seller 9 uses stall F1, the setup/travel cost is 1184.0.\nIf seller 10 uses stall F1, the setup/travel cost is 1443.0.\nIf seller 11 uses stall F1, the setup/travel cost is 1243.0.\nIf seller 12 uses stall F1, the setup/travel cost is 1286.0.\nIf seller 13 uses stall F1, the setup/travel cost is 1066.0.\nIf seller 14 uses stall F1, the setup/travel cost is 758.0.\nIf seller 15 uses stall F1, the setup/travel cost is 948.0.\nIf seller 16 uses stall F1, the setup/travel cost is 701.0.\nIf seller 1 uses stall F2, the setup/travel cost is 113.0.\nIf seller 2 uses stall F2, the setup/travel cost is 43.0.\nIf seller 3 uses stall F2, the setup/travel cost is 390.0.\nIf seller 4 uses stall F2, the setup/travel cost is 477.0.\nIf seller 5 uses stall F2, the setup/travel cost is 152.0.\nIf seller 6 uses stall F2, the setup/travel cost is 179.0.\nIf seller 7 uses stall F2, the setup/travel cost is 501.0.\nIf seller 8 uses stall F2, the setup/travel cost is 46.0.\nIf seller 9 uses stall F2, the setup/travel cost is 331.0.\nIf seller 10 uses stall F2, the setup/travel cost is 349.0.\nIf seller 11 uses stall F2, the setup/travel cost is 52.0.\nIf seller 12 uses stall F2, the setup/travel cost is 613.0.\nIf seller 13 uses stall F2, the setup/travel cost is 410.0.\nIf seller 14 uses stall F2, the setup/travel cost is 111.0.\nIf seller 15 uses stall F2, the setup/travel cost is 475.0.\nIf seller 16 uses stall F2, the setup/travel cost is 156.0.\nIf seller 1 uses stall F3, the setup/travel cost is 84.0.\nIf seller 2 uses stall F3, the setup/travel cost is 154.0.\nIf seller 3 uses stall F3, the setup/travel cost is 610.0.\nIf seller 4 uses stall F3, the setup/travel cost is 463.0.\nIf seller 5 uses stall F3, the setup/travel cost is 116.0.\nIf seller 6 uses stall F3, the setup/travel cost is 725.0.\nIf seller 7 uses stall F3, the setup/travel cost is 927.0.\nIf seller 8 uses stall F3, the setup/travel cost is 89.0.\nIf seller 9 uses stall F3, the setup/travel cost is 563.0.\nIf seller 10 uses stall F3, the setup/travel cost is 985.0.\nIf seller 11 uses stall F3, the setup/travel cost is 715.0.\nIf seller 12 uses stall F3, the setup/travel cost is 728.0.\nIf seller 13 uses stall F3, the setup/travel cost is 500.0.\nIf seller 14 uses stall F3, the setup/travel cost is 138.0.\nIf seller 15 uses stall F3, the setup/travel cost is 817.0.\nIf seller 16 uses stall F3, the setup/travel cost is 151.0.\nIf seller 1 uses stall F4, the setup/travel cost is 76.0.\nIf seller 2 uses stall F4, the setup/travel cost is 87.0.\nIf seller 3 uses stall F4, the setup/travel cost is 171.0.\nIf seller 4 uses stall F4, the setup/travel cost is 340.0.\nIf seller 5 uses stall F4, the setup/travel cost is 100.0.\nIf seller 6 uses stall F4, the setup/travel cost is 107.0.\nIf seller 7 uses stall F4, the setup/travel cost is 638.0.\nIf seller 8 uses stall F4, the setup/travel cost is 74.0.\nIf seller 9 uses stall F4, the setup/travel cost is 120.0.\nIf seller 10 uses stall F4, the setup/travel cost is 457.0.\nIf seller 11 uses stall F4, the setup/travel cost is 190.0.\nIf seller 12 uses stall F4, the setup/travel cost is 401.0.\nIf seller 13 uses stall F4, the setup/travel cost is 227.0.\nIf seller 14 uses stall F4, the setup/travel cost is 39.0.\nIf seller 15 uses stall F4, the setup/travel cost is 604.0.\nIf seller 16 uses stall F4, the setup/travel cost is 58.0.\nIf seller 1 uses stall F5, the setup/travel cost is 213.0.\nIf seller 2 uses stall F5, the setup/travel cost is 136.0.\nIf seller 3 uses stall F5, the setup/travel cost is 815.0.\nIf seller 4 uses stall F5, the setup/travel cost is 750.0.\nIf seller 5 uses stall F5, the setup/travel cost is 293.0.\nIf seller 6 uses stall F5, the setup/travel cost is 651.0.\nIf seller 7 uses stall F5, the setup/travel cost is 206.0.\nIf seller 8 uses stall F5, the setup/travel cost is 67.0.\nIf seller 9 uses stall F5, the setup/travel cost is 756.0.\nIf seller 10 uses stall F5, the setup/travel cost is 549.0.\nIf seller 11 uses stall F5, the setup/travel cost is 527.0.\nIf seller 12 uses stall F5, the setup/travel cost is 1006.0.\nIf seller 13 uses stall F5, the setup/travel cost is 783.0.\nIf seller 14 uses stall F5, the setup/travel cost is 417.0.\nIf seller 15 uses stall F5, the setup/travel cost is 200.0.\nIf seller 16 uses stall F5, the setup/travel cost is 452.0.\nIf seller 1 uses stall F6, the setup/travel cost is 256.0.\nIf seller 2 uses stall F6, the setup/travel cost is 212.0.\nIf seller 3 uses stall F6, the setup/travel cost is 909.0.\nIf seller 4 uses stall F6, the setup/travel cost is 833.0.\nIf seller 5 uses stall F6, the setup/travel cost is 349.0.\nIf seller 6 uses stall F6, the setup/travel cost is 734.0.\nIf seller 7 uses stall F6, the setup/travel cost is 21.0.\nIf seller 8 uses stall F6, the setup/travel cost is 105.0.\nIf seller 9 uses stall F6, the setup/travel cost is 850.0.\nIf seller 10 uses stall F6, the setup/travel cost is 587.0.\nIf seller 11 uses stall F6, the setup/travel cost is 607.0.\nIf seller 12 uses stall F6, the setup/travel cost is 1101.0.\nIf seller 13 uses stall F6, the setup/travel cost is 878.0.\nIf seller 14 uses stall F6, the setup/travel cost is 511.0.\nIf seller 15 uses stall F6, the setup/travel cost is 77.0.\nIf seller 16 uses stall F6, the setup/travel cost is 543.0.\nIf seller 1 uses stall F7, the setup/travel cost is 56.0.\nIf seller 2 uses stall F7, the setup/travel cost is 196.0.\nIf seller 3 uses stall F7, the setup/travel cost is 224.0.\nIf seller 4 uses stall F7, the setup/travel cost is 289.0.\nIf seller 5 uses stall F7, the setup/travel cost is 73.0.\nIf seller 6 uses stall F7, the setup/travel cost is 502.0.\nIf seller 7 uses stall F7, the setup/travel cost is 913.0.\nIf seller 8 uses stall F7, the setup/travel cost is 128.0.\nIf seller 9 uses stall F7, the setup/travel cost is 180.0.\nIf seller 10 uses stall F7, the setup/travel cost is 850.0.\nIf seller 11 uses stall F7, the setup/travel cost is 554.0.\nIf seller 12 uses stall F7, the setup/travel cost is 401.0.\nIf seller 13 uses stall F7, the setup/travel cost is 193.0.\nIf seller 14 uses stall F7, the setup/travel cost is 64.0.\nIf seller 15 uses stall F7, the setup/travel cost is 831.0.\nIf seller 16 uses stall F7, the setup/travel cost is 27.0.\nChoose stalls and assignments that minimize the total of stall rentals plus sellers' setup/travel costs.\n\nAlso, when you send back your answer, just use this simple JSON shape so I can read it easily — nothing more, nothing less.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list the stalls you'll rent. \"assignments\" lists, in the same order as the sellers show up in the instance, which rented stall each seller goes into. Super casual: think of \"selected\" as the list of booths on the lease, and \"assignments\" as the name-tag telling each seller which booth to set up at.\n\nThis JSON is just a sketch of the shape I expect, not the actual solution itself.\n\nPlease make sure to use the exact identifiers from the instance input — do not rename them or invent new ones. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 187.0, 448.0, 1227.0, 839.0, 285.0, 1300.0, 1138.0, 41.0, 1184.0, 1443.0, 1243.0, 1286.0, 1066.0, 758.0, 948.0, 701.0 ], [ 113.0, 43.0, 390.0, 477.0, 152.0, 179.0, 501.0, 46.0, 331.0, 349.0, 52.0, 613.0, 410.0, 111.0, 475.0, 156.0 ], [ 84.0, 154.0, 610.0, 463.0, 116.0, 725.0, 927.0, 89.0, 563.0, 985.0, 715.0, 728.0, 500.0, 138.0, 817.0, 151.0 ], [ 76.0, 87.0, 171.0, 340.0, 100.0, 107.0, 638.0, 74.0, 120.0, 457.0, 190.0, 401.0, 227.0, 39.0, 604.0, 58.0 ], [ 213.0, 136.0, 815.0, 750.0, 293.0, 651.0, 206.0, 67.0, 756.0, 549.0, 527.0, 1006.0, 783.0, 417.0, 200.0, 452.0 ], [ 256.0, 212.0, 909.0, 833.0, 349.0, 734.0, 21.0, 105.0, 850.0, 587.0, 607.0, 1101.0, 878.0, 511.0, 77.0, 543.0 ], [ 56.0, 196.0, 224.0, 289.0, 73.0, 502.0, 913.0, 128.0, 180.0, 850.0, 554.0, 401.0, 193.0, 64.0, 831.0, 27.0 ] ], "demands": [ 18.0, 20.0, 18.0, 20.0, 23.0, 27.0, 10.0, 20.0, 12.0, 23.0, 26.0, 27.0, 21.0, 18.0, 29.0, 13.0 ], "objective": 3745.0 }, "solution": { "open_facilities": [ 3, 5 ], "assignments": [ 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 5, 3 ] }, "obj": 3745.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 16, "facilities": [ { "id": "F1", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F2", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F3", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F4", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F5", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F6", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F7", "opening_cost": 600.0, "capacity": 700.0 } ], "customers": [ { "id": 1, "demand": 18.0 }, { "id": 2, "demand": 20.0 }, { "id": 3, "demand": 18.0 }, { "id": 4, "demand": 20.0 }, { "id": 5, "demand": 23.0 }, { "id": 6, "demand": 27.0 }, { "id": 7, "demand": 10.0 }, { "id": 8, "demand": 20.0 }, { "id": 9, "demand": 12.0 }, { "id": 10, "demand": 23.0 }, { "id": 11, "demand": 26.0 }, { "id": 12, "demand": 27.0 }, { "id": 13, "demand": 21.0 }, { "id": 14, "demand": 18.0 }, { "id": 15, "demand": 29.0 }, { "id": 16, "demand": 13.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 187.0 }, { "facility": "F1", "customer": 2, "cost": 448.0 }, { "facility": "F1", "customer": 3, "cost": 1227.0 }, { "facility": "F1", "customer": 4, "cost": 839.0 }, { "facility": "F1", "customer": 5, "cost": 285.0 }, { "facility": "F1", "customer": 6, "cost": 1300.0 }, { "facility": "F1", "customer": 7, "cost": 1138.0 }, { "facility": "F1", "customer": 8, "cost": 41.0 }, { "facility": "F1", "customer": 9, "cost": 1184.0 }, { "facility": "F1", "customer": 10, "cost": 1443.0 }, { "facility": "F1", "customer": 11, "cost": 1243.0 }, { "facility": "F1", "customer": 12, "cost": 1286.0 }, { "facility": "F1", "customer": 13, "cost": 1066.0 }, { "facility": "F1", "customer": 14, "cost": 758.0 }, { "facility": "F1", "customer": 15, "cost": 948.0 }, { "facility": "F1", "customer": 16, "cost": 701.0 }, { "facility": "F2", "customer": 1, "cost": 113.0 }, { "facility": "F2", "customer": 2, "cost": 43.0 }, { "facility": "F2", "customer": 3, "cost": 390.0 }, { "facility": "F2", "customer": 4, "cost": 477.0 }, { "facility": "F2", "customer": 5, "cost": 152.0 }, { "facility": "F2", "customer": 6, "cost": 179.0 }, { "facility": "F2", "customer": 7, "cost": 501.0 }, { "facility": "F2", "customer": 8, "cost": 46.0 }, { "facility": "F2", "customer": 9, "cost": 331.0 }, { "facility": "F2", "customer": 10, "cost": 349.0 }, { "facility": "F2", "customer": 11, "cost": 52.0 }, { "facility": "F2", "customer": 12, "cost": 613.0 }, { "facility": "F2", "customer": 13, "cost": 410.0 }, { "facility": "F2", "customer": 14, "cost": 111.0 }, { "facility": "F2", "customer": 15, "cost": 475.0 }, { "facility": "F2", "customer": 16, "cost": 156.0 }, { "facility": "F3", "customer": 1, "cost": 84.0 }, { "facility": "F3", "customer": 2, "cost": 154.0 }, { "facility": "F3", "customer": 3, "cost": 610.0 }, { "facility": "F3", "customer": 4, "cost": 463.0 }, { "facility": "F3", "customer": 5, "cost": 116.0 }, { "facility": "F3", "customer": 6, "cost": 725.0 }, { "facility": "F3", "customer": 7, "cost": 927.0 }, { "facility": "F3", "customer": 8, "cost": 89.0 }, { "facility": "F3", "customer": 9, "cost": 563.0 }, { "facility": "F3", "customer": 10, "cost": 985.0 }, { "facility": "F3", "customer": 11, "cost": 715.0 }, { "facility": "F3", "customer": 12, "cost": 728.0 }, { "facility": "F3", "customer": 13, "cost": 500.0 }, { "facility": "F3", "customer": 14, "cost": 138.0 }, { "facility": "F3", "customer": 15, "cost": 817.0 }, { "facility": "F3", "customer": 16, "cost": 151.0 }, { "facility": "F4", "customer": 1, "cost": 76.0 }, { "facility": "F4", "customer": 2, "cost": 87.0 }, { "facility": "F4", "customer": 3, "cost": 171.0 }, { "facility": "F4", "customer": 4, "cost": 340.0 }, { "facility": "F4", "customer": 5, "cost": 100.0 }, { "facility": "F4", "customer": 6, "cost": 107.0 }, { "facility": "F4", "customer": 7, "cost": 638.0 }, { "facility": "F4", "customer": 8, "cost": 74.0 }, { "facility": "F4", "customer": 9, "cost": 120.0 }, { "facility": "F4", "customer": 10, "cost": 457.0 }, { "facility": "F4", "customer": 11, "cost": 190.0 }, { "facility": "F4", "customer": 12, "cost": 401.0 }, { "facility": "F4", "customer": 13, "cost": 227.0 }, { "facility": "F4", "customer": 14, "cost": 39.0 }, { "facility": "F4", "customer": 15, "cost": 604.0 }, { "facility": "F4", "customer": 16, "cost": 58.0 }, { "facility": "F5", "customer": 1, "cost": 213.0 }, { "facility": "F5", "customer": 2, "cost": 136.0 }, { "facility": "F5", "customer": 3, "cost": 815.0 }, { "facility": "F5", "customer": 4, "cost": 750.0 }, { "facility": "F5", "customer": 5, "cost": 293.0 }, { "facility": "F5", "customer": 6, "cost": 651.0 }, { "facility": "F5", "customer": 7, "cost": 206.0 }, { "facility": "F5", "customer": 8, "cost": 67.0 }, { "facility": "F5", "customer": 9, "cost": 756.0 }, { "facility": "F5", "customer": 10, "cost": 549.0 }, { "facility": "F5", "customer": 11, "cost": 527.0 }, { "facility": "F5", "customer": 12, "cost": 1006.0 }, { "facility": "F5", "customer": 13, "cost": 783.0 }, { "facility": "F5", "customer": 14, "cost": 417.0 }, { "facility": "F5", "customer": 15, "cost": 200.0 }, { "facility": "F5", "customer": 16, "cost": 452.0 }, { "facility": "F6", "customer": 1, "cost": 256.0 }, { "facility": "F6", "customer": 2, "cost": 212.0 }, { "facility": "F6", "customer": 3, "cost": 909.0 }, { "facility": "F6", "customer": 4, "cost": 833.0 }, { "facility": "F6", "customer": 5, "cost": 349.0 }, { "facility": "F6", "customer": 6, "cost": 734.0 }, { "facility": "F6", "customer": 7, "cost": 21.0 }, { "facility": "F6", "customer": 8, "cost": 105.0 }, { "facility": "F6", "customer": 9, "cost": 850.0 }, { "facility": "F6", "customer": 10, "cost": 587.0 }, { "facility": "F6", "customer": 11, "cost": 607.0 }, { "facility": "F6", "customer": 12, "cost": 1101.0 }, { "facility": "F6", "customer": 13, "cost": 878.0 }, { "facility": "F6", "customer": 14, "cost": 511.0 }, { "facility": "F6", "customer": 15, "cost": 77.0 }, { "facility": "F6", "customer": 16, "cost": 543.0 }, { "facility": "F7", "customer": 1, "cost": 56.0 }, { "facility": "F7", "customer": 2, "cost": 196.0 }, { "facility": "F7", "customer": 3, "cost": 224.0 }, { "facility": "F7", "customer": 4, "cost": 289.0 }, { "facility": "F7", "customer": 5, "cost": 73.0 }, { "facility": "F7", "customer": 6, "cost": 502.0 }, { "facility": "F7", "customer": 7, "cost": 913.0 }, { "facility": "F7", "customer": 8, "cost": 128.0 }, { "facility": "F7", "customer": 9, "cost": 180.0 }, { "facility": "F7", "customer": 10, "cost": 850.0 }, { "facility": "F7", "customer": 11, "cost": 554.0 }, { "facility": "F7", "customer": 12, "cost": 401.0 }, { "facility": "F7", "customer": 13, "cost": 193.0 }, { "facility": "F7", "customer": 14, "cost": 64.0 }, { "facility": "F7", "customer": 15, "cost": 831.0 }, { "facility": "F7", "customer": 16, "cost": 27.0 } ], "objective": 3745.0 }, "solution_variant": { "selected": [ "F4", "F6" ], "assignments": [ "F4", "F4", "F4", "F4", "F4", "F4", "F6", "F4", "F4", "F4", "F4", "F4", "F4", "F4", "F6", "F4" ] }, "context_index": 27, "input_format": "nl", "input_index_base": 1 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "I run the campus dining operation and have to pick which satellite kitchens to keep cooking and which to close, then decide which whole student groups each open kitchen will feed. No group gets split up, and no kitchen is asked to handle more students than it can actually serve. A good plan is the one that keeps the overall bill low — that bill being the sum of the kitchens’ running costs plus whatever it costs to get food from a kitchen to a group — and the specific kitchen sizes, opening costs, and group demands are shown below.\n\n{\n \"num_kitchens\": 8,\n \"num_student_groups\": 18,\n \"kitchens\": [\n {\n \"kitchen_id\": \"F1\",\n \"kitchen_operating_cost\": 400.0,\n \"kitchen_capacity_students\": 500.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"kitchen_operating_cost\": 400.0,\n \"kitchen_capacity_students\": 500.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"kitchen_operating_cost\": 400.0,\n \"kitchen_capacity_students\": 500.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"kitchen_operating_cost\": 400.0,\n \"kitchen_capacity_students\": 500.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"kitchen_operating_cost\": 400.0,\n \"kitchen_capacity_students\": 500.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"kitchen_operating_cost\": 400.0,\n \"kitchen_capacity_students\": 500.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"kitchen_operating_cost\": 400.0,\n \"kitchen_capacity_students\": 500.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"kitchen_operating_cost\": 400.0,\n \"kitchen_capacity_students\": 500.0\n }\n ],\n \"student_groups\": [\n {\n \"student_group_id\": \"A\",\n \"group_size\": 13.0\n },\n {\n \"student_group_id\": \"B\",\n \"group_size\": 18.0\n },\n {\n \"student_group_id\": \"C\",\n \"group_size\": 12.0\n },\n {\n \"student_group_id\": \"D\",\n \"group_size\": 20.0\n },\n {\n \"student_group_id\": \"E\",\n \"group_size\": 17.0\n },\n {\n \"student_group_id\": \"F\",\n \"group_size\": 27.0\n },\n {\n \"student_group_id\": \"G\",\n \"group_size\": 23.0\n },\n {\n \"student_group_id\": \"H\",\n \"group_size\": 26.0\n },\n {\n \"student_group_id\": \"I\",\n \"group_size\": 17.0\n },\n {\n \"student_group_id\": \"J\",\n \"group_size\": 18.0\n },\n {\n \"student_group_id\": \"K\",\n \"group_size\": 16.0\n },\n {\n \"student_group_id\": \"L\",\n \"group_size\": 27.0\n },\n {\n \"student_group_id\": \"M\",\n \"group_size\": 23.0\n },\n {\n \"student_group_id\": \"N\",\n \"group_size\": 11.0\n },\n {\n \"student_group_id\": \"O\",\n \"group_size\": 16.0\n },\n {\n \"student_group_id\": \"P\",\n \"group_size\": 15.0\n },\n {\n \"student_group_id\": \"Q\",\n \"group_size\": 21.0\n },\n {\n \"student_group_id\": \"R\",\n \"group_size\": 11.0\n }\n ],\n \"distributions\": [\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"A\",\n \"distribution_cost\": 902.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"B\",\n \"distribution_cost\": 97.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"C\",\n \"distribution_cost\": 25.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"D\",\n \"distribution_cost\": 212.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"E\",\n \"distribution_cost\": 639.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"F\",\n \"distribution_cost\": 179.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"G\",\n \"distribution_cost\": 360.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"H\",\n \"distribution_cost\": 234.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"I\",\n \"distribution_cost\": 38.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"J\",\n \"distribution_cost\": 649.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"K\",\n \"distribution_cost\": 219.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"L\",\n \"distribution_cost\": 383.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"M\",\n \"distribution_cost\": 46.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"N\",\n \"distribution_cost\": 266.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"O\",\n \"distribution_cost\": 677.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"P\",\n \"distribution_cost\": 659.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"Q\",\n \"distribution_cost\": 410.0\n },\n {\n \"kitchen_id\": \"F1\",\n \"student_group_id\": \"R\",\n \"distribution_cost\": 606.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"A\",\n \"distribution_cost\": 915.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"B\",\n \"distribution_cost\": 37.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"C\",\n \"distribution_cost\": 328.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"D\",\n \"distribution_cost\": 634.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"E\",\n \"distribution_cost\": 386.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"F\",\n \"distribution_cost\": 429.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"G\",\n \"distribution_cost\": 709.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"H\",\n \"distribution_cost\": 531.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"I\",\n \"distribution_cost\": 186.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"J\",\n \"distribution_cost\": 772.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"K\",\n \"distribution_cost\": 32.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"L\",\n \"distribution_cost\": 781.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"M\",\n \"distribution_cost\": 342.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"N\",\n \"distribution_cost\": 35.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"O\",\n \"distribution_cost\": 123.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"P\",\n \"distribution_cost\": 78.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"Q\",\n \"distribution_cost\": 43.0\n },\n {\n \"kitchen_id\": \"F2\",\n \"student_group_id\": \"R\",\n \"distribution_cost\": 501.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"A\",\n \"distribution_cost\": 1319.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"B\",\n \"distribution_cost\": 188.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"C\",\n \"distribution_cost\": 333.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"D\",\n \"distribution_cost\": 92.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"E\",\n \"distribution_cost\": 1114.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"F\",\n \"distribution_cost\": 651.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"G\",\n \"distribution_cost\": 136.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"H\",\n \"distribution_cost\": 78.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"I\",\n \"distribution_cost\": 211.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"J\",\n \"distribution_cost\": 1070.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"K\",\n \"distribution_cost\": 491.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"L\",\n \"distribution_cost\": 691.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"M\",\n \"distribution_cost\": 288.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"N\",\n \"distribution_cost\": 629.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"O\",\n \"distribution_cost\": 1076.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"P\",\n \"distribution_cost\": 1116.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"Q\",\n \"distribution_cost\": 783.0\n },\n {\n \"kitchen_id\": \"F3\",\n \"student_group_id\": \"R\",\n \"distribution_cost\": 1077.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"A\",\n \"distribution_cost\": 1700.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"B\",\n \"distribution_cost\": 249.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"C\",\n \"distribution_cost\": 627.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"D\",\n \"distribution_cost\": 422.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"E\",\n \"distribution_cost\": 1452.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"F\",\n \"distribution_cost\": 990.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"G\",\n \"distribution_cost\": 74.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"H\",\n \"distribution_cost\": 52.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"I\",\n \"distribution_cost\": 401.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"J\",\n \"distribution_cost\": 1448.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"K\",\n \"distribution_cost\": 671.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"L\",\n \"distribution_cost\": 1078.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"M\",\n \"distribution_cost\": 562.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"N\",\n \"distribution_cost\": 871.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"O\",\n \"distribution_cost\": 1320.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"P\",\n \"distribution_cost\": 1418.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"Q\",\n \"distribution_cost\": 1020.0\n },\n {\n \"kitchen_id\": \"F4\",\n \"student_group_id\": \"R\",\n \"distribution_cost\": 1429.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"A\",\n \"distribution_cost\": 1996.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"B\",\n \"distribution_cost\": 60.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"C\",\n \"distribution_cost\": 1025.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"D\",\n \"distribution_cost\": 1269.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"E\",\n \"distribution_cost\": 1482.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"F\",\n \"distribution_cost\": 1300.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"G\",\n \"distribution_cost\": 1136.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"H\",\n \"distribution_cost\": 912.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"I\",\n \"distribution_cost\": 669.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"J\",\n \"distribution_cost\": 1796.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"K\",\n \"distribution_cost\": 319.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"L\",\n \"distribution_cost\": 1659.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"M\",\n \"distribution_cost\": 992.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"N\",\n \"distribution_cost\": 662.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"O\",\n \"distribution_cost\": 782.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"P\",\n \"distribution_cost\": 1210.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"Q\",\n \"distribution_cost\": 652.0\n },\n {\n \"kitchen_id\": \"F5\",\n \"student_group_id\": \"R\",\n \"distribution_cost\": 1570.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"A\",\n \"distribution_cost\": 2223.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"B\",\n \"distribution_cost\": 257.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"C\",\n \"distribution_cost\": 1057.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"D\",\n \"distribution_cost\": 1025.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"E\",\n \"distribution_cost\": 1866.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"F\",\n \"distribution_cost\": 1449.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"G\",\n \"distribution_cost\": 615.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"H\",\n \"distribution_cost\": 388.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"I\",\n \"distribution_cost\": 680.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"J\",\n \"distribution_cost\": 1972.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"K\",\n \"distribution_cost\": 837.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"L\",\n \"distribution_cost\": 1654.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"M\",\n \"distribution_cost\": 982.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"N\",\n \"distribution_cost\": 1132.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"O\",\n \"distribution_cost\": 1546.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"P\",\n \"distribution_cost\": 1752.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"Q\",\n \"distribution_cost\": 1258.0\n },\n {\n \"kitchen_id\": \"F6\",\n \"student_group_id\": \"R\",\n \"distribution_cost\": 1881.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"A\",\n \"distribution_cost\": 1357.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"B\",\n \"distribution_cost\": 230.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"C\",\n \"distribution_cost\": 428.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"D\",\n \"distribution_cost\": 187.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"E\",\n \"distribution_cost\": 1192.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"F\",\n \"distribution_cost\": 734.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"G\",\n \"distribution_cost\": 62.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"H\",\n \"distribution_cost\": 52.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"I\",\n \"distribution_cost\": 295.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"J\",\n \"distribution_cost\": 1116.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"K\",\n \"distribution_cost\": 577.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"L\",\n \"distribution_cost\": 732.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"M\",\n \"distribution_cost\": 383.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"N\",\n \"distribution_cost\": 724.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"O\",\n \"distribution_cost\": 1171.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"P\",\n \"distribution_cost\": 1206.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"Q\",\n \"distribution_cost\": 878.0\n },\n {\n \"kitchen_id\": \"F7\",\n \"student_group_id\": \"R\",\n \"distribution_cost\": 1147.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"A\",\n \"distribution_cost\": 1364.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"B\",\n \"distribution_cost\": 41.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"C\",\n \"distribution_cost\": 440.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"D\",\n \"distribution_cost\": 735.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"E\",\n \"distribution_cost\": 870.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"F\",\n \"distribution_cost\": 665.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"G\",\n \"distribution_cost\": 741.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"H\",\n \"distribution_cost\": 547.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"I\",\n \"distribution_cost\": 201.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"J\",\n \"distribution_cost\": 1157.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"K\",\n \"distribution_cost\": 43.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"L\",\n \"distribution_cost\": 1034.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"M\",\n \"distribution_cost\": 429.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"N\",\n \"distribution_cost\": 22.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"O\",\n \"distribution_cost\": 472.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"P\",\n \"distribution_cost\": 662.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"Q\",\n \"distribution_cost\": 175.0\n },\n {\n \"kitchen_id\": \"F8\",\n \"student_group_id\": \"R\",\n \"distribution_cost\": 943.0\n }\n ]\n}\n\nOh, and when you reply with a plan, please follow this little JSON layout so I can read it easily — nothing fancy, just a consistent shape. Here's the sketch I like:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list which kitchens you decide to keep running (use the exact kitchen IDs from the instance). \"assignments\" is a list that, in order, says which open kitchen feeds each student group (again, use the exact IDs). This is just the expected shape — a sketch, not the final plan.\n\nPlease make sure you use the identifiers exactly as they appear in the instance input — no renaming and no new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 902.0, 97.0, 25.0, 212.0, 639.0, 179.0, 360.0, 234.0, 38.0, 649.0, 219.0, 383.0, 46.0, 266.0, 677.0, 659.0, 410.0, 606.0 ], [ 915.0, 37.0, 328.0, 634.0, 386.0, 429.0, 709.0, 531.0, 186.0, 772.0, 32.0, 781.0, 342.0, 35.0, 123.0, 78.0, 43.0, 501.0 ], [ 1319.0, 188.0, 333.0, 92.0, 1114.0, 651.0, 136.0, 78.0, 211.0, 1070.0, 491.0, 691.0, 288.0, 629.0, 1076.0, 1116.0, 783.0, 1077.0 ], [ 1700.0, 249.0, 627.0, 422.0, 1452.0, 990.0, 74.0, 52.0, 401.0, 1448.0, 671.0, 1078.0, 562.0, 871.0, 1320.0, 1418.0, 1020.0, 1429.0 ], [ 1996.0, 60.0, 1025.0, 1269.0, 1482.0, 1300.0, 1136.0, 912.0, 669.0, 1796.0, 319.0, 1659.0, 992.0, 662.0, 782.0, 1210.0, 652.0, 1570.0 ], [ 2223.0, 257.0, 1057.0, 1025.0, 1866.0, 1449.0, 615.0, 388.0, 680.0, 1972.0, 837.0, 1654.0, 982.0, 1132.0, 1546.0, 1752.0, 1258.0, 1881.0 ], [ 1357.0, 230.0, 428.0, 187.0, 1192.0, 734.0, 62.0, 52.0, 295.0, 1116.0, 577.0, 732.0, 383.0, 724.0, 1171.0, 1206.0, 878.0, 1147.0 ], [ 1364.0, 41.0, 440.0, 735.0, 870.0, 665.0, 741.0, 547.0, 201.0, 1157.0, 43.0, 1034.0, 429.0, 22.0, 472.0, 662.0, 175.0, 943.0 ] ], "demands": [ 13.0, 18.0, 12.0, 20.0, 17.0, 27.0, 23.0, 26.0, 17.0, 18.0, 16.0, 27.0, 23.0, 11.0, 16.0, 15.0, 21.0, 11.0 ], "objective": 4958.0 }, "solution": { "open_facilities": [ 0, 1, 6 ], "assignments": [ 0, 1, 0, 6, 1, 0, 6, 6, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1 ] }, "obj": 4958.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 18, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F7", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F8", "opening_cost": 400.0, "capacity": 500.0 } ], "customers": [ { "id": "A", "demand": 13.0 }, { "id": "B", "demand": 18.0 }, { "id": "C", "demand": 12.0 }, { "id": "D", "demand": 20.0 }, { "id": "E", "demand": 17.0 }, { "id": "F", "demand": 27.0 }, { "id": "G", "demand": 23.0 }, { "id": "H", "demand": 26.0 }, { "id": "I", "demand": 17.0 }, { "id": "J", "demand": 18.0 }, { "id": "K", "demand": 16.0 }, { "id": "L", "demand": 27.0 }, { "id": "M", "demand": 23.0 }, { "id": "N", "demand": 11.0 }, { "id": "O", "demand": 16.0 }, { "id": "P", "demand": 15.0 }, { "id": "Q", "demand": 21.0 }, { "id": "R", "demand": 11.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 902.0 }, { "facility": "F1", "customer": "B", "cost": 97.0 }, { "facility": "F1", "customer": "C", "cost": 25.0 }, { "facility": "F1", "customer": "D", "cost": 212.0 }, { "facility": "F1", "customer": "E", "cost": 639.0 }, { "facility": "F1", "customer": "F", "cost": 179.0 }, { "facility": "F1", "customer": "G", "cost": 360.0 }, { "facility": "F1", "customer": "H", "cost": 234.0 }, { "facility": "F1", "customer": "I", "cost": 38.0 }, { "facility": "F1", "customer": "J", "cost": 649.0 }, { "facility": "F1", "customer": "K", "cost": 219.0 }, { "facility": "F1", "customer": "L", "cost": 383.0 }, { "facility": "F1", "customer": "M", "cost": 46.0 }, { "facility": "F1", "customer": "N", "cost": 266.0 }, { "facility": "F1", "customer": "O", "cost": 677.0 }, { "facility": "F1", "customer": "P", "cost": 659.0 }, { "facility": "F1", "customer": "Q", "cost": 410.0 }, { "facility": "F1", "customer": "R", "cost": 606.0 }, { "facility": "F2", "customer": "A", "cost": 915.0 }, { "facility": "F2", "customer": "B", "cost": 37.0 }, { "facility": "F2", "customer": "C", "cost": 328.0 }, { "facility": "F2", "customer": "D", "cost": 634.0 }, { "facility": "F2", "customer": "E", "cost": 386.0 }, { "facility": "F2", "customer": "F", "cost": 429.0 }, { "facility": "F2", "customer": "G", "cost": 709.0 }, { "facility": "F2", "customer": "H", "cost": 531.0 }, { "facility": "F2", "customer": "I", "cost": 186.0 }, { "facility": "F2", "customer": "J", "cost": 772.0 }, { "facility": "F2", "customer": "K", "cost": 32.0 }, { "facility": "F2", "customer": "L", "cost": 781.0 }, { "facility": "F2", "customer": "M", "cost": 342.0 }, { "facility": "F2", "customer": "N", "cost": 35.0 }, { "facility": "F2", "customer": "O", "cost": 123.0 }, { "facility": "F2", "customer": "P", "cost": 78.0 }, { "facility": "F2", "customer": "Q", "cost": 43.0 }, { "facility": "F2", "customer": "R", "cost": 501.0 }, { "facility": "F3", "customer": "A", "cost": 1319.0 }, { "facility": "F3", "customer": "B", "cost": 188.0 }, { "facility": "F3", "customer": "C", "cost": 333.0 }, { "facility": "F3", "customer": "D", "cost": 92.0 }, { "facility": "F3", "customer": "E", "cost": 1114.0 }, { "facility": "F3", "customer": "F", "cost": 651.0 }, { "facility": "F3", "customer": "G", "cost": 136.0 }, { "facility": "F3", "customer": "H", "cost": 78.0 }, { "facility": "F3", "customer": "I", "cost": 211.0 }, { "facility": "F3", "customer": "J", "cost": 1070.0 }, { "facility": "F3", "customer": "K", "cost": 491.0 }, { "facility": "F3", "customer": "L", "cost": 691.0 }, { "facility": "F3", "customer": "M", "cost": 288.0 }, { "facility": "F3", "customer": "N", "cost": 629.0 }, { "facility": "F3", "customer": "O", "cost": 1076.0 }, { "facility": "F3", "customer": "P", "cost": 1116.0 }, { "facility": "F3", "customer": "Q", "cost": 783.0 }, { "facility": "F3", "customer": "R", "cost": 1077.0 }, { "facility": "F4", "customer": "A", "cost": 1700.0 }, { "facility": "F4", "customer": "B", "cost": 249.0 }, { "facility": "F4", "customer": "C", "cost": 627.0 }, { "facility": "F4", "customer": "D", "cost": 422.0 }, { "facility": "F4", "customer": "E", "cost": 1452.0 }, { "facility": "F4", "customer": "F", "cost": 990.0 }, { "facility": "F4", "customer": "G", "cost": 74.0 }, { "facility": "F4", "customer": "H", "cost": 52.0 }, { "facility": "F4", "customer": "I", "cost": 401.0 }, { "facility": "F4", "customer": "J", "cost": 1448.0 }, { "facility": "F4", "customer": "K", "cost": 671.0 }, { "facility": "F4", "customer": "L", "cost": 1078.0 }, { "facility": "F4", "customer": "M", "cost": 562.0 }, { "facility": "F4", "customer": "N", "cost": 871.0 }, { "facility": "F4", "customer": "O", "cost": 1320.0 }, { "facility": "F4", "customer": "P", "cost": 1418.0 }, { "facility": "F4", "customer": "Q", "cost": 1020.0 }, { "facility": "F4", "customer": "R", "cost": 1429.0 }, { "facility": "F5", "customer": "A", "cost": 1996.0 }, { "facility": "F5", "customer": "B", "cost": 60.0 }, { "facility": "F5", "customer": "C", "cost": 1025.0 }, { "facility": "F5", "customer": "D", "cost": 1269.0 }, { "facility": "F5", "customer": "E", "cost": 1482.0 }, { "facility": "F5", "customer": "F", "cost": 1300.0 }, { "facility": "F5", "customer": "G", "cost": 1136.0 }, { "facility": "F5", "customer": "H", "cost": 912.0 }, { "facility": "F5", "customer": "I", "cost": 669.0 }, { "facility": "F5", "customer": "J", "cost": 1796.0 }, { "facility": "F5", "customer": "K", "cost": 319.0 }, { "facility": "F5", "customer": "L", "cost": 1659.0 }, { "facility": "F5", "customer": "M", "cost": 992.0 }, { "facility": "F5", "customer": "N", "cost": 662.0 }, { "facility": "F5", "customer": "O", "cost": 782.0 }, { "facility": "F5", "customer": "P", "cost": 1210.0 }, { "facility": "F5", "customer": "Q", "cost": 652.0 }, { "facility": "F5", "customer": "R", "cost": 1570.0 }, { "facility": "F6", "customer": "A", "cost": 2223.0 }, { "facility": "F6", "customer": "B", "cost": 257.0 }, { "facility": "F6", "customer": "C", "cost": 1057.0 }, { "facility": "F6", "customer": "D", "cost": 1025.0 }, { "facility": "F6", "customer": "E", "cost": 1866.0 }, { "facility": "F6", "customer": "F", "cost": 1449.0 }, { "facility": "F6", "customer": "G", "cost": 615.0 }, { "facility": "F6", "customer": "H", "cost": 388.0 }, { "facility": "F6", "customer": "I", "cost": 680.0 }, { "facility": "F6", "customer": "J", "cost": 1972.0 }, { "facility": "F6", "customer": "K", "cost": 837.0 }, { "facility": "F6", "customer": "L", "cost": 1654.0 }, { "facility": "F6", "customer": "M", "cost": 982.0 }, { "facility": "F6", "customer": "N", "cost": 1132.0 }, { "facility": "F6", "customer": "O", "cost": 1546.0 }, { "facility": "F6", "customer": "P", "cost": 1752.0 }, { "facility": "F6", "customer": "Q", "cost": 1258.0 }, { "facility": "F6", "customer": "R", "cost": 1881.0 }, { "facility": "F7", "customer": "A", "cost": 1357.0 }, { "facility": "F7", "customer": "B", "cost": 230.0 }, { "facility": "F7", "customer": "C", "cost": 428.0 }, { "facility": "F7", "customer": "D", "cost": 187.0 }, { "facility": "F7", "customer": "E", "cost": 1192.0 }, { "facility": "F7", "customer": "F", "cost": 734.0 }, { "facility": "F7", "customer": "G", "cost": 62.0 }, { "facility": "F7", "customer": "H", "cost": 52.0 }, { "facility": "F7", "customer": "I", "cost": 295.0 }, { "facility": "F7", "customer": "J", "cost": 1116.0 }, { "facility": "F7", "customer": "K", "cost": 577.0 }, { "facility": "F7", "customer": "L", "cost": 732.0 }, { "facility": "F7", "customer": "M", "cost": 383.0 }, { "facility": "F7", "customer": "N", "cost": 724.0 }, { "facility": "F7", "customer": "O", "cost": 1171.0 }, { "facility": "F7", "customer": "P", "cost": 1206.0 }, { "facility": "F7", "customer": "Q", "cost": 878.0 }, { "facility": "F7", "customer": "R", "cost": 1147.0 }, { "facility": "F8", "customer": "A", "cost": 1364.0 }, { "facility": "F8", "customer": "B", "cost": 41.0 }, { "facility": "F8", "customer": "C", "cost": 440.0 }, { "facility": "F8", "customer": "D", "cost": 735.0 }, { "facility": "F8", "customer": "E", "cost": 870.0 }, { "facility": "F8", "customer": "F", "cost": 665.0 }, { "facility": "F8", "customer": "G", "cost": 741.0 }, { "facility": "F8", "customer": "H", "cost": 547.0 }, { "facility": "F8", "customer": "I", "cost": 201.0 }, { "facility": "F8", "customer": "J", "cost": 1157.0 }, { "facility": "F8", "customer": "K", "cost": 43.0 }, { "facility": "F8", "customer": "L", "cost": 1034.0 }, { "facility": "F8", "customer": "M", "cost": 429.0 }, { "facility": "F8", "customer": "N", "cost": 22.0 }, { "facility": "F8", "customer": "O", "cost": 472.0 }, { "facility": "F8", "customer": "P", "cost": 662.0 }, { "facility": "F8", "customer": "Q", "cost": 175.0 }, { "facility": "F8", "customer": "R", "cost": 943.0 } ], "objective": 4958.0 }, "solution_variant": { "selected": [ "F1", "F2", "F7" ], "assignments": [ "F1", "F2", "F1", "F7", "F2", "F1", "F7", "F7", "F1", "F1", "F2", "F1", "F1", "F2", "F2", "F2", "F2", "F2" ] }, "context_index": 28, "input_format": "json", "input_index_base": "names" }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "We manage a cluster of possible driver stations and have to choose which ones to bring people in to staff, then send each rider to exactly one staffed station for pickup. Staffing a station costs money and each station can only cover so many riders, while every rider assigned to a station creates an extra pickup detour cost. A good plan keeps the overall expense as small as possible — sum up the staffing charges for the stations opened and the detour costs for all rider pickups — while making sure every rider is tied to a single staffed station and no station exceeds its driver limit. The specific numbers and scenarios follow below.\n\n# num_hubs=7\n# num_riders=18\n# HUBS\nhub_id,staffing_cost,driver_capacity\nF1,400.0,800.0\nF2,400.0,800.0\nF3,400.0,800.0\nF4,400.0,800.0\nF5,400.0,800.0\nF6,400.0,800.0\nF7,400.0,800.0\n# RIDERS\nrider_id,rider_demand\nA,30.0\nB,14.0\nC,17.0\nD,49.0\nE,42.0\nF,19.0\nG,25.0\nH,45.0\nI,26.0\nJ,15.0\nK,38.0\nL,33.0\nM,36.0\nN,14.0\nO,17.0\nP,40.0\nQ,16.0\nR,48.0\n# PICKUP_DETOURS\nhub_id,rider_id,pickup_detour_cost\nF1,A,359.0\nF1,B,265.0\nF1,C,264.0\nF1,D,133.0\nF1,E,237.0\nF1,F,367.0\nF1,G,371.0\nF1,H,204.0\nF1,I,364.0\nF1,J,397.0\nF1,K,288.0\nF1,L,361.0\nF1,M,353.0\nF1,N,353.0\nF1,O,324.0\nF1,P,574.0\nF1,Q,463.0\nF1,R,475.0\nF2,A,11.0\nF2,B,504.0\nF2,C,464.0\nF2,D,392.0\nF2,E,501.0\nF2,F,354.0\nF2,G,716.0\nF2,H,563.0\nF2,I,644.0\nF2,J,453.0\nF2,K,599.0\nF2,L,685.0\nF2,M,648.0\nF2,N,131.0\nF2,O,91.0\nF2,P,679.0\nF2,Q,640.0\nF2,R,829.0\nF3,A,123.0\nF3,B,524.0\nF3,C,351.0\nF3,D,394.0\nF3,E,400.0\nF3,F,221.0\nF3,G,637.0\nF3,H,516.0\nF3,I,538.0\nF3,J,321.0\nF3,K,507.0\nF3,L,595.0\nF3,M,548.0\nF3,N,36.0\nF3,O,42.0\nF3,P,547.0\nF3,Q,514.0\nF3,R,758.0\nF4,A,341.0\nF4,B,488.0\nF4,C,118.0\nF4,D,353.0\nF4,E,173.0\nF4,F,152.0\nF4,G,426.0\nF4,H,362.0\nF4,I,306.0\nF4,J,175.0\nF4,K,286.0\nF4,L,373.0\nF4,M,319.0\nF4,N,261.0\nF4,O,267.0\nF4,P,375.0\nF4,Q,300.0\nF4,R,554.0\nF5,A,364.0\nF5,B,365.0\nF5,C,164.0\nF5,D,235.0\nF5,E,152.0\nF5,F,281.0\nF5,G,350.0\nF5,H,241.0\nF5,I,293.0\nF5,J,299.0\nF5,K,234.0\nF5,L,318.0\nF5,M,289.0\nF5,N,324.0\nF5,O,309.0\nF5,P,473.0\nF5,Q,365.0\nF5,R,470.0\nF6,A,404.0\nF6,B,106.0\nF6,C,475.0\nF6,D,82.0\nF6,E,443.0\nF6,F,549.0\nF6,G,508.0\nF6,H,297.0\nF6,I,557.0\nF6,J,598.0\nF6,K,470.0\nF6,L,525.0\nF6,M,538.0\nF6,N,457.0\nF6,O,412.0\nF6,P,784.0\nF6,Q,672.0\nF6,R,577.0\nF7,A,533.0\nF7,B,250.0\nF7,C,324.0\nF7,D,196.0\nF7,E,256.0\nF7,F,496.0\nF7,G,240.0\nF7,H,32.0\nF7,I,322.0\nF7,J,496.0\nF7,K,229.0\nF7,L,264.0\nF7,M,295.0\nF7,N,524.0\nF7,O,498.0\nF7,P,622.0\nF7,Q,484.0\nF7,R,318.0\n\nOh, and one more practical thing — when you send back your plan, please put it in a little JSON package so it's easy to read by humans or tools. Something casual like this shape will do:\n\n{\n \"solution\": {\n \"selected\": [\"\", \"\", ...],\n \"assignments\": [\"\", \"\", ...]\n }\n}\n\nThink of \"selected\" as the list of stations you're deciding to staff, and \"assignments\" as which staffed station each rider gets sent to (one entry per rider). This is just the shape we want — a sketch, not the final numbers.\n\nPlease remember: use the exact identifiers from the instance input when you fill those placeholders — don't rename them or invent new labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 800.0, 800.0, 800.0, 800.0, 800.0, 800.0, 800.0 ], "connection_costs": [ [ 359.0, 265.0, 264.0, 133.0, 237.0, 367.0, 371.0, 204.0, 364.0, 397.0, 288.0, 361.0, 353.0, 353.0, 324.0, 574.0, 463.0, 475.0 ], [ 11.0, 504.0, 464.0, 392.0, 501.0, 354.0, 716.0, 563.0, 644.0, 453.0, 599.0, 685.0, 648.0, 131.0, 91.0, 679.0, 640.0, 829.0 ], [ 123.0, 524.0, 351.0, 394.0, 400.0, 221.0, 637.0, 516.0, 538.0, 321.0, 507.0, 595.0, 548.0, 36.0, 42.0, 547.0, 514.0, 758.0 ], [ 341.0, 488.0, 118.0, 353.0, 173.0, 152.0, 426.0, 362.0, 306.0, 175.0, 286.0, 373.0, 319.0, 261.0, 267.0, 375.0, 300.0, 554.0 ], [ 364.0, 365.0, 164.0, 235.0, 152.0, 281.0, 350.0, 241.0, 293.0, 299.0, 234.0, 318.0, 289.0, 324.0, 309.0, 473.0, 365.0, 470.0 ], [ 404.0, 106.0, 475.0, 82.0, 443.0, 549.0, 508.0, 297.0, 557.0, 598.0, 470.0, 525.0, 538.0, 457.0, 412.0, 784.0, 672.0, 577.0 ], [ 533.0, 250.0, 324.0, 196.0, 256.0, 496.0, 240.0, 32.0, 322.0, 496.0, 229.0, 264.0, 295.0, 524.0, 498.0, 622.0, 484.0, 318.0 ] ], "demands": [ 30.0, 14.0, 17.0, 49.0, 42.0, 19.0, 25.0, 45.0, 26.0, 15.0, 38.0, 33.0, 36.0, 14.0, 17.0, 40.0, 16.0, 48.0 ], "objective": 4824.0 }, "solution": { "open_facilities": [ 2, 3, 6 ], "assignments": [ 2, 6, 3, 6, 3, 3, 6, 6, 3, 3, 6, 6, 6, 2, 2, 3, 3, 6 ] }, "obj": 4824.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 18, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 800.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 800.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 800.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 800.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 800.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 800.0 }, { "id": "F7", "opening_cost": 400.0, "capacity": 800.0 } ], "customers": [ { "id": "A", "demand": 30.0 }, { "id": "B", "demand": 14.0 }, { "id": "C", "demand": 17.0 }, { "id": "D", "demand": 49.0 }, { "id": "E", "demand": 42.0 }, { "id": "F", "demand": 19.0 }, { "id": "G", "demand": 25.0 }, { "id": "H", "demand": 45.0 }, { "id": "I", "demand": 26.0 }, { "id": "J", "demand": 15.0 }, { "id": "K", "demand": 38.0 }, { "id": "L", "demand": 33.0 }, { "id": "M", "demand": 36.0 }, { "id": "N", "demand": 14.0 }, { "id": "O", "demand": 17.0 }, { "id": "P", "demand": 40.0 }, { "id": "Q", "demand": 16.0 }, { "id": "R", "demand": 48.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 359.0 }, { "facility": "F1", "customer": "B", "cost": 265.0 }, { "facility": "F1", "customer": "C", "cost": 264.0 }, { "facility": "F1", "customer": "D", "cost": 133.0 }, { "facility": "F1", "customer": "E", "cost": 237.0 }, { "facility": "F1", "customer": "F", "cost": 367.0 }, { "facility": "F1", "customer": "G", "cost": 371.0 }, { "facility": "F1", "customer": "H", "cost": 204.0 }, { "facility": "F1", "customer": "I", "cost": 364.0 }, { "facility": "F1", "customer": "J", "cost": 397.0 }, { "facility": "F1", "customer": "K", "cost": 288.0 }, { "facility": "F1", "customer": "L", "cost": 361.0 }, { "facility": "F1", "customer": "M", "cost": 353.0 }, { "facility": "F1", "customer": "N", "cost": 353.0 }, { "facility": "F1", "customer": "O", "cost": 324.0 }, { "facility": "F1", "customer": "P", "cost": 574.0 }, { "facility": "F1", "customer": "Q", "cost": 463.0 }, { "facility": "F1", "customer": "R", "cost": 475.0 }, { "facility": "F2", "customer": "A", "cost": 11.0 }, { "facility": "F2", "customer": "B", "cost": 504.0 }, { "facility": "F2", "customer": "C", "cost": 464.0 }, { "facility": "F2", "customer": "D", "cost": 392.0 }, { "facility": "F2", "customer": "E", "cost": 501.0 }, { "facility": "F2", "customer": "F", "cost": 354.0 }, { "facility": "F2", "customer": "G", "cost": 716.0 }, { "facility": "F2", "customer": "H", "cost": 563.0 }, { "facility": "F2", "customer": "I", "cost": 644.0 }, { "facility": "F2", "customer": "J", "cost": 453.0 }, { "facility": "F2", "customer": "K", "cost": 599.0 }, { "facility": "F2", "customer": "L", "cost": 685.0 }, { "facility": "F2", "customer": "M", "cost": 648.0 }, { "facility": "F2", "customer": "N", "cost": 131.0 }, { "facility": "F2", "customer": "O", "cost": 91.0 }, { "facility": "F2", "customer": "P", "cost": 679.0 }, { "facility": "F2", "customer": "Q", "cost": 640.0 }, { "facility": "F2", "customer": "R", "cost": 829.0 }, { "facility": "F3", "customer": "A", "cost": 123.0 }, { "facility": "F3", "customer": "B", "cost": 524.0 }, { "facility": "F3", "customer": "C", "cost": 351.0 }, { "facility": "F3", "customer": "D", "cost": 394.0 }, { "facility": "F3", "customer": "E", "cost": 400.0 }, { "facility": "F3", "customer": "F", "cost": 221.0 }, { "facility": "F3", "customer": "G", "cost": 637.0 }, { "facility": "F3", "customer": "H", "cost": 516.0 }, { "facility": "F3", "customer": "I", "cost": 538.0 }, { "facility": "F3", "customer": "J", "cost": 321.0 }, { "facility": "F3", "customer": "K", "cost": 507.0 }, { "facility": "F3", "customer": "L", "cost": 595.0 }, { "facility": "F3", "customer": "M", "cost": 548.0 }, { "facility": "F3", "customer": "N", "cost": 36.0 }, { "facility": "F3", "customer": "O", "cost": 42.0 }, { "facility": "F3", "customer": "P", "cost": 547.0 }, { "facility": "F3", "customer": "Q", "cost": 514.0 }, { "facility": "F3", "customer": "R", "cost": 758.0 }, { "facility": "F4", "customer": "A", "cost": 341.0 }, { "facility": "F4", "customer": "B", "cost": 488.0 }, { "facility": "F4", "customer": "C", "cost": 118.0 }, { "facility": "F4", "customer": "D", "cost": 353.0 }, { "facility": "F4", "customer": "E", "cost": 173.0 }, { "facility": "F4", "customer": "F", "cost": 152.0 }, { "facility": "F4", "customer": "G", "cost": 426.0 }, { "facility": "F4", "customer": "H", "cost": 362.0 }, { "facility": "F4", "customer": "I", "cost": 306.0 }, { "facility": "F4", "customer": "J", "cost": 175.0 }, { "facility": "F4", "customer": "K", "cost": 286.0 }, { "facility": "F4", "customer": "L", "cost": 373.0 }, { "facility": "F4", "customer": "M", "cost": 319.0 }, { "facility": "F4", "customer": "N", "cost": 261.0 }, { "facility": "F4", "customer": "O", "cost": 267.0 }, { "facility": "F4", "customer": "P", "cost": 375.0 }, { "facility": "F4", "customer": "Q", "cost": 300.0 }, { "facility": "F4", "customer": "R", "cost": 554.0 }, { "facility": "F5", "customer": "A", "cost": 364.0 }, { "facility": "F5", "customer": "B", "cost": 365.0 }, { "facility": "F5", "customer": "C", "cost": 164.0 }, { "facility": "F5", "customer": "D", "cost": 235.0 }, { "facility": "F5", "customer": "E", "cost": 152.0 }, { "facility": "F5", "customer": "F", "cost": 281.0 }, { "facility": "F5", "customer": "G", "cost": 350.0 }, { "facility": "F5", "customer": "H", "cost": 241.0 }, { "facility": "F5", "customer": "I", "cost": 293.0 }, { "facility": "F5", "customer": "J", "cost": 299.0 }, { "facility": "F5", "customer": "K", "cost": 234.0 }, { "facility": "F5", "customer": "L", "cost": 318.0 }, { "facility": "F5", "customer": "M", "cost": 289.0 }, { "facility": "F5", "customer": "N", "cost": 324.0 }, { "facility": "F5", "customer": "O", "cost": 309.0 }, { "facility": "F5", "customer": "P", "cost": 473.0 }, { "facility": "F5", "customer": "Q", "cost": 365.0 }, { "facility": "F5", "customer": "R", "cost": 470.0 }, { "facility": "F6", "customer": "A", "cost": 404.0 }, { "facility": "F6", "customer": "B", "cost": 106.0 }, { "facility": "F6", "customer": "C", "cost": 475.0 }, { "facility": "F6", "customer": "D", "cost": 82.0 }, { "facility": "F6", "customer": "E", "cost": 443.0 }, { "facility": "F6", "customer": "F", "cost": 549.0 }, { "facility": "F6", "customer": "G", "cost": 508.0 }, { "facility": "F6", "customer": "H", "cost": 297.0 }, { "facility": "F6", "customer": "I", "cost": 557.0 }, { "facility": "F6", "customer": "J", "cost": 598.0 }, { "facility": "F6", "customer": "K", "cost": 470.0 }, { "facility": "F6", "customer": "L", "cost": 525.0 }, { "facility": "F6", "customer": "M", "cost": 538.0 }, { "facility": "F6", "customer": "N", "cost": 457.0 }, { "facility": "F6", "customer": "O", "cost": 412.0 }, { "facility": "F6", "customer": "P", "cost": 784.0 }, { "facility": "F6", "customer": "Q", "cost": 672.0 }, { "facility": "F6", "customer": "R", "cost": 577.0 }, { "facility": "F7", "customer": "A", "cost": 533.0 }, { "facility": "F7", "customer": "B", "cost": 250.0 }, { "facility": "F7", "customer": "C", "cost": 324.0 }, { "facility": "F7", "customer": "D", "cost": 196.0 }, { "facility": "F7", "customer": "E", "cost": 256.0 }, { "facility": "F7", "customer": "F", "cost": 496.0 }, { "facility": "F7", "customer": "G", "cost": 240.0 }, { "facility": "F7", "customer": "H", "cost": 32.0 }, { "facility": "F7", "customer": "I", "cost": 322.0 }, { "facility": "F7", "customer": "J", "cost": 496.0 }, { "facility": "F7", "customer": "K", "cost": 229.0 }, { "facility": "F7", "customer": "L", "cost": 264.0 }, { "facility": "F7", "customer": "M", "cost": 295.0 }, { "facility": "F7", "customer": "N", "cost": 524.0 }, { "facility": "F7", "customer": "O", "cost": 498.0 }, { "facility": "F7", "customer": "P", "cost": 622.0 }, { "facility": "F7", "customer": "Q", "cost": 484.0 }, { "facility": "F7", "customer": "R", "cost": 318.0 } ], "objective": 4824.0 }, "solution_variant": { "selected": [ "F3", "F4", "F7" ], "assignments": [ "F3", "F7", "F4", "F7", "F4", "F4", "F7", "F7", "F4", "F4", "F7", "F7", "F7", "F3", "F3", "F4", "F4", "F7" ] }, "context_index": 29, "input_format": "csv", "input_index_base": "names" }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "There’s a neighborhood project where a few bookmobile stops can be set up, but not all of them at once. The team needs to decide which stops to operate, send each reader to exactly one of the active stops (no splitting visits), and watch that no stop handles more visitors or checkouts than it can manage. Better choices are the ones that keep total spending down — add the cost to run the chosen stops and the travel time for every reader, and aim for the smallest total. The concrete details about stops, costs, and reader counts appear below.\n\n# num_candidate_stops=7\n# num_reader_groups=16\n# STOPS\nstop_id,stop_operation_cost,circulation_capacity\nF1,258.0,366.0\nF2,128.0,314.0\nF3,225.0,504.0\nF4,373.0,415.0\nF5,329.0,456.0\nF6,179.0,549.0\nF7,114.0,310.0\n# READER_GROUPS\nreader_group_id,visitor_count\n0,31.0\n1,14.0\n2,39.0\n3,45.0\n4,40.0\n5,24.0\n6,28.0\n7,13.0\n8,27.0\n9,22.0\n10,14.0\n11,37.0\n12,13.0\n13,21.0\n14,17.0\n15,49.0\n# TRAVEL_TIMES\nstop_id,reader_group_id,travel_time\nF1,0,392.0\nF1,1,122.0\nF1,2,143.0\nF1,3,29.0\nF1,4,656.0\nF1,5,329.0\nF1,6,318.0\nF1,7,414.0\nF1,8,458.0\nF1,9,758.0\nF1,10,28.0\nF1,11,502.0\nF1,12,139.0\nF1,13,88.0\nF1,14,370.0\nF1,15,68.0\nF2,0,28.0\nF2,1,319.0\nF2,2,242.0\nF2,3,401.0\nF2,4,551.0\nF2,5,200.0\nF2,6,80.0\nF2,7,107.0\nF2,8,387.0\nF2,9,516.0\nF2,10,374.0\nF2,11,584.0\nF2,12,459.0\nF2,13,463.0\nF2,14,574.0\nF2,15,344.0\nF3,0,219.0\nF3,1,117.0\nF3,2,59.0\nF3,3,205.0\nF3,4,611.0\nF3,5,229.0\nF3,6,135.0\nF3,7,261.0\nF3,8,414.0\nF3,9,653.0\nF3,10,170.0\nF3,11,540.0\nF3,12,286.0\nF3,13,258.0\nF3,14,466.0\nF3,15,138.0\nF4,0,157.0\nF4,1,464.0\nF4,2,357.0\nF4,3,501.0\nF4,4,399.0\nF4,5,184.0\nF4,6,255.0\nF4,7,88.0\nF4,8,281.0\nF4,9,332.0\nF4,10,492.0\nF4,11,510.0\nF4,12,522.0\nF4,13,580.0\nF4,14,560.0\nF4,15,474.0\nF5,0,387.0\nF5,1,643.0\nF5,2,523.0\nF5,3,632.0\nF5,4,200.0\nF5,5,311.0\nF5,6,476.0\nF5,7,309.0\nF5,8,222.0\nF5,9,124.0\nF5,10,642.0\nF5,11,425.0\nF5,12,612.0\nF5,13,720.0\nF5,14,551.0\nF5,15,637.0\nF6,0,742.0\nF6,1,700.0\nF6,2,622.0\nF6,3,567.0\nF6,4,458.0\nF6,5,562.0\nF6,6,751.0\nF6,7,693.0\nF6,8,428.0\nF6,9,702.0\nF6,10,620.0\nF6,11,197.0\nF6,12,460.0\nF6,13,627.0\nF6,14,223.0\nF6,15,652.0\nF7,0,535.0\nF7,1,295.0\nF7,2,296.0\nF7,3,148.0\nF7,4,664.0\nF7,5,423.0\nF7,6,477.0\nF7,7,539.0\nF7,8,485.0\nF7,9,816.0\nF7,10,200.0\nF7,11,443.0\nF7,12,83.0\nF7,13,161.0\nF7,14,269.0\nF7,15,242.0\n\nOh, and just so we're on the same page, please send the solution in this simple JSON layout (just a little form I like to use):\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThis little sketch means: \"selected\" lists the stops you'll run, and \"assignments\" gives, for each reader in the same order as the input, which open stop they should go to. It's just the shape I need — not the final numbers or choices.\n\nPlease remember to use the exact identifiers from the instance input — do not rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 258.0, 128.0, 225.0, 373.0, 329.0, 179.0, 114.0 ], "capacities": [ 366.0, 314.0, 504.0, 415.0, 456.0, 549.0, 310.0 ], "connection_costs": [ [ 392.0, 122.0, 143.0, 29.0, 656.0, 329.0, 318.0, 414.0, 458.0, 758.0, 28.0, 502.0, 139.0, 88.0, 370.0, 68.0 ], [ 28.0, 319.0, 242.0, 401.0, 551.0, 200.0, 80.0, 107.0, 387.0, 516.0, 374.0, 584.0, 459.0, 463.0, 574.0, 344.0 ], [ 219.0, 117.0, 59.0, 205.0, 611.0, 229.0, 135.0, 261.0, 414.0, 653.0, 170.0, 540.0, 286.0, 258.0, 466.0, 138.0 ], [ 157.0, 464.0, 357.0, 501.0, 399.0, 184.0, 255.0, 88.0, 281.0, 332.0, 492.0, 510.0, 522.0, 580.0, 560.0, 474.0 ], [ 387.0, 643.0, 523.0, 632.0, 200.0, 311.0, 476.0, 309.0, 222.0, 124.0, 642.0, 425.0, 612.0, 720.0, 551.0, 637.0 ], [ 742.0, 700.0, 622.0, 567.0, 458.0, 562.0, 751.0, 693.0, 428.0, 702.0, 620.0, 197.0, 460.0, 627.0, 223.0, 652.0 ], [ 535.0, 295.0, 296.0, 148.0, 664.0, 423.0, 477.0, 539.0, 485.0, 816.0, 200.0, 443.0, 83.0, 161.0, 269.0, 242.0 ] ], "demands": [ 31.0, 14.0, 39.0, 45.0, 40.0, 24.0, 28.0, 13.0, 27.0, 22.0, 14.0, 37.0, 13.0, 21.0, 17.0, 49.0 ], "objective": 2892.0 }, "solution": { "open_facilities": [ 0, 1, 4, 5 ], "assignments": [ 1, 0, 0, 0, 4, 1, 1, 1, 4, 4, 0, 5, 0, 0, 5, 0 ] }, "obj": 2892.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 16, "facilities": [ { "id": "F1", "opening_cost": 258.0, "capacity": 366.0 }, { "id": "F2", "opening_cost": 128.0, "capacity": 314.0 }, { "id": "F3", "opening_cost": 225.0, "capacity": 504.0 }, { "id": "F4", "opening_cost": 373.0, "capacity": 415.0 }, { "id": "F5", "opening_cost": 329.0, "capacity": 456.0 }, { "id": "F6", "opening_cost": 179.0, "capacity": 549.0 }, { "id": "F7", "opening_cost": 114.0, "capacity": 310.0 } ], "customers": [ { "id": 0, "demand": 31.0 }, { "id": 1, "demand": 14.0 }, { "id": 2, "demand": 39.0 }, { "id": 3, "demand": 45.0 }, { "id": 4, "demand": 40.0 }, { "id": 5, "demand": 24.0 }, { "id": 6, "demand": 28.0 }, { "id": 7, "demand": 13.0 }, { "id": 8, "demand": 27.0 }, { "id": 9, "demand": 22.0 }, { "id": 10, "demand": 14.0 }, { "id": 11, "demand": 37.0 }, { "id": 12, "demand": 13.0 }, { "id": 13, "demand": 21.0 }, { "id": 14, "demand": 17.0 }, { "id": 15, "demand": 49.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 392.0 }, { "facility": "F1", "customer": 1, "cost": 122.0 }, { "facility": "F1", "customer": 2, "cost": 143.0 }, { "facility": "F1", "customer": 3, "cost": 29.0 }, { "facility": "F1", "customer": 4, "cost": 656.0 }, { "facility": "F1", "customer": 5, "cost": 329.0 }, { "facility": "F1", "customer": 6, "cost": 318.0 }, { "facility": "F1", "customer": 7, "cost": 414.0 }, { "facility": "F1", "customer": 8, "cost": 458.0 }, { "facility": "F1", "customer": 9, "cost": 758.0 }, { "facility": "F1", "customer": 10, "cost": 28.0 }, { "facility": "F1", "customer": 11, "cost": 502.0 }, { "facility": "F1", "customer": 12, "cost": 139.0 }, { "facility": "F1", "customer": 13, "cost": 88.0 }, { "facility": "F1", "customer": 14, "cost": 370.0 }, { "facility": "F1", "customer": 15, "cost": 68.0 }, { "facility": "F2", "customer": 0, "cost": 28.0 }, { "facility": "F2", "customer": 1, "cost": 319.0 }, { "facility": "F2", "customer": 2, "cost": 242.0 }, { "facility": "F2", "customer": 3, "cost": 401.0 }, { "facility": "F2", "customer": 4, "cost": 551.0 }, { "facility": "F2", "customer": 5, "cost": 200.0 }, { "facility": "F2", "customer": 6, "cost": 80.0 }, { "facility": "F2", "customer": 7, "cost": 107.0 }, { "facility": "F2", "customer": 8, "cost": 387.0 }, { "facility": "F2", "customer": 9, "cost": 516.0 }, { "facility": "F2", "customer": 10, "cost": 374.0 }, { "facility": "F2", "customer": 11, "cost": 584.0 }, { "facility": "F2", "customer": 12, "cost": 459.0 }, { "facility": "F2", "customer": 13, "cost": 463.0 }, { "facility": "F2", "customer": 14, "cost": 574.0 }, { "facility": "F2", "customer": 15, "cost": 344.0 }, { "facility": "F3", "customer": 0, "cost": 219.0 }, { "facility": "F3", "customer": 1, "cost": 117.0 }, { "facility": "F3", "customer": 2, "cost": 59.0 }, { "facility": "F3", "customer": 3, "cost": 205.0 }, { "facility": "F3", "customer": 4, "cost": 611.0 }, { "facility": "F3", "customer": 5, "cost": 229.0 }, { "facility": "F3", "customer": 6, "cost": 135.0 }, { "facility": "F3", "customer": 7, "cost": 261.0 }, { "facility": "F3", "customer": 8, "cost": 414.0 }, { "facility": "F3", "customer": 9, "cost": 653.0 }, { "facility": "F3", "customer": 10, "cost": 170.0 }, { "facility": "F3", "customer": 11, "cost": 540.0 }, { "facility": "F3", "customer": 12, "cost": 286.0 }, { "facility": "F3", "customer": 13, "cost": 258.0 }, { "facility": "F3", "customer": 14, "cost": 466.0 }, { "facility": "F3", "customer": 15, "cost": 138.0 }, { "facility": "F4", "customer": 0, "cost": 157.0 }, { "facility": "F4", "customer": 1, "cost": 464.0 }, { "facility": "F4", "customer": 2, "cost": 357.0 }, { "facility": "F4", "customer": 3, "cost": 501.0 }, { "facility": "F4", "customer": 4, "cost": 399.0 }, { "facility": "F4", "customer": 5, "cost": 184.0 }, { "facility": "F4", "customer": 6, "cost": 255.0 }, { "facility": "F4", "customer": 7, "cost": 88.0 }, { "facility": "F4", "customer": 8, "cost": 281.0 }, { "facility": "F4", "customer": 9, "cost": 332.0 }, { "facility": "F4", "customer": 10, "cost": 492.0 }, { "facility": "F4", "customer": 11, "cost": 510.0 }, { "facility": "F4", "customer": 12, "cost": 522.0 }, { "facility": "F4", "customer": 13, "cost": 580.0 }, { "facility": "F4", "customer": 14, "cost": 560.0 }, { "facility": "F4", "customer": 15, "cost": 474.0 }, { "facility": "F5", "customer": 0, "cost": 387.0 }, { "facility": "F5", "customer": 1, "cost": 643.0 }, { "facility": "F5", "customer": 2, "cost": 523.0 }, { "facility": "F5", "customer": 3, "cost": 632.0 }, { "facility": "F5", "customer": 4, "cost": 200.0 }, { "facility": "F5", "customer": 5, "cost": 311.0 }, { "facility": "F5", "customer": 6, "cost": 476.0 }, { "facility": "F5", "customer": 7, "cost": 309.0 }, { "facility": "F5", "customer": 8, "cost": 222.0 }, { "facility": "F5", "customer": 9, "cost": 124.0 }, { "facility": "F5", "customer": 10, "cost": 642.0 }, { "facility": "F5", "customer": 11, "cost": 425.0 }, { "facility": "F5", "customer": 12, "cost": 612.0 }, { "facility": "F5", "customer": 13, "cost": 720.0 }, { "facility": "F5", "customer": 14, "cost": 551.0 }, { "facility": "F5", "customer": 15, "cost": 637.0 }, { "facility": "F6", "customer": 0, "cost": 742.0 }, { "facility": "F6", "customer": 1, "cost": 700.0 }, { "facility": "F6", "customer": 2, "cost": 622.0 }, { "facility": "F6", "customer": 3, "cost": 567.0 }, { "facility": "F6", "customer": 4, "cost": 458.0 }, { "facility": "F6", "customer": 5, "cost": 562.0 }, { "facility": "F6", "customer": 6, "cost": 751.0 }, { "facility": "F6", "customer": 7, "cost": 693.0 }, { "facility": "F6", "customer": 8, "cost": 428.0 }, { "facility": "F6", "customer": 9, "cost": 702.0 }, { "facility": "F6", "customer": 10, "cost": 620.0 }, { "facility": "F6", "customer": 11, "cost": 197.0 }, { "facility": "F6", "customer": 12, "cost": 460.0 }, { "facility": "F6", "customer": 13, "cost": 627.0 }, { "facility": "F6", "customer": 14, "cost": 223.0 }, { "facility": "F6", "customer": 15, "cost": 652.0 }, { "facility": "F7", "customer": 0, "cost": 535.0 }, { "facility": "F7", "customer": 1, "cost": 295.0 }, { "facility": "F7", "customer": 2, "cost": 296.0 }, { "facility": "F7", "customer": 3, "cost": 148.0 }, { "facility": "F7", "customer": 4, "cost": 664.0 }, { "facility": "F7", "customer": 5, "cost": 423.0 }, { "facility": "F7", "customer": 6, "cost": 477.0 }, { "facility": "F7", "customer": 7, "cost": 539.0 }, { "facility": "F7", "customer": 8, "cost": 485.0 }, { "facility": "F7", "customer": 9, "cost": 816.0 }, { "facility": "F7", "customer": 10, "cost": 200.0 }, { "facility": "F7", "customer": 11, "cost": 443.0 }, { "facility": "F7", "customer": 12, "cost": 83.0 }, { "facility": "F7", "customer": 13, "cost": 161.0 }, { "facility": "F7", "customer": 14, "cost": 269.0 }, { "facility": "F7", "customer": 15, "cost": 242.0 } ], "objective": 2892.0 }, "solution_variant": { "selected": [ "F1", "F2", "F5", "F6" ], "assignments": [ "F2", "F1", "F1", "F1", "F5", "F2", "F2", "F2", "F5", "F5", "F1", "F6", "F1", "F1", "F6", "F1" ] }, "context_index": 30, "input_format": "csv", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Someone running a local cloud-kitchen brand needs to decide which ghost kitchens to pay to activate and which active kitchen will handle each incoming order. Orders can’t be split across kitchens — each goes to one kitchen — and no kitchen should be overloaded beyond its capacity. What makes one setup preferable is simple money math: the total bill is the sum of every kitchen’s activation fee that’s paid plus the fulfillment cost for every order, and the goal is to keep that total as small as possible. The detailed instance — kitchens, costs, capacities and orders — follows below.\n\nThere are 8 kitchens and 19 orders in this instance.\n\n**Kitchens**\n| kitchen_id | activation_fee | kitchen_capacity |\n|---|---|---|\n| F1 | 600.0 | 500.0 |\n| F2 | 600.0 | 500.0 |\n| F3 | 600.0 | 500.0 |\n| F4 | 600.0 | 500.0 |\n| F5 | 600.0 | 500.0 |\n| F6 | 600.0 | 500.0 |\n| F7 | 600.0 | 500.0 |\n| F8 | 600.0 | 500.0 |\n\n**Orders**\n| order_id | order_size |\n|---|---|\n| 1 | 38.0 |\n| 2 | 44.0 |\n| 3 | 42.0 |\n| 4 | 37.0 |\n| 5 | 28.0 |\n| 6 | 32.0 |\n| 7 | 21.0 |\n| 8 | 19.0 |\n| 9 | 27.0 |\n| 10 | 46.0 |\n| 11 | 20.0 |\n| 12 | 32.0 |\n| 13 | 27.0 |\n| 14 | 33.0 |\n| 15 | 42.0 |\n| 16 | 48.0 |\n| 17 | 36.0 |\n| 18 | 25.0 |\n| 19 | 47.0 |\n\n**Fulfillment Cost**\n| kitchen_id | order_id | fulfillment_cost |\n|---|---|---|\n| F1 | 1 | 428.0 |\n| F1 | 2 | 161.0 |\n| F1 | 3 | 373.0 |\n| F1 | 4 | 465.0 |\n| F1 | 5 | 337.0 |\n| F1 | 6 | 304.0 |\n| F1 | 7 | 245.0 |\n| F1 | 8 | 333.0 |\n| F1 | 9 | 466.0 |\n| F1 | 10 | 457.0 |\n| F1 | 11 | 244.0 |\n| F1 | 12 | 408.0 |\n| F1 | 13 | 265.0 |\n| F1 | 14 | 294.0 |\n| F1 | 15 | 294.0 |\n| F1 | 16 | 146.0 |\n| F1 | 17 | 406.0 |\n| F1 | 18 | 476.0 |\n| F1 | 19 | 532.0 |\n| F2 | 1 | 560.0 |\n| F2 | 2 | 584.0 |\n| F2 | 3 | 245.0 |\n| F2 | 4 | 142.0 |\n| F2 | 5 | 353.0 |\n| F2 | 6 | 422.0 |\n| F2 | 7 | 521.0 |\n| F2 | 8 | 389.0 |\n| F2 | 9 | 292.0 |\n| F2 | 10 | 125.0 |\n| F2 | 11 | 751.0 |\n| F2 | 12 | 485.0 |\n| F2 | 13 | 342.0 |\n| F2 | 14 | 612.0 |\n| F2 | 15 | 537.0 |\n| F2 | 16 | 549.0 |\n| F2 | 17 | 590.0 |\n| F2 | 18 | 326.0 |\n| F2 | 19 | 254.0 |\n| F3 | 1 | 666.0 |\n| F3 | 2 | 528.0 |\n| F3 | 3 | 362.0 |\n| F3 | 4 | 351.0 |\n| F3 | 5 | 93.0 |\n| F3 | 6 | 134.0 |\n| F3 | 7 | 531.0 |\n| F3 | 8 | 478.0 |\n| F3 | 9 | 492.0 |\n| F3 | 10 | 302.0 |\n| F3 | 11 | 665.0 |\n| F3 | 12 | 140.0 |\n| F3 | 13 | 189.0 |\n| F3 | 14 | 625.0 |\n| F3 | 15 | 574.0 |\n| F3 | 16 | 492.0 |\n| F3 | 17 | 249.0 |\n| F3 | 18 | 51.0 |\n| F3 | 19 | 507.0 |\n| F4 | 1 | 539.0 |\n| F4 | 2 | 368.0 |\n| F4 | 3 | 288.0 |\n| F4 | 4 | 326.0 |\n| F4 | 5 | 72.0 |\n| F4 | 6 | 68.0 |\n| F4 | 7 | 385.0 |\n| F4 | 8 | 363.0 |\n| F4 | 9 | 422.0 |\n| F4 | 10 | 292.0 |\n| F4 | 11 | 501.0 |\n| F4 | 12 | 191.0 |\n| F4 | 13 | 63.0 |\n| F4 | 14 | 473.0 |\n| F4 | 15 | 431.0 |\n| F4 | 16 | 333.0 |\n| F4 | 17 | 254.0 |\n| F4 | 18 | 211.0 |\n| F4 | 19 | 459.0 |\n| F5 | 1 | 651.0 |\n| F5 | 2 | 459.0 |\n| F5 | 3 | 400.0 |\n| F5 | 4 | 425.0 |\n| F5 | 5 | 109.0 |\n| F5 | 6 | 49.0 |\n| F5 | 7 | 490.0 |\n| F5 | 8 | 478.0 |\n| F5 | 9 | 535.0 |\n| F5 | 10 | 384.0 |\n| F5 | 11 | 572.0 |\n| F5 | 12 | 82.0 |\n| F5 | 13 | 177.0 |\n| F5 | 14 | 574.0 |\n| F5 | 15 | 538.0 |\n| F5 | 16 | 427.0 |\n| F5 | 17 | 141.0 |\n| F5 | 18 | 194.0 |\n| F5 | 19 | 567.0 |\n| F6 | 1 | 360.0 |\n| F6 | 2 | 122.0 |\n| F6 | 3 | 467.0 |\n| F6 | 4 | 571.0 |\n| F6 | 5 | 522.0 |\n| F6 | 6 | 497.0 |\n| F6 | 7 | 219.0 |\n| F6 | 8 | 363.0 |\n| F6 | 9 | 514.0 |\n| F6 | 10 | 579.0 |\n| F6 | 11 | 51.0 |\n| F6 | 12 | 604.0 |\n| F6 | 13 | 438.0 |\n| F6 | 14 | 193.0 |\n| F6 | 15 | 244.0 |\n| F6 | 16 | 156.0 |\n| F6 | 17 | 599.0 |\n| F6 | 18 | 661.0 |\n| F6 | 19 | 587.0 |\n| F7 | 1 | 296.0 |\n| F7 | 2 | 25.0 |\n| F7 | 3 | 335.0 |\n| F7 | 4 | 438.0 |\n| F7 | 5 | 412.0 |\n| F7 | 6 | 399.0 |\n| F7 | 7 | 118.0 |\n| F7 | 8 | 243.0 |\n| F7 | 9 | 391.0 |\n| F7 | 10 | 446.0 |\n| F7 | 11 | 181.0 |\n| F7 | 12 | 516.0 |\n| F7 | 13 | 320.0 |\n| F7 | 14 | 156.0 |\n| F7 | 15 | 162.0 |\n| F7 | 16 | 23.0 |\n| F7 | 17 | 532.0 |\n| F7 | 18 | 547.0 |\n| F7 | 19 | 464.0 |\n| F8 | 1 | 174.0 |\n| F8 | 2 | 129.0 |\n| F8 | 3 | 256.0 |\n| F8 | 4 | 360.0 |\n| F8 | 5 | 437.0 |\n| F8 | 6 | 446.0 |\n| F8 | 7 | 23.0 |\n| F8 | 8 | 125.0 |\n| F8 | 9 | 274.0 |\n| F8 | 10 | 382.0 |\n| F8 | 11 | 278.0 |\n| F8 | 12 | 569.0 |\n| F8 | 13 | 336.0 |\n| F8 | 14 | 113.0 |\n| F8 | 15 | 51.0 |\n| F8 | 16 | 118.0 |\n| F8 | 17 | 607.0 |\n| F8 | 18 | 557.0 |\n| F8 | 19 | 348.0 |\n\nAlso, to keep things machine-friendly, please return the result in this simple JSON shape so I can pick out which kitchens you turned on and which kitchen handles each order:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThe idea is straightforward: \"selected\" is the list of ghost kitchens you decide to activate, and \"assignments\" is a list (in the same order as the orders in the instance) naming which active kitchen handles each order. Think of it like a short form: which kitchens are paid for, and who cooks each order.\n\nThis JSON is just a sketch of the expected shape — not the final plan. One important rule: use the exact identifiers from the instance input when you fill this in — do not rename them or invent new labels. Valid identifiers look like plain numbers such as \"1\" or \"23\", single capital letters like \"A\" or \"B\", or a capital letter followed by digits like \"A1\" or \"X7\".", "instance": { "opening_costs": [ 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 428.0, 161.0, 373.0, 465.0, 337.0, 304.0, 245.0, 333.0, 466.0, 457.0, 244.0, 408.0, 265.0, 294.0, 294.0, 146.0, 406.0, 476.0, 532.0 ], [ 560.0, 584.0, 245.0, 142.0, 353.0, 422.0, 521.0, 389.0, 292.0, 125.0, 751.0, 485.0, 342.0, 612.0, 537.0, 549.0, 590.0, 326.0, 254.0 ], [ 666.0, 528.0, 362.0, 351.0, 93.0, 134.0, 531.0, 478.0, 492.0, 302.0, 665.0, 140.0, 189.0, 625.0, 574.0, 492.0, 249.0, 51.0, 507.0 ], [ 539.0, 368.0, 288.0, 326.0, 72.0, 68.0, 385.0, 363.0, 422.0, 292.0, 501.0, 191.0, 63.0, 473.0, 431.0, 333.0, 254.0, 211.0, 459.0 ], [ 651.0, 459.0, 400.0, 425.0, 109.0, 49.0, 490.0, 478.0, 535.0, 384.0, 572.0, 82.0, 177.0, 574.0, 538.0, 427.0, 141.0, 194.0, 567.0 ], [ 360.0, 122.0, 467.0, 571.0, 522.0, 497.0, 219.0, 363.0, 514.0, 579.0, 51.0, 604.0, 438.0, 193.0, 244.0, 156.0, 599.0, 661.0, 587.0 ], [ 296.0, 25.0, 335.0, 438.0, 412.0, 399.0, 118.0, 243.0, 391.0, 446.0, 181.0, 516.0, 320.0, 156.0, 162.0, 23.0, 532.0, 547.0, 464.0 ], [ 174.0, 129.0, 256.0, 360.0, 437.0, 446.0, 23.0, 125.0, 274.0, 382.0, 278.0, 569.0, 336.0, 113.0, 51.0, 118.0, 607.0, 557.0, 348.0 ] ], "demands": [ 38.0, 44.0, 42.0, 37.0, 28.0, 32.0, 21.0, 19.0, 27.0, 46.0, 20.0, 32.0, 27.0, 33.0, 42.0, 48.0, 36.0, 25.0, 47.0 ], "objective": 4566.0 }, "solution": { "open_facilities": [ 3, 7 ], "assignments": [ 7, 7, 7, 3, 3, 3, 7, 7, 7, 3, 7, 3, 3, 7, 7, 7, 3, 3, 7 ] }, "obj": 4566.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 19, "facilities": [ { "id": "F1", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F2", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F3", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F4", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F5", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F6", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F7", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F8", "opening_cost": 600.0, "capacity": 500.0 } ], "customers": [ { "id": 1, "demand": 38.0 }, { "id": 2, "demand": 44.0 }, { "id": 3, "demand": 42.0 }, { "id": 4, "demand": 37.0 }, { "id": 5, "demand": 28.0 }, { "id": 6, "demand": 32.0 }, { "id": 7, "demand": 21.0 }, { "id": 8, "demand": 19.0 }, { "id": 9, "demand": 27.0 }, { "id": 10, "demand": 46.0 }, { "id": 11, "demand": 20.0 }, { "id": 12, "demand": 32.0 }, { "id": 13, "demand": 27.0 }, { "id": 14, "demand": 33.0 }, { "id": 15, "demand": 42.0 }, { "id": 16, "demand": 48.0 }, { "id": 17, "demand": 36.0 }, { "id": 18, "demand": 25.0 }, { "id": 19, "demand": 47.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 428.0 }, { "facility": "F1", "customer": 2, "cost": 161.0 }, { "facility": "F1", "customer": 3, "cost": 373.0 }, { "facility": "F1", "customer": 4, "cost": 465.0 }, { "facility": "F1", "customer": 5, "cost": 337.0 }, { "facility": "F1", "customer": 6, "cost": 304.0 }, { "facility": "F1", "customer": 7, "cost": 245.0 }, { "facility": "F1", "customer": 8, "cost": 333.0 }, { "facility": "F1", "customer": 9, "cost": 466.0 }, { "facility": "F1", "customer": 10, "cost": 457.0 }, { "facility": "F1", "customer": 11, "cost": 244.0 }, { "facility": "F1", "customer": 12, "cost": 408.0 }, { "facility": "F1", "customer": 13, "cost": 265.0 }, { "facility": "F1", "customer": 14, "cost": 294.0 }, { "facility": "F1", "customer": 15, "cost": 294.0 }, { "facility": "F1", "customer": 16, "cost": 146.0 }, { "facility": "F1", "customer": 17, "cost": 406.0 }, { "facility": "F1", "customer": 18, "cost": 476.0 }, { "facility": "F1", "customer": 19, "cost": 532.0 }, { "facility": "F2", "customer": 1, "cost": 560.0 }, { "facility": "F2", "customer": 2, "cost": 584.0 }, { "facility": "F2", "customer": 3, "cost": 245.0 }, { "facility": "F2", "customer": 4, "cost": 142.0 }, { "facility": "F2", "customer": 5, "cost": 353.0 }, { "facility": "F2", "customer": 6, "cost": 422.0 }, { "facility": "F2", "customer": 7, "cost": 521.0 }, { "facility": "F2", "customer": 8, "cost": 389.0 }, { "facility": "F2", "customer": 9, "cost": 292.0 }, { "facility": "F2", "customer": 10, "cost": 125.0 }, { "facility": "F2", "customer": 11, "cost": 751.0 }, { "facility": "F2", "customer": 12, "cost": 485.0 }, { "facility": "F2", "customer": 13, "cost": 342.0 }, { "facility": "F2", "customer": 14, "cost": 612.0 }, { "facility": "F2", "customer": 15, "cost": 537.0 }, { "facility": "F2", "customer": 16, "cost": 549.0 }, { "facility": "F2", "customer": 17, "cost": 590.0 }, { "facility": "F2", "customer": 18, "cost": 326.0 }, { "facility": "F2", "customer": 19, "cost": 254.0 }, { "facility": "F3", "customer": 1, "cost": 666.0 }, { "facility": "F3", "customer": 2, "cost": 528.0 }, { "facility": "F3", "customer": 3, "cost": 362.0 }, { "facility": "F3", "customer": 4, "cost": 351.0 }, { "facility": "F3", "customer": 5, "cost": 93.0 }, { "facility": "F3", "customer": 6, "cost": 134.0 }, { "facility": "F3", "customer": 7, "cost": 531.0 }, { "facility": "F3", "customer": 8, "cost": 478.0 }, { "facility": "F3", "customer": 9, "cost": 492.0 }, { "facility": "F3", "customer": 10, "cost": 302.0 }, { "facility": "F3", "customer": 11, "cost": 665.0 }, { "facility": "F3", "customer": 12, "cost": 140.0 }, { "facility": "F3", "customer": 13, "cost": 189.0 }, { "facility": "F3", "customer": 14, "cost": 625.0 }, { "facility": "F3", "customer": 15, "cost": 574.0 }, { "facility": "F3", "customer": 16, "cost": 492.0 }, { "facility": "F3", "customer": 17, "cost": 249.0 }, { "facility": "F3", "customer": 18, "cost": 51.0 }, { "facility": "F3", "customer": 19, "cost": 507.0 }, { "facility": "F4", "customer": 1, "cost": 539.0 }, { "facility": "F4", "customer": 2, "cost": 368.0 }, { "facility": "F4", "customer": 3, "cost": 288.0 }, { "facility": "F4", "customer": 4, "cost": 326.0 }, { "facility": "F4", "customer": 5, "cost": 72.0 }, { "facility": "F4", "customer": 6, "cost": 68.0 }, { "facility": "F4", "customer": 7, "cost": 385.0 }, { "facility": "F4", "customer": 8, "cost": 363.0 }, { "facility": "F4", "customer": 9, "cost": 422.0 }, { "facility": "F4", "customer": 10, "cost": 292.0 }, { "facility": "F4", "customer": 11, "cost": 501.0 }, { "facility": "F4", "customer": 12, "cost": 191.0 }, { "facility": "F4", "customer": 13, "cost": 63.0 }, { "facility": "F4", "customer": 14, "cost": 473.0 }, { "facility": "F4", "customer": 15, "cost": 431.0 }, { "facility": "F4", "customer": 16, "cost": 333.0 }, { "facility": "F4", "customer": 17, "cost": 254.0 }, { "facility": "F4", "customer": 18, "cost": 211.0 }, { "facility": "F4", "customer": 19, "cost": 459.0 }, { "facility": "F5", "customer": 1, "cost": 651.0 }, { "facility": "F5", "customer": 2, "cost": 459.0 }, { "facility": "F5", "customer": 3, "cost": 400.0 }, { "facility": "F5", "customer": 4, "cost": 425.0 }, { "facility": "F5", "customer": 5, "cost": 109.0 }, { "facility": "F5", "customer": 6, "cost": 49.0 }, { "facility": "F5", "customer": 7, "cost": 490.0 }, { "facility": "F5", "customer": 8, "cost": 478.0 }, { "facility": "F5", "customer": 9, "cost": 535.0 }, { "facility": "F5", "customer": 10, "cost": 384.0 }, { "facility": "F5", "customer": 11, "cost": 572.0 }, { "facility": "F5", "customer": 12, "cost": 82.0 }, { "facility": "F5", "customer": 13, "cost": 177.0 }, { "facility": "F5", "customer": 14, "cost": 574.0 }, { "facility": "F5", "customer": 15, "cost": 538.0 }, { "facility": "F5", "customer": 16, "cost": 427.0 }, { "facility": "F5", "customer": 17, "cost": 141.0 }, { "facility": "F5", "customer": 18, "cost": 194.0 }, { "facility": "F5", "customer": 19, "cost": 567.0 }, { "facility": "F6", "customer": 1, "cost": 360.0 }, { "facility": "F6", "customer": 2, "cost": 122.0 }, { "facility": "F6", "customer": 3, "cost": 467.0 }, { "facility": "F6", "customer": 4, "cost": 571.0 }, { "facility": "F6", "customer": 5, "cost": 522.0 }, { "facility": "F6", "customer": 6, "cost": 497.0 }, { "facility": "F6", "customer": 7, "cost": 219.0 }, { "facility": "F6", "customer": 8, "cost": 363.0 }, { "facility": "F6", "customer": 9, "cost": 514.0 }, { "facility": "F6", "customer": 10, "cost": 579.0 }, { "facility": "F6", "customer": 11, "cost": 51.0 }, { "facility": "F6", "customer": 12, "cost": 604.0 }, { "facility": "F6", "customer": 13, "cost": 438.0 }, { "facility": "F6", "customer": 14, "cost": 193.0 }, { "facility": "F6", "customer": 15, "cost": 244.0 }, { "facility": "F6", "customer": 16, "cost": 156.0 }, { "facility": "F6", "customer": 17, "cost": 599.0 }, { "facility": "F6", "customer": 18, "cost": 661.0 }, { "facility": "F6", "customer": 19, "cost": 587.0 }, { "facility": "F7", "customer": 1, "cost": 296.0 }, { "facility": "F7", "customer": 2, "cost": 25.0 }, { "facility": "F7", "customer": 3, "cost": 335.0 }, { "facility": "F7", "customer": 4, "cost": 438.0 }, { "facility": "F7", "customer": 5, "cost": 412.0 }, { "facility": "F7", "customer": 6, "cost": 399.0 }, { "facility": "F7", "customer": 7, "cost": 118.0 }, { "facility": "F7", "customer": 8, "cost": 243.0 }, { "facility": "F7", "customer": 9, "cost": 391.0 }, { "facility": "F7", "customer": 10, "cost": 446.0 }, { "facility": "F7", "customer": 11, "cost": 181.0 }, { "facility": "F7", "customer": 12, "cost": 516.0 }, { "facility": "F7", "customer": 13, "cost": 320.0 }, { "facility": "F7", "customer": 14, "cost": 156.0 }, { "facility": "F7", "customer": 15, "cost": 162.0 }, { "facility": "F7", "customer": 16, "cost": 23.0 }, { "facility": "F7", "customer": 17, "cost": 532.0 }, { "facility": "F7", "customer": 18, "cost": 547.0 }, { "facility": "F7", "customer": 19, "cost": 464.0 }, { "facility": "F8", "customer": 1, "cost": 174.0 }, { "facility": "F8", "customer": 2, "cost": 129.0 }, { "facility": "F8", "customer": 3, "cost": 256.0 }, { "facility": "F8", "customer": 4, "cost": 360.0 }, { "facility": "F8", "customer": 5, "cost": 437.0 }, { "facility": "F8", "customer": 6, "cost": 446.0 }, { "facility": "F8", "customer": 7, "cost": 23.0 }, { "facility": "F8", "customer": 8, "cost": 125.0 }, { "facility": "F8", "customer": 9, "cost": 274.0 }, { "facility": "F8", "customer": 10, "cost": 382.0 }, { "facility": "F8", "customer": 11, "cost": 278.0 }, { "facility": "F8", "customer": 12, "cost": 569.0 }, { "facility": "F8", "customer": 13, "cost": 336.0 }, { "facility": "F8", "customer": 14, "cost": 113.0 }, { "facility": "F8", "customer": 15, "cost": 51.0 }, { "facility": "F8", "customer": 16, "cost": 118.0 }, { "facility": "F8", "customer": 17, "cost": 607.0 }, { "facility": "F8", "customer": 18, "cost": 557.0 }, { "facility": "F8", "customer": 19, "cost": 348.0 } ], "objective": 4566.0 }, "solution_variant": { "selected": [ "F4", "F8" ], "assignments": [ "F8", "F8", "F8", "F4", "F4", "F4", "F8", "F8", "F8", "F4", "F8", "F4", "F4", "F8", "F8", "F8", "F4", "F4", "F8" ] }, "context_index": 31, "input_format": "markdown_table", "input_index_base": 1 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Someone has to map out which recycling points should be up and running and which households will use each one. Every household must be assigned to one open point only, and each point has a maximum intake it can’t exceed. The “better” solution is the one with the lowest total cost: tally the costs to open the selected points plus all residents’ hauling effort to their assigned spots, and choose the assignment with the smallest total. The exact data and choices are shown below.\n\nThere are 8 collection points and 19 households in this instance.\n\n**Collection Points**\n| collection_point_id | point_opening_cost | point_intake_capacity |\n|---|---|---|\n| F1 | 400.0 | 1183.0 |\n| F2 | 400.0 | 911.0 |\n| F3 | 400.0 | 1105.0 |\n| F4 | 400.0 | 751.0 |\n| F5 | 400.0 | 1067.0 |\n| F6 | 400.0 | 1311.0 |\n| F7 | 400.0 | 596.0 |\n| F8 | 400.0 | 727.0 |\n\n**Households**\n| household_id | household_recycling_amount |\n|---|---|\n| A | 11.0 |\n| B | 30.0 |\n| C | 14.0 |\n| D | 17.0 |\n| E | 35.0 |\n| F | 44.0 |\n| G | 45.0 |\n| H | 23.0 |\n| I | 35.0 |\n| J | 45.0 |\n| K | 43.0 |\n| L | 49.0 |\n| M | 38.0 |\n| N | 42.0 |\n| O | 47.0 |\n| P | 31.0 |\n| Q | 49.0 |\n| R | 12.0 |\n| S | 44.0 |\n\n**Hauling Cost**\n| collection_point_id | household_id | hauling_cost |\n|---|---|---|\n| F1 | A | 557.0 |\n| F1 | B | 473.0 |\n| F1 | C | 617.0 |\n| F1 | D | 553.0 |\n| F1 | E | 294.0 |\n| F1 | F | 471.0 |\n| F1 | G | 675.0 |\n| F1 | H | 318.0 |\n| F1 | I | 593.0 |\n| F1 | J | 563.0 |\n| F1 | K | 511.0 |\n| F1 | L | 333.0 |\n| F1 | M | 465.0 |\n| F1 | N | 93.0 |\n| F1 | O | 353.0 |\n| F1 | P | 153.0 |\n| F1 | Q | 601.0 |\n| F1 | R | 399.0 |\n| F1 | S | 637.0 |\n| F2 | A | 426.0 |\n| F2 | B | 289.0 |\n| F2 | C | 449.0 |\n| F2 | D | 347.0 |\n| F2 | E | 113.0 |\n| F2 | F | 368.0 |\n| F2 | G | 481.0 |\n| F2 | H | 163.0 |\n| F2 | I | 389.0 |\n| F2 | J | 406.0 |\n| F2 | K | 312.0 |\n| F2 | L | 293.0 |\n| F2 | M | 263.0 |\n| F2 | N | 150.0 |\n| F2 | O | 164.0 |\n| F2 | P | 201.0 |\n| F2 | Q | 402.0 |\n| F2 | R | 374.0 |\n| F2 | S | 426.0 |\n| F3 | A | 380.0 |\n| F3 | B | 245.0 |\n| F3 | C | 269.0 |\n| F3 | D | 262.0 |\n| F3 | E | 424.0 |\n| F3 | F | 437.0 |\n| F3 | G | 350.0 |\n| F3 | H | 381.0 |\n| F3 | I | 270.0 |\n| F3 | J | 302.0 |\n| F3 | K | 182.0 |\n| F3 | L | 527.0 |\n| F3 | M | 305.0 |\n| F3 | N | 582.0 |\n| F3 | O | 324.0 |\n| F3 | P | 589.0 |\n| F3 | Q | 305.0 |\n| F3 | R | 572.0 |\n| F3 | S | 39.0 |\n| F4 | A | 528.0 |\n| F4 | B | 404.0 |\n| F4 | C | 561.0 |\n| F4 | D | 424.0 |\n| F4 | E | 164.0 |\n| F4 | F | 459.0 |\n| F4 | G | 543.0 |\n| F4 | H | 267.0 |\n| F4 | I | 464.0 |\n| F4 | J | 516.0 |\n| F4 | K | 428.0 |\n| F4 | L | 353.0 |\n| F4 | M | 336.0 |\n| F4 | N | 122.0 |\n| F4 | O | 279.0 |\n| F4 | P | 204.0 |\n| F4 | Q | 470.0 |\n| F4 | R | 431.0 |\n| F4 | S | 539.0 |\n| F5 | A | 345.0 |\n| F5 | B | 434.0 |\n| F5 | C | 468.0 |\n| F5 | D | 730.0 |\n| F5 | E | 558.0 |\n| F5 | F | 252.0 |\n| F5 | G | 877.0 |\n| F5 | H | 347.0 |\n| F5 | I | 771.0 |\n| F5 | J | 408.0 |\n| F5 | K | 499.0 |\n| F5 | L | 167.0 |\n| F5 | M | 668.0 |\n| F5 | N | 367.0 |\n| F5 | O | 409.0 |\n| F5 | P | 283.0 |\n| F5 | Q | 796.0 |\n| F5 | R | 105.0 |\n| F5 | S | 638.0 |\n| F6 | A | 88.0 |\n| F6 | B | 278.0 |\n| F6 | C | 176.0 |\n| F6 | D | 617.0 |\n| F6 | E | 580.0 |\n| F6 | F | 156.0 |\n| F6 | G | 752.0 |\n| F6 | H | 347.0 |\n| F6 | I | 648.0 |\n| F6 | J | 150.0 |\n| F6 | K | 320.0 |\n| F6 | L | 309.0 |\n| F6 | M | 596.0 |\n| F6 | N | 537.0 |\n| F6 | O | 364.0 |\n| F6 | P | 480.0 |\n| F6 | Q | 682.0 |\n| F6 | R | 281.0 |\n| F6 | S | 408.0 |\n| F7 | A | 422.0 |\n| F7 | B | 319.0 |\n| F7 | C | 468.0 |\n| F7 | D | 428.0 |\n| F7 | E | 192.0 |\n| F7 | F | 348.0 |\n| F7 | G | 563.0 |\n| F7 | H | 167.0 |\n| F7 | I | 471.0 |\n| F7 | J | 418.0 |\n| F7 | K | 355.0 |\n| F7 | L | 242.0 |\n| F7 | M | 345.0 |\n| F7 | N | 72.0 |\n| F7 | O | 198.0 |\n| F7 | P | 120.0 |\n| F7 | Q | 484.0 |\n| F7 | R | 322.0 |\n| F7 | S | 482.0 |\n| F8 | A | 121.0 |\n| F8 | B | 199.0 |\n| F8 | C | 228.0 |\n| F8 | D | 529.0 |\n| F8 | E | 430.0 |\n| F8 | F | 25.0 |\n| F8 | G | 675.0 |\n| F8 | H | 186.0 |\n| F8 | I | 567.0 |\n| F8 | J | 166.0 |\n| F8 | K | 262.0 |\n| F8 | L | 137.0 |\n| F8 | M | 486.0 |\n| F8 | N | 356.0 |\n| F8 | O | 224.0 |\n| F8 | P | 300.0 |\n| F8 | Q | 597.0 |\n| F8 | R | 144.0 |\n| F8 | S | 395.0 |\n\nWhen you send your solution, please follow this simple JSON layout so I can read it easily:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list the recycling points you want to open. \"assignments\" is a list that, for each household in the instance (in the same order as the input), says which open point that household will use. Think of it like filling out a short form: which sites are active, and then which active site each household goes to.\n\nThis JSON is just a sketch of the shape I expect, not the actual answer — replace the placeholders with the real identifiers from the instance.\n\nPlease make sure all identifiers are used exactly as they appear in the instance input — no renaming and no new labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 1183.0, 911.0, 1105.0, 751.0, 1067.0, 1311.0, 596.0, 727.0 ], "connection_costs": [ [ 557.0, 473.0, 617.0, 553.0, 294.0, 471.0, 675.0, 318.0, 593.0, 563.0, 511.0, 333.0, 465.0, 93.0, 353.0, 153.0, 601.0, 399.0, 637.0 ], [ 426.0, 289.0, 449.0, 347.0, 113.0, 368.0, 481.0, 163.0, 389.0, 406.0, 312.0, 293.0, 263.0, 150.0, 164.0, 201.0, 402.0, 374.0, 426.0 ], [ 380.0, 245.0, 269.0, 262.0, 424.0, 437.0, 350.0, 381.0, 270.0, 302.0, 182.0, 527.0, 305.0, 582.0, 324.0, 589.0, 305.0, 572.0, 39.0 ], [ 528.0, 404.0, 561.0, 424.0, 164.0, 459.0, 543.0, 267.0, 464.0, 516.0, 428.0, 353.0, 336.0, 122.0, 279.0, 204.0, 470.0, 431.0, 539.0 ], [ 345.0, 434.0, 468.0, 730.0, 558.0, 252.0, 877.0, 347.0, 771.0, 408.0, 499.0, 167.0, 668.0, 367.0, 409.0, 283.0, 796.0, 105.0, 638.0 ], [ 88.0, 278.0, 176.0, 617.0, 580.0, 156.0, 752.0, 347.0, 648.0, 150.0, 320.0, 309.0, 596.0, 537.0, 364.0, 480.0, 682.0, 281.0, 408.0 ], [ 422.0, 319.0, 468.0, 428.0, 192.0, 348.0, 563.0, 167.0, 471.0, 418.0, 355.0, 242.0, 345.0, 72.0, 198.0, 120.0, 484.0, 322.0, 482.0 ], [ 121.0, 199.0, 228.0, 529.0, 430.0, 25.0, 675.0, 186.0, 567.0, 166.0, 262.0, 137.0, 486.0, 356.0, 224.0, 300.0, 597.0, 144.0, 395.0 ] ], "demands": [ 11.0, 30.0, 14.0, 17.0, 35.0, 44.0, 45.0, 23.0, 35.0, 45.0, 43.0, 49.0, 38.0, 42.0, 47.0, 31.0, 49.0, 12.0, 44.0 ], "objective": 4682.0 }, "solution": { "open_facilities": [ 2, 6, 7 ], "assignments": [ 7, 7, 7, 2, 6, 7, 2, 6, 2, 7, 2, 7, 2, 6, 6, 6, 2, 7, 2 ] }, "obj": 4682.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 19, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 1183.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 911.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 1105.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 751.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 1067.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 1311.0 }, { "id": "F7", "opening_cost": 400.0, "capacity": 596.0 }, { "id": "F8", "opening_cost": 400.0, "capacity": 727.0 } ], "customers": [ { "id": "A", "demand": 11.0 }, { "id": "B", "demand": 30.0 }, { "id": "C", "demand": 14.0 }, { "id": "D", "demand": 17.0 }, { "id": "E", "demand": 35.0 }, { "id": "F", "demand": 44.0 }, { "id": "G", "demand": 45.0 }, { "id": "H", "demand": 23.0 }, { "id": "I", "demand": 35.0 }, { "id": "J", "demand": 45.0 }, { "id": "K", "demand": 43.0 }, { "id": "L", "demand": 49.0 }, { "id": "M", "demand": 38.0 }, { "id": "N", "demand": 42.0 }, { "id": "O", "demand": 47.0 }, { "id": "P", "demand": 31.0 }, { "id": "Q", "demand": 49.0 }, { "id": "R", "demand": 12.0 }, { "id": "S", "demand": 44.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 557.0 }, { "facility": "F1", "customer": "B", "cost": 473.0 }, { "facility": "F1", "customer": "C", "cost": 617.0 }, { "facility": "F1", "customer": "D", "cost": 553.0 }, { "facility": "F1", "customer": "E", "cost": 294.0 }, { "facility": "F1", "customer": "F", "cost": 471.0 }, { "facility": "F1", "customer": "G", "cost": 675.0 }, { "facility": "F1", "customer": "H", "cost": 318.0 }, { "facility": "F1", "customer": "I", "cost": 593.0 }, { "facility": "F1", "customer": "J", "cost": 563.0 }, { "facility": "F1", "customer": "K", "cost": 511.0 }, { "facility": "F1", "customer": "L", "cost": 333.0 }, { "facility": "F1", "customer": "M", "cost": 465.0 }, { "facility": "F1", "customer": "N", "cost": 93.0 }, { "facility": "F1", "customer": "O", "cost": 353.0 }, { "facility": "F1", "customer": "P", "cost": 153.0 }, { "facility": "F1", "customer": "Q", "cost": 601.0 }, { "facility": "F1", "customer": "R", "cost": 399.0 }, { "facility": "F1", "customer": "S", "cost": 637.0 }, { "facility": "F2", "customer": "A", "cost": 426.0 }, { "facility": "F2", "customer": "B", "cost": 289.0 }, { "facility": "F2", "customer": "C", "cost": 449.0 }, { "facility": "F2", "customer": "D", "cost": 347.0 }, { "facility": "F2", "customer": "E", "cost": 113.0 }, { "facility": "F2", "customer": "F", "cost": 368.0 }, { "facility": "F2", "customer": "G", "cost": 481.0 }, { "facility": "F2", "customer": "H", "cost": 163.0 }, { "facility": "F2", "customer": "I", "cost": 389.0 }, { "facility": "F2", "customer": "J", "cost": 406.0 }, { "facility": "F2", "customer": "K", "cost": 312.0 }, { "facility": "F2", "customer": "L", "cost": 293.0 }, { "facility": "F2", "customer": "M", "cost": 263.0 }, { "facility": "F2", "customer": "N", "cost": 150.0 }, { "facility": "F2", "customer": "O", "cost": 164.0 }, { "facility": "F2", "customer": "P", "cost": 201.0 }, { "facility": "F2", "customer": "Q", "cost": 402.0 }, { "facility": "F2", "customer": "R", "cost": 374.0 }, { "facility": "F2", "customer": "S", "cost": 426.0 }, { "facility": "F3", "customer": "A", "cost": 380.0 }, { "facility": "F3", "customer": "B", "cost": 245.0 }, { "facility": "F3", "customer": "C", "cost": 269.0 }, { "facility": "F3", "customer": "D", "cost": 262.0 }, { "facility": "F3", "customer": "E", "cost": 424.0 }, { "facility": "F3", "customer": "F", "cost": 437.0 }, { "facility": "F3", "customer": "G", "cost": 350.0 }, { "facility": "F3", "customer": "H", "cost": 381.0 }, { "facility": "F3", "customer": "I", "cost": 270.0 }, { "facility": "F3", "customer": "J", "cost": 302.0 }, { "facility": "F3", "customer": "K", "cost": 182.0 }, { "facility": "F3", "customer": "L", "cost": 527.0 }, { "facility": "F3", "customer": "M", "cost": 305.0 }, { "facility": "F3", "customer": "N", "cost": 582.0 }, { "facility": "F3", "customer": "O", "cost": 324.0 }, { "facility": "F3", "customer": "P", "cost": 589.0 }, { "facility": "F3", "customer": "Q", "cost": 305.0 }, { "facility": "F3", "customer": "R", "cost": 572.0 }, { "facility": "F3", "customer": "S", "cost": 39.0 }, { "facility": "F4", "customer": "A", "cost": 528.0 }, { "facility": "F4", "customer": "B", "cost": 404.0 }, { "facility": "F4", "customer": "C", "cost": 561.0 }, { "facility": "F4", "customer": "D", "cost": 424.0 }, { "facility": "F4", "customer": "E", "cost": 164.0 }, { "facility": "F4", "customer": "F", "cost": 459.0 }, { "facility": "F4", "customer": "G", "cost": 543.0 }, { "facility": "F4", "customer": "H", "cost": 267.0 }, { "facility": "F4", "customer": "I", "cost": 464.0 }, { "facility": "F4", "customer": "J", "cost": 516.0 }, { "facility": "F4", "customer": "K", "cost": 428.0 }, { "facility": "F4", "customer": "L", "cost": 353.0 }, { "facility": "F4", "customer": "M", "cost": 336.0 }, { "facility": "F4", "customer": "N", "cost": 122.0 }, { "facility": "F4", "customer": "O", "cost": 279.0 }, { "facility": "F4", "customer": "P", "cost": 204.0 }, { "facility": "F4", "customer": "Q", "cost": 470.0 }, { "facility": "F4", "customer": "R", "cost": 431.0 }, { "facility": "F4", "customer": "S", "cost": 539.0 }, { "facility": "F5", "customer": "A", "cost": 345.0 }, { "facility": "F5", "customer": "B", "cost": 434.0 }, { "facility": "F5", "customer": "C", "cost": 468.0 }, { "facility": "F5", "customer": "D", "cost": 730.0 }, { "facility": "F5", "customer": "E", "cost": 558.0 }, { "facility": "F5", "customer": "F", "cost": 252.0 }, { "facility": "F5", "customer": "G", "cost": 877.0 }, { "facility": "F5", "customer": "H", "cost": 347.0 }, { "facility": "F5", "customer": "I", "cost": 771.0 }, { "facility": "F5", "customer": "J", "cost": 408.0 }, { "facility": "F5", "customer": "K", "cost": 499.0 }, { "facility": "F5", "customer": "L", "cost": 167.0 }, { "facility": "F5", "customer": "M", "cost": 668.0 }, { "facility": "F5", "customer": "N", "cost": 367.0 }, { "facility": "F5", "customer": "O", "cost": 409.0 }, { "facility": "F5", "customer": "P", "cost": 283.0 }, { "facility": "F5", "customer": "Q", "cost": 796.0 }, { "facility": "F5", "customer": "R", "cost": 105.0 }, { "facility": "F5", "customer": "S", "cost": 638.0 }, { "facility": "F6", "customer": "A", "cost": 88.0 }, { "facility": "F6", "customer": "B", "cost": 278.0 }, { "facility": "F6", "customer": "C", "cost": 176.0 }, { "facility": "F6", "customer": "D", "cost": 617.0 }, { "facility": "F6", "customer": "E", "cost": 580.0 }, { "facility": "F6", "customer": "F", "cost": 156.0 }, { "facility": "F6", "customer": "G", "cost": 752.0 }, { "facility": "F6", "customer": "H", "cost": 347.0 }, { "facility": "F6", "customer": "I", "cost": 648.0 }, { "facility": "F6", "customer": "J", "cost": 150.0 }, { "facility": "F6", "customer": "K", "cost": 320.0 }, { "facility": "F6", "customer": "L", "cost": 309.0 }, { "facility": "F6", "customer": "M", "cost": 596.0 }, { "facility": "F6", "customer": "N", "cost": 537.0 }, { "facility": "F6", "customer": "O", "cost": 364.0 }, { "facility": "F6", "customer": "P", "cost": 480.0 }, { "facility": "F6", "customer": "Q", "cost": 682.0 }, { "facility": "F6", "customer": "R", "cost": 281.0 }, { "facility": "F6", "customer": "S", "cost": 408.0 }, { "facility": "F7", "customer": "A", "cost": 422.0 }, { "facility": "F7", "customer": "B", "cost": 319.0 }, { "facility": "F7", "customer": "C", "cost": 468.0 }, { "facility": "F7", "customer": "D", "cost": 428.0 }, { "facility": "F7", "customer": "E", "cost": 192.0 }, { "facility": "F7", "customer": "F", "cost": 348.0 }, { "facility": "F7", "customer": "G", "cost": 563.0 }, { "facility": "F7", "customer": "H", "cost": 167.0 }, { "facility": "F7", "customer": "I", "cost": 471.0 }, { "facility": "F7", "customer": "J", "cost": 418.0 }, { "facility": "F7", "customer": "K", "cost": 355.0 }, { "facility": "F7", "customer": "L", "cost": 242.0 }, { "facility": "F7", "customer": "M", "cost": 345.0 }, { "facility": "F7", "customer": "N", "cost": 72.0 }, { "facility": "F7", "customer": "O", "cost": 198.0 }, { "facility": "F7", "customer": "P", "cost": 120.0 }, { "facility": "F7", "customer": "Q", "cost": 484.0 }, { "facility": "F7", "customer": "R", "cost": 322.0 }, { "facility": "F7", "customer": "S", "cost": 482.0 }, { "facility": "F8", "customer": "A", "cost": 121.0 }, { "facility": "F8", "customer": "B", "cost": 199.0 }, { "facility": "F8", "customer": "C", "cost": 228.0 }, { "facility": "F8", "customer": "D", "cost": 529.0 }, { "facility": "F8", "customer": "E", "cost": 430.0 }, { "facility": "F8", "customer": "F", "cost": 25.0 }, { "facility": "F8", "customer": "G", "cost": 675.0 }, { "facility": "F8", "customer": "H", "cost": 186.0 }, { "facility": "F8", "customer": "I", "cost": 567.0 }, { "facility": "F8", "customer": "J", "cost": 166.0 }, { "facility": "F8", "customer": "K", "cost": 262.0 }, { "facility": "F8", "customer": "L", "cost": 137.0 }, { "facility": "F8", "customer": "M", "cost": 486.0 }, { "facility": "F8", "customer": "N", "cost": 356.0 }, { "facility": "F8", "customer": "O", "cost": 224.0 }, { "facility": "F8", "customer": "P", "cost": 300.0 }, { "facility": "F8", "customer": "Q", "cost": 597.0 }, { "facility": "F8", "customer": "R", "cost": 144.0 }, { "facility": "F8", "customer": "S", "cost": 395.0 } ], "objective": 4682.0 }, "solution_variant": { "selected": [ "F3", "F7", "F8" ], "assignments": [ "F8", "F8", "F8", "F3", "F7", "F8", "F3", "F7", "F3", "F8", "F3", "F8", "F3", "F7", "F7", "F7", "F3", "F8", "F3" ] }, "context_index": 32, "input_format": "markdown_table", "input_index_base": "names" }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "We’ve got a list of possible charging locations around town and a fleet of electric vehicles that need to be sent to stations for service. The decision is which of those locations to open (each one costs money to commission) and which station each vehicle should visit; every vehicle must go to one open station only, and every station can only take so many vehicles. A good choice is the one that keeps the overall expense down — tally the commissioning fees for the opened stations plus all the extra driving each vehicle does, and make that total as small as possible. Full specifics about sites, their limits, and the cost numbers appear below.\n\n# num_candidate_stations=7\n# num_vehicles=18\n# STATIONS\nstation_id,commissioning_cost,charging_capacity\nF1,400.0,911.0\nF2,400.0,1105.0\nF3,400.0,588.0\nF4,400.0,1017.0\nF5,400.0,1388.0\nF6,400.0,1331.0\nF7,400.0,620.0\n# VEHICLES\nvehicle_id,charging_demand\nA,30.0\nB,22.0\nC,31.0\nD,14.0\nE,31.0\nF,25.0\nG,19.0\nH,27.0\nI,15.0\nJ,18.0\nK,13.0\nL,35.0\nM,45.0\nN,42.0\nO,18.0\nP,13.0\nQ,15.0\nR,48.0\n# DETOURS\nstation_id,vehicle_id,detour_cost\nF1,A,289.0\nF1,B,56.0\nF1,C,332.0\nF1,D,449.0\nF1,E,557.0\nF1,F,399.0\nF1,G,193.0\nF1,H,440.0\nF1,I,269.0\nF1,J,269.0\nF1,K,195.0\nF1,L,324.0\nF1,M,16.0\nF1,N,253.0\nF1,O,241.0\nF1,P,305.0\nF1,Q,371.0\nF1,R,642.0\nF2,A,245.0\nF2,B,458.0\nF2,C,427.0\nF2,D,269.0\nF2,E,373.0\nF2,F,368.0\nF2,G,434.0\nF2,H,284.0\nF2,I,367.0\nF2,J,212.0\nF2,K,617.0\nF2,L,302.0\nF2,M,466.0\nF2,N,495.0\nF2,O,576.0\nF2,P,147.0\nF2,Q,564.0\nF2,R,285.0\nF3,A,115.0\nF3,B,208.0\nF3,C,218.0\nF3,D,277.0\nF3,E,391.0\nF3,F,402.0\nF3,G,281.0\nF3,H,398.0\nF3,I,299.0\nF3,J,102.0\nF3,K,367.0\nF3,L,162.0\nF3,M,184.0\nF3,N,215.0\nF3,O,275.0\nF3,P,178.0\nF3,Q,317.0\nF3,R,470.0\nF4,A,339.0\nF4,B,34.0\nF4,C,413.0\nF4,D,502.0\nF4,E,617.0\nF4,F,331.0\nF4,G,109.0\nF4,H,389.0\nF4,I,200.0\nF4,J,305.0\nF4,K,161.0\nF4,L,387.0\nF4,M,98.0\nF4,N,342.0\nF4,O,327.0\nF4,P,310.0\nF4,Q,460.0\nF4,R,678.0\nF5,A,316.0\nF5,B,421.0\nF5,C,137.0\nF5,D,358.0\nF5,E,388.0\nF5,F,711.0\nF5,G,549.0\nF5,H,708.0\nF5,I,598.0\nF5,J,363.0\nF5,K,517.0\nF5,L,260.0\nF5,M,361.0\nF5,N,113.0\nF5,O,173.0\nF5,P,469.0\nF5,Q,6.0\nF5,R,577.0\nF6,A,123.0\nF6,B,423.0\nF6,C,134.0\nF6,D,94.0\nF6,E,177.0\nF6,F,573.0\nF6,G,496.0\nF6,H,534.0\nF6,I,496.0\nF6,J,181.0\nF6,K,575.0\nF6,L,57.0\nF6,M,387.0\nF6,N,250.0\nF6,O,355.0\nF6,P,278.0\nF6,Q,272.0\nF6,R,318.0\nF7,A,475.0\nF7,B,424.0\nF7,C,650.0\nF7,D,586.0\nF7,E,705.0\nF7,F,73.0\nF7,G,301.0\nF7,H,68.0\nF7,I,199.0\nF7,J,416.0\nF7,K,520.0\nF7,L,550.0\nF7,M,475.0\nF7,N,652.0\nF7,O,685.0\nF7,P,315.0\nF7,Q,759.0\nF7,R,636.0\n\nYou can just return the answer in this little JSON layout so it's easy to read and machine-friendly:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is the list of charging sites you decide to open (those cost money to commission). \"assignments\" is a list with one entry per vehicle saying which open site that vehicle will go to. Think of it like filling out a form — which stations are active, and where each vehicle is assigned. This is only a sketch of the shape I need, not the actual answer.\n\nPlease make sure to use the exact identifiers from the instance input — do not rename them or invent new labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 911.0, 1105.0, 588.0, 1017.0, 1388.0, 1331.0, 620.0 ], "connection_costs": [ [ 289.0, 56.0, 332.0, 449.0, 557.0, 399.0, 193.0, 440.0, 269.0, 269.0, 195.0, 324.0, 16.0, 253.0, 241.0, 305.0, 371.0, 642.0 ], [ 245.0, 458.0, 427.0, 269.0, 373.0, 368.0, 434.0, 284.0, 367.0, 212.0, 617.0, 302.0, 466.0, 495.0, 576.0, 147.0, 564.0, 285.0 ], [ 115.0, 208.0, 218.0, 277.0, 391.0, 402.0, 281.0, 398.0, 299.0, 102.0, 367.0, 162.0, 184.0, 215.0, 275.0, 178.0, 317.0, 470.0 ], [ 339.0, 34.0, 413.0, 502.0, 617.0, 331.0, 109.0, 389.0, 200.0, 305.0, 161.0, 387.0, 98.0, 342.0, 327.0, 310.0, 460.0, 678.0 ], [ 316.0, 421.0, 137.0, 358.0, 388.0, 711.0, 549.0, 708.0, 598.0, 363.0, 517.0, 260.0, 361.0, 113.0, 173.0, 469.0, 6.0, 577.0 ], [ 123.0, 423.0, 134.0, 94.0, 177.0, 573.0, 496.0, 534.0, 496.0, 181.0, 575.0, 57.0, 387.0, 250.0, 355.0, 278.0, 272.0, 318.0 ], [ 475.0, 424.0, 650.0, 586.0, 705.0, 73.0, 301.0, 68.0, 199.0, 416.0, 520.0, 550.0, 475.0, 652.0, 685.0, 315.0, 759.0, 636.0 ] ], "demands": [ 30.0, 22.0, 31.0, 14.0, 31.0, 25.0, 19.0, 27.0, 15.0, 18.0, 13.0, 35.0, 45.0, 42.0, 18.0, 13.0, 15.0, 48.0 ], "objective": 3996.0 }, "solution": { "open_facilities": [ 3, 4, 5, 6 ], "assignments": [ 5, 3, 5, 5, 5, 6, 3, 6, 6, 5, 3, 5, 3, 4, 4, 5, 4, 5 ] }, "obj": 3996.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 18, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 911.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 1105.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 588.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 1017.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 1388.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 1331.0 }, { "id": "F7", "opening_cost": 400.0, "capacity": 620.0 } ], "customers": [ { "id": "A", "demand": 30.0 }, { "id": "B", "demand": 22.0 }, { "id": "C", "demand": 31.0 }, { "id": "D", "demand": 14.0 }, { "id": "E", "demand": 31.0 }, { "id": "F", "demand": 25.0 }, { "id": "G", "demand": 19.0 }, { "id": "H", "demand": 27.0 }, { "id": "I", "demand": 15.0 }, { "id": "J", "demand": 18.0 }, { "id": "K", "demand": 13.0 }, { "id": "L", "demand": 35.0 }, { "id": "M", "demand": 45.0 }, { "id": "N", "demand": 42.0 }, { "id": "O", "demand": 18.0 }, { "id": "P", "demand": 13.0 }, { "id": "Q", "demand": 15.0 }, { "id": "R", "demand": 48.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 289.0 }, { "facility": "F1", "customer": "B", "cost": 56.0 }, { "facility": "F1", "customer": "C", "cost": 332.0 }, { "facility": "F1", "customer": "D", "cost": 449.0 }, { "facility": "F1", "customer": "E", "cost": 557.0 }, { "facility": "F1", "customer": "F", "cost": 399.0 }, { "facility": "F1", "customer": "G", "cost": 193.0 }, { "facility": "F1", "customer": "H", "cost": 440.0 }, { "facility": "F1", "customer": "I", "cost": 269.0 }, { "facility": "F1", "customer": "J", "cost": 269.0 }, { "facility": "F1", "customer": "K", "cost": 195.0 }, { "facility": "F1", "customer": "L", "cost": 324.0 }, { "facility": "F1", "customer": "M", "cost": 16.0 }, { "facility": "F1", "customer": "N", "cost": 253.0 }, { "facility": "F1", "customer": "O", "cost": 241.0 }, { "facility": "F1", "customer": "P", "cost": 305.0 }, { "facility": "F1", "customer": "Q", "cost": 371.0 }, { "facility": "F1", "customer": "R", "cost": 642.0 }, { "facility": "F2", "customer": "A", "cost": 245.0 }, { "facility": "F2", "customer": "B", "cost": 458.0 }, { "facility": "F2", "customer": "C", "cost": 427.0 }, { "facility": "F2", "customer": "D", "cost": 269.0 }, { "facility": "F2", "customer": "E", "cost": 373.0 }, { "facility": "F2", "customer": "F", "cost": 368.0 }, { "facility": "F2", "customer": "G", "cost": 434.0 }, { "facility": "F2", "customer": "H", "cost": 284.0 }, { "facility": "F2", "customer": "I", "cost": 367.0 }, { "facility": "F2", "customer": "J", "cost": 212.0 }, { "facility": "F2", "customer": "K", "cost": 617.0 }, { "facility": "F2", "customer": "L", "cost": 302.0 }, { "facility": "F2", "customer": "M", "cost": 466.0 }, { "facility": "F2", "customer": "N", "cost": 495.0 }, { "facility": "F2", "customer": "O", "cost": 576.0 }, { "facility": "F2", "customer": "P", "cost": 147.0 }, { "facility": "F2", "customer": "Q", "cost": 564.0 }, { "facility": "F2", "customer": "R", "cost": 285.0 }, { "facility": "F3", "customer": "A", "cost": 115.0 }, { "facility": "F3", "customer": "B", "cost": 208.0 }, { "facility": "F3", "customer": "C", "cost": 218.0 }, { "facility": "F3", "customer": "D", "cost": 277.0 }, { "facility": "F3", "customer": "E", "cost": 391.0 }, { "facility": "F3", "customer": "F", "cost": 402.0 }, { "facility": "F3", "customer": "G", "cost": 281.0 }, { "facility": "F3", "customer": "H", "cost": 398.0 }, { "facility": "F3", "customer": "I", "cost": 299.0 }, { "facility": "F3", "customer": "J", "cost": 102.0 }, { "facility": "F3", "customer": "K", "cost": 367.0 }, { "facility": "F3", "customer": "L", "cost": 162.0 }, { "facility": "F3", "customer": "M", "cost": 184.0 }, { "facility": "F3", "customer": "N", "cost": 215.0 }, { "facility": "F3", "customer": "O", "cost": 275.0 }, { "facility": "F3", "customer": "P", "cost": 178.0 }, { "facility": "F3", "customer": "Q", "cost": 317.0 }, { "facility": "F3", "customer": "R", "cost": 470.0 }, { "facility": "F4", "customer": "A", "cost": 339.0 }, { "facility": "F4", "customer": "B", "cost": 34.0 }, { "facility": "F4", "customer": "C", "cost": 413.0 }, { "facility": "F4", "customer": "D", "cost": 502.0 }, { "facility": "F4", "customer": "E", "cost": 617.0 }, { "facility": "F4", "customer": "F", "cost": 331.0 }, { "facility": "F4", "customer": "G", "cost": 109.0 }, { "facility": "F4", "customer": "H", "cost": 389.0 }, { "facility": "F4", "customer": "I", "cost": 200.0 }, { "facility": "F4", "customer": "J", "cost": 305.0 }, { "facility": "F4", "customer": "K", "cost": 161.0 }, { "facility": "F4", "customer": "L", "cost": 387.0 }, { "facility": "F4", "customer": "M", "cost": 98.0 }, { "facility": "F4", "customer": "N", "cost": 342.0 }, { "facility": "F4", "customer": "O", "cost": 327.0 }, { "facility": "F4", "customer": "P", "cost": 310.0 }, { "facility": "F4", "customer": "Q", "cost": 460.0 }, { "facility": "F4", "customer": "R", "cost": 678.0 }, { "facility": "F5", "customer": "A", "cost": 316.0 }, { "facility": "F5", "customer": "B", "cost": 421.0 }, { "facility": "F5", "customer": "C", "cost": 137.0 }, { "facility": "F5", "customer": "D", "cost": 358.0 }, { "facility": "F5", "customer": "E", "cost": 388.0 }, { "facility": "F5", "customer": "F", "cost": 711.0 }, { "facility": "F5", "customer": "G", "cost": 549.0 }, { "facility": "F5", "customer": "H", "cost": 708.0 }, { "facility": "F5", "customer": "I", "cost": 598.0 }, { "facility": "F5", "customer": "J", "cost": 363.0 }, { "facility": "F5", "customer": "K", "cost": 517.0 }, { "facility": "F5", "customer": "L", "cost": 260.0 }, { "facility": "F5", "customer": "M", "cost": 361.0 }, { "facility": "F5", "customer": "N", "cost": 113.0 }, { "facility": "F5", "customer": "O", "cost": 173.0 }, { "facility": "F5", "customer": "P", "cost": 469.0 }, { "facility": "F5", "customer": "Q", "cost": 6.0 }, { "facility": "F5", "customer": "R", "cost": 577.0 }, { "facility": "F6", "customer": "A", "cost": 123.0 }, { "facility": "F6", "customer": "B", "cost": 423.0 }, { "facility": "F6", "customer": "C", "cost": 134.0 }, { "facility": "F6", "customer": "D", "cost": 94.0 }, { "facility": "F6", "customer": "E", "cost": 177.0 }, { "facility": "F6", "customer": "F", "cost": 573.0 }, { "facility": "F6", "customer": "G", "cost": 496.0 }, { "facility": "F6", "customer": "H", "cost": 534.0 }, { "facility": "F6", "customer": "I", "cost": 496.0 }, { "facility": "F6", "customer": "J", "cost": 181.0 }, { "facility": "F6", "customer": "K", "cost": 575.0 }, { "facility": "F6", "customer": "L", "cost": 57.0 }, { "facility": "F6", "customer": "M", "cost": 387.0 }, { "facility": "F6", "customer": "N", "cost": 250.0 }, { "facility": "F6", "customer": "O", "cost": 355.0 }, { "facility": "F6", "customer": "P", "cost": 278.0 }, { "facility": "F6", "customer": "Q", "cost": 272.0 }, { "facility": "F6", "customer": "R", "cost": 318.0 }, { "facility": "F7", "customer": "A", "cost": 475.0 }, { "facility": "F7", "customer": "B", "cost": 424.0 }, { "facility": "F7", "customer": "C", "cost": 650.0 }, { "facility": "F7", "customer": "D", "cost": 586.0 }, { "facility": "F7", "customer": "E", "cost": 705.0 }, { "facility": "F7", "customer": "F", "cost": 73.0 }, { "facility": "F7", "customer": "G", "cost": 301.0 }, { "facility": "F7", "customer": "H", "cost": 68.0 }, { "facility": "F7", "customer": "I", "cost": 199.0 }, { "facility": "F7", "customer": "J", "cost": 416.0 }, { "facility": "F7", "customer": "K", "cost": 520.0 }, { "facility": "F7", "customer": "L", "cost": 550.0 }, { "facility": "F7", "customer": "M", "cost": 475.0 }, { "facility": "F7", "customer": "N", "cost": 652.0 }, { "facility": "F7", "customer": "O", "cost": 685.0 }, { "facility": "F7", "customer": "P", "cost": 315.0 }, { "facility": "F7", "customer": "Q", "cost": 759.0 }, { "facility": "F7", "customer": "R", "cost": 636.0 } ], "objective": 3996.0 }, "solution_variant": { "selected": [ "F4", "F5", "F6", "F7" ], "assignments": [ "F6", "F4", "F6", "F6", "F6", "F7", "F4", "F7", "F7", "F6", "F4", "F6", "F4", "F5", "F5", "F6", "F5", "F6" ] }, "context_index": 33, "input_format": "csv", "input_index_base": "names" }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Recently the campus IT group had to map out which shared printers to install and how to route staff print jobs to those printers. The goal was to minimize the overall cost, which is just the sum of the installation costs for the printers that are put in plus the transfer or delay cost for each document sent to its chosen printer. Every print job must be sent as a whole to a single installed printer, no printer can exceed its duty capacity, and no job can be left unassigned. The full list of printer options, costs, capacities and the print jobs is provided below.\n\nThere are 8 printers and 18 jobs in this instance.\n\n**Printers**\n| printer_id | installation_cost | duty_capacity_pages |\n|---|---|---|\n| F1 | 258.0 | 366.0 |\n| F2 | 296.0 | 504.0 |\n| F3 | 225.0 | 504.0 |\n| F4 | 310.0 | 580.0 |\n| F5 | 373.0 | 415.0 |\n| F6 | 179.0 | 549.0 |\n| F7 | 114.0 | 310.0 |\n| F8 | 321.0 | 316.0 |\n\n**Jobs**\n| job_id | job_size_pages |\n|---|---|\n| 0 | 29.0 |\n| 1 | 48.0 |\n| 2 | 14.0 |\n| 3 | 39.0 |\n| 4 | 33.0 |\n| 5 | 40.0 |\n| 6 | 43.0 |\n| 7 | 47.0 |\n| 8 | 24.0 |\n| 9 | 32.0 |\n| 10 | 26.0 |\n| 11 | 13.0 |\n| 12 | 27.0 |\n| 13 | 37.0 |\n| 14 | 45.0 |\n| 15 | 38.0 |\n| 16 | 42.0 |\n| 17 | 10.0 |\n\n**Transfer Delay Cost**\n| printer_id | job_id | transfer_delay_cost |\n|---|---|---|\n| F1 | 0 | 239.0 |\n| F1 | 1 | 288.0 |\n| F1 | 2 | 122.0 |\n| F1 | 3 | 143.0 |\n| F1 | 4 | 393.0 |\n| F1 | 5 | 656.0 |\n| F1 | 6 | 654.0 |\n| F1 | 7 | 640.0 |\n| F1 | 8 | 329.0 |\n| F1 | 9 | 524.0 |\n| F1 | 10 | 516.0 |\n| F1 | 11 | 414.0 |\n| F1 | 12 | 458.0 |\n| F1 | 13 | 502.0 |\n| F1 | 14 | 475.0 |\n| F1 | 15 | 94.0 |\n| F1 | 16 | 519.0 |\n| F1 | 17 | 494.0 |\n| F2 | 0 | 212.0 |\n| F2 | 1 | 33.0 |\n| F2 | 2 | 376.0 |\n| F2 | 3 | 262.0 |\n| F2 | 4 | 140.0 |\n| F2 | 5 | 335.0 |\n| F2 | 6 | 466.0 |\n| F2 | 7 | 328.0 |\n| F2 | 8 | 149.0 |\n| F2 | 9 | 274.0 |\n| F2 | 10 | 337.0 |\n| F2 | 11 | 284.0 |\n| F2 | 12 | 140.0 |\n| F2 | 13 | 243.0 |\n| F2 | 14 | 267.0 |\n| F2 | 15 | 244.0 |\n| F2 | 16 | 267.0 |\n| F2 | 17 | 364.0 |\n| F3 | 0 | 347.0 |\n| F3 | 1 | 281.0 |\n| F3 | 2 | 117.0 |\n| F3 | 3 | 59.0 |\n| F3 | 4 | 428.0 |\n| F3 | 5 | 611.0 |\n| F3 | 6 | 738.0 |\n| F3 | 7 | 569.0 |\n| F3 | 8 | 229.0 |\n| F3 | 9 | 409.0 |\n| F3 | 10 | 367.0 |\n| F3 | 11 | 261.0 |\n| F3 | 12 | 414.0 |\n| F3 | 13 | 540.0 |\n| F3 | 14 | 541.0 |\n| F3 | 15 | 218.0 |\n| F3 | 16 | 406.0 |\n| F3 | 17 | 598.0 |\n| F4 | 0 | 276.0 |\n| F4 | 1 | 258.0 |\n| F4 | 2 | 582.0 |\n| F4 | 3 | 484.0 |\n| F4 | 4 | 108.0 |\n| F4 | 5 | 294.0 |\n| F4 | 6 | 237.0 |\n| F4 | 7 | 354.0 |\n| F4 | 8 | 383.0 |\n| F4 | 9 | 432.0 |\n| F4 | 10 | 532.0 |\n| F4 | 11 | 508.0 |\n| F4 | 12 | 235.0 |\n| F4 | 13 | 9.0 |\n| F4 | 14 | 72.0 |\n| F4 | 15 | 402.0 |\n| F4 | 16 | 424.0 |\n| F4 | 17 | 200.0 |\n| F5 | 0 | 507.0 |\n| F5 | 1 | 323.0 |\n| F5 | 2 | 464.0 |\n| F5 | 3 | 357.0 |\n| F5 | 4 | 436.0 |\n| F5 | 5 | 399.0 |\n| F5 | 6 | 748.0 |\n| F5 | 7 | 317.0 |\n| F5 | 8 | 184.0 |\n| F5 | 9 | 113.0 |\n| F5 | 10 | 25.0 |\n| F5 | 11 | 88.0 |\n| F5 | 12 | 281.0 |\n| F5 | 13 | 510.0 |\n| F5 | 14 | 559.0 |\n| F5 | 15 | 466.0 |\n| F5 | 16 | 118.0 |\n| F5 | 17 | 671.0 |\n| F6 | 0 | 354.0 |\n| F6 | 1 | 422.0 |\n| F6 | 2 | 700.0 |\n| F6 | 3 | 622.0 |\n| F6 | 4 | 274.0 |\n| F6 | 5 | 458.0 |\n| F6 | 6 | 61.0 |\n| F6 | 7 | 533.0 |\n| F6 | 8 | 562.0 |\n| F6 | 9 | 625.0 |\n| F6 | 10 | 724.0 |\n| F6 | 11 | 693.0 |\n| F6 | 12 | 428.0 |\n| F6 | 13 | 197.0 |\n| F6 | 14 | 147.0 |\n| F6 | 15 | 501.0 |\n| F6 | 16 | 617.0 |\n| F6 | 17 | 113.0 |\n| F7 | 0 | 162.0 |\n| F7 | 1 | 320.0 |\n| F7 | 2 | 295.0 |\n| F7 | 3 | 296.0 |\n| F7 | 4 | 356.0 |\n| F7 | 5 | 664.0 |\n| F7 | 6 | 538.0 |\n| F7 | 7 | 673.0 |\n| F7 | 8 | 423.0 |\n| F7 | 9 | 607.0 |\n| F7 | 10 | 630.0 |\n| F7 | 11 | 539.0 |\n| F7 | 12 | 485.0 |\n| F7 | 13 | 443.0 |\n| F7 | 14 | 392.0 |\n| F7 | 15 | 142.0 |\n| F7 | 16 | 600.0 |\n| F7 | 17 | 368.0 |\n| F8 | 0 | 462.0 |\n| F8 | 1 | 357.0 |\n| F8 | 2 | 701.0 |\n| F8 | 3 | 585.0 |\n| F8 | 4 | 268.0 |\n| F8 | 5 | 96.0 |\n| F8 | 6 | 381.0 |\n| F8 | 7 | 187.0 |\n| F8 | 8 | 412.0 |\n| F8 | 9 | 354.0 |\n| F8 | 10 | 474.0 |\n| F8 | 11 | 496.0 |\n| F8 | 12 | 213.0 |\n| F8 | 13 | 209.0 |\n| F8 | 14 | 289.0 |\n| F8 | 15 | 555.0 |\n| F8 | 16 | 347.0 |\n| F8 | 17 | 411.0 |\n\nIf you could return the plan in a simple machine-friendly way, that would be great — something like this JSON layout so it's easy to check and parse.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of printers you'll actually install, and \"assignments\" as, for each print job in the same order they were listed in the instance, which installed printer that job gets sent to. Super casual: selected = which printers we put in, assignments = where each job goes.\n\nThis JSON is just a sketch of the shape I want your answer to follow — not the final plan itself.\n\nPlease be careful to use the exact identifiers from the instance input when filling in those placeholders — do not rename or invent labels. For example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 258.0, 296.0, 225.0, 310.0, 373.0, 179.0, 114.0, 321.0 ], "capacities": [ 366.0, 504.0, 504.0, 580.0, 415.0, 549.0, 310.0, 316.0 ], "connection_costs": [ [ 239.0, 288.0, 122.0, 143.0, 393.0, 656.0, 654.0, 640.0, 329.0, 524.0, 516.0, 414.0, 458.0, 502.0, 475.0, 94.0, 519.0, 494.0 ], [ 212.0, 33.0, 376.0, 262.0, 140.0, 335.0, 466.0, 328.0, 149.0, 274.0, 337.0, 284.0, 140.0, 243.0, 267.0, 244.0, 267.0, 364.0 ], [ 347.0, 281.0, 117.0, 59.0, 428.0, 611.0, 738.0, 569.0, 229.0, 409.0, 367.0, 261.0, 414.0, 540.0, 541.0, 218.0, 406.0, 598.0 ], [ 276.0, 258.0, 582.0, 484.0, 108.0, 294.0, 237.0, 354.0, 383.0, 432.0, 532.0, 508.0, 235.0, 9.0, 72.0, 402.0, 424.0, 200.0 ], [ 507.0, 323.0, 464.0, 357.0, 436.0, 399.0, 748.0, 317.0, 184.0, 113.0, 25.0, 88.0, 281.0, 510.0, 559.0, 466.0, 118.0, 671.0 ], [ 354.0, 422.0, 700.0, 622.0, 274.0, 458.0, 61.0, 533.0, 562.0, 625.0, 724.0, 693.0, 428.0, 197.0, 147.0, 501.0, 617.0, 113.0 ], [ 162.0, 320.0, 295.0, 296.0, 356.0, 664.0, 538.0, 673.0, 423.0, 607.0, 630.0, 539.0, 485.0, 443.0, 392.0, 142.0, 600.0, 368.0 ], [ 462.0, 357.0, 701.0, 585.0, 268.0, 96.0, 381.0, 187.0, 412.0, 354.0, 474.0, 496.0, 213.0, 209.0, 289.0, 555.0, 347.0, 411.0 ] ], "demands": [ 29.0, 48.0, 14.0, 39.0, 33.0, 40.0, 43.0, 47.0, 24.0, 32.0, 26.0, 13.0, 27.0, 37.0, 45.0, 38.0, 42.0, 10.0 ], "objective": 3595.0 }, "solution": { "open_facilities": [ 1, 2, 4, 5, 6, 7 ], "assignments": [ 6, 1, 2, 2, 1, 7, 5, 7, 1, 4, 4, 4, 1, 5, 5, 6, 4, 5 ] }, "obj": 3595.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 18, "facilities": [ { "id": "F1", "opening_cost": 258.0, "capacity": 366.0 }, { "id": "F2", "opening_cost": 296.0, "capacity": 504.0 }, { "id": "F3", "opening_cost": 225.0, "capacity": 504.0 }, { "id": "F4", "opening_cost": 310.0, "capacity": 580.0 }, { "id": "F5", "opening_cost": 373.0, "capacity": 415.0 }, { "id": "F6", "opening_cost": 179.0, "capacity": 549.0 }, { "id": "F7", "opening_cost": 114.0, "capacity": 310.0 }, { "id": "F8", "opening_cost": 321.0, "capacity": 316.0 } ], "customers": [ { "id": 0, "demand": 29.0 }, { "id": 1, "demand": 48.0 }, { "id": 2, "demand": 14.0 }, { "id": 3, "demand": 39.0 }, { "id": 4, "demand": 33.0 }, { "id": 5, "demand": 40.0 }, { "id": 6, "demand": 43.0 }, { "id": 7, "demand": 47.0 }, { "id": 8, "demand": 24.0 }, { "id": 9, "demand": 32.0 }, { "id": 10, "demand": 26.0 }, { "id": 11, "demand": 13.0 }, { "id": 12, "demand": 27.0 }, { "id": 13, "demand": 37.0 }, { "id": 14, "demand": 45.0 }, { "id": 15, "demand": 38.0 }, { "id": 16, "demand": 42.0 }, { "id": 17, "demand": 10.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 239.0 }, { "facility": "F1", "customer": 1, "cost": 288.0 }, { "facility": "F1", "customer": 2, "cost": 122.0 }, { "facility": "F1", "customer": 3, "cost": 143.0 }, { "facility": "F1", "customer": 4, "cost": 393.0 }, { "facility": "F1", "customer": 5, "cost": 656.0 }, { "facility": "F1", "customer": 6, "cost": 654.0 }, { "facility": "F1", "customer": 7, "cost": 640.0 }, { "facility": "F1", "customer": 8, "cost": 329.0 }, { "facility": "F1", "customer": 9, "cost": 524.0 }, { "facility": "F1", "customer": 10, "cost": 516.0 }, { "facility": "F1", "customer": 11, "cost": 414.0 }, { "facility": "F1", "customer": 12, "cost": 458.0 }, { "facility": "F1", "customer": 13, "cost": 502.0 }, { "facility": "F1", "customer": 14, "cost": 475.0 }, { "facility": "F1", "customer": 15, "cost": 94.0 }, { "facility": "F1", "customer": 16, "cost": 519.0 }, { "facility": "F1", "customer": 17, "cost": 494.0 }, { "facility": "F2", "customer": 0, "cost": 212.0 }, { "facility": "F2", "customer": 1, "cost": 33.0 }, { "facility": "F2", "customer": 2, "cost": 376.0 }, { "facility": "F2", "customer": 3, "cost": 262.0 }, { "facility": "F2", "customer": 4, "cost": 140.0 }, { "facility": "F2", "customer": 5, "cost": 335.0 }, { "facility": "F2", "customer": 6, "cost": 466.0 }, { "facility": "F2", "customer": 7, "cost": 328.0 }, { "facility": "F2", "customer": 8, "cost": 149.0 }, { "facility": "F2", "customer": 9, "cost": 274.0 }, { "facility": "F2", "customer": 10, "cost": 337.0 }, { "facility": "F2", "customer": 11, "cost": 284.0 }, { "facility": "F2", "customer": 12, "cost": 140.0 }, { "facility": "F2", "customer": 13, "cost": 243.0 }, { "facility": "F2", "customer": 14, "cost": 267.0 }, { "facility": "F2", "customer": 15, "cost": 244.0 }, { "facility": "F2", "customer": 16, "cost": 267.0 }, { "facility": "F2", "customer": 17, "cost": 364.0 }, { "facility": "F3", "customer": 0, "cost": 347.0 }, { "facility": "F3", "customer": 1, "cost": 281.0 }, { "facility": "F3", "customer": 2, "cost": 117.0 }, { "facility": "F3", "customer": 3, "cost": 59.0 }, { "facility": "F3", "customer": 4, "cost": 428.0 }, { "facility": "F3", "customer": 5, "cost": 611.0 }, { "facility": "F3", "customer": 6, "cost": 738.0 }, { "facility": "F3", "customer": 7, "cost": 569.0 }, { "facility": "F3", "customer": 8, "cost": 229.0 }, { "facility": "F3", "customer": 9, "cost": 409.0 }, { "facility": "F3", "customer": 10, "cost": 367.0 }, { "facility": "F3", "customer": 11, "cost": 261.0 }, { "facility": "F3", "customer": 12, "cost": 414.0 }, { "facility": "F3", "customer": 13, "cost": 540.0 }, { "facility": "F3", "customer": 14, "cost": 541.0 }, { "facility": "F3", "customer": 15, "cost": 218.0 }, { "facility": "F3", "customer": 16, "cost": 406.0 }, { "facility": "F3", "customer": 17, "cost": 598.0 }, { "facility": "F4", "customer": 0, "cost": 276.0 }, { "facility": "F4", "customer": 1, "cost": 258.0 }, { "facility": "F4", "customer": 2, "cost": 582.0 }, { "facility": "F4", "customer": 3, "cost": 484.0 }, { "facility": "F4", "customer": 4, "cost": 108.0 }, { "facility": "F4", "customer": 5, "cost": 294.0 }, { "facility": "F4", "customer": 6, "cost": 237.0 }, { "facility": "F4", "customer": 7, "cost": 354.0 }, { "facility": "F4", "customer": 8, "cost": 383.0 }, { "facility": "F4", "customer": 9, "cost": 432.0 }, { "facility": "F4", "customer": 10, "cost": 532.0 }, { "facility": "F4", "customer": 11, "cost": 508.0 }, { "facility": "F4", "customer": 12, "cost": 235.0 }, { "facility": "F4", "customer": 13, "cost": 9.0 }, { "facility": "F4", "customer": 14, "cost": 72.0 }, { "facility": "F4", "customer": 15, "cost": 402.0 }, { "facility": "F4", "customer": 16, "cost": 424.0 }, { "facility": "F4", "customer": 17, "cost": 200.0 }, { "facility": "F5", "customer": 0, "cost": 507.0 }, { "facility": "F5", "customer": 1, "cost": 323.0 }, { "facility": "F5", "customer": 2, "cost": 464.0 }, { "facility": "F5", "customer": 3, "cost": 357.0 }, { "facility": "F5", "customer": 4, "cost": 436.0 }, { "facility": "F5", "customer": 5, "cost": 399.0 }, { "facility": "F5", "customer": 6, "cost": 748.0 }, { "facility": "F5", "customer": 7, "cost": 317.0 }, { "facility": "F5", "customer": 8, "cost": 184.0 }, { "facility": "F5", "customer": 9, "cost": 113.0 }, { "facility": "F5", "customer": 10, "cost": 25.0 }, { "facility": "F5", "customer": 11, "cost": 88.0 }, { "facility": "F5", "customer": 12, "cost": 281.0 }, { "facility": "F5", "customer": 13, "cost": 510.0 }, { "facility": "F5", "customer": 14, "cost": 559.0 }, { "facility": "F5", "customer": 15, "cost": 466.0 }, { "facility": "F5", "customer": 16, "cost": 118.0 }, { "facility": "F5", "customer": 17, "cost": 671.0 }, { "facility": "F6", "customer": 0, "cost": 354.0 }, { "facility": "F6", "customer": 1, "cost": 422.0 }, { "facility": "F6", "customer": 2, "cost": 700.0 }, { "facility": "F6", "customer": 3, "cost": 622.0 }, { "facility": "F6", "customer": 4, "cost": 274.0 }, { "facility": "F6", "customer": 5, "cost": 458.0 }, { "facility": "F6", "customer": 6, "cost": 61.0 }, { "facility": "F6", "customer": 7, "cost": 533.0 }, { "facility": "F6", "customer": 8, "cost": 562.0 }, { "facility": "F6", "customer": 9, "cost": 625.0 }, { "facility": "F6", "customer": 10, "cost": 724.0 }, { "facility": "F6", "customer": 11, "cost": 693.0 }, { "facility": "F6", "customer": 12, "cost": 428.0 }, { "facility": "F6", "customer": 13, "cost": 197.0 }, { "facility": "F6", "customer": 14, "cost": 147.0 }, { "facility": "F6", "customer": 15, "cost": 501.0 }, { "facility": "F6", "customer": 16, "cost": 617.0 }, { "facility": "F6", "customer": 17, "cost": 113.0 }, { "facility": "F7", "customer": 0, "cost": 162.0 }, { "facility": "F7", "customer": 1, "cost": 320.0 }, { "facility": "F7", "customer": 2, "cost": 295.0 }, { "facility": "F7", "customer": 3, "cost": 296.0 }, { "facility": "F7", "customer": 4, "cost": 356.0 }, { "facility": "F7", "customer": 5, "cost": 664.0 }, { "facility": "F7", "customer": 6, "cost": 538.0 }, { "facility": "F7", "customer": 7, "cost": 673.0 }, { "facility": "F7", "customer": 8, "cost": 423.0 }, { "facility": "F7", "customer": 9, "cost": 607.0 }, { "facility": "F7", "customer": 10, "cost": 630.0 }, { "facility": "F7", "customer": 11, "cost": 539.0 }, { "facility": "F7", "customer": 12, "cost": 485.0 }, { "facility": "F7", "customer": 13, "cost": 443.0 }, { "facility": "F7", "customer": 14, "cost": 392.0 }, { "facility": "F7", "customer": 15, "cost": 142.0 }, { "facility": "F7", "customer": 16, "cost": 600.0 }, { "facility": "F7", "customer": 17, "cost": 368.0 }, { "facility": "F8", "customer": 0, "cost": 462.0 }, { "facility": "F8", "customer": 1, "cost": 357.0 }, { "facility": "F8", "customer": 2, "cost": 701.0 }, { "facility": "F8", "customer": 3, "cost": 585.0 }, { "facility": "F8", "customer": 4, "cost": 268.0 }, { "facility": "F8", "customer": 5, "cost": 96.0 }, { "facility": "F8", "customer": 6, "cost": 381.0 }, { "facility": "F8", "customer": 7, "cost": 187.0 }, { "facility": "F8", "customer": 8, "cost": 412.0 }, { "facility": "F8", "customer": 9, "cost": 354.0 }, { "facility": "F8", "customer": 10, "cost": 474.0 }, { "facility": "F8", "customer": 11, "cost": 496.0 }, { "facility": "F8", "customer": 12, "cost": 213.0 }, { "facility": "F8", "customer": 13, "cost": 209.0 }, { "facility": "F8", "customer": 14, "cost": 289.0 }, { "facility": "F8", "customer": 15, "cost": 555.0 }, { "facility": "F8", "customer": 16, "cost": 347.0 }, { "facility": "F8", "customer": 17, "cost": 411.0 } ], "objective": 3595.0 }, "solution_variant": { "selected": [ "F2", "F3", "F5", "F6", "F7", "F8" ], "assignments": [ "F7", "F2", "F3", "F3", "F2", "F8", "F6", "F8", "F2", "F5", "F5", "F5", "F2", "F6", "F6", "F7", "F5", "F6" ] }, "context_index": 34, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "There’s a simple trade-off in town: keep more drop-off centers so neighborhoods travel less, or keep fewer centers to save on upkeep — but whichever plan is chosen, each neighborhood’s trash must go to one place and no center can take more than its limit. Each open center has a maintenance cost, each neighborhood-to-center route adds hauling distance, and the aim is the plan that makes the combined upkeep plus hauling as small as possible while respecting site capacities and keeping every neighborhood’s trash intact and unsplit. The actual list of centers, capacities, costs, and neighborhood demands appears below.\n\n# num_dropoff_centers=8\n# num_neighborhoods=19\n# CENTERS\ncenter_id,maintenance_cost,processing_capacity\nF1,400.0,1500.0\nF2,400.0,1500.0\nF3,400.0,1500.0\nF4,400.0,1500.0\nF5,400.0,1500.0\nF6,400.0,1500.0\nF7,400.0,1500.0\nF8,400.0,1500.0\n# NEIGHBORHOODS\nneighborhood_id,waste_demand\nA,33.0\nB,40.0\nC,40.0\nD,18.0\nE,17.0\nF,43.0\nG,39.0\nH,12.0\nI,45.0\nJ,13.0\nK,17.0\nL,45.0\nM,46.0\nN,36.0\nO,45.0\nP,40.0\nQ,44.0\nR,16.0\nS,22.0\n# HAULINGS\ncenter_id,neighborhood_id,hauling_cost\nF1,A,273.0\nF1,B,549.0\nF1,C,594.0\nF1,D,349.0\nF1,E,423.0\nF1,F,124.0\nF1,G,711.0\nF1,H,400.0\nF1,I,231.0\nF1,J,780.0\nF1,K,724.0\nF1,L,600.0\nF1,M,265.0\nF1,N,837.0\nF1,O,529.0\nF1,P,583.0\nF1,Q,241.0\nF1,R,481.0\nF1,S,69.0\nF2,A,688.0\nF2,B,235.0\nF2,C,250.0\nF2,D,393.0\nF2,E,247.0\nF2,F,548.0\nF2,G,207.0\nF2,H,634.0\nF2,I,549.0\nF2,J,232.0\nF2,K,287.0\nF2,L,238.0\nF2,M,500.0\nF2,N,354.0\nF2,O,190.0\nF2,P,148.0\nF2,Q,447.0\nF2,R,320.0\nF2,S,736.0\nF3,A,321.0\nF3,B,373.0\nF3,C,436.0\nF3,D,193.0\nF3,E,238.0\nF3,F,73.0\nF3,G,543.0\nF3,H,385.0\nF3,I,194.0\nF3,J,611.0\nF3,K,567.0\nF3,L,440.0\nF3,M,189.0\nF3,N,681.0\nF3,O,357.0\nF3,P,400.0\nF3,Q,75.0\nF3,R,318.0\nF3,S,251.0\nF4,A,497.0\nF4,B,168.0\nF4,C,293.0\nF4,D,163.0\nF4,E,30.0\nF4,F,308.0\nF4,G,358.0\nF4,H,492.0\nF4,I,351.0\nF4,J,417.0\nF4,K,408.0\nF4,L,290.0\nF4,M,310.0\nF4,N,514.0\nF4,O,182.0\nF4,P,164.0\nF4,Q,198.0\nF4,R,172.0\nF4,S,491.0\nF5,A,203.0\nF5,B,575.0\nF5,C,333.0\nF5,D,486.0\nF5,E,382.0\nF5,F,316.0\nF5,G,460.0\nF5,H,93.0\nF5,I,166.0\nF5,J,526.0\nF5,K,433.0\nF5,L,345.0\nF5,M,150.0\nF5,N,532.0\nF5,O,350.0\nF5,P,548.0\nF5,Q,395.0\nF5,R,569.0\nF5,S,450.0\nF6,A,354.0\nF6,B,433.0\nF6,C,544.0\nF6,D,228.0\nF6,E,332.0\nF6,F,105.0\nF6,G,649.0\nF6,H,451.0\nF6,I,260.0\nF6,J,716.0\nF6,K,675.0\nF6,L,547.0\nF6,M,272.0\nF6,N,788.0\nF6,O,461.0\nF6,P,476.0\nF6,Q,131.0\nF6,R,360.0\nF6,S,176.0\nF7,A,343.0\nF7,B,320.0\nF7,C,287.0\nF7,D,224.0\nF7,E,135.0\nF7,F,193.0\nF7,G,396.0\nF7,H,343.0\nF7,I,197.0\nF7,J,465.0\nF7,K,418.0\nF7,L,291.0\nF7,M,156.0\nF7,N,532.0\nF7,O,212.0\nF7,P,315.0\nF7,Q,162.0\nF7,R,303.0\nF7,S,386.0\nF8,A,740.0\nF8,B,88.0\nF8,C,483.0\nF8,D,260.0\nF8,E,281.0\nF8,F,515.0\nF8,G,487.0\nF8,H,745.0\nF8,I,594.0\nF8,J,520.0\nF8,K,561.0\nF8,L,475.0\nF8,M,559.0\nF8,N,641.0\nF8,O,377.0\nF8,P,152.0\nF8,Q,372.0\nF8,R,128.0\nF8,S,664.0\n\nWhen you send the plan back, do it in this little JSON shape so it's easy to check automatically and still human-readable:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nHere, \"selected\" is where you list the drop-off centers you decide to keep open, and \"assignments\" is, in order, which open center each neighborhood sends its trash to. Think of it like a simple form: selected = open centers, assignments = each neighborhood's chosen center. This JSON is just a sketch of the shape I need — not the final plan itself.\n\nPlease use the exact identifiers from the instance input when you fill this in — do not rename them or invent new labels. For example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 1500.0, 1500.0, 1500.0, 1500.0, 1500.0, 1500.0, 1500.0, 1500.0 ], "connection_costs": [ [ 273.0, 549.0, 594.0, 349.0, 423.0, 124.0, 711.0, 400.0, 231.0, 780.0, 724.0, 600.0, 265.0, 837.0, 529.0, 583.0, 241.0, 481.0, 69.0 ], [ 688.0, 235.0, 250.0, 393.0, 247.0, 548.0, 207.0, 634.0, 549.0, 232.0, 287.0, 238.0, 500.0, 354.0, 190.0, 148.0, 447.0, 320.0, 736.0 ], [ 321.0, 373.0, 436.0, 193.0, 238.0, 73.0, 543.0, 385.0, 194.0, 611.0, 567.0, 440.0, 189.0, 681.0, 357.0, 400.0, 75.0, 318.0, 251.0 ], [ 497.0, 168.0, 293.0, 163.0, 30.0, 308.0, 358.0, 492.0, 351.0, 417.0, 408.0, 290.0, 310.0, 514.0, 182.0, 164.0, 198.0, 172.0, 491.0 ], [ 203.0, 575.0, 333.0, 486.0, 382.0, 316.0, 460.0, 93.0, 166.0, 526.0, 433.0, 345.0, 150.0, 532.0, 350.0, 548.0, 395.0, 569.0, 450.0 ], [ 354.0, 433.0, 544.0, 228.0, 332.0, 105.0, 649.0, 451.0, 260.0, 716.0, 675.0, 547.0, 272.0, 788.0, 461.0, 476.0, 131.0, 360.0, 176.0 ], [ 343.0, 320.0, 287.0, 224.0, 135.0, 193.0, 396.0, 343.0, 197.0, 465.0, 418.0, 291.0, 156.0, 532.0, 212.0, 315.0, 162.0, 303.0, 386.0 ], [ 740.0, 88.0, 483.0, 260.0, 281.0, 515.0, 487.0, 745.0, 594.0, 520.0, 561.0, 475.0, 559.0, 641.0, 377.0, 152.0, 372.0, 128.0, 664.0 ] ], "demands": [ 33.0, 40.0, 40.0, 18.0, 17.0, 43.0, 39.0, 12.0, 45.0, 13.0, 17.0, 45.0, 46.0, 36.0, 45.0, 40.0, 44.0, 16.0, 22.0 ], "objective": 5034.0 }, "solution": { "open_facilities": [ 0, 1, 3, 4 ], "assignments": [ 4, 3, 1, 3, 3, 0, 1, 4, 4, 1, 1, 1, 4, 1, 3, 1, 3, 3, 0 ] }, "obj": 5034.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 19, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 1500.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 1500.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 1500.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 1500.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 1500.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 1500.0 }, { "id": "F7", "opening_cost": 400.0, "capacity": 1500.0 }, { "id": "F8", "opening_cost": 400.0, "capacity": 1500.0 } ], "customers": [ { "id": "A", "demand": 33.0 }, { "id": "B", "demand": 40.0 }, { "id": "C", "demand": 40.0 }, { "id": "D", "demand": 18.0 }, { "id": "E", "demand": 17.0 }, { "id": "F", "demand": 43.0 }, { "id": "G", "demand": 39.0 }, { "id": "H", "demand": 12.0 }, { "id": "I", "demand": 45.0 }, { "id": "J", "demand": 13.0 }, { "id": "K", "demand": 17.0 }, { "id": "L", "demand": 45.0 }, { "id": "M", "demand": 46.0 }, { "id": "N", "demand": 36.0 }, { "id": "O", "demand": 45.0 }, { "id": "P", "demand": 40.0 }, { "id": "Q", "demand": 44.0 }, { "id": "R", "demand": 16.0 }, { "id": "S", "demand": 22.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 273.0 }, { "facility": "F1", "customer": "B", "cost": 549.0 }, { "facility": "F1", "customer": "C", "cost": 594.0 }, { "facility": "F1", "customer": "D", "cost": 349.0 }, { "facility": "F1", "customer": "E", "cost": 423.0 }, { "facility": "F1", "customer": "F", "cost": 124.0 }, { "facility": "F1", "customer": "G", "cost": 711.0 }, { "facility": "F1", "customer": "H", "cost": 400.0 }, { "facility": "F1", "customer": "I", "cost": 231.0 }, { "facility": "F1", "customer": "J", "cost": 780.0 }, { "facility": "F1", "customer": "K", "cost": 724.0 }, { "facility": "F1", "customer": "L", "cost": 600.0 }, { "facility": "F1", "customer": "M", "cost": 265.0 }, { "facility": "F1", "customer": "N", "cost": 837.0 }, { "facility": "F1", "customer": "O", "cost": 529.0 }, { "facility": "F1", "customer": "P", "cost": 583.0 }, { "facility": "F1", "customer": "Q", "cost": 241.0 }, { "facility": "F1", "customer": "R", "cost": 481.0 }, { "facility": "F1", "customer": "S", "cost": 69.0 }, { "facility": "F2", "customer": "A", "cost": 688.0 }, { "facility": "F2", "customer": "B", "cost": 235.0 }, { "facility": "F2", "customer": "C", "cost": 250.0 }, { "facility": "F2", "customer": "D", "cost": 393.0 }, { "facility": "F2", "customer": "E", "cost": 247.0 }, { "facility": "F2", "customer": "F", "cost": 548.0 }, { "facility": "F2", "customer": "G", "cost": 207.0 }, { "facility": "F2", "customer": "H", "cost": 634.0 }, { "facility": "F2", "customer": "I", "cost": 549.0 }, { "facility": "F2", "customer": "J", "cost": 232.0 }, { "facility": "F2", "customer": "K", "cost": 287.0 }, { "facility": "F2", "customer": "L", "cost": 238.0 }, { "facility": "F2", "customer": "M", "cost": 500.0 }, { "facility": "F2", "customer": "N", "cost": 354.0 }, { "facility": "F2", "customer": "O", "cost": 190.0 }, { "facility": "F2", "customer": "P", "cost": 148.0 }, { "facility": "F2", "customer": "Q", "cost": 447.0 }, { "facility": "F2", "customer": "R", "cost": 320.0 }, { "facility": "F2", "customer": "S", "cost": 736.0 }, { "facility": "F3", "customer": "A", "cost": 321.0 }, { "facility": "F3", "customer": "B", "cost": 373.0 }, { "facility": "F3", "customer": "C", "cost": 436.0 }, { "facility": "F3", "customer": "D", "cost": 193.0 }, { "facility": "F3", "customer": "E", "cost": 238.0 }, { "facility": "F3", "customer": "F", "cost": 73.0 }, { "facility": "F3", "customer": "G", "cost": 543.0 }, { "facility": "F3", "customer": "H", "cost": 385.0 }, { "facility": "F3", "customer": "I", "cost": 194.0 }, { "facility": "F3", "customer": "J", "cost": 611.0 }, { "facility": "F3", "customer": "K", "cost": 567.0 }, { "facility": "F3", "customer": "L", "cost": 440.0 }, { "facility": "F3", "customer": "M", "cost": 189.0 }, { "facility": "F3", "customer": "N", "cost": 681.0 }, { "facility": "F3", "customer": "O", "cost": 357.0 }, { "facility": "F3", "customer": "P", "cost": 400.0 }, { "facility": "F3", "customer": "Q", "cost": 75.0 }, { "facility": "F3", "customer": "R", "cost": 318.0 }, { "facility": "F3", "customer": "S", "cost": 251.0 }, { "facility": "F4", "customer": "A", "cost": 497.0 }, { "facility": "F4", "customer": "B", "cost": 168.0 }, { "facility": "F4", "customer": "C", "cost": 293.0 }, { "facility": "F4", "customer": "D", "cost": 163.0 }, { "facility": "F4", "customer": "E", "cost": 30.0 }, { "facility": "F4", "customer": "F", "cost": 308.0 }, { "facility": "F4", "customer": "G", "cost": 358.0 }, { "facility": "F4", "customer": "H", "cost": 492.0 }, { "facility": "F4", "customer": "I", "cost": 351.0 }, { "facility": "F4", "customer": "J", "cost": 417.0 }, { "facility": "F4", "customer": "K", "cost": 408.0 }, { "facility": "F4", "customer": "L", "cost": 290.0 }, { "facility": "F4", "customer": "M", "cost": 310.0 }, { "facility": "F4", "customer": "N", "cost": 514.0 }, { "facility": "F4", "customer": "O", "cost": 182.0 }, { "facility": "F4", "customer": "P", "cost": 164.0 }, { "facility": "F4", "customer": "Q", "cost": 198.0 }, { "facility": "F4", "customer": "R", "cost": 172.0 }, { "facility": "F4", "customer": "S", "cost": 491.0 }, { "facility": "F5", "customer": "A", "cost": 203.0 }, { "facility": "F5", "customer": "B", "cost": 575.0 }, { "facility": "F5", "customer": "C", "cost": 333.0 }, { "facility": "F5", "customer": "D", "cost": 486.0 }, { "facility": "F5", "customer": "E", "cost": 382.0 }, { "facility": "F5", "customer": "F", "cost": 316.0 }, { "facility": "F5", "customer": "G", "cost": 460.0 }, { "facility": "F5", "customer": "H", "cost": 93.0 }, { "facility": "F5", "customer": "I", "cost": 166.0 }, { "facility": "F5", "customer": "J", "cost": 526.0 }, { "facility": "F5", "customer": "K", "cost": 433.0 }, { "facility": "F5", "customer": "L", "cost": 345.0 }, { "facility": "F5", "customer": "M", "cost": 150.0 }, { "facility": "F5", "customer": "N", "cost": 532.0 }, { "facility": "F5", "customer": "O", "cost": 350.0 }, { "facility": "F5", "customer": "P", "cost": 548.0 }, { "facility": "F5", "customer": "Q", "cost": 395.0 }, { "facility": "F5", "customer": "R", "cost": 569.0 }, { "facility": "F5", "customer": "S", "cost": 450.0 }, { "facility": "F6", "customer": "A", "cost": 354.0 }, { "facility": "F6", "customer": "B", "cost": 433.0 }, { "facility": "F6", "customer": "C", "cost": 544.0 }, { "facility": "F6", "customer": "D", "cost": 228.0 }, { "facility": "F6", "customer": "E", "cost": 332.0 }, { "facility": "F6", "customer": "F", "cost": 105.0 }, { "facility": "F6", "customer": "G", "cost": 649.0 }, { "facility": "F6", "customer": "H", "cost": 451.0 }, { "facility": "F6", "customer": "I", "cost": 260.0 }, { "facility": "F6", "customer": "J", "cost": 716.0 }, { "facility": "F6", "customer": "K", "cost": 675.0 }, { "facility": "F6", "customer": "L", "cost": 547.0 }, { "facility": "F6", "customer": "M", "cost": 272.0 }, { "facility": "F6", "customer": "N", "cost": 788.0 }, { "facility": "F6", "customer": "O", "cost": 461.0 }, { "facility": "F6", "customer": "P", "cost": 476.0 }, { "facility": "F6", "customer": "Q", "cost": 131.0 }, { "facility": "F6", "customer": "R", "cost": 360.0 }, { "facility": "F6", "customer": "S", "cost": 176.0 }, { "facility": "F7", "customer": "A", "cost": 343.0 }, { "facility": "F7", "customer": "B", "cost": 320.0 }, { "facility": "F7", "customer": "C", "cost": 287.0 }, { "facility": "F7", "customer": "D", "cost": 224.0 }, { "facility": "F7", "customer": "E", "cost": 135.0 }, { "facility": "F7", "customer": "F", "cost": 193.0 }, { "facility": "F7", "customer": "G", "cost": 396.0 }, { "facility": "F7", "customer": "H", "cost": 343.0 }, { "facility": "F7", "customer": "I", "cost": 197.0 }, { "facility": "F7", "customer": "J", "cost": 465.0 }, { "facility": "F7", "customer": "K", "cost": 418.0 }, { "facility": "F7", "customer": "L", "cost": 291.0 }, { "facility": "F7", "customer": "M", "cost": 156.0 }, { "facility": "F7", "customer": "N", "cost": 532.0 }, { "facility": "F7", "customer": "O", "cost": 212.0 }, { "facility": "F7", "customer": "P", "cost": 315.0 }, { "facility": "F7", "customer": "Q", "cost": 162.0 }, { "facility": "F7", "customer": "R", "cost": 303.0 }, { "facility": "F7", "customer": "S", "cost": 386.0 }, { "facility": "F8", "customer": "A", "cost": 740.0 }, { "facility": "F8", "customer": "B", "cost": 88.0 }, { "facility": "F8", "customer": "C", "cost": 483.0 }, { "facility": "F8", "customer": "D", "cost": 260.0 }, { "facility": "F8", "customer": "E", "cost": 281.0 }, { "facility": "F8", "customer": "F", "cost": 515.0 }, { "facility": "F8", "customer": "G", "cost": 487.0 }, { "facility": "F8", "customer": "H", "cost": 745.0 }, { "facility": "F8", "customer": "I", "cost": 594.0 }, { "facility": "F8", "customer": "J", "cost": 520.0 }, { "facility": "F8", "customer": "K", "cost": 561.0 }, { "facility": "F8", "customer": "L", "cost": 475.0 }, { "facility": "F8", "customer": "M", "cost": 559.0 }, { "facility": "F8", "customer": "N", "cost": 641.0 }, { "facility": "F8", "customer": "O", "cost": 377.0 }, { "facility": "F8", "customer": "P", "cost": 152.0 }, { "facility": "F8", "customer": "Q", "cost": 372.0 }, { "facility": "F8", "customer": "R", "cost": 128.0 }, { "facility": "F8", "customer": "S", "cost": 664.0 } ], "objective": 5034.0 }, "solution_variant": { "selected": [ "F1", "F2", "F4", "F5" ], "assignments": [ "F5", "F4", "F2", "F4", "F4", "F1", "F2", "F5", "F5", "F2", "F2", "F2", "F5", "F2", "F4", "F2", "F4", "F4", "F1" ] }, "context_index": 35, "input_format": "csv", "input_index_base": "names" }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Recently the team had to map out where to put service stations and how to assign arriving guest groups so nobody ends up split between stations and no station gets swamped. Each potential station comes with a setup charge and a cap on how many people it can serve, while each guest group has a cost to be served from each station. The idea is to open some stations and send every group to exactly one of the opened stations, keeping assignments within capacity, and then total up the cost: station setup charges for those opened plus the service/travel costs for all group assignments — the lower that total, the better. The specific station choices, capacities, costs, and guest group list are below.\n\n{\n \"num_stations\": 6,\n \"num_guest_groups\": 15,\n \"stations\": [\n {\n \"station_id\": \"F1\",\n \"setup_cost\": 525.0,\n \"station_capacity\": 700.0\n },\n {\n \"station_id\": \"F2\",\n \"setup_cost\": 365.0,\n \"station_capacity\": 700.0\n },\n {\n \"station_id\": \"F3\",\n \"setup_cost\": 213.0,\n \"station_capacity\": 700.0\n },\n {\n \"station_id\": \"F4\",\n \"setup_cost\": 487.0,\n \"station_capacity\": 700.0\n },\n {\n \"station_id\": \"F5\",\n \"setup_cost\": 201.0,\n \"station_capacity\": 700.0\n },\n {\n \"station_id\": \"F6\",\n \"setup_cost\": 351.0,\n \"station_capacity\": 700.0\n }\n ],\n \"groups\": [\n {\n \"group_id\": 0,\n \"group_size\": 28.0\n },\n {\n \"group_id\": 1,\n \"group_size\": 24.0\n },\n {\n \"group_id\": 2,\n \"group_size\": 17.0\n },\n {\n \"group_id\": 3,\n \"group_size\": 20.0\n },\n {\n \"group_id\": 4,\n \"group_size\": 13.0\n },\n {\n \"group_id\": 5,\n \"group_size\": 18.0\n },\n {\n \"group_id\": 6,\n \"group_size\": 23.0\n },\n {\n \"group_id\": 7,\n \"group_size\": 26.0\n },\n {\n \"group_id\": 8,\n \"group_size\": 17.0\n },\n {\n \"group_id\": 9,\n \"group_size\": 13.0\n },\n {\n \"group_id\": 10,\n \"group_size\": 16.0\n },\n {\n \"group_id\": 11,\n \"group_size\": 27.0\n },\n {\n \"group_id\": 12,\n \"group_size\": 11.0\n },\n {\n \"group_id\": 13,\n \"group_size\": 18.0\n },\n {\n \"group_id\": 14,\n \"group_size\": 17.0\n }\n ],\n \"services\": [\n {\n \"station_id\": \"F1\",\n \"group_id\": 0,\n \"service_cost\": 1017.0\n },\n {\n \"station_id\": \"F1\",\n \"group_id\": 1,\n \"service_cost\": 166.0\n },\n {\n \"station_id\": \"F1\",\n \"group_id\": 2,\n \"service_cost\": 924.0\n },\n {\n \"station_id\": \"F1\",\n \"group_id\": 3,\n \"service_cost\": 463.0\n },\n {\n \"station_id\": \"F1\",\n \"group_id\": 4,\n \"service_cost\": 36.0\n },\n {\n \"station_id\": \"F1\",\n \"group_id\": 5,\n \"service_cost\": 685.0\n },\n {\n \"station_id\": \"F1\",\n \"group_id\": 6,\n \"service_cost\": 116.0\n },\n {\n \"station_id\": \"F1\",\n \"group_id\": 7,\n \"service_cost\": 463.0\n },\n {\n \"station_id\": \"F1\",\n \"group_id\": 8,\n \"service_cost\": 583.0\n },\n {\n \"station_id\": \"F1\",\n \"group_id\": 9,\n \"service_cost\": 335.0\n },\n {\n \"station_id\": \"F1\",\n \"group_id\": 10,\n \"service_cost\": 275.0\n },\n {\n \"station_id\": \"F1\",\n \"group_id\": 11,\n \"service_cost\": 728.0\n },\n {\n \"station_id\": \"F1\",\n \"group_id\": 12,\n \"service_cost\": 656.0\n },\n {\n \"station_id\": \"F1\",\n \"group_id\": 13,\n \"service_cost\": 138.0\n },\n {\n \"station_id\": \"F1\",\n \"group_id\": 14,\n \"service_cost\": 800.0\n },\n {\n \"station_id\": \"F2\",\n \"group_id\": 0,\n \"service_cost\": 262.0\n },\n {\n \"station_id\": \"F2\",\n \"group_id\": 1,\n \"service_cost\": 63.0\n },\n {\n \"station_id\": \"F2\",\n \"group_id\": 2,\n \"service_cost\": 232.0\n },\n {\n \"station_id\": \"F2\",\n \"group_id\": 3,\n \"service_cost\": 142.0\n },\n {\n \"station_id\": \"F2\",\n \"group_id\": 4,\n \"service_cost\": 38.0\n },\n {\n \"station_id\": \"F2\",\n \"group_id\": 5,\n \"service_cost\": 122.0\n },\n {\n \"station_id\": \"F2\",\n \"group_id\": 6,\n \"service_cost\": 49.0\n },\n {\n \"station_id\": \"F2\",\n \"group_id\": 7,\n \"service_cost\": 542.0\n },\n {\n \"station_id\": \"F2\",\n \"group_id\": 8,\n \"service_cost\": 399.0\n },\n {\n \"station_id\": \"F2\",\n \"group_id\": 9,\n \"service_cost\": 96.0\n },\n {\n \"station_id\": \"F2\",\n \"group_id\": 10,\n \"service_cost\": 235.0\n },\n {\n \"station_id\": \"F2\",\n \"group_id\": 11,\n \"service_cost\": 101.0\n },\n {\n \"station_id\": \"F2\",\n \"group_id\": 12,\n \"service_cost\": 720.0\n },\n {\n \"station_id\": \"F2\",\n \"group_id\": 13,\n \"service_cost\": 123.0\n },\n {\n \"station_id\": \"F2\",\n \"group_id\": 14,\n \"service_cost\": 734.0\n },\n {\n \"station_id\": \"F3\",\n \"group_id\": 0,\n \"service_cost\": 1770.0\n },\n {\n \"station_id\": \"F3\",\n \"group_id\": 1,\n \"service_cost\": 555.0\n },\n {\n \"station_id\": \"F3\",\n \"group_id\": 2,\n \"service_cost\": 1664.0\n },\n {\n \"station_id\": \"F3\",\n \"group_id\": 3,\n \"service_cost\": 1051.0\n },\n {\n \"station_id\": \"F3\",\n \"group_id\": 4,\n \"service_cost\": 381.0\n },\n {\n \"station_id\": \"F3\",\n \"group_id\": 5,\n \"service_cost\": 1451.0\n },\n {\n \"station_id\": \"F3\",\n \"group_id\": 6,\n \"service_cost\": 467.0\n },\n {\n \"station_id\": \"F3\",\n \"group_id\": 7,\n \"service_cost\": 456.0\n },\n {\n \"station_id\": \"F3\",\n \"group_id\": 8,\n \"service_cost\": 1184.0\n },\n {\n \"station_id\": \"F3\",\n \"group_id\": 9,\n \"service_cost\": 1109.0\n },\n {\n \"station_id\": \"F3\",\n \"group_id\": 10,\n \"service_cost\": 953.0\n },\n {\n \"station_id\": \"F3\",\n \"group_id\": 11,\n \"service_cost\": 1483.0\n },\n {\n \"station_id\": \"F3\",\n \"group_id\": 12,\n \"service_cost\": 526.0\n },\n {\n \"station_id\": \"F3\",\n \"group_id\": 13,\n \"service_cost\": 915.0\n },\n {\n \"station_id\": \"F3\",\n \"group_id\": 14,\n \"service_cost\": 1064.0\n },\n {\n \"station_id\": \"F4\",\n \"group_id\": 0,\n \"service_cost\": 1439.0\n },\n {\n \"station_id\": \"F4\",\n \"group_id\": 1,\n \"service_cost\": 465.0\n },\n {\n \"station_id\": \"F4\",\n \"group_id\": 2,\n \"service_cost\": 1444.0\n },\n {\n \"station_id\": \"F4\",\n \"group_id\": 3,\n \"service_cost\": 909.0\n },\n {\n \"station_id\": \"F4\",\n \"group_id\": 4,\n \"service_cost\": 280.0\n },\n {\n \"station_id\": \"F4\",\n \"group_id\": 5,\n \"service_cost\": 1143.0\n },\n {\n \"station_id\": \"F4\",\n \"group_id\": 6,\n \"service_cost\": 383.0\n },\n {\n \"station_id\": \"F4\",\n \"group_id\": 7,\n \"service_cost\": 118.0\n },\n {\n \"station_id\": \"F4\",\n \"group_id\": 8,\n \"service_cost\": 813.0\n },\n {\n \"station_id\": \"F4\",\n \"group_id\": 9,\n \"service_cost\": 829.0\n },\n {\n \"station_id\": \"F4\",\n \"group_id\": 10,\n \"service_cost\": 641.0\n },\n {\n \"station_id\": \"F4\",\n \"group_id\": 11,\n \"service_cost\": 1248.0\n },\n {\n \"station_id\": \"F4\",\n \"group_id\": 12,\n \"service_cost\": 22.0\n },\n {\n \"station_id\": \"F4\",\n \"group_id\": 13,\n \"service_cost\": 651.0\n },\n {\n \"station_id\": \"F4\",\n \"group_id\": 14,\n \"service_cost\": 603.0\n },\n {\n \"station_id\": \"F5\",\n \"group_id\": 0,\n \"service_cost\": 223.0\n },\n {\n \"station_id\": \"F5\",\n \"group_id\": 1,\n \"service_cost\": 146.0\n },\n {\n \"station_id\": \"F5\",\n \"group_id\": 2,\n \"service_cost\": 518.0\n },\n {\n \"station_id\": \"F5\",\n \"group_id\": 3,\n \"service_cost\": 332.0\n },\n {\n \"station_id\": \"F5\",\n \"group_id\": 4,\n \"service_cost\": 37.0\n },\n {\n \"station_id\": \"F5\",\n \"group_id\": 5,\n \"service_cost\": 128.0\n },\n {\n \"station_id\": \"F5\",\n \"group_id\": 6,\n \"service_cost\": 107.0\n },\n {\n \"station_id\": \"F5\",\n \"group_id\": 7,\n \"service_cost\": 232.0\n },\n {\n \"station_id\": \"F5\",\n \"group_id\": 8,\n \"service_cost\": 47.0\n },\n {\n \"station_id\": \"F5\",\n \"group_id\": 9,\n \"service_cost\": 59.0\n },\n {\n \"station_id\": \"F5\",\n \"group_id\": 10,\n \"service_cost\": 33.0\n },\n {\n \"station_id\": \"F5\",\n \"group_id\": 11,\n \"service_cost\": 350.0\n },\n {\n \"station_id\": \"F5\",\n \"group_id\": 12,\n \"service_cost\": 351.0\n },\n {\n \"station_id\": \"F5\",\n \"group_id\": 13,\n \"service_cost\": 45.0\n },\n {\n \"station_id\": \"F5\",\n \"group_id\": 14,\n \"service_cost\": 256.0\n },\n {\n \"station_id\": \"F6\",\n \"group_id\": 0,\n \"service_cost\": 1591.0\n },\n {\n \"station_id\": \"F6\",\n \"group_id\": 1,\n \"service_cost\": 216.0\n },\n {\n \"station_id\": \"F6\",\n \"group_id\": 2,\n \"service_cost\": 1317.0\n },\n {\n \"station_id\": \"F6\",\n \"group_id\": 3,\n \"service_cost\": 670.0\n },\n {\n \"station_id\": \"F6\",\n \"group_id\": 4,\n \"service_cost\": 40.0\n },\n {\n \"station_id\": \"F6\",\n \"group_id\": 5,\n \"service_cost\": 1253.0\n },\n {\n \"station_id\": \"F6\",\n \"group_id\": 6,\n \"service_cost\": 145.0\n },\n {\n \"station_id\": \"F6\",\n \"group_id\": 7,\n \"service_cost\": 804.0\n },\n {\n \"station_id\": \"F6\",\n \"group_id\": 8,\n \"service_cost\": 1176.0\n },\n {\n \"station_id\": \"F6\",\n \"group_id\": 9,\n \"service_cost\": 905.0\n },\n {\n \"station_id\": \"F6\",\n \"group_id\": 10,\n \"service_cost\": 870.0\n },\n {\n \"station_id\": \"F6\",\n \"group_id\": 11,\n \"service_cost\": 1160.0\n },\n {\n \"station_id\": \"F6\",\n \"group_id\": 12,\n \"service_cost\": 995.0\n },\n {\n \"station_id\": \"F6\",\n \"group_id\": 13,\n \"service_cost\": 722.0\n },\n {\n \"station_id\": \"F6\",\n \"group_id\": 14,\n \"service_cost\": 1302.0\n }\n ]\n}\n\nOh, and when you send the actual picks and assignments back, please follow this little JSON layout so it's easy to parse and check — just a simple sketch of the shape I expect:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nPretty straightforward: \"selected\" is the list of stations you decide to set up, and \"assignments\" is the list (in the same order as the guest groups were given) of which opened station each group goes to. Think of it like filling out a form: pick the stations you open, then for each guest group write the station you assigned them to.\n\nThis JSON is just a sketch of the expected shape, not the actual solution — fill in the real station identifiers from the instance when you reply.\n\nPlease make sure you use the exact identifiers from the instance input — do not rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 525.0, 365.0, 213.0, 487.0, 201.0, 351.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 1017.0, 166.0, 924.0, 463.0, 36.0, 685.0, 116.0, 463.0, 583.0, 335.0, 275.0, 728.0, 656.0, 138.0, 800.0 ], [ 262.0, 63.0, 232.0, 142.0, 38.0, 122.0, 49.0, 542.0, 399.0, 96.0, 235.0, 101.0, 720.0, 123.0, 734.0 ], [ 1770.0, 555.0, 1664.0, 1051.0, 381.0, 1451.0, 467.0, 456.0, 1184.0, 1109.0, 953.0, 1483.0, 526.0, 915.0, 1064.0 ], [ 1439.0, 465.0, 1444.0, 909.0, 280.0, 1143.0, 383.0, 118.0, 813.0, 829.0, 641.0, 1248.0, 22.0, 651.0, 603.0 ], [ 223.0, 146.0, 518.0, 332.0, 37.0, 128.0, 107.0, 232.0, 47.0, 59.0, 33.0, 350.0, 351.0, 45.0, 256.0 ], [ 1591.0, 216.0, 1317.0, 670.0, 40.0, 1253.0, 145.0, 804.0, 1176.0, 905.0, 870.0, 1160.0, 995.0, 722.0, 1302.0 ] ], "demands": [ 28.0, 24.0, 17.0, 20.0, 13.0, 18.0, 23.0, 26.0, 17.0, 13.0, 16.0, 27.0, 11.0, 18.0, 17.0 ], "objective": 2558.0 }, "solution": { "open_facilities": [ 1, 4 ], "assignments": [ 4, 1, 1, 1, 4, 1, 1, 4, 4, 4, 4, 1, 4, 4, 4 ] }, "obj": 2558.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 6, "num_customers": 15, "facilities": [ { "id": "F1", "opening_cost": 525.0, "capacity": 700.0 }, { "id": "F2", "opening_cost": 365.0, "capacity": 700.0 }, { "id": "F3", "opening_cost": 213.0, "capacity": 700.0 }, { "id": "F4", "opening_cost": 487.0, "capacity": 700.0 }, { "id": "F5", "opening_cost": 201.0, "capacity": 700.0 }, { "id": "F6", "opening_cost": 351.0, "capacity": 700.0 } ], "customers": [ { "id": 0, "demand": 28.0 }, { "id": 1, "demand": 24.0 }, { "id": 2, "demand": 17.0 }, { "id": 3, "demand": 20.0 }, { "id": 4, "demand": 13.0 }, { "id": 5, "demand": 18.0 }, { "id": 6, "demand": 23.0 }, { "id": 7, "demand": 26.0 }, { "id": 8, "demand": 17.0 }, { "id": 9, "demand": 13.0 }, { "id": 10, "demand": 16.0 }, { "id": 11, "demand": 27.0 }, { "id": 12, "demand": 11.0 }, { "id": 13, "demand": 18.0 }, { "id": 14, "demand": 17.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 1017.0 }, { "facility": "F1", "customer": 1, "cost": 166.0 }, { "facility": "F1", "customer": 2, "cost": 924.0 }, { "facility": "F1", "customer": 3, "cost": 463.0 }, { "facility": "F1", "customer": 4, "cost": 36.0 }, { "facility": "F1", "customer": 5, "cost": 685.0 }, { "facility": "F1", "customer": 6, "cost": 116.0 }, { "facility": "F1", "customer": 7, "cost": 463.0 }, { "facility": "F1", "customer": 8, "cost": 583.0 }, { "facility": "F1", "customer": 9, "cost": 335.0 }, { "facility": "F1", "customer": 10, "cost": 275.0 }, { "facility": "F1", "customer": 11, "cost": 728.0 }, { "facility": "F1", "customer": 12, "cost": 656.0 }, { "facility": "F1", "customer": 13, "cost": 138.0 }, { "facility": "F1", "customer": 14, "cost": 800.0 }, { "facility": "F2", "customer": 0, "cost": 262.0 }, { "facility": "F2", "customer": 1, "cost": 63.0 }, { "facility": "F2", "customer": 2, "cost": 232.0 }, { "facility": "F2", "customer": 3, "cost": 142.0 }, { "facility": "F2", "customer": 4, "cost": 38.0 }, { "facility": "F2", "customer": 5, "cost": 122.0 }, { "facility": "F2", "customer": 6, "cost": 49.0 }, { "facility": "F2", "customer": 7, "cost": 542.0 }, { "facility": "F2", "customer": 8, "cost": 399.0 }, { "facility": "F2", "customer": 9, "cost": 96.0 }, { "facility": "F2", "customer": 10, "cost": 235.0 }, { "facility": "F2", "customer": 11, "cost": 101.0 }, { "facility": "F2", "customer": 12, "cost": 720.0 }, { "facility": "F2", "customer": 13, "cost": 123.0 }, { "facility": "F2", "customer": 14, "cost": 734.0 }, { "facility": "F3", "customer": 0, "cost": 1770.0 }, { "facility": "F3", "customer": 1, "cost": 555.0 }, { "facility": "F3", "customer": 2, "cost": 1664.0 }, { "facility": "F3", "customer": 3, "cost": 1051.0 }, { "facility": "F3", "customer": 4, "cost": 381.0 }, { "facility": "F3", "customer": 5, "cost": 1451.0 }, { "facility": "F3", "customer": 6, "cost": 467.0 }, { "facility": "F3", "customer": 7, "cost": 456.0 }, { "facility": "F3", "customer": 8, "cost": 1184.0 }, { "facility": "F3", "customer": 9, "cost": 1109.0 }, { "facility": "F3", "customer": 10, "cost": 953.0 }, { "facility": "F3", "customer": 11, "cost": 1483.0 }, { "facility": "F3", "customer": 12, "cost": 526.0 }, { "facility": "F3", "customer": 13, "cost": 915.0 }, { "facility": "F3", "customer": 14, "cost": 1064.0 }, { "facility": "F4", "customer": 0, "cost": 1439.0 }, { "facility": "F4", "customer": 1, "cost": 465.0 }, { "facility": "F4", "customer": 2, "cost": 1444.0 }, { "facility": "F4", "customer": 3, "cost": 909.0 }, { "facility": "F4", "customer": 4, "cost": 280.0 }, { "facility": "F4", "customer": 5, "cost": 1143.0 }, { "facility": "F4", "customer": 6, "cost": 383.0 }, { "facility": "F4", "customer": 7, "cost": 118.0 }, { "facility": "F4", "customer": 8, "cost": 813.0 }, { "facility": "F4", "customer": 9, "cost": 829.0 }, { "facility": "F4", "customer": 10, "cost": 641.0 }, { "facility": "F4", "customer": 11, "cost": 1248.0 }, { "facility": "F4", "customer": 12, "cost": 22.0 }, { "facility": "F4", "customer": 13, "cost": 651.0 }, { "facility": "F4", "customer": 14, "cost": 603.0 }, { "facility": "F5", "customer": 0, "cost": 223.0 }, { "facility": "F5", "customer": 1, "cost": 146.0 }, { "facility": "F5", "customer": 2, "cost": 518.0 }, { "facility": "F5", "customer": 3, "cost": 332.0 }, { "facility": "F5", "customer": 4, "cost": 37.0 }, { "facility": "F5", "customer": 5, "cost": 128.0 }, { "facility": "F5", "customer": 6, "cost": 107.0 }, { "facility": "F5", "customer": 7, "cost": 232.0 }, { "facility": "F5", "customer": 8, "cost": 47.0 }, { "facility": "F5", "customer": 9, "cost": 59.0 }, { "facility": "F5", "customer": 10, "cost": 33.0 }, { "facility": "F5", "customer": 11, "cost": 350.0 }, { "facility": "F5", "customer": 12, "cost": 351.0 }, { "facility": "F5", "customer": 13, "cost": 45.0 }, { "facility": "F5", "customer": 14, "cost": 256.0 }, { "facility": "F6", "customer": 0, "cost": 1591.0 }, { "facility": "F6", "customer": 1, "cost": 216.0 }, { "facility": "F6", "customer": 2, "cost": 1317.0 }, { "facility": "F6", "customer": 3, "cost": 670.0 }, { "facility": "F6", "customer": 4, "cost": 40.0 }, { "facility": "F6", "customer": 5, "cost": 1253.0 }, { "facility": "F6", "customer": 6, "cost": 145.0 }, { "facility": "F6", "customer": 7, "cost": 804.0 }, { "facility": "F6", "customer": 8, "cost": 1176.0 }, { "facility": "F6", "customer": 9, "cost": 905.0 }, { "facility": "F6", "customer": 10, "cost": 870.0 }, { "facility": "F6", "customer": 11, "cost": 1160.0 }, { "facility": "F6", "customer": 12, "cost": 995.0 }, { "facility": "F6", "customer": 13, "cost": 722.0 }, { "facility": "F6", "customer": 14, "cost": 1302.0 } ], "objective": 2558.0 }, "solution_variant": { "selected": [ "F2", "F5" ], "assignments": [ "F5", "F2", "F2", "F2", "F5", "F2", "F2", "F5", "F5", "F5", "F5", "F2", "F5", "F5", "F5" ] }, "context_index": 36, "input_format": "json", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Out in the district planners are choosing which pantry locations to operate and routing every family to a single open pantry, taking care not to overload any pantry’s storage. A good plan is judged by total cost — the sum of the running charges for the open sites plus the cost to serve all the families — so the plan with the lowest combined cost wins. The concrete inputs and figures come after this.\n\n# total_pantry_sites=9\n# total_families=18\n# PANTRYS\npantry_id,operating_charge,storage_limit\nF1,600.0,700.0\nF2,600.0,700.0\nF3,600.0,700.0\nF4,600.0,700.0\nF5,600.0,700.0\nF6,600.0,700.0\nF7,600.0,700.0\nF8,600.0,700.0\nF9,600.0,700.0\n# FAMILYS\nfamily_id,family_demand\n1,28.0\n2,13.0\n3,12.0\n4,25.0\n5,24.0\n6,13.0\n7,24.0\n8,28.0\n9,14.0\n10,17.0\n11,10.0\n12,18.0\n13,10.0\n14,23.0\n15,24.0\n16,15.0\n17,21.0\n18,25.0\n# SERVICES\npantry_id,family_id,service_cost\nF1,1,75.0\nF1,2,1688.0\nF1,3,261.0\nF1,4,1025.0\nF1,5,121.0\nF1,6,901.0\nF1,7,218.0\nF1,8,751.0\nF1,9,926.0\nF1,10,1128.0\nF1,11,969.0\nF1,12,1614.0\nF1,13,195.0\nF1,14,476.0\nF1,15,1076.0\nF1,16,1162.0\nF1,17,690.0\nF1,18,950.0\nF2,1,140.0\nF2,2,1319.0\nF2,3,27.0\nF2,4,558.0\nF2,5,237.0\nF2,6,1000.0\nF2,7,366.0\nF2,8,116.0\nF2,9,525.0\nF2,10,415.0\nF2,11,206.0\nF2,12,1262.0\nF2,13,359.0\nF2,14,288.0\nF2,15,1148.0\nF2,16,1116.0\nF2,17,783.0\nF2,18,449.0\nF3,1,109.0\nF3,2,590.0\nF3,3,257.0\nF3,4,389.0\nF3,5,65.0\nF3,6,242.0\nF3,7,102.0\nF3,8,576.0\nF3,9,290.0\nF3,10,632.0\nF3,11,706.0\nF3,12,517.0\nF3,13,57.0\nF3,14,165.0\nF3,15,315.0\nF3,16,157.0\nF3,17,115.0\nF3,18,396.0\nF4,1,838.0\nF4,2,2629.0\nF4,3,865.0\nF4,4,1973.0\nF4,5,232.0\nF4,6,1569.0\nF4,7,436.0\nF4,8,1511.0\nF4,9,1876.0\nF4,10,2035.0\nF4,11,1760.0\nF4,12,2553.0\nF4,13,567.0\nF4,14,1425.0\nF4,15,1772.0\nF4,16,1990.0\nF4,17,1428.0\nF4,18,1891.0\nF5,1,67.0\nF5,2,848.0\nF5,3,66.0\nF5,4,120.0\nF5,5,161.0\nF5,6,712.0\nF5,7,258.0\nF5,8,224.0\nF5,9,120.0\nF5,10,186.0\nF5,11,298.0\nF5,12,794.0\nF5,13,229.0\nF5,14,79.0\nF5,15,835.0\nF5,16,745.0\nF5,17,507.0\nF5,18,61.0\nF6,1,443.0\nF6,2,2223.0\nF6,3,232.0\nF6,4,1489.0\nF6,5,333.0\nF6,6,1455.0\nF6,7,509.0\nF6,8,880.0\nF6,9,1412.0\nF6,10,1472.0\nF6,11,1131.0\nF6,12,2153.0\nF6,13,558.0\nF6,14,982.0\nF6,15,1641.0\nF6,16,1752.0\nF6,17,1258.0\nF6,18,1390.0\nF7,1,255.0\nF7,2,1775.0\nF7,3,456.0\nF7,4,1197.0\nF7,5,60.0\nF7,6,756.0\nF7,7,108.0\nF7,8,986.0\nF7,9,1087.0\nF7,10,1342.0\nF7,11,1206.0\nF7,12,1698.0\nF7,13,65.0\nF7,14,667.0\nF7,15,947.0\nF7,16,1115.0\nF7,17,571.0\nF7,18,1137.0\nF8,1,346.0\nF8,2,2102.0\nF8,3,493.0\nF8,4,1456.0\nF8,5,102.0\nF8,6,1130.0\nF8,7,216.0\nF8,8,1090.0\nF8,9,1356.0\nF8,10,1545.0\nF8,11,1329.0\nF8,12,2027.0\nF8,13,225.0\nF8,14,907.0\nF8,15,1324.0\nF8,16,1493.0\nF8,17,953.0\nF8,18,1378.0\nF9,1,738.0\nF9,2,2444.0\nF9,3,840.0\nF9,4,1837.0\nF9,5,79.0\nF9,6,1295.0\nF9,7,141.0\nF9,8,1467.0\nF9,9,1733.0\nF9,10,1938.0\nF9,11,1711.0\nF9,12,2367.0\nF9,13,308.0\nF9,14,1290.0\nF9,15,1499.0\nF9,16,1750.0\nF9,17,1178.0\nF9,18,1764.0\n\nOh, and when you send the plan back, please follow this simple JSON layout so I can read it easily:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of pantry sites you'll keep running, and \"assignments\" as which open pantry each family goes to (one entry per family, in the same order as the family list). This is just a sketch of the shape I expect — not the final plan itself.\n\nPlease be sure to use the exact identifiers from the instance input when filling this out — don't rename sites or invent new labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 75.0, 1688.0, 261.0, 1025.0, 121.0, 901.0, 218.0, 751.0, 926.0, 1128.0, 969.0, 1614.0, 195.0, 476.0, 1076.0, 1162.0, 690.0, 950.0 ], [ 140.0, 1319.0, 27.0, 558.0, 237.0, 1000.0, 366.0, 116.0, 525.0, 415.0, 206.0, 1262.0, 359.0, 288.0, 1148.0, 1116.0, 783.0, 449.0 ], [ 109.0, 590.0, 257.0, 389.0, 65.0, 242.0, 102.0, 576.0, 290.0, 632.0, 706.0, 517.0, 57.0, 165.0, 315.0, 157.0, 115.0, 396.0 ], [ 838.0, 2629.0, 865.0, 1973.0, 232.0, 1569.0, 436.0, 1511.0, 1876.0, 2035.0, 1760.0, 2553.0, 567.0, 1425.0, 1772.0, 1990.0, 1428.0, 1891.0 ], [ 67.0, 848.0, 66.0, 120.0, 161.0, 712.0, 258.0, 224.0, 120.0, 186.0, 298.0, 794.0, 229.0, 79.0, 835.0, 745.0, 507.0, 61.0 ], [ 443.0, 2223.0, 232.0, 1489.0, 333.0, 1455.0, 509.0, 880.0, 1412.0, 1472.0, 1131.0, 2153.0, 558.0, 982.0, 1641.0, 1752.0, 1258.0, 1390.0 ], [ 255.0, 1775.0, 456.0, 1197.0, 60.0, 756.0, 108.0, 986.0, 1087.0, 1342.0, 1206.0, 1698.0, 65.0, 667.0, 947.0, 1115.0, 571.0, 1137.0 ], [ 346.0, 2102.0, 493.0, 1456.0, 102.0, 1130.0, 216.0, 1090.0, 1356.0, 1545.0, 1329.0, 2027.0, 225.0, 907.0, 1324.0, 1493.0, 953.0, 1378.0 ], [ 738.0, 2444.0, 840.0, 1837.0, 79.0, 1295.0, 141.0, 1467.0, 1733.0, 1938.0, 1711.0, 2367.0, 308.0, 1290.0, 1499.0, 1750.0, 1178.0, 1764.0 ] ], "demands": [ 28.0, 13.0, 12.0, 25.0, 24.0, 13.0, 24.0, 28.0, 14.0, 17.0, 10.0, 18.0, 10.0, 23.0, 24.0, 15.0, 21.0, 25.0 ], "objective": 4581.0 }, "solution": { "open_facilities": [ 2, 4 ], "assignments": [ 4, 2, 4, 4, 2, 2, 2, 4, 4, 4, 4, 2, 2, 4, 2, 2, 2, 4 ] }, "obj": 4581.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 9, "num_customers": 18, "facilities": [ { "id": "F1", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F2", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F3", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F4", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F5", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F6", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F7", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F8", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F9", "opening_cost": 600.0, "capacity": 700.0 } ], "customers": [ { "id": 1, "demand": 28.0 }, { "id": 2, "demand": 13.0 }, { "id": 3, "demand": 12.0 }, { "id": 4, "demand": 25.0 }, { "id": 5, "demand": 24.0 }, { "id": 6, "demand": 13.0 }, { "id": 7, "demand": 24.0 }, { "id": 8, "demand": 28.0 }, { "id": 9, "demand": 14.0 }, { "id": 10, "demand": 17.0 }, { "id": 11, "demand": 10.0 }, { "id": 12, "demand": 18.0 }, { "id": 13, "demand": 10.0 }, { "id": 14, "demand": 23.0 }, { "id": 15, "demand": 24.0 }, { "id": 16, "demand": 15.0 }, { "id": 17, "demand": 21.0 }, { "id": 18, "demand": 25.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 75.0 }, { "facility": "F1", "customer": 2, "cost": 1688.0 }, { "facility": "F1", "customer": 3, "cost": 261.0 }, { "facility": "F1", "customer": 4, "cost": 1025.0 }, { "facility": "F1", "customer": 5, "cost": 121.0 }, { "facility": "F1", "customer": 6, "cost": 901.0 }, { "facility": "F1", "customer": 7, "cost": 218.0 }, { "facility": "F1", "customer": 8, "cost": 751.0 }, { "facility": "F1", "customer": 9, "cost": 926.0 }, { "facility": "F1", "customer": 10, "cost": 1128.0 }, { "facility": "F1", "customer": 11, "cost": 969.0 }, { "facility": "F1", "customer": 12, "cost": 1614.0 }, { "facility": "F1", "customer": 13, "cost": 195.0 }, { "facility": "F1", "customer": 14, "cost": 476.0 }, { "facility": "F1", "customer": 15, "cost": 1076.0 }, { "facility": "F1", "customer": 16, "cost": 1162.0 }, { "facility": "F1", "customer": 17, "cost": 690.0 }, { "facility": "F1", "customer": 18, "cost": 950.0 }, { "facility": "F2", "customer": 1, "cost": 140.0 }, { "facility": "F2", "customer": 2, "cost": 1319.0 }, { "facility": "F2", "customer": 3, "cost": 27.0 }, { "facility": "F2", "customer": 4, "cost": 558.0 }, { "facility": "F2", "customer": 5, "cost": 237.0 }, { "facility": "F2", "customer": 6, "cost": 1000.0 }, { "facility": "F2", "customer": 7, "cost": 366.0 }, { "facility": "F2", "customer": 8, "cost": 116.0 }, { "facility": "F2", "customer": 9, "cost": 525.0 }, { "facility": "F2", "customer": 10, "cost": 415.0 }, { "facility": "F2", "customer": 11, "cost": 206.0 }, { "facility": "F2", "customer": 12, "cost": 1262.0 }, { "facility": "F2", "customer": 13, "cost": 359.0 }, { "facility": "F2", "customer": 14, "cost": 288.0 }, { "facility": "F2", "customer": 15, "cost": 1148.0 }, { "facility": "F2", "customer": 16, "cost": 1116.0 }, { "facility": "F2", "customer": 17, "cost": 783.0 }, { "facility": "F2", "customer": 18, "cost": 449.0 }, { "facility": "F3", "customer": 1, "cost": 109.0 }, { "facility": "F3", "customer": 2, "cost": 590.0 }, { "facility": "F3", "customer": 3, "cost": 257.0 }, { "facility": "F3", "customer": 4, "cost": 389.0 }, { "facility": "F3", "customer": 5, "cost": 65.0 }, { "facility": "F3", "customer": 6, "cost": 242.0 }, { "facility": "F3", "customer": 7, "cost": 102.0 }, { "facility": "F3", "customer": 8, "cost": 576.0 }, { "facility": "F3", "customer": 9, "cost": 290.0 }, { "facility": "F3", "customer": 10, "cost": 632.0 }, { "facility": "F3", "customer": 11, "cost": 706.0 }, { "facility": "F3", "customer": 12, "cost": 517.0 }, { "facility": "F3", "customer": 13, "cost": 57.0 }, { "facility": "F3", "customer": 14, "cost": 165.0 }, { "facility": "F3", "customer": 15, "cost": 315.0 }, { "facility": "F3", "customer": 16, "cost": 157.0 }, { "facility": "F3", "customer": 17, "cost": 115.0 }, { "facility": "F3", "customer": 18, "cost": 396.0 }, { "facility": "F4", "customer": 1, "cost": 838.0 }, { "facility": "F4", "customer": 2, "cost": 2629.0 }, { "facility": "F4", "customer": 3, "cost": 865.0 }, { "facility": "F4", "customer": 4, "cost": 1973.0 }, { "facility": "F4", "customer": 5, "cost": 232.0 }, { "facility": "F4", "customer": 6, "cost": 1569.0 }, { "facility": "F4", "customer": 7, "cost": 436.0 }, { "facility": "F4", "customer": 8, "cost": 1511.0 }, { "facility": "F4", "customer": 9, "cost": 1876.0 }, { "facility": "F4", "customer": 10, "cost": 2035.0 }, { "facility": "F4", "customer": 11, "cost": 1760.0 }, { "facility": "F4", "customer": 12, "cost": 2553.0 }, { "facility": "F4", "customer": 13, "cost": 567.0 }, { "facility": "F4", "customer": 14, "cost": 1425.0 }, { "facility": "F4", "customer": 15, "cost": 1772.0 }, { "facility": "F4", "customer": 16, "cost": 1990.0 }, { "facility": "F4", "customer": 17, "cost": 1428.0 }, { "facility": "F4", "customer": 18, "cost": 1891.0 }, { "facility": "F5", "customer": 1, "cost": 67.0 }, { "facility": "F5", "customer": 2, "cost": 848.0 }, { "facility": "F5", "customer": 3, "cost": 66.0 }, { "facility": "F5", "customer": 4, "cost": 120.0 }, { "facility": "F5", "customer": 5, "cost": 161.0 }, { "facility": "F5", "customer": 6, "cost": 712.0 }, { "facility": "F5", "customer": 7, "cost": 258.0 }, { "facility": "F5", "customer": 8, "cost": 224.0 }, { "facility": "F5", "customer": 9, "cost": 120.0 }, { "facility": "F5", "customer": 10, "cost": 186.0 }, { "facility": "F5", "customer": 11, "cost": 298.0 }, { "facility": "F5", "customer": 12, "cost": 794.0 }, { "facility": "F5", "customer": 13, "cost": 229.0 }, { "facility": "F5", "customer": 14, "cost": 79.0 }, { "facility": "F5", "customer": 15, "cost": 835.0 }, { "facility": "F5", "customer": 16, "cost": 745.0 }, { "facility": "F5", "customer": 17, "cost": 507.0 }, { "facility": "F5", "customer": 18, "cost": 61.0 }, { "facility": "F6", "customer": 1, "cost": 443.0 }, { "facility": "F6", "customer": 2, "cost": 2223.0 }, { "facility": "F6", "customer": 3, "cost": 232.0 }, { "facility": "F6", "customer": 4, "cost": 1489.0 }, { "facility": "F6", "customer": 5, "cost": 333.0 }, { "facility": "F6", "customer": 6, "cost": 1455.0 }, { "facility": "F6", "customer": 7, "cost": 509.0 }, { "facility": "F6", "customer": 8, "cost": 880.0 }, { "facility": "F6", "customer": 9, "cost": 1412.0 }, { "facility": "F6", "customer": 10, "cost": 1472.0 }, { "facility": "F6", "customer": 11, "cost": 1131.0 }, { "facility": "F6", "customer": 12, "cost": 2153.0 }, { "facility": "F6", "customer": 13, "cost": 558.0 }, { "facility": "F6", "customer": 14, "cost": 982.0 }, { "facility": "F6", "customer": 15, "cost": 1641.0 }, { "facility": "F6", "customer": 16, "cost": 1752.0 }, { "facility": "F6", "customer": 17, "cost": 1258.0 }, { "facility": "F6", "customer": 18, "cost": 1390.0 }, { "facility": "F7", "customer": 1, "cost": 255.0 }, { "facility": "F7", "customer": 2, "cost": 1775.0 }, { "facility": "F7", "customer": 3, "cost": 456.0 }, { "facility": "F7", "customer": 4, "cost": 1197.0 }, { "facility": "F7", "customer": 5, "cost": 60.0 }, { "facility": "F7", "customer": 6, "cost": 756.0 }, { "facility": "F7", "customer": 7, "cost": 108.0 }, { "facility": "F7", "customer": 8, "cost": 986.0 }, { "facility": "F7", "customer": 9, "cost": 1087.0 }, { "facility": "F7", "customer": 10, "cost": 1342.0 }, { "facility": "F7", "customer": 11, "cost": 1206.0 }, { "facility": "F7", "customer": 12, "cost": 1698.0 }, { "facility": "F7", "customer": 13, "cost": 65.0 }, { "facility": "F7", "customer": 14, "cost": 667.0 }, { "facility": "F7", "customer": 15, "cost": 947.0 }, { "facility": "F7", "customer": 16, "cost": 1115.0 }, { "facility": "F7", "customer": 17, "cost": 571.0 }, { "facility": "F7", "customer": 18, "cost": 1137.0 }, { "facility": "F8", "customer": 1, "cost": 346.0 }, { "facility": "F8", "customer": 2, "cost": 2102.0 }, { "facility": "F8", "customer": 3, "cost": 493.0 }, { "facility": "F8", "customer": 4, "cost": 1456.0 }, { "facility": "F8", "customer": 5, "cost": 102.0 }, { "facility": "F8", "customer": 6, "cost": 1130.0 }, { "facility": "F8", "customer": 7, "cost": 216.0 }, { "facility": "F8", "customer": 8, "cost": 1090.0 }, { "facility": "F8", "customer": 9, "cost": 1356.0 }, { "facility": "F8", "customer": 10, "cost": 1545.0 }, { "facility": "F8", "customer": 11, "cost": 1329.0 }, { "facility": "F8", "customer": 12, "cost": 2027.0 }, { "facility": "F8", "customer": 13, "cost": 225.0 }, { "facility": "F8", "customer": 14, "cost": 907.0 }, { "facility": "F8", "customer": 15, "cost": 1324.0 }, { "facility": "F8", "customer": 16, "cost": 1493.0 }, { "facility": "F8", "customer": 17, "cost": 953.0 }, { "facility": "F8", "customer": 18, "cost": 1378.0 }, { "facility": "F9", "customer": 1, "cost": 738.0 }, { "facility": "F9", "customer": 2, "cost": 2444.0 }, { "facility": "F9", "customer": 3, "cost": 840.0 }, { "facility": "F9", "customer": 4, "cost": 1837.0 }, { "facility": "F9", "customer": 5, "cost": 79.0 }, { "facility": "F9", "customer": 6, "cost": 1295.0 }, { "facility": "F9", "customer": 7, "cost": 141.0 }, { "facility": "F9", "customer": 8, "cost": 1467.0 }, { "facility": "F9", "customer": 9, "cost": 1733.0 }, { "facility": "F9", "customer": 10, "cost": 1938.0 }, { "facility": "F9", "customer": 11, "cost": 1711.0 }, { "facility": "F9", "customer": 12, "cost": 2367.0 }, { "facility": "F9", "customer": 13, "cost": 308.0 }, { "facility": "F9", "customer": 14, "cost": 1290.0 }, { "facility": "F9", "customer": 15, "cost": 1499.0 }, { "facility": "F9", "customer": 16, "cost": 1750.0 }, { "facility": "F9", "customer": 17, "cost": 1178.0 }, { "facility": "F9", "customer": 18, "cost": 1764.0 } ], "objective": 4581.0 }, "solution_variant": { "selected": [ "F3", "F5" ], "assignments": [ "F5", "F3", "F5", "F5", "F3", "F3", "F3", "F5", "F5", "F5", "F5", "F3", "F3", "F5", "F3", "F3", "F3", "F5" ] }, "context_index": 37, "input_format": "csv", "input_index_base": 1 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "One day the ops team had to trim costs: there are several data centers that can be kept on for a fee and each has finite server capacity, and every application must be assigned to a single active center. The task is to pick which centers to keep running and assign every app to exactly one of them, without exceeding any center’s capacity or duplicating assignments. The goal is to minimize the overall outlay — total cost equals the sum of running fees for the centers that are on plus the latency/connection cost for each app’s assignment — so choose the setup with the smallest total. The detailed instance information follows below.\n\n# num_data_centers=8\n# num_applications=20\n# DATA_CENTERS\ndata_center_id,running_fee,server_capacity\nF1,600.0,700.0\nF2,600.0,700.0\nF3,600.0,700.0\nF4,600.0,700.0\nF5,600.0,700.0\nF6,600.0,700.0\nF7,600.0,700.0\nF8,600.0,700.0\n# APPLICATIONS\napplication_id,app_demand\nA,12.0\nB,28.0\nC,18.0\nD,12.0\nE,18.0\nF,13.0\nG,29.0\nH,27.0\nI,22.0\nJ,30.0\nK,24.0\nL,27.0\nM,16.0\nN,22.0\nO,16.0\nP,23.0\nQ,21.0\nR,16.0\nS,14.0\nT,18.0\n# LATENCYS\ndata_center_id,application_id,latency_cost\nF1,A,74.0\nF1,B,530.0\nF1,C,36.0\nF1,D,699.0\nF1,E,822.0\nF1,F,624.0\nF1,G,373.0\nF1,H,735.0\nF1,I,1574.0\nF1,J,307.0\nF1,K,428.0\nF1,L,610.0\nF1,M,468.0\nF1,N,486.0\nF1,O,450.0\nF1,P,476.0\nF1,Q,1267.0\nF1,R,988.0\nF1,S,44.0\nF1,T,1551.0\nF2,A,94.0\nF2,B,478.0\nF2,C,58.0\nF2,D,660.0\nF2,E,610.0\nF2,F,412.0\nF2,G,391.0\nF2,H,728.0\nF2,I,1374.0\nF2,J,325.0\nF2,K,443.0\nF2,L,480.0\nF2,M,298.0\nF2,N,299.0\nF2,O,275.0\nF2,P,352.0\nF2,Q,1057.0\nF2,R,799.0\nF2,S,29.0\nF2,T,1361.0\nF3,A,73.0\nF3,B,341.0\nF3,C,382.0\nF3,D,232.0\nF3,E,1095.0\nF3,F,904.0\nF3,G,61.0\nF3,H,116.0\nF3,I,1653.0\nF3,J,64.0\nF3,K,57.0\nF3,L,949.0\nF3,M,641.0\nF3,N,689.0\nF3,O,641.0\nF3,P,562.0\nF3,Q,1434.0\nF3,R,1320.0\nF3,S,280.0\nF3,T,1574.0\nF4,A,96.0\nF4,B,858.0\nF4,C,626.0\nF4,D,907.0\nF4,E,1412.0\nF4,F,1214.0\nF4,G,260.0\nF4,H,764.0\nF4,I,2131.0\nF4,J,232.0\nF4,K,337.0\nF4,L,1075.0\nF4,M,1022.0\nF4,N,1055.0\nF4,O,1012.0\nF4,P,982.0\nF4,Q,1846.0\nF4,R,1546.0\nF4,S,368.0\nF4,T,2088.0\nF5,A,60.0\nF5,B,186.0\nF5,C,289.0\nF5,D,55.0\nF5,E,909.0\nF5,F,732.0\nF5,G,61.0\nF5,H,76.0\nF5,I,1343.0\nF5,J,61.0\nF5,K,56.0\nF5,L,861.0\nF5,M,463.0\nF5,N,514.0\nF5,O,468.0\nF5,P,383.0\nF5,Q,1177.0\nF5,R,1171.0\nF5,S,234.0\nF5,T,1244.0\nF6,A,193.0\nF6,B,924.0\nF6,C,466.0\nF6,D,1066.0\nF6,E,1159.0\nF6,F,973.0\nF6,G,579.0\nF6,H,1032.0\nF6,I,1975.0\nF6,J,524.0\nF6,K,650.0\nF6,L,729.0\nF6,M,891.0\nF6,N,901.0\nF6,O,870.0\nF6,P,907.0\nF6,Q,1646.0\nF6,R,1223.0\nF6,S,33.0\nF6,T,1966.0\nF7,A,134.0\nF7,B,474.0\nF7,C,104.0\nF7,D,656.0\nF7,E,224.0\nF7,F,26.0\nF7,G,436.0\nF7,H,753.0\nF7,I,1051.0\nF7,J,371.0\nF7,K,487.0\nF7,L,287.0\nF7,M,213.0\nF7,N,190.0\nF7,O,192.0\nF7,P,305.0\nF7,Q,704.0\nF7,R,469.0\nF7,S,34.0\nF7,T,1070.0\nF8,A,172.0\nF8,B,586.0\nF8,C,165.0\nF8,D,770.0\nF8,E,336.0\nF8,F,192.0\nF8,G,500.0\nF8,H,848.0\nF8,I,1206.0\nF8,J,435.0\nF8,K,557.0\nF8,L,251.0\nF8,M,342.0\nF8,N,320.0\nF8,O,317.0\nF8,P,429.0\nF8,Q,849.0\nF8,R,472.0\nF8,S,49.0\nF8,T,1232.0\n\nAlso, just so we're on the same page, please give the solution using this simple JSON shape when you answer — nothing fancy, just that structure so it's easy to parse:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of data centers you decide to keep running (one placeholder per center), and \"assignments\" as, in order, which running center each application gets assigned to. Super informal: \"selected\" = which centers are on, \"assignments\" = where each app goes.\n\nThis JSON is only a sketch of the expected shape, not the actual answer.\n\nPlease make sure to use the exact identifiers from the instance input — do not rename them and do not invent new labels.\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 74.0, 530.0, 36.0, 699.0, 822.0, 624.0, 373.0, 735.0, 1574.0, 307.0, 428.0, 610.0, 468.0, 486.0, 450.0, 476.0, 1267.0, 988.0, 44.0, 1551.0 ], [ 94.0, 478.0, 58.0, 660.0, 610.0, 412.0, 391.0, 728.0, 1374.0, 325.0, 443.0, 480.0, 298.0, 299.0, 275.0, 352.0, 1057.0, 799.0, 29.0, 1361.0 ], [ 73.0, 341.0, 382.0, 232.0, 1095.0, 904.0, 61.0, 116.0, 1653.0, 64.0, 57.0, 949.0, 641.0, 689.0, 641.0, 562.0, 1434.0, 1320.0, 280.0, 1574.0 ], [ 96.0, 858.0, 626.0, 907.0, 1412.0, 1214.0, 260.0, 764.0, 2131.0, 232.0, 337.0, 1075.0, 1022.0, 1055.0, 1012.0, 982.0, 1846.0, 1546.0, 368.0, 2088.0 ], [ 60.0, 186.0, 289.0, 55.0, 909.0, 732.0, 61.0, 76.0, 1343.0, 61.0, 56.0, 861.0, 463.0, 514.0, 468.0, 383.0, 1177.0, 1171.0, 234.0, 1244.0 ], [ 193.0, 924.0, 466.0, 1066.0, 1159.0, 973.0, 579.0, 1032.0, 1975.0, 524.0, 650.0, 729.0, 891.0, 901.0, 870.0, 907.0, 1646.0, 1223.0, 33.0, 1966.0 ], [ 134.0, 474.0, 104.0, 656.0, 224.0, 26.0, 436.0, 753.0, 1051.0, 371.0, 487.0, 287.0, 213.0, 190.0, 192.0, 305.0, 704.0, 469.0, 34.0, 1070.0 ], [ 172.0, 586.0, 165.0, 770.0, 336.0, 192.0, 500.0, 848.0, 1206.0, 435.0, 557.0, 251.0, 342.0, 320.0, 317.0, 429.0, 849.0, 472.0, 49.0, 1232.0 ] ], "demands": [ 12.0, 28.0, 18.0, 12.0, 18.0, 13.0, 29.0, 27.0, 22.0, 30.0, 24.0, 27.0, 16.0, 22.0, 16.0, 23.0, 21.0, 16.0, 14.0, 18.0 ], "objective": 6624.0 }, "solution": { "open_facilities": [ 4, 6 ], "assignments": [ 4, 4, 6, 4, 6, 6, 4, 4, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6 ] }, "obj": 6624.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 20, "facilities": [ { "id": "F1", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F2", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F3", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F4", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F5", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F6", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F7", "opening_cost": 600.0, "capacity": 700.0 }, { "id": "F8", "opening_cost": 600.0, "capacity": 700.0 } ], "customers": [ { "id": "A", "demand": 12.0 }, { "id": "B", "demand": 28.0 }, { "id": "C", "demand": 18.0 }, { "id": "D", "demand": 12.0 }, { "id": "E", "demand": 18.0 }, { "id": "F", "demand": 13.0 }, { "id": "G", "demand": 29.0 }, { "id": "H", "demand": 27.0 }, { "id": "I", "demand": 22.0 }, { "id": "J", "demand": 30.0 }, { "id": "K", "demand": 24.0 }, { "id": "L", "demand": 27.0 }, { "id": "M", "demand": 16.0 }, { "id": "N", "demand": 22.0 }, { "id": "O", "demand": 16.0 }, { "id": "P", "demand": 23.0 }, { "id": "Q", "demand": 21.0 }, { "id": "R", "demand": 16.0 }, { "id": "S", "demand": 14.0 }, { "id": "T", "demand": 18.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 74.0 }, { "facility": "F1", "customer": "B", "cost": 530.0 }, { "facility": "F1", "customer": "C", "cost": 36.0 }, { "facility": "F1", "customer": "D", "cost": 699.0 }, { "facility": "F1", "customer": "E", "cost": 822.0 }, { "facility": "F1", "customer": "F", "cost": 624.0 }, { "facility": "F1", "customer": "G", "cost": 373.0 }, { "facility": "F1", "customer": "H", "cost": 735.0 }, { "facility": "F1", "customer": "I", "cost": 1574.0 }, { "facility": "F1", "customer": "J", "cost": 307.0 }, { "facility": "F1", "customer": "K", "cost": 428.0 }, { "facility": "F1", "customer": "L", "cost": 610.0 }, { "facility": "F1", "customer": "M", "cost": 468.0 }, { "facility": "F1", "customer": "N", "cost": 486.0 }, { "facility": "F1", "customer": "O", "cost": 450.0 }, { "facility": "F1", "customer": "P", "cost": 476.0 }, { "facility": "F1", "customer": "Q", "cost": 1267.0 }, { "facility": "F1", "customer": "R", "cost": 988.0 }, { "facility": "F1", "customer": "S", "cost": 44.0 }, { "facility": "F1", "customer": "T", "cost": 1551.0 }, { "facility": "F2", "customer": "A", "cost": 94.0 }, { "facility": "F2", "customer": "B", "cost": 478.0 }, { "facility": "F2", "customer": "C", "cost": 58.0 }, { "facility": "F2", "customer": "D", "cost": 660.0 }, { "facility": "F2", "customer": "E", "cost": 610.0 }, { "facility": "F2", "customer": "F", "cost": 412.0 }, { "facility": "F2", "customer": "G", "cost": 391.0 }, { "facility": "F2", "customer": "H", "cost": 728.0 }, { "facility": "F2", "customer": "I", "cost": 1374.0 }, { "facility": "F2", "customer": "J", "cost": 325.0 }, { "facility": "F2", "customer": "K", "cost": 443.0 }, { "facility": "F2", "customer": "L", "cost": 480.0 }, { "facility": "F2", "customer": "M", "cost": 298.0 }, { "facility": "F2", "customer": "N", "cost": 299.0 }, { "facility": "F2", "customer": "O", "cost": 275.0 }, { "facility": "F2", "customer": "P", "cost": 352.0 }, { "facility": "F2", "customer": "Q", "cost": 1057.0 }, { "facility": "F2", "customer": "R", "cost": 799.0 }, { "facility": "F2", "customer": "S", "cost": 29.0 }, { "facility": "F2", "customer": "T", "cost": 1361.0 }, { "facility": "F3", "customer": "A", "cost": 73.0 }, { "facility": "F3", "customer": "B", "cost": 341.0 }, { "facility": "F3", "customer": "C", "cost": 382.0 }, { "facility": "F3", "customer": "D", "cost": 232.0 }, { "facility": "F3", "customer": "E", "cost": 1095.0 }, { "facility": "F3", "customer": "F", "cost": 904.0 }, { "facility": "F3", "customer": "G", "cost": 61.0 }, { "facility": "F3", "customer": "H", "cost": 116.0 }, { "facility": "F3", "customer": "I", "cost": 1653.0 }, { "facility": "F3", "customer": "J", "cost": 64.0 }, { "facility": "F3", "customer": "K", "cost": 57.0 }, { "facility": "F3", "customer": "L", "cost": 949.0 }, { "facility": "F3", "customer": "M", "cost": 641.0 }, { "facility": "F3", "customer": "N", "cost": 689.0 }, { "facility": "F3", "customer": "O", "cost": 641.0 }, { "facility": "F3", "customer": "P", "cost": 562.0 }, { "facility": "F3", "customer": "Q", "cost": 1434.0 }, { "facility": "F3", "customer": "R", "cost": 1320.0 }, { "facility": "F3", "customer": "S", "cost": 280.0 }, { "facility": "F3", "customer": "T", "cost": 1574.0 }, { "facility": "F4", "customer": "A", "cost": 96.0 }, { "facility": "F4", "customer": "B", "cost": 858.0 }, { "facility": "F4", "customer": "C", "cost": 626.0 }, { "facility": "F4", "customer": "D", "cost": 907.0 }, { "facility": "F4", "customer": "E", "cost": 1412.0 }, { "facility": "F4", "customer": "F", "cost": 1214.0 }, { "facility": "F4", "customer": "G", "cost": 260.0 }, { "facility": "F4", "customer": "H", "cost": 764.0 }, { "facility": "F4", "customer": "I", "cost": 2131.0 }, { "facility": "F4", "customer": "J", "cost": 232.0 }, { "facility": "F4", "customer": "K", "cost": 337.0 }, { "facility": "F4", "customer": "L", "cost": 1075.0 }, { "facility": "F4", "customer": "M", "cost": 1022.0 }, { "facility": "F4", "customer": "N", "cost": 1055.0 }, { "facility": "F4", "customer": "O", "cost": 1012.0 }, { "facility": "F4", "customer": "P", "cost": 982.0 }, { "facility": "F4", "customer": "Q", "cost": 1846.0 }, { "facility": "F4", "customer": "R", "cost": 1546.0 }, { "facility": "F4", "customer": "S", "cost": 368.0 }, { "facility": "F4", "customer": "T", "cost": 2088.0 }, { "facility": "F5", "customer": "A", "cost": 60.0 }, { "facility": "F5", "customer": "B", "cost": 186.0 }, { "facility": "F5", "customer": "C", "cost": 289.0 }, { "facility": "F5", "customer": "D", "cost": 55.0 }, { "facility": "F5", "customer": "E", "cost": 909.0 }, { "facility": "F5", "customer": "F", "cost": 732.0 }, { "facility": "F5", "customer": "G", "cost": 61.0 }, { "facility": "F5", "customer": "H", "cost": 76.0 }, { "facility": "F5", "customer": "I", "cost": 1343.0 }, { "facility": "F5", "customer": "J", "cost": 61.0 }, { "facility": "F5", "customer": "K", "cost": 56.0 }, { "facility": "F5", "customer": "L", "cost": 861.0 }, { "facility": "F5", "customer": "M", "cost": 463.0 }, { "facility": "F5", "customer": "N", "cost": 514.0 }, { "facility": "F5", "customer": "O", "cost": 468.0 }, { "facility": "F5", "customer": "P", "cost": 383.0 }, { "facility": "F5", "customer": "Q", "cost": 1177.0 }, { "facility": "F5", "customer": "R", "cost": 1171.0 }, { "facility": "F5", "customer": "S", "cost": 234.0 }, { "facility": "F5", "customer": "T", "cost": 1244.0 }, { "facility": "F6", "customer": "A", "cost": 193.0 }, { "facility": "F6", "customer": "B", "cost": 924.0 }, { "facility": "F6", "customer": "C", "cost": 466.0 }, { "facility": "F6", "customer": "D", "cost": 1066.0 }, { "facility": "F6", "customer": "E", "cost": 1159.0 }, { "facility": "F6", "customer": "F", "cost": 973.0 }, { "facility": "F6", "customer": "G", "cost": 579.0 }, { "facility": "F6", "customer": "H", "cost": 1032.0 }, { "facility": "F6", "customer": "I", "cost": 1975.0 }, { "facility": "F6", "customer": "J", "cost": 524.0 }, { "facility": "F6", "customer": "K", "cost": 650.0 }, { "facility": "F6", "customer": "L", "cost": 729.0 }, { "facility": "F6", "customer": "M", "cost": 891.0 }, { "facility": "F6", "customer": "N", "cost": 901.0 }, { "facility": "F6", "customer": "O", "cost": 870.0 }, { "facility": "F6", "customer": "P", "cost": 907.0 }, { "facility": "F6", "customer": "Q", "cost": 1646.0 }, { "facility": "F6", "customer": "R", "cost": 1223.0 }, { "facility": "F6", "customer": "S", "cost": 33.0 }, { "facility": "F6", "customer": "T", "cost": 1966.0 }, { "facility": "F7", "customer": "A", "cost": 134.0 }, { "facility": "F7", "customer": "B", "cost": 474.0 }, { "facility": "F7", "customer": "C", "cost": 104.0 }, { "facility": "F7", "customer": "D", "cost": 656.0 }, { "facility": "F7", "customer": "E", "cost": 224.0 }, { "facility": "F7", "customer": "F", "cost": 26.0 }, { "facility": "F7", "customer": "G", "cost": 436.0 }, { "facility": "F7", "customer": "H", "cost": 753.0 }, { "facility": "F7", "customer": "I", "cost": 1051.0 }, { "facility": "F7", "customer": "J", "cost": 371.0 }, { "facility": "F7", "customer": "K", "cost": 487.0 }, { "facility": "F7", "customer": "L", "cost": 287.0 }, { "facility": "F7", "customer": "M", "cost": 213.0 }, { "facility": "F7", "customer": "N", "cost": 190.0 }, { "facility": "F7", "customer": "O", "cost": 192.0 }, { "facility": "F7", "customer": "P", "cost": 305.0 }, { "facility": "F7", "customer": "Q", "cost": 704.0 }, { "facility": "F7", "customer": "R", "cost": 469.0 }, { "facility": "F7", "customer": "S", "cost": 34.0 }, { "facility": "F7", "customer": "T", "cost": 1070.0 }, { "facility": "F8", "customer": "A", "cost": 172.0 }, { "facility": "F8", "customer": "B", "cost": 586.0 }, { "facility": "F8", "customer": "C", "cost": 165.0 }, { "facility": "F8", "customer": "D", "cost": 770.0 }, { "facility": "F8", "customer": "E", "cost": 336.0 }, { "facility": "F8", "customer": "F", "cost": 192.0 }, { "facility": "F8", "customer": "G", "cost": 500.0 }, { "facility": "F8", "customer": "H", "cost": 848.0 }, { "facility": "F8", "customer": "I", "cost": 1206.0 }, { "facility": "F8", "customer": "J", "cost": 435.0 }, { "facility": "F8", "customer": "K", "cost": 557.0 }, { "facility": "F8", "customer": "L", "cost": 251.0 }, { "facility": "F8", "customer": "M", "cost": 342.0 }, { "facility": "F8", "customer": "N", "cost": 320.0 }, { "facility": "F8", "customer": "O", "cost": 317.0 }, { "facility": "F8", "customer": "P", "cost": 429.0 }, { "facility": "F8", "customer": "Q", "cost": 849.0 }, { "facility": "F8", "customer": "R", "cost": 472.0 }, { "facility": "F8", "customer": "S", "cost": 49.0 }, { "facility": "F8", "customer": "T", "cost": 1232.0 } ], "objective": 6624.0 }, "solution_variant": { "selected": [ "F5", "F7" ], "assignments": [ "F5", "F5", "F7", "F5", "F7", "F7", "F5", "F5", "F7", "F5", "F5", "F7", "F7", "F7", "F7", "F7", "F7", "F7", "F7", "F7" ] }, "context_index": 38, "input_format": "csv", "input_index_base": "names" }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Someone in operations has to map orders to active micro-fulfillment centers and decide which centers to open. Opening a center carries a fixed fee and each center can only process a limited number of parcels; each order must go to exactly one open center and centers can’t take on more than their throughput allows. The quality of any decision is judged by the total expense: add the activation fees for the centers that are opened plus the routing cost for all orders — the plan with the lowest total is preferred. The exact center fees, capacities, and order list are shown below.\n\n{\n \"num_micro_centers\": 7,\n \"num_orders\": 16,\n \"connection_centers\": [\n {\n \"connection_center_id\": \"F1\",\n \"activation_fee\": 400.0,\n \"center_throughput\": 800.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"activation_fee\": 400.0,\n \"center_throughput\": 800.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"activation_fee\": 400.0,\n \"center_throughput\": 800.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"activation_fee\": 400.0,\n \"center_throughput\": 800.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"activation_fee\": 400.0,\n \"center_throughput\": 800.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"activation_fee\": 400.0,\n \"center_throughput\": 800.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"activation_fee\": 400.0,\n \"center_throughput\": 800.0\n }\n ],\n \"connection_orders\": [\n {\n \"connection_order_id\": \"A\",\n \"order_parcel_count\": 11.0\n },\n {\n \"connection_order_id\": \"B\",\n \"order_parcel_count\": 46.0\n },\n {\n \"connection_order_id\": \"C\",\n \"order_parcel_count\": 44.0\n },\n {\n \"connection_order_id\": \"D\",\n \"order_parcel_count\": 10.0\n },\n {\n \"connection_order_id\": \"E\",\n \"order_parcel_count\": 14.0\n },\n {\n \"connection_order_id\": \"F\",\n \"order_parcel_count\": 27.0\n },\n {\n \"connection_order_id\": \"G\",\n \"order_parcel_count\": 33.0\n },\n {\n \"connection_order_id\": \"H\",\n \"order_parcel_count\": 25.0\n },\n {\n \"connection_order_id\": \"I\",\n \"order_parcel_count\": 39.0\n },\n {\n \"connection_order_id\": \"J\",\n \"order_parcel_count\": 34.0\n },\n {\n \"connection_order_id\": \"K\",\n \"order_parcel_count\": 44.0\n },\n {\n \"connection_order_id\": \"L\",\n \"order_parcel_count\": 21.0\n },\n {\n \"connection_order_id\": \"M\",\n \"order_parcel_count\": 25.0\n },\n {\n \"connection_order_id\": \"N\",\n \"order_parcel_count\": 18.0\n },\n {\n \"connection_order_id\": \"O\",\n \"order_parcel_count\": 48.0\n },\n {\n \"connection_order_id\": \"P\",\n \"order_parcel_count\": 12.0\n }\n ],\n \"routings\": [\n {\n \"connection_center_id\": \"F1\",\n \"connection_order_id\": \"A\",\n \"routing_cost\": 211.0\n },\n {\n \"connection_center_id\": \"F1\",\n \"connection_order_id\": \"B\",\n \"routing_cost\": 189.0\n },\n {\n \"connection_center_id\": \"F1\",\n \"connection_order_id\": \"C\",\n \"routing_cost\": 288.0\n },\n {\n \"connection_center_id\": \"F1\",\n \"connection_order_id\": \"D\",\n \"routing_cost\": 563.0\n },\n {\n \"connection_center_id\": \"F1\",\n \"connection_order_id\": \"E\",\n \"routing_cost\": 265.0\n },\n {\n \"connection_center_id\": \"F1\",\n \"connection_order_id\": \"F\",\n \"routing_cost\": 400.0\n },\n {\n \"connection_center_id\": \"F1\",\n \"connection_order_id\": \"G\",\n \"routing_cost\": 405.0\n },\n {\n \"connection_center_id\": \"F1\",\n \"connection_order_id\": \"H\",\n \"routing_cost\": 504.0\n },\n {\n \"connection_center_id\": \"F1\",\n \"connection_order_id\": \"I\",\n \"routing_cost\": 338.0\n },\n {\n \"connection_center_id\": \"F1\",\n \"connection_order_id\": \"J\",\n \"routing_cost\": 206.0\n },\n {\n \"connection_center_id\": \"F1\",\n \"connection_order_id\": \"K\",\n \"routing_cost\": 402.0\n },\n {\n \"connection_center_id\": \"F1\",\n \"connection_order_id\": \"L\",\n \"routing_cost\": 386.0\n },\n {\n \"connection_center_id\": \"F1\",\n \"connection_order_id\": \"M\",\n \"routing_cost\": 344.0\n },\n {\n \"connection_center_id\": \"F1\",\n \"connection_order_id\": \"N\",\n \"routing_cost\": 163.0\n },\n {\n \"connection_center_id\": \"F1\",\n \"connection_order_id\": \"O\",\n \"routing_cost\": 121.0\n },\n {\n \"connection_center_id\": \"F1\",\n \"connection_order_id\": \"P\",\n \"routing_cost\": 222.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"connection_order_id\": \"A\",\n \"routing_cost\": 571.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"connection_order_id\": \"B\",\n \"routing_cost\": 626.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"connection_order_id\": \"C\",\n \"routing_cost\": 737.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"connection_order_id\": \"D\",\n \"routing_cost\": 116.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"connection_order_id\": \"E\",\n \"routing_cost\": 709.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"connection_order_id\": \"F\",\n \"routing_cost\": 346.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"connection_order_id\": \"G\",\n \"routing_cost\": 377.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"connection_order_id\": \"H\",\n \"routing_cost\": 90.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"connection_order_id\": \"I\",\n \"routing_cost\": 432.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"connection_order_id\": \"J\",\n \"routing_cost\": 255.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"connection_order_id\": \"K\",\n \"routing_cost\": 595.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"connection_order_id\": \"L\",\n \"routing_cost\": 204.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"connection_order_id\": \"M\",\n \"routing_cost\": 148.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"connection_order_id\": \"N\",\n \"routing_cost\": 324.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"connection_order_id\": \"O\",\n \"routing_cost\": 549.0\n },\n {\n \"connection_center_id\": \"F2\",\n \"connection_order_id\": \"P\",\n \"routing_cost\": 675.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"connection_order_id\": \"A\",\n \"routing_cost\": 285.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"connection_order_id\": \"B\",\n \"routing_cost\": 567.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"connection_order_id\": \"C\",\n \"routing_cost\": 610.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"connection_order_id\": \"D\",\n \"routing_cost\": 637.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"connection_order_id\": \"E\",\n \"routing_cost\": 480.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"connection_order_id\": \"F\",\n \"routing_cost\": 718.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"connection_order_id\": \"G\",\n \"routing_cost\": 737.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"connection_order_id\": \"H\",\n \"routing_cost\": 621.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"connection_order_id\": \"I\",\n \"routing_cost\": 711.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"connection_order_id\": \"J\",\n \"routing_cost\": 459.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"connection_order_id\": \"K\",\n \"routing_cost\": 94.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"connection_order_id\": \"L\",\n \"routing_cost\": 625.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"connection_order_id\": \"M\",\n \"routing_cost\": 391.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"connection_order_id\": \"N\",\n \"routing_cost\": 323.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"connection_order_id\": \"O\",\n \"routing_cost\": 380.0\n },\n {\n \"connection_center_id\": \"F3\",\n \"connection_order_id\": \"P\",\n \"routing_cost\": 536.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"connection_order_id\": \"A\",\n \"routing_cost\": 426.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"connection_order_id\": \"B\",\n \"routing_cost\": 294.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"connection_order_id\": \"C\",\n \"routing_cost\": 411.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"connection_order_id\": \"D\",\n \"routing_cost\": 471.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"connection_order_id\": \"E\",\n \"routing_cost\": 453.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"connection_order_id\": \"F\",\n \"routing_cost\": 193.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"connection_order_id\": \"G\",\n \"routing_cost\": 192.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"connection_order_id\": \"H\",\n \"routing_cost\": 399.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"connection_order_id\": \"I\",\n \"routing_cost\": 125.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"connection_order_id\": \"J\",\n \"routing_cost\": 166.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"connection_order_id\": \"K\",\n \"routing_cost\": 594.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"connection_order_id\": \"L\",\n \"routing_cost\": 233.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"connection_order_id\": \"M\",\n \"routing_cost\": 348.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"connection_order_id\": \"N\",\n \"routing_cost\": 269.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"connection_order_id\": \"O\",\n \"routing_cost\": 333.0\n },\n {\n \"connection_center_id\": \"F4\",\n \"connection_order_id\": \"P\",\n \"routing_cost\": 374.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"connection_order_id\": \"A\",\n \"routing_cost\": 414.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"connection_order_id\": \"B\",\n \"routing_cost\": 472.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"connection_order_id\": \"C\",\n \"routing_cost\": 580.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"connection_order_id\": \"D\",\n \"routing_cost\": 276.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"connection_order_id\": \"E\",\n \"routing_cost\": 547.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"connection_order_id\": \"F\",\n \"routing_cost\": 317.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"connection_order_id\": \"G\",\n \"routing_cost\": 343.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"connection_order_id\": \"H\",\n \"routing_cost\": 228.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"connection_order_id\": \"I\",\n \"routing_cost\": 358.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"connection_order_id\": \"J\",\n \"routing_cost\": 113.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"connection_order_id\": \"K\",\n \"routing_cost\": 470.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"connection_order_id\": \"L\",\n \"routing_cost\": 202.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"connection_order_id\": \"M\",\n \"routing_cost\": 75.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"connection_order_id\": \"N\",\n \"routing_cost\": 165.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"connection_order_id\": \"O\",\n \"routing_cost\": 387.0\n },\n {\n \"connection_center_id\": \"F5\",\n \"connection_order_id\": \"P\",\n \"routing_cost\": 516.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"connection_order_id\": \"A\",\n \"routing_cost\": 121.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"connection_order_id\": \"B\",\n \"routing_cost\": 176.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"connection_order_id\": \"C\",\n \"routing_cost\": 220.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"connection_order_id\": \"D\",\n \"routing_cost\": 684.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"connection_order_id\": \"E\",\n \"routing_cost\": 139.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"connection_order_id\": \"F\",\n \"routing_cost\": 533.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"connection_order_id\": \"G\",\n \"routing_cost\": 536.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"connection_order_id\": \"H\",\n \"routing_cost\": 629.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"connection_order_id\": \"I\",\n \"routing_cost\": 460.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"connection_order_id\": \"J\",\n \"routing_cost\": 336.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"connection_order_id\": \"K\",\n \"routing_cost\": 349.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"connection_order_id\": \"L\",\n \"routing_cost\": 521.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"connection_order_id\": \"M\",\n \"routing_cost\": 445.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"connection_order_id\": \"N\",\n \"routing_cost\": 253.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"connection_order_id\": \"O\",\n \"routing_cost\": 23.0\n },\n {\n \"connection_center_id\": \"F6\",\n \"connection_order_id\": \"P\",\n \"routing_cost\": 144.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"connection_order_id\": \"A\",\n \"routing_cost\": 70.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"connection_order_id\": \"B\",\n \"routing_cost\": 304.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"connection_order_id\": \"C\",\n \"routing_cost\": 356.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"connection_order_id\": \"D\",\n \"routing_cost\": 617.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"connection_order_id\": \"E\",\n \"routing_cost\": 250.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"connection_order_id\": \"F\",\n \"routing_cost\": 549.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"connection_order_id\": \"G\",\n \"routing_cost\": 560.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"connection_order_id\": \"H\",\n \"routing_cost\": 573.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"connection_order_id\": \"I\",\n \"routing_cost\": 505.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"connection_order_id\": \"J\",\n \"routing_cost\": 308.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"connection_order_id\": \"K\",\n \"routing_cost\": 230.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"connection_order_id\": \"L\",\n \"routing_cost\": 501.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"connection_order_id\": \"M\",\n \"routing_cost\": 361.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"connection_order_id\": \"N\",\n \"routing_cost\": 181.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"connection_order_id\": \"O\",\n \"routing_cost\": 118.0\n },\n {\n \"connection_center_id\": \"F7\",\n \"connection_order_id\": \"P\",\n \"routing_cost\": 280.0\n }\n ]\n}\n\nAlso, when you send back the plan, please use this little JSON layout so I can read it automatically — just a casual shape for the answer:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is where you list the centers you decide to open (one identifier per opened center). \"assignments\" is a list that, for each order in the same order as the input, gives the identifier of the open center that will handle that order. Super informal: think of \"selected\" as the checkboxes you tick and \"assignments\" as the column where you write which box each order goes into.\n\nThis JSON is just a sketch of the expected shape — not the actual answer. Make sure every identifier you put in here matches the instance input exactly — no renaming and no new labels.\n\nValid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 800.0, 800.0, 800.0, 800.0, 800.0, 800.0, 800.0 ], "connection_costs": [ [ 211.0, 189.0, 288.0, 563.0, 265.0, 400.0, 405.0, 504.0, 338.0, 206.0, 402.0, 386.0, 344.0, 163.0, 121.0, 222.0 ], [ 571.0, 626.0, 737.0, 116.0, 709.0, 346.0, 377.0, 90.0, 432.0, 255.0, 595.0, 204.0, 148.0, 324.0, 549.0, 675.0 ], [ 285.0, 567.0, 610.0, 637.0, 480.0, 718.0, 737.0, 621.0, 711.0, 459.0, 94.0, 625.0, 391.0, 323.0, 380.0, 536.0 ], [ 426.0, 294.0, 411.0, 471.0, 453.0, 193.0, 192.0, 399.0, 125.0, 166.0, 594.0, 233.0, 348.0, 269.0, 333.0, 374.0 ], [ 414.0, 472.0, 580.0, 276.0, 547.0, 317.0, 343.0, 228.0, 358.0, 113.0, 470.0, 202.0, 75.0, 165.0, 387.0, 516.0 ], [ 121.0, 176.0, 220.0, 684.0, 139.0, 533.0, 536.0, 629.0, 460.0, 336.0, 349.0, 521.0, 445.0, 253.0, 23.0, 144.0 ], [ 70.0, 304.0, 356.0, 617.0, 250.0, 549.0, 560.0, 573.0, 505.0, 308.0, 230.0, 501.0, 361.0, 181.0, 118.0, 280.0 ] ], "demands": [ 11.0, 46.0, 44.0, 10.0, 14.0, 27.0, 33.0, 25.0, 39.0, 34.0, 44.0, 21.0, 25.0, 18.0, 48.0, 12.0 ], "objective": 3859.0 }, "solution": { "open_facilities": [ 1, 3, 5 ], "assignments": [ 5, 5, 5, 1, 5, 3, 3, 1, 3, 3, 5, 1, 1, 5, 5, 5 ] }, "obj": 3859.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 16, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 800.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 800.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 800.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 800.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 800.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 800.0 }, { "id": "F7", "opening_cost": 400.0, "capacity": 800.0 } ], "customers": [ { "id": "A", "demand": 11.0 }, { "id": "B", "demand": 46.0 }, { "id": "C", "demand": 44.0 }, { "id": "D", "demand": 10.0 }, { "id": "E", "demand": 14.0 }, { "id": "F", "demand": 27.0 }, { "id": "G", "demand": 33.0 }, { "id": "H", "demand": 25.0 }, { "id": "I", "demand": 39.0 }, { "id": "J", "demand": 34.0 }, { "id": "K", "demand": 44.0 }, { "id": "L", "demand": 21.0 }, { "id": "M", "demand": 25.0 }, { "id": "N", "demand": 18.0 }, { "id": "O", "demand": 48.0 }, { "id": "P", "demand": 12.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 211.0 }, { "facility": "F1", "customer": "B", "cost": 189.0 }, { "facility": "F1", "customer": "C", "cost": 288.0 }, { "facility": "F1", "customer": "D", "cost": 563.0 }, { "facility": "F1", "customer": "E", "cost": 265.0 }, { "facility": "F1", "customer": "F", "cost": 400.0 }, { "facility": "F1", "customer": "G", "cost": 405.0 }, { "facility": "F1", "customer": "H", "cost": 504.0 }, { "facility": "F1", "customer": "I", "cost": 338.0 }, { "facility": "F1", "customer": "J", "cost": 206.0 }, { "facility": "F1", "customer": "K", "cost": 402.0 }, { "facility": "F1", "customer": "L", "cost": 386.0 }, { "facility": "F1", "customer": "M", "cost": 344.0 }, { "facility": "F1", "customer": "N", "cost": 163.0 }, { "facility": "F1", "customer": "O", "cost": 121.0 }, { "facility": "F1", "customer": "P", "cost": 222.0 }, { "facility": "F2", "customer": "A", "cost": 571.0 }, { "facility": "F2", "customer": "B", "cost": 626.0 }, { "facility": "F2", "customer": "C", "cost": 737.0 }, { "facility": "F2", "customer": "D", "cost": 116.0 }, { "facility": "F2", "customer": "E", "cost": 709.0 }, { "facility": "F2", "customer": "F", "cost": 346.0 }, { "facility": "F2", "customer": "G", "cost": 377.0 }, { "facility": "F2", "customer": "H", "cost": 90.0 }, { "facility": "F2", "customer": "I", "cost": 432.0 }, { "facility": "F2", "customer": "J", "cost": 255.0 }, { "facility": "F2", "customer": "K", "cost": 595.0 }, { "facility": "F2", "customer": "L", "cost": 204.0 }, { "facility": "F2", "customer": "M", "cost": 148.0 }, { "facility": "F2", "customer": "N", "cost": 324.0 }, { "facility": "F2", "customer": "O", "cost": 549.0 }, { "facility": "F2", "customer": "P", "cost": 675.0 }, { "facility": "F3", "customer": "A", "cost": 285.0 }, { "facility": "F3", "customer": "B", "cost": 567.0 }, { "facility": "F3", "customer": "C", "cost": 610.0 }, { "facility": "F3", "customer": "D", "cost": 637.0 }, { "facility": "F3", "customer": "E", "cost": 480.0 }, { "facility": "F3", "customer": "F", "cost": 718.0 }, { "facility": "F3", "customer": "G", "cost": 737.0 }, { "facility": "F3", "customer": "H", "cost": 621.0 }, { "facility": "F3", "customer": "I", "cost": 711.0 }, { "facility": "F3", "customer": "J", "cost": 459.0 }, { "facility": "F3", "customer": "K", "cost": 94.0 }, { "facility": "F3", "customer": "L", "cost": 625.0 }, { "facility": "F3", "customer": "M", "cost": 391.0 }, { "facility": "F3", "customer": "N", "cost": 323.0 }, { "facility": "F3", "customer": "O", "cost": 380.0 }, { "facility": "F3", "customer": "P", "cost": 536.0 }, { "facility": "F4", "customer": "A", "cost": 426.0 }, { "facility": "F4", "customer": "B", "cost": 294.0 }, { "facility": "F4", "customer": "C", "cost": 411.0 }, { "facility": "F4", "customer": "D", "cost": 471.0 }, { "facility": "F4", "customer": "E", "cost": 453.0 }, { "facility": "F4", "customer": "F", "cost": 193.0 }, { "facility": "F4", "customer": "G", "cost": 192.0 }, { "facility": "F4", "customer": "H", "cost": 399.0 }, { "facility": "F4", "customer": "I", "cost": 125.0 }, { "facility": "F4", "customer": "J", "cost": 166.0 }, { "facility": "F4", "customer": "K", "cost": 594.0 }, { "facility": "F4", "customer": "L", "cost": 233.0 }, { "facility": "F4", "customer": "M", "cost": 348.0 }, { "facility": "F4", "customer": "N", "cost": 269.0 }, { "facility": "F4", "customer": "O", "cost": 333.0 }, { "facility": "F4", "customer": "P", "cost": 374.0 }, { "facility": "F5", "customer": "A", "cost": 414.0 }, { "facility": "F5", "customer": "B", "cost": 472.0 }, { "facility": "F5", "customer": "C", "cost": 580.0 }, { "facility": "F5", "customer": "D", "cost": 276.0 }, { "facility": "F5", "customer": "E", "cost": 547.0 }, { "facility": "F5", "customer": "F", "cost": 317.0 }, { "facility": "F5", "customer": "G", "cost": 343.0 }, { "facility": "F5", "customer": "H", "cost": 228.0 }, { "facility": "F5", "customer": "I", "cost": 358.0 }, { "facility": "F5", "customer": "J", "cost": 113.0 }, { "facility": "F5", "customer": "K", "cost": 470.0 }, { "facility": "F5", "customer": "L", "cost": 202.0 }, { "facility": "F5", "customer": "M", "cost": 75.0 }, { "facility": "F5", "customer": "N", "cost": 165.0 }, { "facility": "F5", "customer": "O", "cost": 387.0 }, { "facility": "F5", "customer": "P", "cost": 516.0 }, { "facility": "F6", "customer": "A", "cost": 121.0 }, { "facility": "F6", "customer": "B", "cost": 176.0 }, { "facility": "F6", "customer": "C", "cost": 220.0 }, { "facility": "F6", "customer": "D", "cost": 684.0 }, { "facility": "F6", "customer": "E", "cost": 139.0 }, { "facility": "F6", "customer": "F", "cost": 533.0 }, { "facility": "F6", "customer": "G", "cost": 536.0 }, { "facility": "F6", "customer": "H", "cost": 629.0 }, { "facility": "F6", "customer": "I", "cost": 460.0 }, { "facility": "F6", "customer": "J", "cost": 336.0 }, { "facility": "F6", "customer": "K", "cost": 349.0 }, { "facility": "F6", "customer": "L", "cost": 521.0 }, { "facility": "F6", "customer": "M", "cost": 445.0 }, { "facility": "F6", "customer": "N", "cost": 253.0 }, { "facility": "F6", "customer": "O", "cost": 23.0 }, { "facility": "F6", "customer": "P", "cost": 144.0 }, { "facility": "F7", "customer": "A", "cost": 70.0 }, { "facility": "F7", "customer": "B", "cost": 304.0 }, { "facility": "F7", "customer": "C", "cost": 356.0 }, { "facility": "F7", "customer": "D", "cost": 617.0 }, { "facility": "F7", "customer": "E", "cost": 250.0 }, { "facility": "F7", "customer": "F", "cost": 549.0 }, { "facility": "F7", "customer": "G", "cost": 560.0 }, { "facility": "F7", "customer": "H", "cost": 573.0 }, { "facility": "F7", "customer": "I", "cost": 505.0 }, { "facility": "F7", "customer": "J", "cost": 308.0 }, { "facility": "F7", "customer": "K", "cost": 230.0 }, { "facility": "F7", "customer": "L", "cost": 501.0 }, { "facility": "F7", "customer": "M", "cost": 361.0 }, { "facility": "F7", "customer": "N", "cost": 181.0 }, { "facility": "F7", "customer": "O", "cost": 118.0 }, { "facility": "F7", "customer": "P", "cost": 280.0 } ], "objective": 3859.0 }, "solution_variant": { "selected": [ "F2", "F4", "F6" ], "assignments": [ "F6", "F6", "F6", "F2", "F6", "F4", "F4", "F2", "F4", "F4", "F6", "F2", "F2", "F6", "F6", "F6" ] }, "context_index": 39, "input_format": "json", "input_index_base": "names" }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Across the county the goal is to set up a handful of mobile clinic locations and then send each patient to exactly one of the opened locations, making sure no location is overloaded. Each possible location has a cost to deploy and a capacity limit, and routing a patient to a location brings a travel or treatment cost. One rollout is better than another if its overall cost — the sum of the deployment costs for the chosen locations plus the travel/treatment costs for everyone scheduled there — is lower, with every patient assigned to a single open location and each location kept within its capacity. The concrete details are shown below.\n\n{\n \"total_mobile_clinic_sites\": 7,\n \"total_patients\": 15,\n \"sites\": [\n {\n \"site_id\": \"F1\",\n \"deployment_cost\": 400.0,\n \"site_capacity\": 384.0\n },\n {\n \"site_id\": \"F2\",\n \"deployment_cost\": 400.0,\n \"site_capacity\": 494.0\n },\n {\n \"site_id\": \"F3\",\n \"deployment_cost\": 400.0,\n \"site_capacity\": 427.0\n },\n {\n \"site_id\": \"F4\",\n \"deployment_cost\": 400.0,\n \"site_capacity\": 491.0\n },\n {\n \"site_id\": \"F5\",\n \"deployment_cost\": 400.0,\n \"site_capacity\": 244.0\n },\n {\n \"site_id\": \"F6\",\n \"deployment_cost\": 400.0,\n \"site_capacity\": 404.0\n },\n {\n \"site_id\": \"F7\",\n \"deployment_cost\": 400.0,\n \"site_capacity\": 410.0\n }\n ],\n \"patients\": [\n {\n \"patient_id\": \"A\",\n \"patient_demand\": 17.0\n },\n {\n \"patient_id\": \"B\",\n \"patient_demand\": 12.0\n },\n {\n \"patient_id\": \"C\",\n \"patient_demand\": 28.0\n },\n {\n \"patient_id\": \"D\",\n \"patient_demand\": 13.0\n },\n {\n \"patient_id\": \"E\",\n \"patient_demand\": 14.0\n },\n {\n \"patient_id\": \"F\",\n \"patient_demand\": 10.0\n },\n {\n \"patient_id\": \"G\",\n \"patient_demand\": 27.0\n },\n {\n \"patient_id\": \"H\",\n \"patient_demand\": 25.0\n },\n {\n \"patient_id\": \"I\",\n \"patient_demand\": 18.0\n },\n {\n \"patient_id\": \"J\",\n \"patient_demand\": 20.0\n },\n {\n \"patient_id\": \"K\",\n \"patient_demand\": 17.0\n },\n {\n \"patient_id\": \"L\",\n \"patient_demand\": 14.0\n },\n {\n \"patient_id\": \"M\",\n \"patient_demand\": 18.0\n },\n {\n \"patient_id\": \"N\",\n \"patient_demand\": 14.0\n },\n {\n \"patient_id\": \"O\",\n \"patient_demand\": 29.0\n }\n ],\n \"travel_or_treatments\": [\n {\n \"site_id\": \"F1\",\n \"patient_id\": \"A\",\n \"travel_or_treatment_cost\": 472.0\n },\n {\n \"site_id\": \"F1\",\n \"patient_id\": \"B\",\n \"travel_or_treatment_cost\": 127.0\n },\n {\n \"site_id\": \"F1\",\n \"patient_id\": \"C\",\n \"travel_or_treatment_cost\": 145.0\n },\n {\n \"site_id\": \"F1\",\n \"patient_id\": \"D\",\n \"travel_or_treatment_cost\": 613.0\n },\n {\n \"site_id\": \"F1\",\n \"patient_id\": \"E\",\n \"travel_or_treatment_cost\": 112.0\n },\n {\n \"site_id\": \"F1\",\n \"patient_id\": \"F\",\n \"travel_or_treatment_cost\": 501.0\n },\n {\n \"site_id\": \"F1\",\n \"patient_id\": \"G\",\n \"travel_or_treatment_cost\": 383.0\n },\n {\n \"site_id\": \"F1\",\n \"patient_id\": \"H\",\n \"travel_or_treatment_cost\": 162.0\n },\n {\n \"site_id\": \"F1\",\n \"patient_id\": \"I\",\n \"travel_or_treatment_cost\": 63.0\n },\n {\n \"site_id\": \"F1\",\n \"patient_id\": \"J\",\n \"travel_or_treatment_cost\": 546.0\n },\n {\n \"site_id\": \"F1\",\n \"patient_id\": \"K\",\n \"travel_or_treatment_cost\": 271.0\n },\n {\n \"site_id\": \"F1\",\n \"patient_id\": \"L\",\n \"travel_or_treatment_cost\": 49.0\n },\n {\n \"site_id\": \"F1\",\n \"patient_id\": \"M\",\n \"travel_or_treatment_cost\": 111.0\n },\n {\n \"site_id\": \"F1\",\n \"patient_id\": \"N\",\n \"travel_or_treatment_cost\": 95.0\n },\n {\n \"site_id\": \"F1\",\n \"patient_id\": \"O\",\n \"travel_or_treatment_cost\": 91.0\n },\n {\n \"site_id\": \"F2\",\n \"patient_id\": \"A\",\n \"travel_or_treatment_cost\": 676.0\n },\n {\n \"site_id\": \"F2\",\n \"patient_id\": \"B\",\n \"travel_or_treatment_cost\": 261.0\n },\n {\n \"site_id\": \"F2\",\n \"patient_id\": \"C\",\n \"travel_or_treatment_cost\": 530.0\n },\n {\n \"site_id\": \"F2\",\n \"patient_id\": \"D\",\n \"travel_or_treatment_cost\": 901.0\n },\n {\n \"site_id\": \"F2\",\n \"patient_id\": \"E\",\n \"travel_or_treatment_cost\": 926.0\n },\n {\n \"site_id\": \"F2\",\n \"patient_id\": \"F\",\n \"travel_or_treatment_cost\": 969.0\n },\n {\n \"site_id\": \"F2\",\n \"patient_id\": \"G\",\n \"travel_or_treatment_cost\": 1193.0\n },\n {\n \"site_id\": \"F2\",\n \"patient_id\": \"H\",\n \"travel_or_treatment_cost\": 504.0\n },\n {\n \"site_id\": \"F2\",\n \"patient_id\": \"I\",\n \"travel_or_treatment_cost\": 56.0\n },\n {\n \"site_id\": \"F2\",\n \"patient_id\": \"J\",\n \"travel_or_treatment_cost\": 653.0\n },\n {\n \"site_id\": \"F2\",\n \"patient_id\": \"K\",\n \"travel_or_treatment_cost\": 591.0\n },\n {\n \"site_id\": \"F2\",\n \"patient_id\": \"L\",\n \"travel_or_treatment_cost\": 44.0\n },\n {\n \"site_id\": \"F2\",\n \"patient_id\": \"M\",\n \"travel_or_treatment_cost\": 350.0\n },\n {\n \"site_id\": \"F2\",\n \"patient_id\": \"N\",\n \"travel_or_treatment_cost\": 155.0\n },\n {\n \"site_id\": \"F2\",\n \"patient_id\": \"O\",\n \"travel_or_treatment_cost\": 85.0\n },\n {\n \"site_id\": \"F3\",\n \"patient_id\": \"A\",\n \"travel_or_treatment_cost\": 183.0\n },\n {\n \"site_id\": \"F3\",\n \"patient_id\": \"B\",\n \"travel_or_treatment_cost\": 257.0\n },\n {\n \"site_id\": \"F3\",\n \"patient_id\": \"C\",\n \"travel_or_treatment_cost\": 324.0\n },\n {\n \"site_id\": \"F3\",\n \"patient_id\": \"D\",\n \"travel_or_treatment_cost\": 242.0\n },\n {\n \"site_id\": \"F3\",\n \"patient_id\": \"E\",\n \"travel_or_treatment_cost\": 290.0\n },\n {\n \"site_id\": \"F3\",\n \"patient_id\": \"F\",\n \"travel_or_treatment_cost\": 706.0\n },\n {\n \"site_id\": \"F3\",\n \"patient_id\": \"G\",\n \"travel_or_treatment_cost\": 482.0\n },\n {\n \"site_id\": \"F3\",\n \"patient_id\": \"H\",\n \"travel_or_treatment_cost\": 339.0\n },\n {\n \"site_id\": \"F3\",\n \"patient_id\": \"I\",\n \"travel_or_treatment_cost\": 37.0\n },\n {\n \"site_id\": \"F3\",\n \"patient_id\": \"J\",\n \"travel_or_treatment_cost\": 299.0\n },\n {\n \"site_id\": \"F3\",\n \"patient_id\": \"K\",\n \"travel_or_treatment_cost\": 44.0\n },\n {\n \"site_id\": \"F3\",\n \"patient_id\": \"L\",\n \"travel_or_treatment_cost\": 31.0\n },\n {\n \"site_id\": \"F3\",\n \"patient_id\": \"M\",\n \"travel_or_treatment_cost\": 42.0\n },\n {\n \"site_id\": \"F3\",\n \"patient_id\": \"N\",\n \"travel_or_treatment_cost\": 28.0\n },\n {\n \"site_id\": \"F3\",\n \"patient_id\": \"O\",\n \"travel_or_treatment_cost\": 64.0\n },\n {\n \"site_id\": \"F4\",\n \"patient_id\": \"A\",\n \"travel_or_treatment_cost\": 567.0\n },\n {\n \"site_id\": \"F4\",\n \"patient_id\": \"B\",\n \"travel_or_treatment_cost\": 66.0\n },\n {\n \"site_id\": \"F4\",\n \"patient_id\": \"C\",\n \"travel_or_treatment_cost\": 66.0\n },\n {\n \"site_id\": \"F4\",\n \"patient_id\": \"D\",\n \"travel_or_treatment_cost\": 712.0\n },\n {\n \"site_id\": \"F4\",\n \"patient_id\": \"E\",\n \"travel_or_treatment_cost\": 120.0\n },\n {\n \"site_id\": \"F4\",\n \"patient_id\": \"F\",\n \"travel_or_treatment_cost\": 298.0\n },\n {\n \"site_id\": \"F4\",\n \"patient_id\": \"G\",\n \"travel_or_treatment_cost\": 220.0\n },\n {\n \"site_id\": \"F4\",\n \"patient_id\": \"H\",\n \"travel_or_treatment_cost\": 74.0\n },\n {\n \"site_id\": \"F4\",\n \"patient_id\": \"I\",\n \"travel_or_treatment_cost\": 87.0\n },\n {\n \"site_id\": \"F4\",\n \"patient_id\": \"J\",\n \"travel_or_treatment_cost\": 631.0\n },\n {\n \"site_id\": \"F4\",\n \"patient_id\": \"K\",\n \"travel_or_treatment_cost\": 368.0\n },\n {\n \"site_id\": \"F4\",\n \"patient_id\": \"L\",\n \"travel_or_treatment_cost\": 83.0\n },\n {\n \"site_id\": \"F4\",\n \"patient_id\": \"M\",\n \"travel_or_treatment_cost\": 191.0\n },\n {\n \"site_id\": \"F4\",\n \"patient_id\": \"N\",\n \"travel_or_treatment_cost\": 159.0\n },\n {\n \"site_id\": \"F4\",\n \"patient_id\": \"O\",\n \"travel_or_treatment_cost\": 110.0\n },\n {\n \"site_id\": \"F5\",\n \"patient_id\": \"A\",\n \"travel_or_treatment_cost\": 433.0\n },\n {\n \"site_id\": \"F5\",\n \"patient_id\": \"B\",\n \"travel_or_treatment_cost\": 736.0\n },\n {\n \"site_id\": \"F5\",\n \"patient_id\": \"C\",\n \"travel_or_treatment_cost\": 1095.0\n },\n {\n \"site_id\": \"F5\",\n \"patient_id\": \"D\",\n \"travel_or_treatment_cost\": 692.0\n },\n {\n \"site_id\": \"F5\",\n \"patient_id\": \"E\",\n \"travel_or_treatment_cost\": 1389.0\n },\n {\n \"site_id\": \"F5\",\n \"patient_id\": \"F\",\n \"travel_or_treatment_cost\": 1533.0\n },\n {\n \"site_id\": \"F5\",\n \"patient_id\": \"G\",\n \"travel_or_treatment_cost\": 1659.0\n },\n {\n \"site_id\": \"F5\",\n \"patient_id\": \"H\",\n \"travel_or_treatment_cost\": 1069.0\n },\n {\n \"site_id\": \"F5\",\n \"patient_id\": \"I\",\n \"travel_or_treatment_cost\": 108.0\n },\n {\n \"site_id\": \"F5\",\n \"patient_id\": \"J\",\n \"travel_or_treatment_cost\": 113.0\n },\n {\n \"site_id\": \"F5\",\n \"patient_id\": \"K\",\n \"travel_or_treatment_cost\": 737.0\n },\n {\n \"site_id\": \"F5\",\n \"patient_id\": \"L\",\n \"travel_or_treatment_cost\": 277.0\n },\n {\n \"site_id\": \"F5\",\n \"patient_id\": \"M\",\n \"travel_or_treatment_cost\": 703.0\n },\n {\n \"site_id\": \"F5\",\n \"patient_id\": \"N\",\n \"travel_or_treatment_cost\": 430.0\n },\n {\n \"site_id\": \"F5\",\n \"patient_id\": \"O\",\n \"travel_or_treatment_cost\": 77.0\n },\n {\n \"site_id\": \"F6\",\n \"patient_id\": \"A\",\n \"travel_or_treatment_cost\": 1113.0\n },\n {\n \"site_id\": \"F6\",\n \"patient_id\": \"B\",\n \"travel_or_treatment_cost\": 24.0\n },\n {\n \"site_id\": \"F6\",\n \"patient_id\": \"C\",\n \"travel_or_treatment_cost\": 663.0\n },\n {\n \"site_id\": \"F6\",\n \"patient_id\": \"D\",\n \"travel_or_treatment_cost\": 1355.0\n },\n {\n \"site_id\": \"F6\",\n \"patient_id\": \"E\",\n \"travel_or_treatment_cost\": 1228.0\n },\n {\n \"site_id\": \"F6\",\n \"patient_id\": \"F\",\n \"travel_or_treatment_cost\": 926.0\n },\n {\n \"site_id\": \"F6\",\n \"patient_id\": \"G\",\n \"travel_or_treatment_cost\": 1462.0\n },\n {\n \"site_id\": \"F6\",\n \"patient_id\": \"H\",\n \"travel_or_treatment_cost\": 575.0\n },\n {\n \"site_id\": \"F6\",\n \"patient_id\": \"I\",\n \"travel_or_treatment_cost\": 191.0\n },\n {\n \"site_id\": \"F6\",\n \"patient_id\": \"J\",\n \"travel_or_treatment_cost\": 1022.0\n },\n {\n \"site_id\": \"F6\",\n \"patient_id\": \"K\",\n \"travel_or_treatment_cost\": 1053.0\n },\n {\n \"site_id\": \"F6\",\n \"patient_id\": \"L\",\n \"travel_or_treatment_cost\": 305.0\n },\n {\n \"site_id\": \"F6\",\n \"patient_id\": \"M\",\n \"travel_or_treatment_cost\": 808.0\n },\n {\n \"site_id\": \"F6\",\n \"patient_id\": \"N\",\n \"travel_or_treatment_cost\": 587.0\n },\n {\n \"site_id\": \"F6\",\n \"patient_id\": \"O\",\n \"travel_or_treatment_cost\": 175.0\n },\n {\n \"site_id\": \"F7\",\n \"patient_id\": \"A\",\n \"travel_or_treatment_cost\": 867.0\n },\n {\n \"site_id\": \"F7\",\n \"patient_id\": \"B\",\n \"travel_or_treatment_cost\": 493.0\n },\n {\n \"site_id\": \"F7\",\n \"patient_id\": \"C\",\n \"travel_or_treatment_cost\": 924.0\n },\n {\n \"site_id\": \"F7\",\n \"patient_id\": \"D\",\n \"travel_or_treatment_cost\": 1130.0\n },\n {\n \"site_id\": \"F7\",\n \"patient_id\": \"E\",\n \"travel_or_treatment_cost\": 1356.0\n },\n {\n \"site_id\": \"F7\",\n \"patient_id\": \"F\",\n \"travel_or_treatment_cost\": 1329.0\n },\n {\n \"site_id\": \"F7\",\n \"patient_id\": \"G\",\n \"travel_or_treatment_cost\": 1623.0\n },\n {\n \"site_id\": \"F7\",\n \"patient_id\": \"H\",\n \"travel_or_treatment_cost\": 878.0\n },\n {\n \"site_id\": \"F7\",\n \"patient_id\": \"I\",\n \"travel_or_treatment_cost\": 43.0\n },\n {\n \"site_id\": \"F7\",\n \"patient_id\": \"J\",\n \"travel_or_treatment_cost\": 739.0\n },\n {\n \"site_id\": \"F7\",\n \"patient_id\": \"K\",\n \"travel_or_treatment_cost\": 911.0\n },\n {\n \"site_id\": \"F7\",\n \"patient_id\": \"L\",\n \"travel_or_treatment_cost\": 33.0\n },\n {\n \"site_id\": \"F7\",\n \"patient_id\": \"M\",\n \"travel_or_treatment_cost\": 722.0\n },\n {\n \"site_id\": \"F7\",\n \"patient_id\": \"N\",\n \"travel_or_treatment_cost\": 404.0\n },\n {\n \"site_id\": \"F7\",\n \"patient_id\": \"O\",\n \"travel_or_treatment_cost\": 72.0\n }\n ]\n}\n\nAlso, when you send the rollout back, please follow this little JSON layout so it's easy to check automatically. Here's the shape I expect:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of clinic sites you decide to deploy, and \"assignments\" as who goes to which opened site (one entry per patient, in the same order the patients appear in the instance). This is just the format sketch — not the actual numbers or choices.\n\nPlease make sure all identifiers you use match the instance input exactly — no renaming and no invented labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”. \"", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 384.0, 494.0, 427.0, 491.0, 244.0, 404.0, 410.0 ], "connection_costs": [ [ 472.0, 127.0, 145.0, 613.0, 112.0, 501.0, 383.0, 162.0, 63.0, 546.0, 271.0, 49.0, 111.0, 95.0, 91.0 ], [ 676.0, 261.0, 530.0, 901.0, 926.0, 969.0, 1193.0, 504.0, 56.0, 653.0, 591.0, 44.0, 350.0, 155.0, 85.0 ], [ 183.0, 257.0, 324.0, 242.0, 290.0, 706.0, 482.0, 339.0, 37.0, 299.0, 44.0, 31.0, 42.0, 28.0, 64.0 ], [ 567.0, 66.0, 66.0, 712.0, 120.0, 298.0, 220.0, 74.0, 87.0, 631.0, 368.0, 83.0, 191.0, 159.0, 110.0 ], [ 433.0, 736.0, 1095.0, 692.0, 1389.0, 1533.0, 1659.0, 1069.0, 108.0, 113.0, 737.0, 277.0, 703.0, 430.0, 77.0 ], [ 1113.0, 24.0, 663.0, 1355.0, 1228.0, 926.0, 1462.0, 575.0, 191.0, 1022.0, 1053.0, 305.0, 808.0, 587.0, 175.0 ], [ 867.0, 493.0, 924.0, 1130.0, 1356.0, 1329.0, 1623.0, 878.0, 43.0, 739.0, 911.0, 33.0, 722.0, 404.0, 72.0 ] ], "demands": [ 17.0, 12.0, 28.0, 13.0, 14.0, 10.0, 27.0, 25.0, 18.0, 20.0, 17.0, 14.0, 18.0, 14.0, 29.0 ], "objective": 2614.0 }, "solution": { "open_facilities": [ 2, 3 ], "assignments": [ 2, 3, 3, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2 ] }, "obj": 2614.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 15, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 384.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 494.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 427.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 491.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 244.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 404.0 }, { "id": "F7", "opening_cost": 400.0, "capacity": 410.0 } ], "customers": [ { "id": "A", "demand": 17.0 }, { "id": "B", "demand": 12.0 }, { "id": "C", "demand": 28.0 }, { "id": "D", "demand": 13.0 }, { "id": "E", "demand": 14.0 }, { "id": "F", "demand": 10.0 }, { "id": "G", "demand": 27.0 }, { "id": "H", "demand": 25.0 }, { "id": "I", "demand": 18.0 }, { "id": "J", "demand": 20.0 }, { "id": "K", "demand": 17.0 }, { "id": "L", "demand": 14.0 }, { "id": "M", "demand": 18.0 }, { "id": "N", "demand": 14.0 }, { "id": "O", "demand": 29.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 472.0 }, { "facility": "F1", "customer": "B", "cost": 127.0 }, { "facility": "F1", "customer": "C", "cost": 145.0 }, { "facility": "F1", "customer": "D", "cost": 613.0 }, { "facility": "F1", "customer": "E", "cost": 112.0 }, { "facility": "F1", "customer": "F", "cost": 501.0 }, { "facility": "F1", "customer": "G", "cost": 383.0 }, { "facility": "F1", "customer": "H", "cost": 162.0 }, { "facility": "F1", "customer": "I", "cost": 63.0 }, { "facility": "F1", "customer": "J", "cost": 546.0 }, { "facility": "F1", "customer": "K", "cost": 271.0 }, { "facility": "F1", "customer": "L", "cost": 49.0 }, { "facility": "F1", "customer": "M", "cost": 111.0 }, { "facility": "F1", "customer": "N", "cost": 95.0 }, { "facility": "F1", "customer": "O", "cost": 91.0 }, { "facility": "F2", "customer": "A", "cost": 676.0 }, { "facility": "F2", "customer": "B", "cost": 261.0 }, { "facility": "F2", "customer": "C", "cost": 530.0 }, { "facility": "F2", "customer": "D", "cost": 901.0 }, { "facility": "F2", "customer": "E", "cost": 926.0 }, { "facility": "F2", "customer": "F", "cost": 969.0 }, { "facility": "F2", "customer": "G", "cost": 1193.0 }, { "facility": "F2", "customer": "H", "cost": 504.0 }, { "facility": "F2", "customer": "I", "cost": 56.0 }, { "facility": "F2", "customer": "J", "cost": 653.0 }, { "facility": "F2", "customer": "K", "cost": 591.0 }, { "facility": "F2", "customer": "L", "cost": 44.0 }, { "facility": "F2", "customer": "M", "cost": 350.0 }, { "facility": "F2", "customer": "N", "cost": 155.0 }, { "facility": "F2", "customer": "O", "cost": 85.0 }, { "facility": "F3", "customer": "A", "cost": 183.0 }, { "facility": "F3", "customer": "B", "cost": 257.0 }, { "facility": "F3", "customer": "C", "cost": 324.0 }, { "facility": "F3", "customer": "D", "cost": 242.0 }, { "facility": "F3", "customer": "E", "cost": 290.0 }, { "facility": "F3", "customer": "F", "cost": 706.0 }, { "facility": "F3", "customer": "G", "cost": 482.0 }, { "facility": "F3", "customer": "H", "cost": 339.0 }, { "facility": "F3", "customer": "I", "cost": 37.0 }, { "facility": "F3", "customer": "J", "cost": 299.0 }, { "facility": "F3", "customer": "K", "cost": 44.0 }, { "facility": "F3", "customer": "L", "cost": 31.0 }, { "facility": "F3", "customer": "M", "cost": 42.0 }, { "facility": "F3", "customer": "N", "cost": 28.0 }, { "facility": "F3", "customer": "O", "cost": 64.0 }, { "facility": "F4", "customer": "A", "cost": 567.0 }, { "facility": "F4", "customer": "B", "cost": 66.0 }, { "facility": "F4", "customer": "C", "cost": 66.0 }, { "facility": "F4", "customer": "D", "cost": 712.0 }, { "facility": "F4", "customer": "E", "cost": 120.0 }, { "facility": "F4", "customer": "F", "cost": 298.0 }, { "facility": "F4", "customer": "G", "cost": 220.0 }, { "facility": "F4", "customer": "H", "cost": 74.0 }, { "facility": "F4", "customer": "I", "cost": 87.0 }, { "facility": "F4", "customer": "J", "cost": 631.0 }, { "facility": "F4", "customer": "K", "cost": 368.0 }, { "facility": "F4", "customer": "L", "cost": 83.0 }, { "facility": "F4", "customer": "M", "cost": 191.0 }, { "facility": "F4", "customer": "N", "cost": 159.0 }, { "facility": "F4", "customer": "O", "cost": 110.0 }, { "facility": "F5", "customer": "A", "cost": 433.0 }, { "facility": "F5", "customer": "B", "cost": 736.0 }, { "facility": "F5", "customer": "C", "cost": 1095.0 }, { "facility": "F5", "customer": "D", "cost": 692.0 }, { "facility": "F5", "customer": "E", "cost": 1389.0 }, { "facility": "F5", "customer": "F", "cost": 1533.0 }, { "facility": "F5", "customer": "G", "cost": 1659.0 }, { "facility": "F5", "customer": "H", "cost": 1069.0 }, { "facility": "F5", "customer": "I", "cost": 108.0 }, { "facility": "F5", "customer": "J", "cost": 113.0 }, { "facility": "F5", "customer": "K", "cost": 737.0 }, { "facility": "F5", "customer": "L", "cost": 277.0 }, { "facility": "F5", "customer": "M", "cost": 703.0 }, { "facility": "F5", "customer": "N", "cost": 430.0 }, { "facility": "F5", "customer": "O", "cost": 77.0 }, { "facility": "F6", "customer": "A", "cost": 1113.0 }, { "facility": "F6", "customer": "B", "cost": 24.0 }, { "facility": "F6", "customer": "C", "cost": 663.0 }, { "facility": "F6", "customer": "D", "cost": 1355.0 }, { "facility": "F6", "customer": "E", "cost": 1228.0 }, { "facility": "F6", "customer": "F", "cost": 926.0 }, { "facility": "F6", "customer": "G", "cost": 1462.0 }, { "facility": "F6", "customer": "H", "cost": 575.0 }, { "facility": "F6", "customer": "I", "cost": 191.0 }, { "facility": "F6", "customer": "J", "cost": 1022.0 }, { "facility": "F6", "customer": "K", "cost": 1053.0 }, { "facility": "F6", "customer": "L", "cost": 305.0 }, { "facility": "F6", "customer": "M", "cost": 808.0 }, { "facility": "F6", "customer": "N", "cost": 587.0 }, { "facility": "F6", "customer": "O", "cost": 175.0 }, { "facility": "F7", "customer": "A", "cost": 867.0 }, { "facility": "F7", "customer": "B", "cost": 493.0 }, { "facility": "F7", "customer": "C", "cost": 924.0 }, { "facility": "F7", "customer": "D", "cost": 1130.0 }, { "facility": "F7", "customer": "E", "cost": 1356.0 }, { "facility": "F7", "customer": "F", "cost": 1329.0 }, { "facility": "F7", "customer": "G", "cost": 1623.0 }, { "facility": "F7", "customer": "H", "cost": 878.0 }, { "facility": "F7", "customer": "I", "cost": 43.0 }, { "facility": "F7", "customer": "J", "cost": 739.0 }, { "facility": "F7", "customer": "K", "cost": 911.0 }, { "facility": "F7", "customer": "L", "cost": 33.0 }, { "facility": "F7", "customer": "M", "cost": 722.0 }, { "facility": "F7", "customer": "N", "cost": 404.0 }, { "facility": "F7", "customer": "O", "cost": 72.0 } ], "objective": 2614.0 }, "solution_variant": { "selected": [ "F3", "F4" ], "assignments": [ "F3", "F4", "F4", "F3", "F4", "F4", "F4", "F4", "F3", "F3", "F3", "F3", "F3", "F3", "F3" ] }, "context_index": 40, "input_format": "json", "input_index_base": "names" }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Recently the planners talked about which docking stations to activate and how to group riders around them. Every station that’s turned on comes with a fixed cost, and each rider’s distance or inconvenience to their dock adds a small extra cost, so the plan that’s preferred is the one with the lowest combined cost — station start-up fees plus all riders’ access costs. It’s required that each rider be matched to a single open station and that no station be asked to handle more riders than its capacity. The detailed numbers are provided below.\n\nThere are 7 candidate docking stations and 15 riders to assign.\nDocking station F1 would cost 432.0 to activate and can serve up to 466.0 riders.\nDocking station F2 would cost 114.0 to activate and can serve up to 307.0 riders.\nDocking station F3 would cost 121.0 to activate and can serve up to 311.0 riders.\nDocking station F4 would cost 312.0 to activate and can serve up to 406.0 riders.\nDocking station F5 would cost 103.0 to activate and can serve up to 302.0 riders.\nDocking station F6 would cost 336.0 to activate and can serve up to 418.0 riders.\nDocking station F7 would cost 472.0 to activate and can serve up to 486.0 riders.\nRider 0 requires 20.0 capacity units.\nRider 1 requires 20.0 capacity units.\nRider 2 requires 10.0 capacity units.\nRider 3 requires 20.0 capacity units.\nRider 4 requires 19.0 capacity units.\nRider 5 requires 16.0 capacity units.\nRider 6 requires 9.0 capacity units.\nRider 7 requires 21.0 capacity units.\nRider 8 requires 23.0 capacity units.\nRider 9 requires 5.0 capacity units.\nRider 10 requires 8.0 capacity units.\nRider 11 requires 19.0 capacity units.\nRider 12 requires 26.0 capacity units.\nRider 13 requires 35.0 capacity units.\nRider 14 requires 15.0 capacity units.\nAssigning rider 0 to docking station F1 incurs access cost 100.0.\nAssigning rider 1 to docking station F1 incurs access cost 117.0.\nAssigning rider 2 to docking station F1 incurs access cost 241.0.\nAssigning rider 3 to docking station F1 incurs access cost 277.0.\nAssigning rider 4 to docking station F1 incurs access cost 126.0.\nAssigning rider 5 to docking station F1 incurs access cost 70.0.\nAssigning rider 6 to docking station F1 incurs access cost 163.0.\nAssigning rider 7 to docking station F1 incurs access cost 134.0.\nAssigning rider 8 to docking station F1 incurs access cost 161.0.\nAssigning rider 9 to docking station F1 incurs access cost 151.0.\nAssigning rider 10 to docking station F1 incurs access cost 45.0.\nAssigning rider 11 to docking station F1 incurs access cost 112.0.\nAssigning rider 12 to docking station F1 incurs access cost 154.0.\nAssigning rider 13 to docking station F1 incurs access cost 97.0.\nAssigning rider 14 to docking station F1 incurs access cost 20.0.\nAssigning rider 0 to docking station F2 incurs access cost 193.0.\nAssigning rider 1 to docking station F2 incurs access cost 204.0.\nAssigning rider 2 to docking station F2 incurs access cost 146.0.\nAssigning rider 3 to docking station F2 incurs access cost 211.0.\nAssigning rider 4 to docking station F2 incurs access cost 63.0.\nAssigning rider 5 to docking station F2 incurs access cost 37.0.\nAssigning rider 6 to docking station F2 incurs access cost 63.0.\nAssigning rider 7 to docking station F2 incurs access cost 108.0.\nAssigning rider 8 to docking station F2 incurs access cost 149.0.\nAssigning rider 9 to docking station F2 incurs access cost 216.0.\nAssigning rider 10 to docking station F2 incurs access cost 134.0.\nAssigning rider 11 to docking station F2 incurs access cost 139.0.\nAssigning rider 12 to docking station F2 incurs access cost 79.0.\nAssigning rider 13 to docking station F2 incurs access cost 196.0.\nAssigning rider 14 to docking station F2 incurs access cost 96.0.\nAssigning rider 0 to docking station F3 incurs access cost 131.0.\nAssigning rider 1 to docking station F3 incurs access cost 152.0.\nAssigning rider 2 to docking station F3 incurs access cost 286.0.\nAssigning rider 3 to docking station F3 incurs access cost 365.0.\nAssigning rider 4 to docking station F3 incurs access cost 165.0.\nAssigning rider 5 to docking station F3 incurs access cost 150.0.\nAssigning rider 6 to docking station F3 incurs access cost 234.0.\nAssigning rider 7 to docking station F3 incurs access cost 224.0.\nAssigning rider 8 to docking station F3 incurs access cost 249.0.\nAssigning rider 9 to docking station F3 incurs access cost 207.0.\nAssigning rider 10 to docking station F3 incurs access cost 45.0.\nAssigning rider 11 to docking station F3 incurs access cost 195.0.\nAssigning rider 12 to docking station F3 incurs access cost 238.0.\nAssigning rider 13 to docking station F3 incurs access cost 54.0.\nAssigning rider 14 to docking station F3 incurs access cost 109.0.\nAssigning rider 0 to docking station F4 incurs access cost 86.0.\nAssigning rider 1 to docking station F4 incurs access cost 108.0.\nAssigning rider 2 to docking station F4 incurs access cost 301.0.\nAssigning rider 3 to docking station F4 incurs access cost 346.0.\nAssigning rider 4 to docking station F4 incurs access cost 180.0.\nAssigning rider 5 to docking station F4 incurs access cost 141.0.\nAssigning rider 6 to docking station F4 incurs access cost 233.0.\nAssigning rider 7 to docking station F4 incurs access cost 200.0.\nAssigning rider 8 to docking station F4 incurs access cost 220.0.\nAssigning rider 9 to docking station F4 incurs access cost 163.0.\nAssigning rider 10 to docking station F4 incurs access cost 40.0.\nAssigning rider 11 to docking station F4 incurs access cost 162.0.\nAssigning rider 12 to docking station F4 incurs access cost 226.0.\nAssigning rider 13 to docking station F4 incurs access cost 25.0.\nAssigning rider 14 to docking station F4 incurs access cost 88.0.\nAssigning rider 0 to docking station F5 incurs access cost 264.0.\nAssigning rider 1 to docking station F5 incurs access cost 279.0.\nAssigning rider 2 to docking station F5 incurs access cost 82.0.\nAssigning rider 3 to docking station F5 incurs access cost 260.0.\nAssigning rider 4 to docking station F5 incurs access cost 40.0.\nAssigning rider 5 to docking station F5 incurs access cost 118.0.\nAssigning rider 6 to docking station F5 incurs access cost 88.0.\nAssigning rider 7 to docking station F5 incurs access cost 189.0.\nAssigning rider 8 to docking station F5 incurs access cost 230.0.\nAssigning rider 9 to docking station F5 incurs access cost 299.0.\nAssigning rider 10 to docking station F5 incurs access cost 180.0.\nAssigning rider 11 to docking station F5 incurs access cost 224.0.\nAssigning rider 12 to docking station F5 incurs access cost 142.0.\nAssigning rider 13 to docking station F5 incurs access cost 244.0.\nAssigning rider 14 to docking station F5 incurs access cost 167.0.\nAssigning rider 0 to docking station F6 incurs access cost 204.0.\nAssigning rider 1 to docking station F6 incurs access cost 212.0.\nAssigning rider 2 to docking station F6 incurs access cost 147.0.\nAssigning rider 3 to docking station F6 incurs access cost 177.0.\nAssigning rider 4 to docking station F6 incurs access cost 92.0.\nAssigning rider 5 to docking station F6 incurs access cost 54.0.\nAssigning rider 6 to docking station F6 incurs access cost 44.0.\nAssigning rider 7 to docking station F6 incurs access cost 86.0.\nAssigning rider 8 to docking station F6 incurs access cost 126.0.\nAssigning rider 9 to docking station F6 incurs access cost 215.0.\nAssigning rider 10 to docking station F6 incurs access cost 161.0.\nAssigning rider 11 to docking station F6 incurs access cost 131.0.\nAssigning rider 12 to docking station F6 incurs access cost 45.0.\nAssigning rider 13 to docking station F6 incurs access cost 220.0.\nAssigning rider 14 to docking station F6 incurs access cost 113.0.\nAssigning rider 0 to docking station F7 incurs access cost 107.0.\nAssigning rider 1 to docking station F7 incurs access cost 108.0.\nAssigning rider 2 to docking station F7 incurs access cost 260.0.\nAssigning rider 3 to docking station F7 incurs access cost 211.0.\nAssigning rider 4 to docking station F7 incurs access cost 173.0.\nAssigning rider 5 to docking station F7 incurs access cost 85.0.\nAssigning rider 6 to docking station F7 incurs access cost 157.0.\nAssigning rider 7 to docking station F7 incurs access cost 64.0.\nAssigning rider 8 to docking station F7 incurs access cost 77.0.\nAssigning rider 9 to docking station F7 incurs access cost 101.0.\nAssigning rider 10 to docking station F7 incurs access cost 130.0.\nAssigning rider 11 to docking station F7 incurs access cost 25.0.\nAssigning rider 12 to docking station F7 incurs access cost 116.0.\nAssigning rider 13 to docking station F7 incurs access cost 162.0.\nAssigning rider 14 to docking station F7 incurs access cost 68.0.\nThe planners will prefer the assignment with the lowest combined station activation and riders' access costs.\n\nAlso, when you reply with the plan, please stick to this simple JSON layout so it's easy to parse:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThis just sketches the shape we expect—nothing more. In plain terms: \"selected\" is the list of docking stations you decide to turn on, and \"assignments\" gives, for each rider (in the same order as the input), the identifier of the open station they're assigned to. Keep it casual and concise.\n\nPlease make sure to use the exact identifiers from the instance input — do not rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”\n- single capital letters like “A” or “B”\n- or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 432.0, 114.0, 121.0, 312.0, 103.0, 336.0, 472.0 ], "capacities": [ 466.0, 307.0, 311.0, 406.0, 302.0, 418.0, 486.0 ], "connection_costs": [ [ 100.0, 117.0, 241.0, 277.0, 126.0, 70.0, 163.0, 134.0, 161.0, 151.0, 45.0, 112.0, 154.0, 97.0, 20.0 ], [ 193.0, 204.0, 146.0, 211.0, 63.0, 37.0, 63.0, 108.0, 149.0, 216.0, 134.0, 139.0, 79.0, 196.0, 96.0 ], [ 131.0, 152.0, 286.0, 365.0, 165.0, 150.0, 234.0, 224.0, 249.0, 207.0, 45.0, 195.0, 238.0, 54.0, 109.0 ], [ 86.0, 108.0, 301.0, 346.0, 180.0, 141.0, 233.0, 200.0, 220.0, 163.0, 40.0, 162.0, 226.0, 25.0, 88.0 ], [ 264.0, 279.0, 82.0, 260.0, 40.0, 118.0, 88.0, 189.0, 230.0, 299.0, 180.0, 224.0, 142.0, 244.0, 167.0 ], [ 204.0, 212.0, 147.0, 177.0, 92.0, 54.0, 44.0, 86.0, 126.0, 215.0, 161.0, 131.0, 45.0, 220.0, 113.0 ], [ 107.0, 108.0, 260.0, 211.0, 173.0, 85.0, 157.0, 64.0, 77.0, 101.0, 130.0, 25.0, 116.0, 162.0, 68.0 ] ], "demands": [ 20.0, 20.0, 10.0, 20.0, 19.0, 16.0, 9.0, 21.0, 23.0, 5.0, 8.0, 19.0, 26.0, 35.0, 15.0 ], "objective": 1915.0 }, "solution": { "open_facilities": [ 1, 2 ], "assignments": [ 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1 ] }, "obj": 1915.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 15, "facilities": [ { "id": "F1", "opening_cost": 432.0, "capacity": 466.0 }, { "id": "F2", "opening_cost": 114.0, "capacity": 307.0 }, { "id": "F3", "opening_cost": 121.0, "capacity": 311.0 }, { "id": "F4", "opening_cost": 312.0, "capacity": 406.0 }, { "id": "F5", "opening_cost": 103.0, "capacity": 302.0 }, { "id": "F6", "opening_cost": 336.0, "capacity": 418.0 }, { "id": "F7", "opening_cost": 472.0, "capacity": 486.0 } ], "customers": [ { "id": 0, "demand": 20.0 }, { "id": 1, "demand": 20.0 }, { "id": 2, "demand": 10.0 }, { "id": 3, "demand": 20.0 }, { "id": 4, "demand": 19.0 }, { "id": 5, "demand": 16.0 }, { "id": 6, "demand": 9.0 }, { "id": 7, "demand": 21.0 }, { "id": 8, "demand": 23.0 }, { "id": 9, "demand": 5.0 }, { "id": 10, "demand": 8.0 }, { "id": 11, "demand": 19.0 }, { "id": 12, "demand": 26.0 }, { "id": 13, "demand": 35.0 }, { "id": 14, "demand": 15.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 100.0 }, { "facility": "F1", "customer": 1, "cost": 117.0 }, { "facility": "F1", "customer": 2, "cost": 241.0 }, { "facility": "F1", "customer": 3, "cost": 277.0 }, { "facility": "F1", "customer": 4, "cost": 126.0 }, { "facility": "F1", "customer": 5, "cost": 70.0 }, { "facility": "F1", "customer": 6, "cost": 163.0 }, { "facility": "F1", "customer": 7, "cost": 134.0 }, { "facility": "F1", "customer": 8, "cost": 161.0 }, { "facility": "F1", "customer": 9, "cost": 151.0 }, { "facility": "F1", "customer": 10, "cost": 45.0 }, { "facility": "F1", "customer": 11, "cost": 112.0 }, { "facility": "F1", "customer": 12, "cost": 154.0 }, { "facility": "F1", "customer": 13, "cost": 97.0 }, { "facility": "F1", "customer": 14, "cost": 20.0 }, { "facility": "F2", "customer": 0, "cost": 193.0 }, { "facility": "F2", "customer": 1, "cost": 204.0 }, { "facility": "F2", "customer": 2, "cost": 146.0 }, { "facility": "F2", "customer": 3, "cost": 211.0 }, { "facility": "F2", "customer": 4, "cost": 63.0 }, { "facility": "F2", "customer": 5, "cost": 37.0 }, { "facility": "F2", "customer": 6, "cost": 63.0 }, { "facility": "F2", "customer": 7, "cost": 108.0 }, { "facility": "F2", "customer": 8, "cost": 149.0 }, { "facility": "F2", "customer": 9, "cost": 216.0 }, { "facility": "F2", "customer": 10, "cost": 134.0 }, { "facility": "F2", "customer": 11, "cost": 139.0 }, { "facility": "F2", "customer": 12, "cost": 79.0 }, { "facility": "F2", "customer": 13, "cost": 196.0 }, { "facility": "F2", "customer": 14, "cost": 96.0 }, { "facility": "F3", "customer": 0, "cost": 131.0 }, { "facility": "F3", "customer": 1, "cost": 152.0 }, { "facility": "F3", "customer": 2, "cost": 286.0 }, { "facility": "F3", "customer": 3, "cost": 365.0 }, { "facility": "F3", "customer": 4, "cost": 165.0 }, { "facility": "F3", "customer": 5, "cost": 150.0 }, { "facility": "F3", "customer": 6, "cost": 234.0 }, { "facility": "F3", "customer": 7, "cost": 224.0 }, { "facility": "F3", "customer": 8, "cost": 249.0 }, { "facility": "F3", "customer": 9, "cost": 207.0 }, { "facility": "F3", "customer": 10, "cost": 45.0 }, { "facility": "F3", "customer": 11, "cost": 195.0 }, { "facility": "F3", "customer": 12, "cost": 238.0 }, { "facility": "F3", "customer": 13, "cost": 54.0 }, { "facility": "F3", "customer": 14, "cost": 109.0 }, { "facility": "F4", "customer": 0, "cost": 86.0 }, { "facility": "F4", "customer": 1, "cost": 108.0 }, { "facility": "F4", "customer": 2, "cost": 301.0 }, { "facility": "F4", "customer": 3, "cost": 346.0 }, { "facility": "F4", "customer": 4, "cost": 180.0 }, { "facility": "F4", "customer": 5, "cost": 141.0 }, { "facility": "F4", "customer": 6, "cost": 233.0 }, { "facility": "F4", "customer": 7, "cost": 200.0 }, { "facility": "F4", "customer": 8, "cost": 220.0 }, { "facility": "F4", "customer": 9, "cost": 163.0 }, { "facility": "F4", "customer": 10, "cost": 40.0 }, { "facility": "F4", "customer": 11, "cost": 162.0 }, { "facility": "F4", "customer": 12, "cost": 226.0 }, { "facility": "F4", "customer": 13, "cost": 25.0 }, { "facility": "F4", "customer": 14, "cost": 88.0 }, { "facility": "F5", "customer": 0, "cost": 264.0 }, { "facility": "F5", "customer": 1, "cost": 279.0 }, { "facility": "F5", "customer": 2, "cost": 82.0 }, { "facility": "F5", "customer": 3, "cost": 260.0 }, { "facility": "F5", "customer": 4, "cost": 40.0 }, { "facility": "F5", "customer": 5, "cost": 118.0 }, { "facility": "F5", "customer": 6, "cost": 88.0 }, { "facility": "F5", "customer": 7, "cost": 189.0 }, { "facility": "F5", "customer": 8, "cost": 230.0 }, { "facility": "F5", "customer": 9, "cost": 299.0 }, { "facility": "F5", "customer": 10, "cost": 180.0 }, { "facility": "F5", "customer": 11, "cost": 224.0 }, { "facility": "F5", "customer": 12, "cost": 142.0 }, { "facility": "F5", "customer": 13, "cost": 244.0 }, { "facility": "F5", "customer": 14, "cost": 167.0 }, { "facility": "F6", "customer": 0, "cost": 204.0 }, { "facility": "F6", "customer": 1, "cost": 212.0 }, { "facility": "F6", "customer": 2, "cost": 147.0 }, { "facility": "F6", "customer": 3, "cost": 177.0 }, { "facility": "F6", "customer": 4, "cost": 92.0 }, { "facility": "F6", "customer": 5, "cost": 54.0 }, { "facility": "F6", "customer": 6, "cost": 44.0 }, { "facility": "F6", "customer": 7, "cost": 86.0 }, { "facility": "F6", "customer": 8, "cost": 126.0 }, { "facility": "F6", "customer": 9, "cost": 215.0 }, { "facility": "F6", "customer": 10, "cost": 161.0 }, { "facility": "F6", "customer": 11, "cost": 131.0 }, { "facility": "F6", "customer": 12, "cost": 45.0 }, { "facility": "F6", "customer": 13, "cost": 220.0 }, { "facility": "F6", "customer": 14, "cost": 113.0 }, { "facility": "F7", "customer": 0, "cost": 107.0 }, { "facility": "F7", "customer": 1, "cost": 108.0 }, { "facility": "F7", "customer": 2, "cost": 260.0 }, { "facility": "F7", "customer": 3, "cost": 211.0 }, { "facility": "F7", "customer": 4, "cost": 173.0 }, { "facility": "F7", "customer": 5, "cost": 85.0 }, { "facility": "F7", "customer": 6, "cost": 157.0 }, { "facility": "F7", "customer": 7, "cost": 64.0 }, { "facility": "F7", "customer": 8, "cost": 77.0 }, { "facility": "F7", "customer": 9, "cost": 101.0 }, { "facility": "F7", "customer": 10, "cost": 130.0 }, { "facility": "F7", "customer": 11, "cost": 25.0 }, { "facility": "F7", "customer": 12, "cost": 116.0 }, { "facility": "F7", "customer": 13, "cost": 162.0 }, { "facility": "F7", "customer": 14, "cost": 68.0 } ], "objective": 1915.0 }, "solution_variant": { "selected": [ "F2", "F3" ], "assignments": [ "F3", "F3", "F2", "F2", "F2", "F2", "F2", "F2", "F2", "F3", "F3", "F2", "F2", "F3", "F2" ] }, "context_index": 41, "input_format": "nl", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Out in the district the challenge is picking which vending spots to fill and then assigning every customer zone to just one of the stocked spots. Filling a spot comes with a stocking fee, and each zone picks up an inconvenience cost depending on how far its assigned spot is; to judge any arrangement, total up all the stocking fees plus all the inconvenience costs — that combined total determines how good the choice is. It’s also essential that no stocked spot serves beyond its capacity and that every zone is linked to one and only one stocked spot. The instance details follow below.\n\nThere are 7 candidate vending spots and 17 customer zones described below.\nVending site F1 costs 300.0 to stock and can serve up to 300.0 demand.\nVending site F2 costs 300.0 to stock and can serve up to 300.0 demand.\nVending site F3 costs 300.0 to stock and can serve up to 300.0 demand.\nVending site F4 costs 300.0 to stock and can serve up to 300.0 demand.\nVending site F5 costs 300.0 to stock and can serve up to 300.0 demand.\nVending site F6 costs 300.0 to stock and can serve up to 300.0 demand.\nVending site F7 costs 300.0 to stock and can serve up to 300.0 demand.\nCustomer zone 0 has demand 25.0.\nCustomer zone 1 has demand 28.0.\nCustomer zone 2 has demand 17.0.\nCustomer zone 3 has demand 23.0.\nCustomer zone 4 has demand 18.0.\nCustomer zone 5 has demand 17.0.\nCustomer zone 6 has demand 29.0.\nCustomer zone 7 has demand 27.0.\nCustomer zone 8 has demand 13.0.\nCustomer zone 9 has demand 23.0.\nCustomer zone 10 has demand 23.0.\nCustomer zone 11 has demand 17.0.\nCustomer zone 12 has demand 16.0.\nCustomer zone 13 has demand 27.0.\nCustomer zone 14 has demand 17.0.\nCustomer zone 15 has demand 22.0.\nCustomer zone 16 has demand 27.0.\nIf customer zone 0 is linked to vending site F1, the inconvenience cost is 680.0.\nIf customer zone 1 is linked to vending site F1, the inconvenience cost is 75.0.\nIf customer zone 2 is linked to vending site F1, the inconvenience cost is 676.0.\nIf customer zone 3 is linked to vending site F1, the inconvenience cost is 1201.0.\nIf customer zone 4 is linked to vending site F1, the inconvenience cost is 36.0.\nIf customer zone 5 is linked to vending site F1, the inconvenience cost is 1105.0.\nIf customer zone 6 is linked to vending site F1, the inconvenience cost is 61.0.\nIf customer zone 7 is linked to vending site F1, the inconvenience cost is 735.0.\nIf customer zone 8 is linked to vending site F1, the inconvenience cost is 60.0.\nIf customer zone 9 is linked to vending site F1, the inconvenience cost is 156.0.\nIf customer zone 10 is linked to vending site F1, the inconvenience cost is 414.0.\nIf customer zone 11 is linked to vending site F1, the inconvenience cost is 749.0.\nIf customer zone 12 is linked to vending site F1, the inconvenience cost is 328.0.\nIf customer zone 13 is linked to vending site F1, the inconvenience cost is 1193.0.\nIf customer zone 14 is linked to vending site F1, the inconvenience cost is 889.0.\nIf customer zone 15 is linked to vending site F1, the inconvenience cost is 822.0.\nIf customer zone 16 is linked to vending site F1, the inconvenience cost is 862.0.\nIf customer zone 0 is linked to vending site F2, the inconvenience cost is 110.0.\nIf customer zone 1 is linked to vending site F2, the inconvenience cost is 78.0.\nIf customer zone 2 is linked to vending site F2, the inconvenience cost is 301.0.\nIf customer zone 3 is linked to vending site F2, the inconvenience cost is 290.0.\nIf customer zone 4 is linked to vending site F2, the inconvenience cost is 44.0.\nIf customer zone 5 is linked to vending site F2, the inconvenience cost is 590.0.\nIf customer zone 6 is linked to vending site F2, the inconvenience cost is 58.0.\nIf customer zone 7 is linked to vending site F2, the inconvenience cost is 551.0.\nIf customer zone 8 is linked to vending site F2, the inconvenience cost is 46.0.\nIf customer zone 9 is linked to vending site F2, the inconvenience cost is 100.0.\nIf customer zone 10 is linked to vending site F2, the inconvenience cost is 200.0.\nIf customer zone 11 is linked to vending site F2, the inconvenience cost is 102.0.\nIf customer zone 12 is linked to vending site F2, the inconvenience cost is 112.0.\nIf customer zone 13 is linked to vending site F2, the inconvenience cost is 447.0.\nIf customer zone 14 is linked to vending site F2, the inconvenience cost is 419.0.\nIf customer zone 15 is linked to vending site F2, the inconvenience cost is 606.0.\nIf customer zone 16 is linked to vending site F2, the inconvenience cost is 486.0.\nIf customer zone 0 is linked to vending site F3, the inconvenience cost is 686.0.\nIf customer zone 1 is linked to vending site F3, the inconvenience cost is 140.0.\nIf customer zone 2 is linked to vending site F3, the inconvenience cost is 813.0.\nIf customer zone 3 is linked to vending site F3, the inconvenience cost is 867.0.\nIf customer zone 4 is linked to vending site F3, the inconvenience cost is 208.0.\nIf customer zone 5 is linked to vending site F3, the inconvenience cost is 1207.0.\nIf customer zone 6 is linked to vending site F3, the inconvenience cost is 129.0.\nIf customer zone 7 is linked to vending site F3, the inconvenience cost is 176.0.\nIf customer zone 8 is linked to vending site F3, the inconvenience cost is 125.0.\nIf customer zone 9 is linked to vending site F3, the inconvenience cost is 293.0.\nIf customer zone 10 is linked to vending site F3, the inconvenience cost is 584.0.\nIf customer zone 11 is linked to vending site F3, the inconvenience cost is 485.0.\nIf customer zone 12 is linked to vending site F3, the inconvenience cost is 491.0.\nIf customer zone 13 is linked to vending site F3, the inconvenience cost is 691.0.\nIf customer zone 14 is linked to vending site F3, the inconvenience cost is 214.0.\nIf customer zone 15 is linked to vending site F3, the inconvenience cost is 205.0.\nIf customer zone 16 is linked to vending site F3, the inconvenience cost is 54.0.\nIf customer zone 0 is linked to vending site F4, the inconvenience cost is 956.0.\nIf customer zone 1 is linked to vending site F4, the inconvenience cost is 262.0.\nIf customer zone 2 is linked to vending site F4, the inconvenience cost is 1022.0.\nIf customer zone 3 is linked to vending site F4, the inconvenience cost is 1232.0.\nIf customer zone 4 is linked to vending site F4, the inconvenience cost is 382.0.\nIf customer zone 5 is linked to vending site F4, the inconvenience cost is 1444.0.\nIf customer zone 6 is linked to vending site F4, the inconvenience cost is 186.0.\nIf customer zone 7 is linked to vending site F4, the inconvenience cost is 116.0.\nIf customer zone 8 is linked to vending site F4, the inconvenience cost is 162.0.\nIf customer zone 9 is linked to vending site F4, the inconvenience cost is 383.0.\nIf customer zone 10 is linked to vending site F4, the inconvenience cost is 749.0.\nIf customer zone 11 is linked to vending site F4, the inconvenience cost is 813.0.\nIf customer zone 12 is linked to vending site F4, the inconvenience cost is 671.0.\nIf customer zone 13 is linked to vending site F4, the inconvenience cost is 1078.0.\nIf customer zone 14 is linked to vending site F4, the inconvenience cost is 603.0.\nIf customer zone 15 is linked to vending site F4, the inconvenience cost is 175.0.\nIf customer zone 16 is linked to vending site F4, the inconvenience cost is 450.0.\nIf customer zone 0 is linked to vending site F5, the inconvenience cost is 106.0.\nIf customer zone 1 is linked to vending site F5, the inconvenience cost is 66.0.\nIf customer zone 2 is linked to vending site F5, the inconvenience cost is 280.0.\nIf customer zone 3 is linked to vending site F5, the inconvenience cost is 53.0.\nIf customer zone 4 is linked to vending site F5, the inconvenience cost is 37.0.\nIf customer zone 5 is linked to vending site F5, the inconvenience cost is 518.0.\nIf customer zone 6 is linked to vending site F5, the inconvenience cost is 59.0.\nIf customer zone 7 is linked to vending site F5, the inconvenience cost is 445.0.\nIf customer zone 8 is linked to vending site F5, the inconvenience cost is 50.0.\nIf customer zone 9 is linked to vending site F5, the inconvenience cost is 107.0.\nIf customer zone 10 is linked to vending site F5, the inconvenience cost is 200.0.\nIf customer zone 11 is linked to vending site F5, the inconvenience cost is 47.0.\nIf customer zone 12 is linked to vending site F5, the inconvenience cost is 116.0.\nIf customer zone 13 is linked to vending site F5, the inconvenience cost is 189.0.\nIf customer zone 14 is linked to vending site F5, the inconvenience cost is 256.0.\nIf customer zone 15 is linked to vending site F5, the inconvenience cost is 485.0.\nIf customer zone 16 is linked to vending site F5, the inconvenience cost is 337.0.\nIf customer zone 0 is linked to vending site F6, the inconvenience cost is 1270.0.\nIf customer zone 1 is linked to vending site F6, the inconvenience cost is 443.0.\nIf customer zone 2 is linked to vending site F6, the inconvenience cost is 1203.0.\nIf customer zone 3 is linked to vending site F6, the inconvenience cost is 1732.0.\nIf customer zone 4 is linked to vending site F6, the inconvenience cost is 626.0.\nIf customer zone 5 is linked to vending site F6, the inconvenience cost is 1650.0.\nIf customer zone 6 is linked to vending site F6, the inconvenience cost is 199.0.\nIf customer zone 7 is linked to vending site F6, the inconvenience cost is 764.0.\nIf customer zone 8 is linked to vending site F6, the inconvenience cost is 158.0.\nIf customer zone 9 is linked to vending site F6, the inconvenience cost is 421.0.\nIf customer zone 10 is linked to vending site F6, the inconvenience cost is 877.0.\nIf customer zone 11 is linked to vending site F6, the inconvenience cost is 1274.0.\nIf customer zone 12 is linked to vending site F6, the inconvenience cost is 837.0.\nIf customer zone 13 is linked to vending site F6, the inconvenience cost is 1654.0.\nIf customer zone 14 is linked to vending site F6, the inconvenience cost is 1234.0.\nIf customer zone 15 is linked to vending site F6, the inconvenience cost is 873.0.\nIf customer zone 16 is linked to vending site F6, the inconvenience cost is 1125.0.\nIf customer zone 0 is linked to vending site F7, the inconvenience cost is 339.0.\nIf customer zone 1 is linked to vending site F7, the inconvenience cost is 320.0.\nIf customer zone 2 is linked to vending site F7, the inconvenience cost is 34.0.\nIf customer zone 3 is linked to vending site F7, the inconvenience cost is 979.0.\nIf customer zone 4 is linked to vending site F7, the inconvenience cost is 305.0.\nIf customer zone 5 is linked to vending site F7, the inconvenience cost is 167.0.\nIf customer zone 6 is linked to vending site F7, the inconvenience cost is 119.0.\nIf customer zone 7 is linked to vending site F7, the inconvenience cost is 998.0.\nIf customer zone 8 is linked to vending site F7, the inconvenience cost is 27.0.\nIf customer zone 9 is linked to vending site F7, the inconvenience cost is 48.0.\nIf customer zone 10 is linked to vending site F7, the inconvenience cost is 46.0.\nIf customer zone 11 is linked to vending site F7, the inconvenience cost is 697.0.\nIf customer zone 12 is linked to vending site F7, the inconvenience cost is 68.0.\nIf customer zone 13 is linked to vending site F7, the inconvenience cost is 1131.0.\nIf customer zone 14 is linked to vending site F7, the inconvenience cost is 1017.0.\nIf customer zone 15 is linked to vending site F7, the inconvenience cost is 1079.0.\nIf customer zone 16 is linked to vending site F7, the inconvenience cost is 1047.0.\nThese entries let one total stocking fees and inconvenience costs to judge arrangements while ensuring capacities are respected and each zone is assigned to exactly one stocked spot.\n\nAlso, when you send your pick, please follow this little JSON layout so it's easy to read and check:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of vending spots you decide to stock, and \"assignments\" as a parallel list saying which stocked spot each customer zone uses (one entry per zone). This is just a sketch of the shape I need — not the final answer itself.\n\nPlease use the exact identifiers from the instance input when you fill this in; do not rename them or invent new labels.\n- \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "connection_costs": [ [ 680.0, 75.0, 676.0, 1201.0, 36.0, 1105.0, 61.0, 735.0, 60.0, 156.0, 414.0, 749.0, 328.0, 1193.0, 889.0, 822.0, 862.0 ], [ 110.0, 78.0, 301.0, 290.0, 44.0, 590.0, 58.0, 551.0, 46.0, 100.0, 200.0, 102.0, 112.0, 447.0, 419.0, 606.0, 486.0 ], [ 686.0, 140.0, 813.0, 867.0, 208.0, 1207.0, 129.0, 176.0, 125.0, 293.0, 584.0, 485.0, 491.0, 691.0, 214.0, 205.0, 54.0 ], [ 956.0, 262.0, 1022.0, 1232.0, 382.0, 1444.0, 186.0, 116.0, 162.0, 383.0, 749.0, 813.0, 671.0, 1078.0, 603.0, 175.0, 450.0 ], [ 106.0, 66.0, 280.0, 53.0, 37.0, 518.0, 59.0, 445.0, 50.0, 107.0, 200.0, 47.0, 116.0, 189.0, 256.0, 485.0, 337.0 ], [ 1270.0, 443.0, 1203.0, 1732.0, 626.0, 1650.0, 199.0, 764.0, 158.0, 421.0, 877.0, 1274.0, 837.0, 1654.0, 1234.0, 873.0, 1125.0 ], [ 339.0, 320.0, 34.0, 979.0, 305.0, 167.0, 119.0, 998.0, 27.0, 48.0, 46.0, 697.0, 68.0, 1131.0, 1017.0, 1079.0, 1047.0 ] ], "demands": [ 25.0, 28.0, 17.0, 23.0, 18.0, 17.0, 29.0, 27.0, 13.0, 23.0, 23.0, 17.0, 16.0, 27.0, 17.0, 22.0, 27.0 ], "objective": 2496.0 }, "solution": { "open_facilities": [ 2, 4, 6 ], "assignments": [ 4, 4, 6, 4, 4, 6, 4, 2, 6, 6, 6, 4, 6, 4, 2, 2, 2 ] }, "obj": 2496.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 17, "facilities": [ { "id": "F1", "opening_cost": 300.0, "capacity": 300.0 }, { "id": "F2", "opening_cost": 300.0, "capacity": 300.0 }, { "id": "F3", "opening_cost": 300.0, "capacity": 300.0 }, { "id": "F4", "opening_cost": 300.0, "capacity": 300.0 }, { "id": "F5", "opening_cost": 300.0, "capacity": 300.0 }, { "id": "F6", "opening_cost": 300.0, "capacity": 300.0 }, { "id": "F7", "opening_cost": 300.0, "capacity": 300.0 } ], "customers": [ { "id": 0, "demand": 25.0 }, { "id": 1, "demand": 28.0 }, { "id": 2, "demand": 17.0 }, { "id": 3, "demand": 23.0 }, { "id": 4, "demand": 18.0 }, { "id": 5, "demand": 17.0 }, { "id": 6, "demand": 29.0 }, { "id": 7, "demand": 27.0 }, { "id": 8, "demand": 13.0 }, { "id": 9, "demand": 23.0 }, { "id": 10, "demand": 23.0 }, { "id": 11, "demand": 17.0 }, { "id": 12, "demand": 16.0 }, { "id": 13, "demand": 27.0 }, { "id": 14, "demand": 17.0 }, { "id": 15, "demand": 22.0 }, { "id": 16, "demand": 27.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 680.0 }, { "facility": "F1", "customer": 1, "cost": 75.0 }, { "facility": "F1", "customer": 2, "cost": 676.0 }, { "facility": "F1", "customer": 3, "cost": 1201.0 }, { "facility": "F1", "customer": 4, "cost": 36.0 }, { "facility": "F1", "customer": 5, "cost": 1105.0 }, { "facility": "F1", "customer": 6, "cost": 61.0 }, { "facility": "F1", "customer": 7, "cost": 735.0 }, { "facility": "F1", "customer": 8, "cost": 60.0 }, { "facility": "F1", "customer": 9, "cost": 156.0 }, { "facility": "F1", "customer": 10, "cost": 414.0 }, { "facility": "F1", "customer": 11, "cost": 749.0 }, { "facility": "F1", "customer": 12, "cost": 328.0 }, { "facility": "F1", "customer": 13, "cost": 1193.0 }, { "facility": "F1", "customer": 14, "cost": 889.0 }, { "facility": "F1", "customer": 15, "cost": 822.0 }, { "facility": "F1", "customer": 16, "cost": 862.0 }, { "facility": "F2", "customer": 0, "cost": 110.0 }, { "facility": "F2", "customer": 1, "cost": 78.0 }, { "facility": "F2", "customer": 2, "cost": 301.0 }, { "facility": "F2", "customer": 3, "cost": 290.0 }, { "facility": "F2", "customer": 4, "cost": 44.0 }, { "facility": "F2", "customer": 5, "cost": 590.0 }, { "facility": "F2", "customer": 6, "cost": 58.0 }, { "facility": "F2", "customer": 7, "cost": 551.0 }, { "facility": "F2", "customer": 8, "cost": 46.0 }, { "facility": "F2", "customer": 9, "cost": 100.0 }, { "facility": "F2", "customer": 10, "cost": 200.0 }, { "facility": "F2", "customer": 11, "cost": 102.0 }, { "facility": "F2", "customer": 12, "cost": 112.0 }, { "facility": "F2", "customer": 13, "cost": 447.0 }, { "facility": "F2", "customer": 14, "cost": 419.0 }, { "facility": "F2", "customer": 15, "cost": 606.0 }, { "facility": "F2", "customer": 16, "cost": 486.0 }, { "facility": "F3", "customer": 0, "cost": 686.0 }, { "facility": "F3", "customer": 1, "cost": 140.0 }, { "facility": "F3", "customer": 2, "cost": 813.0 }, { "facility": "F3", "customer": 3, "cost": 867.0 }, { "facility": "F3", "customer": 4, "cost": 208.0 }, { "facility": "F3", "customer": 5, "cost": 1207.0 }, { "facility": "F3", "customer": 6, "cost": 129.0 }, { "facility": "F3", "customer": 7, "cost": 176.0 }, { "facility": "F3", "customer": 8, "cost": 125.0 }, { "facility": "F3", "customer": 9, "cost": 293.0 }, { "facility": "F3", "customer": 10, "cost": 584.0 }, { "facility": "F3", "customer": 11, "cost": 485.0 }, { "facility": "F3", "customer": 12, "cost": 491.0 }, { "facility": "F3", "customer": 13, "cost": 691.0 }, { "facility": "F3", "customer": 14, "cost": 214.0 }, { "facility": "F3", "customer": 15, "cost": 205.0 }, { "facility": "F3", "customer": 16, "cost": 54.0 }, { "facility": "F4", "customer": 0, "cost": 956.0 }, { "facility": "F4", "customer": 1, "cost": 262.0 }, { "facility": "F4", "customer": 2, "cost": 1022.0 }, { "facility": "F4", "customer": 3, "cost": 1232.0 }, { "facility": "F4", "customer": 4, "cost": 382.0 }, { "facility": "F4", "customer": 5, "cost": 1444.0 }, { "facility": "F4", "customer": 6, "cost": 186.0 }, { "facility": "F4", "customer": 7, "cost": 116.0 }, { "facility": "F4", "customer": 8, "cost": 162.0 }, { "facility": "F4", "customer": 9, "cost": 383.0 }, { "facility": "F4", "customer": 10, "cost": 749.0 }, { "facility": "F4", "customer": 11, "cost": 813.0 }, { "facility": "F4", "customer": 12, "cost": 671.0 }, { "facility": "F4", "customer": 13, "cost": 1078.0 }, { "facility": "F4", "customer": 14, "cost": 603.0 }, { "facility": "F4", "customer": 15, "cost": 175.0 }, { "facility": "F4", "customer": 16, "cost": 450.0 }, { "facility": "F5", "customer": 0, "cost": 106.0 }, { "facility": "F5", "customer": 1, "cost": 66.0 }, { "facility": "F5", "customer": 2, "cost": 280.0 }, { "facility": "F5", "customer": 3, "cost": 53.0 }, { "facility": "F5", "customer": 4, "cost": 37.0 }, { "facility": "F5", "customer": 5, "cost": 518.0 }, { "facility": "F5", "customer": 6, "cost": 59.0 }, { "facility": "F5", "customer": 7, "cost": 445.0 }, { "facility": "F5", "customer": 8, "cost": 50.0 }, { "facility": "F5", "customer": 9, "cost": 107.0 }, { "facility": "F5", "customer": 10, "cost": 200.0 }, { "facility": "F5", "customer": 11, "cost": 47.0 }, { "facility": "F5", "customer": 12, "cost": 116.0 }, { "facility": "F5", "customer": 13, "cost": 189.0 }, { "facility": "F5", "customer": 14, "cost": 256.0 }, { "facility": "F5", "customer": 15, "cost": 485.0 }, { "facility": "F5", "customer": 16, "cost": 337.0 }, { "facility": "F6", "customer": 0, "cost": 1270.0 }, { "facility": "F6", "customer": 1, "cost": 443.0 }, { "facility": "F6", "customer": 2, "cost": 1203.0 }, { "facility": "F6", "customer": 3, "cost": 1732.0 }, { "facility": "F6", "customer": 4, "cost": 626.0 }, { "facility": "F6", "customer": 5, "cost": 1650.0 }, { "facility": "F6", "customer": 6, "cost": 199.0 }, { "facility": "F6", "customer": 7, "cost": 764.0 }, { "facility": "F6", "customer": 8, "cost": 158.0 }, { "facility": "F6", "customer": 9, "cost": 421.0 }, { "facility": "F6", "customer": 10, "cost": 877.0 }, { "facility": "F6", "customer": 11, "cost": 1274.0 }, { "facility": "F6", "customer": 12, "cost": 837.0 }, { "facility": "F6", "customer": 13, "cost": 1654.0 }, { "facility": "F6", "customer": 14, "cost": 1234.0 }, { "facility": "F6", "customer": 15, "cost": 873.0 }, { "facility": "F6", "customer": 16, "cost": 1125.0 }, { "facility": "F7", "customer": 0, "cost": 339.0 }, { "facility": "F7", "customer": 1, "cost": 320.0 }, { "facility": "F7", "customer": 2, "cost": 34.0 }, { "facility": "F7", "customer": 3, "cost": 979.0 }, { "facility": "F7", "customer": 4, "cost": 305.0 }, { "facility": "F7", "customer": 5, "cost": 167.0 }, { "facility": "F7", "customer": 6, "cost": 119.0 }, { "facility": "F7", "customer": 7, "cost": 998.0 }, { "facility": "F7", "customer": 8, "cost": 27.0 }, { "facility": "F7", "customer": 9, "cost": 48.0 }, { "facility": "F7", "customer": 10, "cost": 46.0 }, { "facility": "F7", "customer": 11, "cost": 697.0 }, { "facility": "F7", "customer": 12, "cost": 68.0 }, { "facility": "F7", "customer": 13, "cost": 1131.0 }, { "facility": "F7", "customer": 14, "cost": 1017.0 }, { "facility": "F7", "customer": 15, "cost": 1079.0 }, { "facility": "F7", "customer": 16, "cost": 1047.0 } ], "objective": 2496.0 }, "solution_variant": { "selected": [ "F3", "F5", "F7" ], "assignments": [ "F5", "F5", "F7", "F5", "F5", "F7", "F5", "F3", "F7", "F7", "F7", "F5", "F7", "F5", "F3", "F3", "F3" ] }, "context_index": 42, "input_format": "nl", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Picture this: a map dotted with possible sorting hubs, each one you can turn on for a fee and each one only able to handle so many deliveries. Every address on the map needs to be sent to one running hub, and if a hub is farther away the trip costs more. The job is to decide which hubs to power up and which hub each address uses so the total spending — the sum of hub running costs and all the per-address routing costs — ends up minimal, and no hub is asked to do more than it can. The exact figures and setup are shown below.\n\n# num_hubs=8\n# num_addresses=18\n# HUB_ID_REFS\nhub_id_ref,hub_running_cost,hub_capacity\nF1,300.0,331.0\nF2,300.0,573.0\nF3,300.0,425.0\nF4,300.0,427.0\nF5,300.0,390.0\nF6,300.0,418.0\nF7,300.0,410.0\nF8,300.0,338.0\n# ADDRESS_ID_REFS\naddress_id_ref,address_demand\n1,23.0\n2,21.0\n3,20.0\n4,12.0\n5,20.0\n6,24.0\n7,19.0\n8,11.0\n9,27.0\n10,23.0\n11,18.0\n12,13.0\n13,19.0\n14,13.0\n15,23.0\n16,21.0\n17,11.0\n18,14.0\n# ROUTINGS\nhub_id_ref,address_id_ref,routing_cost\nF1,1,364.0\nF1,2,858.0\nF1,3,255.0\nF1,4,83.0\nF1,5,51.0\nF1,6,63.0\nF1,7,587.0\nF1,8,395.0\nF1,9,804.0\nF1,10,49.0\nF1,11,92.0\nF1,12,1023.0\nF1,13,145.0\nF1,14,371.0\nF1,15,791.0\nF1,16,374.0\nF1,17,303.0\nF1,18,61.0\nF2,1,547.0\nF2,2,1168.0\nF2,3,488.0\nF2,4,241.0\nF2,5,99.0\nF2,6,49.0\nF2,7,1037.0\nF2,8,1029.0\nF2,9,1064.0\nF2,10,48.0\nF2,11,686.0\nF2,12,1393.0\nF2,13,376.0\nF2,14,621.0\nF2,15,1288.0\nF2,16,1070.0\nF2,17,445.0\nF2,18,199.0\nF3,1,936.0\nF3,2,1642.0\nF3,3,1197.0\nF3,4,1110.0\nF3,5,1523.0\nF3,6,721.0\nF3,7,1935.0\nF3,8,2266.0\nF3,9,1432.0\nF3,10,639.0\nF3,11,2052.0\nF3,12,1953.0\nF3,13,1294.0\nF3,14,1213.0\nF3,15,2192.0\nF3,16,2386.0\nF3,17,705.0\nF3,18,1147.0\nF4,1,243.0\nF4,2,647.0\nF4,3,132.0\nF4,4,30.0\nF4,5,130.0\nF4,6,102.0\nF4,7,335.0\nF4,8,90.0\nF4,9,619.0\nF4,10,73.0\nF4,11,71.0\nF4,12,778.0\nF4,13,57.0\nF4,14,220.0\nF4,15,506.0\nF4,16,42.0\nF4,17,202.0\nF4,18,28.0\nF5,1,262.0\nF5,2,962.0\nF5,3,598.0\nF5,4,625.0\nF5,5,1134.0\nF5,6,509.0\nF5,7,1295.0\nF5,8,1703.0\nF5,9,764.0\nF5,10,421.0\nF5,11,1557.0\nF5,12,1271.0\nF5,13,763.0\nF5,14,559.0\nF5,15,1540.0\nF5,16,1846.0\nF5,17,22.0\nF5,18,688.0\nF6,1,142.0\nF6,2,554.0\nF6,3,48.0\nF6,4,62.0\nF6,5,443.0\nF6,6,210.0\nF6,7,354.0\nF6,8,681.0\nF6,9,509.0\nF6,10,154.0\nF6,11,625.0\nF6,12,729.0\nF6,13,67.0\nF6,14,109.0\nF6,15,618.0\nF6,16,839.0\nF6,17,113.0\nF6,18,104.0\nF7,1,480.0\nF7,2,1182.0\nF7,3,548.0\nF7,4,374.0\nF7,5,807.0\nF7,6,216.0\nF7,7,1277.0\nF7,8,1535.0\nF7,9,1032.0\nF7,10,145.0\nF7,11,1309.0\nF7,12,1456.0\nF7,13,571.0\nF7,14,642.0\nF7,15,1544.0\nF7,16,1646.0\nF7,17,347.0\nF7,18,404.0\nF8,1,504.0\nF8,2,1084.0\nF8,3,421.0\nF8,4,194.0\nF8,5,57.0\nF8,6,48.0\nF8,7,887.0\nF8,8,786.0\nF8,9,998.0\nF8,10,48.0\nF8,11,429.0\nF8,12,1286.0\nF8,13,301.0\nF8,14,552.0\nF8,15,1121.0\nF8,16,794.0\nF8,17,416.0\nF8,18,156.0\n\nOh, and one more practical thing — please give the final plan in this little JSON shape so it's easy to read and check:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nHere \"selected\" is where you list the hubs you decide to power up (use the exact hub IDs from the instance), and \"assignments\" is a list, in customer order, saying which opened hub each address will use. Think of it like filling out a short form: which hubs are on, and for each address which hub handles it. This is just the expected shape — not the final choices.\n\nPlease use the exact identifiers from the instance input — do not rename or invent labels. \nFor example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 331.0, 573.0, 425.0, 427.0, 390.0, 418.0, 410.0, 338.0 ], "connection_costs": [ [ 364.0, 858.0, 255.0, 83.0, 51.0, 63.0, 587.0, 395.0, 804.0, 49.0, 92.0, 1023.0, 145.0, 371.0, 791.0, 374.0, 303.0, 61.0 ], [ 547.0, 1168.0, 488.0, 241.0, 99.0, 49.0, 1037.0, 1029.0, 1064.0, 48.0, 686.0, 1393.0, 376.0, 621.0, 1288.0, 1070.0, 445.0, 199.0 ], [ 936.0, 1642.0, 1197.0, 1110.0, 1523.0, 721.0, 1935.0, 2266.0, 1432.0, 639.0, 2052.0, 1953.0, 1294.0, 1213.0, 2192.0, 2386.0, 705.0, 1147.0 ], [ 243.0, 647.0, 132.0, 30.0, 130.0, 102.0, 335.0, 90.0, 619.0, 73.0, 71.0, 778.0, 57.0, 220.0, 506.0, 42.0, 202.0, 28.0 ], [ 262.0, 962.0, 598.0, 625.0, 1134.0, 509.0, 1295.0, 1703.0, 764.0, 421.0, 1557.0, 1271.0, 763.0, 559.0, 1540.0, 1846.0, 22.0, 688.0 ], [ 142.0, 554.0, 48.0, 62.0, 443.0, 210.0, 354.0, 681.0, 509.0, 154.0, 625.0, 729.0, 67.0, 109.0, 618.0, 839.0, 113.0, 104.0 ], [ 480.0, 1182.0, 548.0, 374.0, 807.0, 216.0, 1277.0, 1535.0, 1032.0, 145.0, 1309.0, 1456.0, 571.0, 642.0, 1544.0, 1646.0, 347.0, 404.0 ], [ 504.0, 1084.0, 421.0, 194.0, 57.0, 48.0, 887.0, 786.0, 998.0, 48.0, 429.0, 1286.0, 301.0, 552.0, 1121.0, 794.0, 416.0, 156.0 ] ], "demands": [ 23.0, 21.0, 20.0, 12.0, 20.0, 24.0, 19.0, 11.0, 27.0, 23.0, 18.0, 13.0, 19.0, 13.0, 23.0, 21.0, 11.0, 14.0 ], "objective": 4268.0 }, "solution": { "open_facilities": [ 3, 5 ], "assignments": [ 5, 5, 5, 3, 3, 3, 3, 3, 5, 3, 3, 5, 3, 5, 3, 3, 5, 3 ] }, "obj": 4268.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 18, "facilities": [ { "id": "F1", "opening_cost": 300.0, "capacity": 331.0 }, { "id": "F2", "opening_cost": 300.0, "capacity": 573.0 }, { "id": "F3", "opening_cost": 300.0, "capacity": 425.0 }, { "id": "F4", "opening_cost": 300.0, "capacity": 427.0 }, { "id": "F5", "opening_cost": 300.0, "capacity": 390.0 }, { "id": "F6", "opening_cost": 300.0, "capacity": 418.0 }, { "id": "F7", "opening_cost": 300.0, "capacity": 410.0 }, { "id": "F8", "opening_cost": 300.0, "capacity": 338.0 } ], "customers": [ { "id": 1, "demand": 23.0 }, { "id": 2, "demand": 21.0 }, { "id": 3, "demand": 20.0 }, { "id": 4, "demand": 12.0 }, { "id": 5, "demand": 20.0 }, { "id": 6, "demand": 24.0 }, { "id": 7, "demand": 19.0 }, { "id": 8, "demand": 11.0 }, { "id": 9, "demand": 27.0 }, { "id": 10, "demand": 23.0 }, { "id": 11, "demand": 18.0 }, { "id": 12, "demand": 13.0 }, { "id": 13, "demand": 19.0 }, { "id": 14, "demand": 13.0 }, { "id": 15, "demand": 23.0 }, { "id": 16, "demand": 21.0 }, { "id": 17, "demand": 11.0 }, { "id": 18, "demand": 14.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 364.0 }, { "facility": "F1", "customer": 2, "cost": 858.0 }, { "facility": "F1", "customer": 3, "cost": 255.0 }, { "facility": "F1", "customer": 4, "cost": 83.0 }, { "facility": "F1", "customer": 5, "cost": 51.0 }, { "facility": "F1", "customer": 6, "cost": 63.0 }, { "facility": "F1", "customer": 7, "cost": 587.0 }, { "facility": "F1", "customer": 8, "cost": 395.0 }, { "facility": "F1", "customer": 9, "cost": 804.0 }, { "facility": "F1", "customer": 10, "cost": 49.0 }, { "facility": "F1", "customer": 11, "cost": 92.0 }, { "facility": "F1", "customer": 12, "cost": 1023.0 }, { "facility": "F1", "customer": 13, "cost": 145.0 }, { "facility": "F1", "customer": 14, "cost": 371.0 }, { "facility": "F1", "customer": 15, "cost": 791.0 }, { "facility": "F1", "customer": 16, "cost": 374.0 }, { "facility": "F1", "customer": 17, "cost": 303.0 }, { "facility": "F1", "customer": 18, "cost": 61.0 }, { "facility": "F2", "customer": 1, "cost": 547.0 }, { "facility": "F2", "customer": 2, "cost": 1168.0 }, { "facility": "F2", "customer": 3, "cost": 488.0 }, { "facility": "F2", "customer": 4, "cost": 241.0 }, { "facility": "F2", "customer": 5, "cost": 99.0 }, { "facility": "F2", "customer": 6, "cost": 49.0 }, { "facility": "F2", "customer": 7, "cost": 1037.0 }, { "facility": "F2", "customer": 8, "cost": 1029.0 }, { "facility": "F2", "customer": 9, "cost": 1064.0 }, { "facility": "F2", "customer": 10, "cost": 48.0 }, { "facility": "F2", "customer": 11, "cost": 686.0 }, { "facility": "F2", "customer": 12, "cost": 1393.0 }, { "facility": "F2", "customer": 13, "cost": 376.0 }, { "facility": "F2", "customer": 14, "cost": 621.0 }, { "facility": "F2", "customer": 15, "cost": 1288.0 }, { "facility": "F2", "customer": 16, "cost": 1070.0 }, { "facility": "F2", "customer": 17, "cost": 445.0 }, { "facility": "F2", "customer": 18, "cost": 199.0 }, { "facility": "F3", "customer": 1, "cost": 936.0 }, { "facility": "F3", "customer": 2, "cost": 1642.0 }, { "facility": "F3", "customer": 3, "cost": 1197.0 }, { "facility": "F3", "customer": 4, "cost": 1110.0 }, { "facility": "F3", "customer": 5, "cost": 1523.0 }, { "facility": "F3", "customer": 6, "cost": 721.0 }, { "facility": "F3", "customer": 7, "cost": 1935.0 }, { "facility": "F3", "customer": 8, "cost": 2266.0 }, { "facility": "F3", "customer": 9, "cost": 1432.0 }, { "facility": "F3", "customer": 10, "cost": 639.0 }, { "facility": "F3", "customer": 11, "cost": 2052.0 }, { "facility": "F3", "customer": 12, "cost": 1953.0 }, { "facility": "F3", "customer": 13, "cost": 1294.0 }, { "facility": "F3", "customer": 14, "cost": 1213.0 }, { "facility": "F3", "customer": 15, "cost": 2192.0 }, { "facility": "F3", "customer": 16, "cost": 2386.0 }, { "facility": "F3", "customer": 17, "cost": 705.0 }, { "facility": "F3", "customer": 18, "cost": 1147.0 }, { "facility": "F4", "customer": 1, "cost": 243.0 }, { "facility": "F4", "customer": 2, "cost": 647.0 }, { "facility": "F4", "customer": 3, "cost": 132.0 }, { "facility": "F4", "customer": 4, "cost": 30.0 }, { "facility": "F4", "customer": 5, "cost": 130.0 }, { "facility": "F4", "customer": 6, "cost": 102.0 }, { "facility": "F4", "customer": 7, "cost": 335.0 }, { "facility": "F4", "customer": 8, "cost": 90.0 }, { "facility": "F4", "customer": 9, "cost": 619.0 }, { "facility": "F4", "customer": 10, "cost": 73.0 }, { "facility": "F4", "customer": 11, "cost": 71.0 }, { "facility": "F4", "customer": 12, "cost": 778.0 }, { "facility": "F4", "customer": 13, "cost": 57.0 }, { "facility": "F4", "customer": 14, "cost": 220.0 }, { "facility": "F4", "customer": 15, "cost": 506.0 }, { "facility": "F4", "customer": 16, "cost": 42.0 }, { "facility": "F4", "customer": 17, "cost": 202.0 }, { "facility": "F4", "customer": 18, "cost": 28.0 }, { "facility": "F5", "customer": 1, "cost": 262.0 }, { "facility": "F5", "customer": 2, "cost": 962.0 }, { "facility": "F5", "customer": 3, "cost": 598.0 }, { "facility": "F5", "customer": 4, "cost": 625.0 }, { "facility": "F5", "customer": 5, "cost": 1134.0 }, { "facility": "F5", "customer": 6, "cost": 509.0 }, { "facility": "F5", "customer": 7, "cost": 1295.0 }, { "facility": "F5", "customer": 8, "cost": 1703.0 }, { "facility": "F5", "customer": 9, "cost": 764.0 }, { "facility": "F5", "customer": 10, "cost": 421.0 }, { "facility": "F5", "customer": 11, "cost": 1557.0 }, { "facility": "F5", "customer": 12, "cost": 1271.0 }, { "facility": "F5", "customer": 13, "cost": 763.0 }, { "facility": "F5", "customer": 14, "cost": 559.0 }, { "facility": "F5", "customer": 15, "cost": 1540.0 }, { "facility": "F5", "customer": 16, "cost": 1846.0 }, { "facility": "F5", "customer": 17, "cost": 22.0 }, { "facility": "F5", "customer": 18, "cost": 688.0 }, { "facility": "F6", "customer": 1, "cost": 142.0 }, { "facility": "F6", "customer": 2, "cost": 554.0 }, { "facility": "F6", "customer": 3, "cost": 48.0 }, { "facility": "F6", "customer": 4, "cost": 62.0 }, { "facility": "F6", "customer": 5, "cost": 443.0 }, { "facility": "F6", "customer": 6, "cost": 210.0 }, { "facility": "F6", "customer": 7, "cost": 354.0 }, { "facility": "F6", "customer": 8, "cost": 681.0 }, { "facility": "F6", "customer": 9, "cost": 509.0 }, { "facility": "F6", "customer": 10, "cost": 154.0 }, { "facility": "F6", "customer": 11, "cost": 625.0 }, { "facility": "F6", "customer": 12, "cost": 729.0 }, { "facility": "F6", "customer": 13, "cost": 67.0 }, { "facility": "F6", "customer": 14, "cost": 109.0 }, { "facility": "F6", "customer": 15, "cost": 618.0 }, { "facility": "F6", "customer": 16, "cost": 839.0 }, { "facility": "F6", "customer": 17, "cost": 113.0 }, { "facility": "F6", "customer": 18, "cost": 104.0 }, { "facility": "F7", "customer": 1, "cost": 480.0 }, { "facility": "F7", "customer": 2, "cost": 1182.0 }, { "facility": "F7", "customer": 3, "cost": 548.0 }, { "facility": "F7", "customer": 4, "cost": 374.0 }, { "facility": "F7", "customer": 5, "cost": 807.0 }, { "facility": "F7", "customer": 6, "cost": 216.0 }, { "facility": "F7", "customer": 7, "cost": 1277.0 }, { "facility": "F7", "customer": 8, "cost": 1535.0 }, { "facility": "F7", "customer": 9, "cost": 1032.0 }, { "facility": "F7", "customer": 10, "cost": 145.0 }, { "facility": "F7", "customer": 11, "cost": 1309.0 }, { "facility": "F7", "customer": 12, "cost": 1456.0 }, { "facility": "F7", "customer": 13, "cost": 571.0 }, { "facility": "F7", "customer": 14, "cost": 642.0 }, { "facility": "F7", "customer": 15, "cost": 1544.0 }, { "facility": "F7", "customer": 16, "cost": 1646.0 }, { "facility": "F7", "customer": 17, "cost": 347.0 }, { "facility": "F7", "customer": 18, "cost": 404.0 }, { "facility": "F8", "customer": 1, "cost": 504.0 }, { "facility": "F8", "customer": 2, "cost": 1084.0 }, { "facility": "F8", "customer": 3, "cost": 421.0 }, { "facility": "F8", "customer": 4, "cost": 194.0 }, { "facility": "F8", "customer": 5, "cost": 57.0 }, { "facility": "F8", "customer": 6, "cost": 48.0 }, { "facility": "F8", "customer": 7, "cost": 887.0 }, { "facility": "F8", "customer": 8, "cost": 786.0 }, { "facility": "F8", "customer": 9, "cost": 998.0 }, { "facility": "F8", "customer": 10, "cost": 48.0 }, { "facility": "F8", "customer": 11, "cost": 429.0 }, { "facility": "F8", "customer": 12, "cost": 1286.0 }, { "facility": "F8", "customer": 13, "cost": 301.0 }, { "facility": "F8", "customer": 14, "cost": 552.0 }, { "facility": "F8", "customer": 15, "cost": 1121.0 }, { "facility": "F8", "customer": 16, "cost": 794.0 }, { "facility": "F8", "customer": 17, "cost": 416.0 }, { "facility": "F8", "customer": 18, "cost": 156.0 } ], "objective": 4268.0 }, "solution_variant": { "selected": [ "F4", "F6" ], "assignments": [ "F6", "F6", "F6", "F4", "F4", "F4", "F4", "F4", "F6", "F4", "F4", "F6", "F4", "F6", "F4", "F4", "F6", "F4" ] }, "context_index": 43, "input_format": "csv", "input_index_base": 1 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "There’s a small town council trying to set up shared garden plots: each plot has an entry fee and can only hold so many people, and each gardener has a different effort cost for working different plots. The decision is which plots to unlock and which single unlocked plot every gardener should be assigned to, while respecting each plot’s capacity limits and making sure everyone is assigned exactly once. The winning layout is the one with the lowest total bill — just add the fees for all unlocked plots plus the effort costs for every gardener’s assignment to get the final total. The specific numbers for fees, capacities, and effort are given below.\n\n{\n \"num_plots\": 8,\n \"num_gardeners\": 20,\n \"plots\": [\n {\n \"plot_id\": \"F1\",\n \"unlock_fee\": 600.0,\n \"plot_capacity\": 300.0\n },\n {\n \"plot_id\": \"F2\",\n \"unlock_fee\": 600.0,\n \"plot_capacity\": 300.0\n },\n {\n \"plot_id\": \"F3\",\n \"unlock_fee\": 600.0,\n \"plot_capacity\": 300.0\n },\n {\n \"plot_id\": \"F4\",\n \"unlock_fee\": 600.0,\n \"plot_capacity\": 300.0\n },\n {\n \"plot_id\": \"F5\",\n \"unlock_fee\": 600.0,\n \"plot_capacity\": 300.0\n },\n {\n \"plot_id\": \"F6\",\n \"unlock_fee\": 600.0,\n \"plot_capacity\": 300.0\n },\n {\n \"plot_id\": \"F7\",\n \"unlock_fee\": 600.0,\n \"plot_capacity\": 300.0\n },\n {\n \"plot_id\": \"F8\",\n \"unlock_fee\": 600.0,\n \"plot_capacity\": 300.0\n }\n ],\n \"gardeners\": [\n {\n \"gardener_id\": 1,\n \"gardener_demand\": 25.0\n },\n {\n \"gardener_id\": 2,\n \"gardener_demand\": 28.0\n },\n {\n \"gardener_id\": 3,\n \"gardener_demand\": 15.0\n },\n {\n \"gardener_id\": 4,\n \"gardener_demand\": 23.0\n },\n {\n \"gardener_id\": 5,\n \"gardener_demand\": 28.0\n },\n {\n \"gardener_id\": 6,\n \"gardener_demand\": 20.0\n },\n {\n \"gardener_id\": 7,\n \"gardener_demand\": 18.0\n },\n {\n \"gardener_id\": 8,\n \"gardener_demand\": 29.0\n },\n {\n \"gardener_id\": 9,\n \"gardener_demand\": 14.0\n },\n {\n \"gardener_id\": 10,\n \"gardener_demand\": 18.0\n },\n {\n \"gardener_id\": 11,\n \"gardener_demand\": 26.0\n },\n {\n \"gardener_id\": 12,\n \"gardener_demand\": 10.0\n },\n {\n \"gardener_id\": 13,\n \"gardener_demand\": 18.0\n },\n {\n \"gardener_id\": 14,\n \"gardener_demand\": 23.0\n },\n {\n \"gardener_id\": 15,\n \"gardener_demand\": 18.0\n },\n {\n \"gardener_id\": 16,\n \"gardener_demand\": 23.0\n },\n {\n \"gardener_id\": 17,\n \"gardener_demand\": 27.0\n },\n {\n \"gardener_id\": 18,\n \"gardener_demand\": 18.0\n },\n {\n \"gardener_id\": 19,\n \"gardener_demand\": 19.0\n },\n {\n \"gardener_id\": 20,\n \"gardener_demand\": 25.0\n }\n ],\n \"efforts\": [\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 1,\n \"effort_cost\": 1087.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 2,\n \"effort_cost\": 974.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 3,\n \"effort_cost\": 408.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 4,\n \"effort_cost\": 910.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 5,\n \"effort_cost\": 892.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 6,\n \"effort_cost\": 1107.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 7,\n \"effort_cost\": 1209.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 8,\n \"effort_cost\": 369.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 9,\n \"effort_cost\": 630.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 10,\n \"effort_cost\": 1307.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 11,\n \"effort_cost\": 1004.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 12,\n \"effort_cost\": 1138.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 13,\n \"effort_cost\": 2008.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 14,\n \"effort_cost\": 993.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 15,\n \"effort_cost\": 37.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 16,\n \"effort_cost\": 1443.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 17,\n \"effort_cost\": 315.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 18,\n \"effort_cost\": 758.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 19,\n \"effort_cost\": 396.0\n },\n {\n \"plot_id\": \"F1\",\n \"gardener_id\": 20,\n \"effort_cost\": 1284.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 1,\n \"effort_cost\": 110.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 2,\n \"effort_cost\": 155.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 3,\n \"effort_cost\": 72.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 4,\n \"effort_cost\": 103.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 5,\n \"effort_cost\": 506.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 6,\n \"effort_cost\": 463.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 7,\n \"effort_cost\": 342.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 8,\n \"effort_cost\": 315.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 9,\n \"effort_cost\": 35.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 10,\n \"effort_cost\": 166.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 11,\n \"effort_cost\": 442.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 12,\n \"effort_cost\": 638.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 13,\n \"effort_cost\": 661.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 14,\n \"effort_cost\": 122.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 15,\n \"effort_cost\": 38.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 16,\n \"effort_cost\": 457.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 17,\n \"effort_cost\": 136.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 18,\n \"effort_cost\": 39.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 19,\n \"effort_cost\": 38.0\n },\n {\n \"plot_id\": \"F2\",\n \"gardener_id\": 20,\n \"effort_cost\": 334.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 1,\n \"effort_cost\": 512.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 2,\n \"effort_cost\": 312.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 3,\n \"effort_cost\": 69.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 4,\n \"effort_cost\": 339.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 5,\n \"effort_cost\": 1078.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 6,\n \"effort_cost\": 198.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 7,\n \"effort_cost\": 1107.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 8,\n \"effort_cost\": 667.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 9,\n \"effort_cost\": 291.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 10,\n \"effort_cost\": 675.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 11,\n \"effort_cost\": 179.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 12,\n \"effort_cost\": 1284.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 13,\n \"effort_cost\": 1533.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 14,\n \"effort_cost\": 798.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 15,\n \"effort_cost\": 63.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 16,\n \"effort_cost\": 1288.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 17,\n \"effort_cost\": 55.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 18,\n \"effort_cost\": 398.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 19,\n \"effort_cost\": 278.0\n },\n {\n \"plot_id\": \"F3\",\n \"gardener_id\": 20,\n \"effort_cost\": 1130.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 1,\n \"effort_cost\": 1542.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 2,\n \"effort_cost\": 1374.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 3,\n \"effort_cost\": 684.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 4,\n \"effort_cost\": 1337.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 5,\n \"effort_cost\": 1511.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 6,\n \"effort_cost\": 1304.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 7,\n \"effort_cost\": 1825.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 8,\n \"effort_cost\": 900.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 9,\n \"effort_cost\": 1093.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 10,\n \"effort_cost\": 1765.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 11,\n \"effort_cost\": 1167.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 12,\n \"effort_cost\": 1760.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 13,\n \"effort_cost\": 2553.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 14,\n \"effort_cost\": 1575.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 15,\n \"effort_cost\": 49.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 16,\n \"effort_cost\": 2054.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 17,\n \"effort_cost\": 328.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 18,\n \"effort_cost\": 1247.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 19,\n \"effort_cost\": 889.0\n },\n {\n \"plot_id\": \"F4\",\n \"gardener_id\": 20,\n \"effort_cost\": 1891.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 1,\n \"effort_cost\": 1136.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 2,\n \"effort_cost\": 1049.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 3,\n \"effort_cost\": 520.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 4,\n \"effort_cost\": 979.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 5,\n \"effort_cost\": 674.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 6,\n \"effort_cost\": 1217.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 7,\n \"effort_cost\": 1109.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 8,\n \"effort_cost\": 138.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 9,\n \"effort_cost\": 699.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 10,\n \"effort_cost\": 1348.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 11,\n \"effort_cost\": 1117.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 12,\n \"effort_cost\": 926.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 13,\n \"effort_cost\": 1976.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 14,\n \"effort_cost\": 956.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 15,\n \"effort_cost\": 47.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 16,\n \"effort_cost\": 1344.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 17,\n \"effort_cost\": 411.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 18,\n \"effort_cost\": 808.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 19,\n \"effort_cost\": 477.0\n },\n {\n \"plot_id\": \"F5\",\n \"gardener_id\": 20,\n \"effort_cost\": 1198.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 1,\n \"effort_cost\": 377.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 2,\n \"effort_cost\": 376.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 3,\n \"effort_cost\": 147.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 4,\n \"effort_cost\": 298.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 5,\n \"effort_cost\": 475.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 6,\n \"effort_cost\": 686.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 7,\n \"effort_cost\": 418.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 8,\n \"effort_cost\": 263.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 9,\n \"effort_cost\": 116.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 10,\n \"effort_cost\": 544.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 11,\n \"effort_cost\": 636.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 12,\n \"effort_cost\": 637.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 13,\n \"effort_cost\": 1121.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 14,\n \"effort_cost\": 113.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 15,\n \"effort_cost\": 36.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 16,\n \"effort_cost\": 618.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 17,\n \"effort_cost\": 194.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 18,\n \"effort_cost\": 137.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 19,\n \"effort_cost\": 57.0\n },\n {\n \"plot_id\": \"F6\",\n \"gardener_id\": 20,\n \"effort_cost\": 453.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 1,\n \"effort_cost\": 665.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 2,\n \"effort_cost\": 498.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 3,\n \"effort_cost\": 40.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 4,\n \"effort_cost\": 459.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 5,\n \"effort_cost\": 986.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 6,\n \"effort_cost\": 623.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 7,\n \"effort_cost\": 1095.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 8,\n \"effort_cost\": 558.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 9,\n \"effort_cost\": 249.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 10,\n \"effort_cost\": 886.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 11,\n \"effort_cost\": 544.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 12,\n \"effort_cost\": 1206.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 13,\n \"effort_cost\": 1698.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 14,\n \"effort_cost\": 797.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 15,\n \"effort_cost\": 45.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 16,\n \"effort_cost\": 1302.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 17,\n \"effort_cost\": 105.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 18,\n \"effort_cost\": 400.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 19,\n \"effort_cost\": 173.0\n },\n {\n \"plot_id\": \"F7\",\n \"gardener_id\": 20,\n \"effort_cost\": 1137.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 1,\n \"effort_cost\": 1329.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 2,\n \"effort_cost\": 1143.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 3,\n \"effort_cost\": 463.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 4,\n \"effort_cost\": 1120.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 5,\n \"effort_cost\": 1467.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 6,\n \"effort_cost\": 1008.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 7,\n \"effort_cost\": 1709.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 8,\n \"effort_cost\": 898.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 9,\n \"effort_cost\": 908.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 10,\n \"effort_cost\": 1545.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 11,\n \"effort_cost\": 866.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 12,\n \"effort_cost\": 1711.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 13,\n \"effort_cost\": 2367.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 14,\n \"effort_cost\": 1433.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 15,\n \"effort_cost\": 71.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 16,\n \"effort_cost\": 1931.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 17,\n \"effort_cost\": 56.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 18,\n \"effort_cost\": 1063.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 19,\n \"effort_cost\": 741.0\n },\n {\n \"plot_id\": \"F8\",\n \"gardener_id\": 20,\n \"effort_cost\": 1764.0\n }\n ]\n}\n\nAlso, when you reply, please follow this little JSON layout so I can read your choices easily — nothing fancy, just a tiny form I can parse:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of garden plots you decide to unlock (one entry per unlocked plot), and \"assignments\" as the single unlocked plot each gardener will be sent to (the i-th entry in that list matches the i-th gardener in the instance). This block is just a sketch of the shape I need, not the actual final answer.\n\nPlease be careful to use the exact identifiers from the instance input — do not rename them or invent new ones. For example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "connection_costs": [ [ 1087.0, 974.0, 408.0, 910.0, 892.0, 1107.0, 1209.0, 369.0, 630.0, 1307.0, 1004.0, 1138.0, 2008.0, 993.0, 37.0, 1443.0, 315.0, 758.0, 396.0, 1284.0 ], [ 110.0, 155.0, 72.0, 103.0, 506.0, 463.0, 342.0, 315.0, 35.0, 166.0, 442.0, 638.0, 661.0, 122.0, 38.0, 457.0, 136.0, 39.0, 38.0, 334.0 ], [ 512.0, 312.0, 69.0, 339.0, 1078.0, 198.0, 1107.0, 667.0, 291.0, 675.0, 179.0, 1284.0, 1533.0, 798.0, 63.0, 1288.0, 55.0, 398.0, 278.0, 1130.0 ], [ 1542.0, 1374.0, 684.0, 1337.0, 1511.0, 1304.0, 1825.0, 900.0, 1093.0, 1765.0, 1167.0, 1760.0, 2553.0, 1575.0, 49.0, 2054.0, 328.0, 1247.0, 889.0, 1891.0 ], [ 1136.0, 1049.0, 520.0, 979.0, 674.0, 1217.0, 1109.0, 138.0, 699.0, 1348.0, 1117.0, 926.0, 1976.0, 956.0, 47.0, 1344.0, 411.0, 808.0, 477.0, 1198.0 ], [ 377.0, 376.0, 147.0, 298.0, 475.0, 686.0, 418.0, 263.0, 116.0, 544.0, 636.0, 637.0, 1121.0, 113.0, 36.0, 618.0, 194.0, 137.0, 57.0, 453.0 ], [ 665.0, 498.0, 40.0, 459.0, 986.0, 623.0, 1095.0, 558.0, 249.0, 886.0, 544.0, 1206.0, 1698.0, 797.0, 45.0, 1302.0, 105.0, 400.0, 173.0, 1137.0 ], [ 1329.0, 1143.0, 463.0, 1120.0, 1467.0, 1008.0, 1709.0, 898.0, 908.0, 1545.0, 866.0, 1711.0, 2367.0, 1433.0, 71.0, 1931.0, 56.0, 1063.0, 741.0, 1764.0 ] ], "demands": [ 25.0, 28.0, 15.0, 23.0, 28.0, 20.0, 18.0, 29.0, 14.0, 18.0, 26.0, 10.0, 18.0, 23.0, 18.0, 23.0, 27.0, 18.0, 19.0, 25.0 ], "objective": 5942.0 }, "solution": { "open_facilities": [ 1, 2 ], "assignments": [ 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1 ] }, "obj": 5942.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 20, "facilities": [ { "id": "F1", "opening_cost": 600.0, "capacity": 300.0 }, { "id": "F2", "opening_cost": 600.0, "capacity": 300.0 }, { "id": "F3", "opening_cost": 600.0, "capacity": 300.0 }, { "id": "F4", "opening_cost": 600.0, "capacity": 300.0 }, { "id": "F5", "opening_cost": 600.0, "capacity": 300.0 }, { "id": "F6", "opening_cost": 600.0, "capacity": 300.0 }, { "id": "F7", "opening_cost": 600.0, "capacity": 300.0 }, { "id": "F8", "opening_cost": 600.0, "capacity": 300.0 } ], "customers": [ { "id": 1, "demand": 25.0 }, { "id": 2, "demand": 28.0 }, { "id": 3, "demand": 15.0 }, { "id": 4, "demand": 23.0 }, { "id": 5, "demand": 28.0 }, { "id": 6, "demand": 20.0 }, { "id": 7, "demand": 18.0 }, { "id": 8, "demand": 29.0 }, { "id": 9, "demand": 14.0 }, { "id": 10, "demand": 18.0 }, { "id": 11, "demand": 26.0 }, { "id": 12, "demand": 10.0 }, { "id": 13, "demand": 18.0 }, { "id": 14, "demand": 23.0 }, { "id": 15, "demand": 18.0 }, { "id": 16, "demand": 23.0 }, { "id": 17, "demand": 27.0 }, { "id": 18, "demand": 18.0 }, { "id": 19, "demand": 19.0 }, { "id": 20, "demand": 25.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 1087.0 }, { "facility": "F1", "customer": 2, "cost": 974.0 }, { "facility": "F1", "customer": 3, "cost": 408.0 }, { "facility": "F1", "customer": 4, "cost": 910.0 }, { "facility": "F1", "customer": 5, "cost": 892.0 }, { "facility": "F1", "customer": 6, "cost": 1107.0 }, { "facility": "F1", "customer": 7, "cost": 1209.0 }, { "facility": "F1", "customer": 8, "cost": 369.0 }, { "facility": "F1", "customer": 9, "cost": 630.0 }, { "facility": "F1", "customer": 10, "cost": 1307.0 }, { "facility": "F1", "customer": 11, "cost": 1004.0 }, { "facility": "F1", "customer": 12, "cost": 1138.0 }, { "facility": "F1", "customer": 13, "cost": 2008.0 }, { "facility": "F1", "customer": 14, "cost": 993.0 }, { "facility": "F1", "customer": 15, "cost": 37.0 }, { "facility": "F1", "customer": 16, "cost": 1443.0 }, { "facility": "F1", "customer": 17, "cost": 315.0 }, { "facility": "F1", "customer": 18, "cost": 758.0 }, { "facility": "F1", "customer": 19, "cost": 396.0 }, { "facility": "F1", "customer": 20, "cost": 1284.0 }, { "facility": "F2", "customer": 1, "cost": 110.0 }, { "facility": "F2", "customer": 2, "cost": 155.0 }, { "facility": "F2", "customer": 3, "cost": 72.0 }, { "facility": "F2", "customer": 4, "cost": 103.0 }, { "facility": "F2", "customer": 5, "cost": 506.0 }, { "facility": "F2", "customer": 6, "cost": 463.0 }, { "facility": "F2", "customer": 7, "cost": 342.0 }, { "facility": "F2", "customer": 8, "cost": 315.0 }, { "facility": "F2", "customer": 9, "cost": 35.0 }, { "facility": "F2", "customer": 10, "cost": 166.0 }, { "facility": "F2", "customer": 11, "cost": 442.0 }, { "facility": "F2", "customer": 12, "cost": 638.0 }, { "facility": "F2", "customer": 13, "cost": 661.0 }, { "facility": "F2", "customer": 14, "cost": 122.0 }, { "facility": "F2", "customer": 15, "cost": 38.0 }, { "facility": "F2", "customer": 16, "cost": 457.0 }, { "facility": "F2", "customer": 17, "cost": 136.0 }, { "facility": "F2", "customer": 18, "cost": 39.0 }, { "facility": "F2", "customer": 19, "cost": 38.0 }, { "facility": "F2", "customer": 20, "cost": 334.0 }, { "facility": "F3", "customer": 1, "cost": 512.0 }, { "facility": "F3", "customer": 2, "cost": 312.0 }, { "facility": "F3", "customer": 3, "cost": 69.0 }, { "facility": "F3", "customer": 4, "cost": 339.0 }, { "facility": "F3", "customer": 5, "cost": 1078.0 }, { "facility": "F3", "customer": 6, "cost": 198.0 }, { "facility": "F3", "customer": 7, "cost": 1107.0 }, { "facility": "F3", "customer": 8, "cost": 667.0 }, { "facility": "F3", "customer": 9, "cost": 291.0 }, { "facility": "F3", "customer": 10, "cost": 675.0 }, { "facility": "F3", "customer": 11, "cost": 179.0 }, { "facility": "F3", "customer": 12, "cost": 1284.0 }, { "facility": "F3", "customer": 13, "cost": 1533.0 }, { "facility": "F3", "customer": 14, "cost": 798.0 }, { "facility": "F3", "customer": 15, "cost": 63.0 }, { "facility": "F3", "customer": 16, "cost": 1288.0 }, { "facility": "F3", "customer": 17, "cost": 55.0 }, { "facility": "F3", "customer": 18, "cost": 398.0 }, { "facility": "F3", "customer": 19, "cost": 278.0 }, { "facility": "F3", "customer": 20, "cost": 1130.0 }, { "facility": "F4", "customer": 1, "cost": 1542.0 }, { "facility": "F4", "customer": 2, "cost": 1374.0 }, { "facility": "F4", "customer": 3, "cost": 684.0 }, { "facility": "F4", "customer": 4, "cost": 1337.0 }, { "facility": "F4", "customer": 5, "cost": 1511.0 }, { "facility": "F4", "customer": 6, "cost": 1304.0 }, { "facility": "F4", "customer": 7, "cost": 1825.0 }, { "facility": "F4", "customer": 8, "cost": 900.0 }, { "facility": "F4", "customer": 9, "cost": 1093.0 }, { "facility": "F4", "customer": 10, "cost": 1765.0 }, { "facility": "F4", "customer": 11, "cost": 1167.0 }, { "facility": "F4", "customer": 12, "cost": 1760.0 }, { "facility": "F4", "customer": 13, "cost": 2553.0 }, { "facility": "F4", "customer": 14, "cost": 1575.0 }, { "facility": "F4", "customer": 15, "cost": 49.0 }, { "facility": "F4", "customer": 16, "cost": 2054.0 }, { "facility": "F4", "customer": 17, "cost": 328.0 }, { "facility": "F4", "customer": 18, "cost": 1247.0 }, { "facility": "F4", "customer": 19, "cost": 889.0 }, { "facility": "F4", "customer": 20, "cost": 1891.0 }, { "facility": "F5", "customer": 1, "cost": 1136.0 }, { "facility": "F5", "customer": 2, "cost": 1049.0 }, { "facility": "F5", "customer": 3, "cost": 520.0 }, { "facility": "F5", "customer": 4, "cost": 979.0 }, { "facility": "F5", "customer": 5, "cost": 674.0 }, { "facility": "F5", "customer": 6, "cost": 1217.0 }, { "facility": "F5", "customer": 7, "cost": 1109.0 }, { "facility": "F5", "customer": 8, "cost": 138.0 }, { "facility": "F5", "customer": 9, "cost": 699.0 }, { "facility": "F5", "customer": 10, "cost": 1348.0 }, { "facility": "F5", "customer": 11, "cost": 1117.0 }, { "facility": "F5", "customer": 12, "cost": 926.0 }, { "facility": "F5", "customer": 13, "cost": 1976.0 }, { "facility": "F5", "customer": 14, "cost": 956.0 }, { "facility": "F5", "customer": 15, "cost": 47.0 }, { "facility": "F5", "customer": 16, "cost": 1344.0 }, { "facility": "F5", "customer": 17, "cost": 411.0 }, { "facility": "F5", "customer": 18, "cost": 808.0 }, { "facility": "F5", "customer": 19, "cost": 477.0 }, { "facility": "F5", "customer": 20, "cost": 1198.0 }, { "facility": "F6", "customer": 1, "cost": 377.0 }, { "facility": "F6", "customer": 2, "cost": 376.0 }, { "facility": "F6", "customer": 3, "cost": 147.0 }, { "facility": "F6", "customer": 4, "cost": 298.0 }, { "facility": "F6", "customer": 5, "cost": 475.0 }, { "facility": "F6", "customer": 6, "cost": 686.0 }, { "facility": "F6", "customer": 7, "cost": 418.0 }, { "facility": "F6", "customer": 8, "cost": 263.0 }, { "facility": "F6", "customer": 9, "cost": 116.0 }, { "facility": "F6", "customer": 10, "cost": 544.0 }, { "facility": "F6", "customer": 11, "cost": 636.0 }, { "facility": "F6", "customer": 12, "cost": 637.0 }, { "facility": "F6", "customer": 13, "cost": 1121.0 }, { "facility": "F6", "customer": 14, "cost": 113.0 }, { "facility": "F6", "customer": 15, "cost": 36.0 }, { "facility": "F6", "customer": 16, "cost": 618.0 }, { "facility": "F6", "customer": 17, "cost": 194.0 }, { "facility": "F6", "customer": 18, "cost": 137.0 }, { "facility": "F6", "customer": 19, "cost": 57.0 }, { "facility": "F6", "customer": 20, "cost": 453.0 }, { "facility": "F7", "customer": 1, "cost": 665.0 }, { "facility": "F7", "customer": 2, "cost": 498.0 }, { "facility": "F7", "customer": 3, "cost": 40.0 }, { "facility": "F7", "customer": 4, "cost": 459.0 }, { "facility": "F7", "customer": 5, "cost": 986.0 }, { "facility": "F7", "customer": 6, "cost": 623.0 }, { "facility": "F7", "customer": 7, "cost": 1095.0 }, { "facility": "F7", "customer": 8, "cost": 558.0 }, { "facility": "F7", "customer": 9, "cost": 249.0 }, { "facility": "F7", "customer": 10, "cost": 886.0 }, { "facility": "F7", "customer": 11, "cost": 544.0 }, { "facility": "F7", "customer": 12, "cost": 1206.0 }, { "facility": "F7", "customer": 13, "cost": 1698.0 }, { "facility": "F7", "customer": 14, "cost": 797.0 }, { "facility": "F7", "customer": 15, "cost": 45.0 }, { "facility": "F7", "customer": 16, "cost": 1302.0 }, { "facility": "F7", "customer": 17, "cost": 105.0 }, { "facility": "F7", "customer": 18, "cost": 400.0 }, { "facility": "F7", "customer": 19, "cost": 173.0 }, { "facility": "F7", "customer": 20, "cost": 1137.0 }, { "facility": "F8", "customer": 1, "cost": 1329.0 }, { "facility": "F8", "customer": 2, "cost": 1143.0 }, { "facility": "F8", "customer": 3, "cost": 463.0 }, { "facility": "F8", "customer": 4, "cost": 1120.0 }, { "facility": "F8", "customer": 5, "cost": 1467.0 }, { "facility": "F8", "customer": 6, "cost": 1008.0 }, { "facility": "F8", "customer": 7, "cost": 1709.0 }, { "facility": "F8", "customer": 8, "cost": 898.0 }, { "facility": "F8", "customer": 9, "cost": 908.0 }, { "facility": "F8", "customer": 10, "cost": 1545.0 }, { "facility": "F8", "customer": 11, "cost": 866.0 }, { "facility": "F8", "customer": 12, "cost": 1711.0 }, { "facility": "F8", "customer": 13, "cost": 2367.0 }, { "facility": "F8", "customer": 14, "cost": 1433.0 }, { "facility": "F8", "customer": 15, "cost": 71.0 }, { "facility": "F8", "customer": 16, "cost": 1931.0 }, { "facility": "F8", "customer": 17, "cost": 56.0 }, { "facility": "F8", "customer": 18, "cost": 1063.0 }, { "facility": "F8", "customer": 19, "cost": 741.0 }, { "facility": "F8", "customer": 20, "cost": 1764.0 } ], "objective": 5942.0 }, "solution_variant": { "selected": [ "F2", "F3" ], "assignments": [ "F2", "F3", "F3", "F2", "F2", "F3", "F2", "F2", "F2", "F2", "F3", "F2", "F2", "F2", "F3", "F2", "F3", "F2", "F2", "F2" ] }, "context_index": 44, "input_format": "json", "input_index_base": 1 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Many people don’t see how much thought goes into placing service vans: pick which vans to put into service, then give each service visit to exactly one of those vans, making sure no van is asked to do more than it can. Each van has a cost to deploy and a cap on workload, and every client visit costs travel money. The goal is the plan with the lowest total expense — simply add up the deployment costs for the vans used and the travel costs for all visits — while covering every request once and not overloading any van. The specific instance information is listed below.\n\nThere are 9 candidate vans and 18 client requests listed below.\nVan F1 has deployment cost 221.0 and capacity 700.0.\nVan F2 has deployment cost 595.0 and capacity 700.0.\nVan F3 has deployment cost 365.0 and capacity 700.0.\nVan F4 has deployment cost 534.0 and capacity 700.0.\nVan F5 has deployment cost 487.0 and capacity 700.0.\nVan F6 has deployment cost 436.0 and capacity 700.0.\nVan F7 has deployment cost 364.0 and capacity 700.0.\nVan F8 has deployment cost 405.0 and capacity 700.0.\nVan F9 has deployment cost 518.0 and capacity 700.0.\nRequest A has service demand 28.0.\nRequest B has service demand 20.0.\nRequest C has service demand 24.0.\nRequest D has service demand 27.0.\nRequest E has service demand 19.0.\nRequest F has service demand 12.0.\nRequest G has service demand 14.0.\nRequest H has service demand 22.0.\nRequest I has service demand 23.0.\nRequest J has service demand 18.0.\nRequest K has service demand 17.0.\nRequest L has service demand 16.0.\nRequest M has service demand 16.0.\nRequest N has service demand 27.0.\nRequest O has service demand 10.0.\nRequest P has service demand 16.0.\nRequest Q has service demand 22.0.\nRequest R has service demand 17.0.\nIf van F1 serves request A, the travel cost is 648.0.\nIf van F1 serves request B, the travel cost is 43.0.\nIf van F1 serves request C, the travel cost is 205.0.\nIf van F1 serves request D, the travel cost is 441.0.\nIf van F1 serves request E, the travel cost is 48.0.\nIf van F1 serves request F, the travel cost is 153.0.\nIf van F1 serves request G, the travel cost is 112.0.\nIf van F1 serves request H, the travel cost is 637.0.\nIf van F1 serves request I, the travel cost is 318.0.\nIf van F1 serves request J, the travel cost is 649.0.\nIf van F1 serves request K, the travel cost is 52.0.\nIf van F1 serves request L, the travel cost is 219.0.\nIf van F1 serves request M, the travel cost is 56.0.\nIf van F1 serves request N, the travel cost is 383.0.\nIf van F1 serves request O, the travel cost is 28.0.\nIf van F1 serves request P, the travel cost is 854.0.\nIf van F1 serves request Q, the travel cost is 102.0.\nIf van F1 serves request R, the travel cost is 281.0.\nIf van F2 serves request A, the travel cost is 1230.0.\nIf van F2 serves request B, the travel cost is 159.0.\nIf van F2 serves request C, the travel cost is 218.0.\nIf van F2 serves request D, the travel cost is 536.0.\nIf van F2 serves request E, the travel cost is 57.0.\nIf van F2 serves request F, the travel cost is 495.0.\nIf van F2 serves request G, the travel cost is 926.0.\nIf van F2 serves request H, the travel cost is 1154.0.\nIf van F2 serves request I, the travel cost is 414.0.\nIf van F2 serves request J, the travel cost is 1446.0.\nIf van F2 serves request K, the travel cost is 749.0.\nIf van F2 serves request L, the travel cost is 328.0.\nIf van F2 serves request M, the travel cost is 450.0.\nIf van F2 serves request N, the travel cost is 1193.0.\nIf van F2 serves request O, the travel cost is 63.0.\nIf van F2 serves request P, the travel cost is 1600.0.\nIf van F2 serves request Q, the travel cost is 191.0.\nIf van F2 serves request R, the travel cost is 889.0.\nIf van F3 serves request A, the travel cost is 262.0.\nIf van F3 serves request B, the travel cost is 255.0.\nIf van F3 serves request C, the travel cost is 63.0.\nIf van F3 serves request D, the travel cost is 132.0.\nIf van F3 serves request E, the travel cost is 107.0.\nIf van F3 serves request F, the travel cost is 519.0.\nIf van F3 serves request G, the travel cost is 558.0.\nIf van F3 serves request H, the travel cost is 1088.0.\nIf van F3 serves request I, the travel cost is 65.0.\nIf van F3 serves request J, the travel cost is 772.0.\nIf van F3 serves request K, the travel cost is 399.0.\nIf van F3 serves request L, the travel cost is 32.0.\nIf van F3 serves request M, the travel cost is 235.0.\nIf van F3 serves request N, the travel cost is 781.0.\nIf van F3 serves request O, the travel cost is 179.0.\nIf van F3 serves request P, the travel cost is 752.0.\nIf van F3 serves request Q, the travel cost is 316.0.\nIf van F3 serves request R, the travel cost is 734.0.\nIf van F4 serves request A, the travel cost is 108.0.\nIf van F4 serves request B, the travel cost is 132.0.\nIf van F4 serves request C, the travel cost is 102.0.\nIf van F4 serves request D, the travel cost is 225.0.\nIf van F4 serves request E, the travel cost is 77.0.\nIf van F4 serves request F, the travel cost is 333.0.\nIf van F4 serves request G, the travel cost is 290.0.\nIf van F4 serves request H, the travel cost is 840.0.\nIf van F4 serves request I, the travel cost is 129.0.\nIf van F4 serves request J, the travel cost is 441.0.\nIf van F4 serves request K, the travel cost is 171.0.\nIf van F4 serves request L, the travel cost is 61.0.\nIf van F4 serves request M, the travel cost is 85.0.\nIf van F4 serves request N, the travel cost is 482.0.\nIf van F4 serves request O, the travel cost is 96.0.\nIf van F4 serves request P, the travel cost is 437.0.\nIf van F4 serves request Q, the travel cost is 209.0.\nIf van F4 serves request R, the travel cost is 485.0.\nIf van F5 serves request A, the travel cost is 1439.0.\nIf van F5 serves request B, the travel cost is 302.0.\nIf van F5 serves request C, the travel cost is 465.0.\nIf van F5 serves request D, the travel cost is 862.0.\nIf van F5 serves request E, the travel cost is 45.0.\nIf van F5 serves request F, the travel cost is 203.0.\nIf van F5 serves request G, the travel cost is 887.0.\nIf van F5 serves request H, the travel cost is 589.0.\nIf van F5 serves request I, the travel cost is 749.0.\nIf van F5 serves request J, the travel cost is 1448.0.\nIf van F5 serves request K, the travel cost is 813.0.\nIf van F5 serves request L, the travel cost is 671.0.\nIf van F5 serves request M, the travel cost is 641.0.\nIf van F5 serves request N, the travel cost is 1078.0.\nIf van F5 serves request O, the travel cost is 118.0.\nIf van F5 serves request P, the travel cost is 1674.0.\nIf van F5 serves request Q, the travel cost is 70.0.\nIf van F5 serves request R, the travel cost is 603.0.\nIf van F6 serves request A, the travel cost is 723.0.\nIf van F6 serves request B, the travel cost is 47.0.\nIf van F6 serves request C, the travel cost is 258.0.\nIf van F6 serves request D, the travel cost is 523.0.\nIf van F6 serves request E, the travel cost is 41.0.\nIf van F6 serves request F, the travel cost is 57.0.\nIf van F6 serves request G, the travel cost is 120.0.\nIf van F6 serves request H, the travel cost is 410.0.\nIf van F6 serves request I, the travel cost is 398.0.\nIf van F6 serves request J, the travel cost is 603.0.\nIf van F6 serves request K, the travel cost is 146.0.\nIf van F6 serves request L, the travel cost is 299.0.\nIf van F6 serves request M, the travel cost is 128.0.\nIf van F6 serves request N, the travel cost is 220.0.\nIf van F6 serves request O, the travel cost is 20.0.\nIf van F6 serves request P, the travel cost is 846.0.\nIf van F6 serves request Q, the travel cost is 62.0.\nIf van F6 serves request R, the travel cost is 85.0.\nIf van F7 serves request A, the travel cost is 837.0.\nIf van F7 serves request B, the travel cost is 48.0.\nIf van F7 serves request C, the travel cost is 210.0.\nIf van F7 serves request D, the travel cost is 469.0.\nIf van F7 serves request E, the travel cost is 50.0.\nIf van F7 serves request F, the travel cost is 221.0.\nIf van F7 serves request G, the travel cost is 413.0.\nIf van F7 serves request H, the travel cost is 796.0.\nIf van F7 serves request I, the travel cost is 343.0.\nIf van F7 serves request J, the travel cost is 944.0.\nIf van F7 serves request K, the travel cost is 242.0.\nIf van F7 serves request L, the travel cost is 243.0.\nIf van F7 serves request M, the travel cost is 75.0.\nIf van F7 serves request N, the travel cost is 682.0.\nIf van F7 serves request O, the travel cost is 33.0.\nIf van F7 serves request P, the travel cost is 1125.0.\nIf van F7 serves request Q, the travel cost is 118.0.\nIf van F7 serves request R, the travel cost is 459.0.\nIf van F8 serves request A, the travel cost is 1334.0.\nIf van F8 serves request B, the travel cost is 612.0.\nIf van F8 serves request C, the travel cost is 49.0.\nIf van F8 serves request D, the travel cost is 183.0.\nIf van F8 serves request E, the travel cost is 149.0.\nIf van F8 serves request F, the travel cost is 949.0.\nIf van F8 serves request G, the travel cost is 1295.0.\nIf van F8 serves request H, the travel cost is 1609.0.\nIf van F8 serves request I, the travel cost is 85.0.\nIf van F8 serves request J, the travel cost is 1726.0.\nIf van F8 serves request K, the travel cost is 1099.0.\nIf van F8 serves request L, the travel cost is 218.0.\nIf van F8 serves request M, the travel cost is 801.0.\nIf van F8 serves request N, the travel cost is 1566.0.\nIf van F8 serves request O, the travel cost is 379.0.\nIf van F8 serves request P, the travel cost is 1807.0.\nIf van F8 serves request Q, the travel cost is 536.0.\nIf van F8 serves request R, the travel cost is 1332.0.\nIf van F9 serves request A, the travel cost is 402.0.\nIf van F9 serves request B, the travel cost is 193.0.\nIf van F9 serves request C, the travel cost is 91.0.\nIf van F9 serves request D, the travel cost is 214.0.\nIf van F9 serves request E, the travel cost is 87.0.\nIf van F9 serves request F, the travel cost is 451.0.\nIf van F9 serves request G, the travel cost is 516.0.\nIf van F9 serves request H, the travel cost is 1027.0.\nIf van F9 serves request I, the travel cost is 116.0.\nIf van F9 serves request J, the travel cost is 817.0.\nIf van F9 serves request K, the travel cost is 343.0.\nIf van F9 serves request L, the travel cost is 49.0.\nIf van F9 serves request M, the travel cost is 168.0.\nIf van F9 serves request N, the travel cost is 759.0.\nIf van F9 serves request O, the travel cost is 132.0.\nIf van F9 serves request P, the travel cost is 867.0.\nIf van F9 serves request Q, the travel cost is 261.0.\nIf van F9 serves request R, the travel cost is 677.0.\nUse these details to pick which vans to deploy and assign each request without exceeding any van's capacity.\n\nYou can just hand the plan back to me in a small JSON snippet like this — I find it the easiest way to keep things straight.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is the list of vans you decide to put into service (one entry per van). \"assignments\" is the list of which van handles each client visit (one entry per client, in the same order as the client list). Think of it like a simple form: pick the vans you open, then for each visit say which opened van covers it.\n\nThis JSON is just a sketch of the shape I expect, not the final plan itself. Please use the exact identifiers from the instance input when you fill it in — do not rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 221.0, 595.0, 365.0, 534.0, 487.0, 436.0, 364.0, 405.0, 518.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 648.0, 43.0, 205.0, 441.0, 48.0, 153.0, 112.0, 637.0, 318.0, 649.0, 52.0, 219.0, 56.0, 383.0, 28.0, 854.0, 102.0, 281.0 ], [ 1230.0, 159.0, 218.0, 536.0, 57.0, 495.0, 926.0, 1154.0, 414.0, 1446.0, 749.0, 328.0, 450.0, 1193.0, 63.0, 1600.0, 191.0, 889.0 ], [ 262.0, 255.0, 63.0, 132.0, 107.0, 519.0, 558.0, 1088.0, 65.0, 772.0, 399.0, 32.0, 235.0, 781.0, 179.0, 752.0, 316.0, 734.0 ], [ 108.0, 132.0, 102.0, 225.0, 77.0, 333.0, 290.0, 840.0, 129.0, 441.0, 171.0, 61.0, 85.0, 482.0, 96.0, 437.0, 209.0, 485.0 ], [ 1439.0, 302.0, 465.0, 862.0, 45.0, 203.0, 887.0, 589.0, 749.0, 1448.0, 813.0, 671.0, 641.0, 1078.0, 118.0, 1674.0, 70.0, 603.0 ], [ 723.0, 47.0, 258.0, 523.0, 41.0, 57.0, 120.0, 410.0, 398.0, 603.0, 146.0, 299.0, 128.0, 220.0, 20.0, 846.0, 62.0, 85.0 ], [ 837.0, 48.0, 210.0, 469.0, 50.0, 221.0, 413.0, 796.0, 343.0, 944.0, 242.0, 243.0, 75.0, 682.0, 33.0, 1125.0, 118.0, 459.0 ], [ 1334.0, 612.0, 49.0, 183.0, 149.0, 949.0, 1295.0, 1609.0, 85.0, 1726.0, 1099.0, 218.0, 801.0, 1566.0, 379.0, 1807.0, 536.0, 1332.0 ], [ 402.0, 193.0, 91.0, 214.0, 87.0, 451.0, 516.0, 1027.0, 116.0, 817.0, 343.0, 49.0, 168.0, 759.0, 132.0, 867.0, 261.0, 677.0 ] ], "demands": [ 28.0, 20.0, 24.0, 27.0, 19.0, 12.0, 14.0, 22.0, 23.0, 18.0, 17.0, 16.0, 16.0, 27.0, 10.0, 16.0, 22.0, 17.0 ], "objective": 3766.0 }, "solution": { "open_facilities": [ 3, 5 ], "assignments": [ 3, 5, 3, 3, 5, 5, 5, 5, 3, 3, 5, 3, 3, 5, 5, 3, 5, 5 ] }, "obj": 3766.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 9, "num_customers": 18, "facilities": [ { "id": "F1", "opening_cost": 221.0, "capacity": 700.0 }, { "id": "F2", "opening_cost": 595.0, "capacity": 700.0 }, { "id": "F3", "opening_cost": 365.0, "capacity": 700.0 }, { "id": "F4", "opening_cost": 534.0, "capacity": 700.0 }, { "id": "F5", "opening_cost": 487.0, "capacity": 700.0 }, { "id": "F6", "opening_cost": 436.0, "capacity": 700.0 }, { "id": "F7", "opening_cost": 364.0, "capacity": 700.0 }, { "id": "F8", "opening_cost": 405.0, "capacity": 700.0 }, { "id": "F9", "opening_cost": 518.0, "capacity": 700.0 } ], "customers": [ { "id": "A", "demand": 28.0 }, { "id": "B", "demand": 20.0 }, { "id": "C", "demand": 24.0 }, { "id": "D", "demand": 27.0 }, { "id": "E", "demand": 19.0 }, { "id": "F", "demand": 12.0 }, { "id": "G", "demand": 14.0 }, { "id": "H", "demand": 22.0 }, { "id": "I", "demand": 23.0 }, { "id": "J", "demand": 18.0 }, { "id": "K", "demand": 17.0 }, { "id": "L", "demand": 16.0 }, { "id": "M", "demand": 16.0 }, { "id": "N", "demand": 27.0 }, { "id": "O", "demand": 10.0 }, { "id": "P", "demand": 16.0 }, { "id": "Q", "demand": 22.0 }, { "id": "R", "demand": 17.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 648.0 }, { "facility": "F1", "customer": "B", "cost": 43.0 }, { "facility": "F1", "customer": "C", "cost": 205.0 }, { "facility": "F1", "customer": "D", "cost": 441.0 }, { "facility": "F1", "customer": "E", "cost": 48.0 }, { "facility": "F1", "customer": "F", "cost": 153.0 }, { "facility": "F1", "customer": "G", "cost": 112.0 }, { "facility": "F1", "customer": "H", "cost": 637.0 }, { "facility": "F1", "customer": "I", "cost": 318.0 }, { "facility": "F1", "customer": "J", "cost": 649.0 }, { "facility": "F1", "customer": "K", "cost": 52.0 }, { "facility": "F1", "customer": "L", "cost": 219.0 }, { "facility": "F1", "customer": "M", "cost": 56.0 }, { "facility": "F1", "customer": "N", "cost": 383.0 }, { "facility": "F1", "customer": "O", "cost": 28.0 }, { "facility": "F1", "customer": "P", "cost": 854.0 }, { "facility": "F1", "customer": "Q", "cost": 102.0 }, { "facility": "F1", "customer": "R", "cost": 281.0 }, { "facility": "F2", "customer": "A", "cost": 1230.0 }, { "facility": "F2", "customer": "B", "cost": 159.0 }, { "facility": "F2", "customer": "C", "cost": 218.0 }, { "facility": "F2", "customer": "D", "cost": 536.0 }, { "facility": "F2", "customer": "E", "cost": 57.0 }, { "facility": "F2", "customer": "F", "cost": 495.0 }, { "facility": "F2", "customer": "G", "cost": 926.0 }, { "facility": "F2", "customer": "H", "cost": 1154.0 }, { "facility": "F2", "customer": "I", "cost": 414.0 }, { "facility": "F2", "customer": "J", "cost": 1446.0 }, { "facility": "F2", "customer": "K", "cost": 749.0 }, { "facility": "F2", "customer": "L", "cost": 328.0 }, { "facility": "F2", "customer": "M", "cost": 450.0 }, { "facility": "F2", "customer": "N", "cost": 1193.0 }, { "facility": "F2", "customer": "O", "cost": 63.0 }, { "facility": "F2", "customer": "P", "cost": 1600.0 }, { "facility": "F2", "customer": "Q", "cost": 191.0 }, { "facility": "F2", "customer": "R", "cost": 889.0 }, { "facility": "F3", "customer": "A", "cost": 262.0 }, { "facility": "F3", "customer": "B", "cost": 255.0 }, { "facility": "F3", "customer": "C", "cost": 63.0 }, { "facility": "F3", "customer": "D", "cost": 132.0 }, { "facility": "F3", "customer": "E", "cost": 107.0 }, { "facility": "F3", "customer": "F", "cost": 519.0 }, { "facility": "F3", "customer": "G", "cost": 558.0 }, { "facility": "F3", "customer": "H", "cost": 1088.0 }, { "facility": "F3", "customer": "I", "cost": 65.0 }, { "facility": "F3", "customer": "J", "cost": 772.0 }, { "facility": "F3", "customer": "K", "cost": 399.0 }, { "facility": "F3", "customer": "L", "cost": 32.0 }, { "facility": "F3", "customer": "M", "cost": 235.0 }, { "facility": "F3", "customer": "N", "cost": 781.0 }, { "facility": "F3", "customer": "O", "cost": 179.0 }, { "facility": "F3", "customer": "P", "cost": 752.0 }, { "facility": "F3", "customer": "Q", "cost": 316.0 }, { "facility": "F3", "customer": "R", "cost": 734.0 }, { "facility": "F4", "customer": "A", "cost": 108.0 }, { "facility": "F4", "customer": "B", "cost": 132.0 }, { "facility": "F4", "customer": "C", "cost": 102.0 }, { "facility": "F4", "customer": "D", "cost": 225.0 }, { "facility": "F4", "customer": "E", "cost": 77.0 }, { "facility": "F4", "customer": "F", "cost": 333.0 }, { "facility": "F4", "customer": "G", "cost": 290.0 }, { "facility": "F4", "customer": "H", "cost": 840.0 }, { "facility": "F4", "customer": "I", "cost": 129.0 }, { "facility": "F4", "customer": "J", "cost": 441.0 }, { "facility": "F4", "customer": "K", "cost": 171.0 }, { "facility": "F4", "customer": "L", "cost": 61.0 }, { "facility": "F4", "customer": "M", "cost": 85.0 }, { "facility": "F4", "customer": "N", "cost": 482.0 }, { "facility": "F4", "customer": "O", "cost": 96.0 }, { "facility": "F4", "customer": "P", "cost": 437.0 }, { "facility": "F4", "customer": "Q", "cost": 209.0 }, { "facility": "F4", "customer": "R", "cost": 485.0 }, { "facility": "F5", "customer": "A", "cost": 1439.0 }, { "facility": "F5", "customer": "B", "cost": 302.0 }, { "facility": "F5", "customer": "C", "cost": 465.0 }, { "facility": "F5", "customer": "D", "cost": 862.0 }, { "facility": "F5", "customer": "E", "cost": 45.0 }, { "facility": "F5", "customer": "F", "cost": 203.0 }, { "facility": "F5", "customer": "G", "cost": 887.0 }, { "facility": "F5", "customer": "H", "cost": 589.0 }, { "facility": "F5", "customer": "I", "cost": 749.0 }, { "facility": "F5", "customer": "J", "cost": 1448.0 }, { "facility": "F5", "customer": "K", "cost": 813.0 }, { "facility": "F5", "customer": "L", "cost": 671.0 }, { "facility": "F5", "customer": "M", "cost": 641.0 }, { "facility": "F5", "customer": "N", "cost": 1078.0 }, { "facility": "F5", "customer": "O", "cost": 118.0 }, { "facility": "F5", "customer": "P", "cost": 1674.0 }, { "facility": "F5", "customer": "Q", "cost": 70.0 }, { "facility": "F5", "customer": "R", "cost": 603.0 }, { "facility": "F6", "customer": "A", "cost": 723.0 }, { "facility": "F6", "customer": "B", "cost": 47.0 }, { "facility": "F6", "customer": "C", "cost": 258.0 }, { "facility": "F6", "customer": "D", "cost": 523.0 }, { "facility": "F6", "customer": "E", "cost": 41.0 }, { "facility": "F6", "customer": "F", "cost": 57.0 }, { "facility": "F6", "customer": "G", "cost": 120.0 }, { "facility": "F6", "customer": "H", "cost": 410.0 }, { "facility": "F6", "customer": "I", "cost": 398.0 }, { "facility": "F6", "customer": "J", "cost": 603.0 }, { "facility": "F6", "customer": "K", "cost": 146.0 }, { "facility": "F6", "customer": "L", "cost": 299.0 }, { "facility": "F6", "customer": "M", "cost": 128.0 }, { "facility": "F6", "customer": "N", "cost": 220.0 }, { "facility": "F6", "customer": "O", "cost": 20.0 }, { "facility": "F6", "customer": "P", "cost": 846.0 }, { "facility": "F6", "customer": "Q", "cost": 62.0 }, { "facility": "F6", "customer": "R", "cost": 85.0 }, { "facility": "F7", "customer": "A", "cost": 837.0 }, { "facility": "F7", "customer": "B", "cost": 48.0 }, { "facility": "F7", "customer": "C", "cost": 210.0 }, { "facility": "F7", "customer": "D", "cost": 469.0 }, { "facility": "F7", "customer": "E", "cost": 50.0 }, { "facility": "F7", "customer": "F", "cost": 221.0 }, { "facility": "F7", "customer": "G", "cost": 413.0 }, { "facility": "F7", "customer": "H", "cost": 796.0 }, { "facility": "F7", "customer": "I", "cost": 343.0 }, { "facility": "F7", "customer": "J", "cost": 944.0 }, { "facility": "F7", "customer": "K", "cost": 242.0 }, { "facility": "F7", "customer": "L", "cost": 243.0 }, { "facility": "F7", "customer": "M", "cost": 75.0 }, { "facility": "F7", "customer": "N", "cost": 682.0 }, { "facility": "F7", "customer": "O", "cost": 33.0 }, { "facility": "F7", "customer": "P", "cost": 1125.0 }, { "facility": "F7", "customer": "Q", "cost": 118.0 }, { "facility": "F7", "customer": "R", "cost": 459.0 }, { "facility": "F8", "customer": "A", "cost": 1334.0 }, { "facility": "F8", "customer": "B", "cost": 612.0 }, { "facility": "F8", "customer": "C", "cost": 49.0 }, { "facility": "F8", "customer": "D", "cost": 183.0 }, { "facility": "F8", "customer": "E", "cost": 149.0 }, { "facility": "F8", "customer": "F", "cost": 949.0 }, { "facility": "F8", "customer": "G", "cost": 1295.0 }, { "facility": "F8", "customer": "H", "cost": 1609.0 }, { "facility": "F8", "customer": "I", "cost": 85.0 }, { "facility": "F8", "customer": "J", "cost": 1726.0 }, { "facility": "F8", "customer": "K", "cost": 1099.0 }, { "facility": "F8", "customer": "L", "cost": 218.0 }, { "facility": "F8", "customer": "M", "cost": 801.0 }, { "facility": "F8", "customer": "N", "cost": 1566.0 }, { "facility": "F8", "customer": "O", "cost": 379.0 }, { "facility": "F8", "customer": "P", "cost": 1807.0 }, { "facility": "F8", "customer": "Q", "cost": 536.0 }, { "facility": "F8", "customer": "R", "cost": 1332.0 }, { "facility": "F9", "customer": "A", "cost": 402.0 }, { "facility": "F9", "customer": "B", "cost": 193.0 }, { "facility": "F9", "customer": "C", "cost": 91.0 }, { "facility": "F9", "customer": "D", "cost": 214.0 }, { "facility": "F9", "customer": "E", "cost": 87.0 }, { "facility": "F9", "customer": "F", "cost": 451.0 }, { "facility": "F9", "customer": "G", "cost": 516.0 }, { "facility": "F9", "customer": "H", "cost": 1027.0 }, { "facility": "F9", "customer": "I", "cost": 116.0 }, { "facility": "F9", "customer": "J", "cost": 817.0 }, { "facility": "F9", "customer": "K", "cost": 343.0 }, { "facility": "F9", "customer": "L", "cost": 49.0 }, { "facility": "F9", "customer": "M", "cost": 168.0 }, { "facility": "F9", "customer": "N", "cost": 759.0 }, { "facility": "F9", "customer": "O", "cost": 132.0 }, { "facility": "F9", "customer": "P", "cost": 867.0 }, { "facility": "F9", "customer": "Q", "cost": 261.0 }, { "facility": "F9", "customer": "R", "cost": 677.0 } ], "objective": 3766.0 }, "solution_variant": { "selected": [ "F4", "F6" ], "assignments": [ "F4", "F6", "F4", "F4", "F6", "F6", "F6", "F6", "F4", "F4", "F6", "F4", "F4", "F6", "F6", "F4", "F6", "F6" ] }, "context_index": 45, "input_format": "nl", "input_index_base": "names" }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "At the planning meeting the task was explained plainly: decide which local switching offices to switch on and make sure every subscriber is assigned to one and only one of the switched-on offices, with no office taking more subscribers than its capacity allows. Turning on an office costs money, and linking each subscriber to a particular office has its own cost, so the total cost for any plan is just the sum of the activation charges for opened offices plus all subscriber connection costs — the plan should minimize that total. The specific numbers for this instance are provided below.\n\n{\n \"num_switching_offices\": 8,\n \"num_subscribers\": 19,\n \"offices\": [\n {\n \"office_id\": \"F1\",\n \"activation_cost\": 400.0,\n \"office_capacity\": 500.0\n },\n {\n \"office_id\": \"F2\",\n \"activation_cost\": 400.0,\n \"office_capacity\": 500.0\n },\n {\n \"office_id\": \"F3\",\n \"activation_cost\": 400.0,\n \"office_capacity\": 500.0\n },\n {\n \"office_id\": \"F4\",\n \"activation_cost\": 400.0,\n \"office_capacity\": 500.0\n },\n {\n \"office_id\": \"F5\",\n \"activation_cost\": 400.0,\n \"office_capacity\": 500.0\n },\n {\n \"office_id\": \"F6\",\n \"activation_cost\": 400.0,\n \"office_capacity\": 500.0\n },\n {\n \"office_id\": \"F7\",\n \"activation_cost\": 400.0,\n \"office_capacity\": 500.0\n },\n {\n \"office_id\": \"F8\",\n \"activation_cost\": 400.0,\n \"office_capacity\": 500.0\n }\n ],\n \"subscribers\": [\n {\n \"subscriber_id\": 1,\n \"subscriber_demand\": 13.0\n },\n {\n \"subscriber_id\": 2,\n \"subscriber_demand\": 26.0\n },\n {\n \"subscriber_id\": 3,\n \"subscriber_demand\": 23.0\n },\n {\n \"subscriber_id\": 4,\n \"subscriber_demand\": 28.0\n },\n {\n \"subscriber_id\": 5,\n \"subscriber_demand\": 28.0\n },\n {\n \"subscriber_id\": 6,\n \"subscriber_demand\": 26.0\n },\n {\n \"subscriber_id\": 7,\n \"subscriber_demand\": 30.0\n },\n {\n \"subscriber_id\": 8,\n \"subscriber_demand\": 27.0\n },\n {\n \"subscriber_id\": 9,\n \"subscriber_demand\": 10.0\n },\n {\n \"subscriber_id\": 10,\n \"subscriber_demand\": 23.0\n },\n {\n \"subscriber_id\": 11,\n \"subscriber_demand\": 23.0\n },\n {\n \"subscriber_id\": 12,\n \"subscriber_demand\": 23.0\n },\n {\n \"subscriber_id\": 13,\n \"subscriber_demand\": 22.0\n },\n {\n \"subscriber_id\": 14,\n \"subscriber_demand\": 26.0\n },\n {\n \"subscriber_id\": 15,\n \"subscriber_demand\": 21.0\n },\n {\n \"subscriber_id\": 16,\n \"subscriber_demand\": 18.0\n },\n {\n \"subscriber_id\": 17,\n \"subscriber_demand\": 24.0\n },\n {\n \"subscriber_id\": 18,\n \"subscriber_demand\": 15.0\n },\n {\n \"subscriber_id\": 19,\n \"subscriber_demand\": 27.0\n }\n ],\n \"connections\": [\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 1,\n \"connection_cost\": 2821.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 2,\n \"connection_cost\": 1022.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 3,\n \"connection_cost\": 2332.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 4,\n \"connection_cost\": 1619.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 5,\n \"connection_cost\": 2333.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 6,\n \"connection_cost\": 795.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 7,\n \"connection_cost\": 913.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 8,\n \"connection_cost\": 2040.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 9,\n \"connection_cost\": 1813.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 10,\n \"connection_cost\": 1203.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 11,\n \"connection_cost\": 1280.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 12,\n \"connection_cost\": 1741.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 13,\n \"connection_cost\": 1619.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 14,\n \"connection_cost\": 1991.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 15,\n \"connection_cost\": 2386.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 16,\n \"connection_cost\": 395.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 17,\n \"connection_cost\": 2041.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 18,\n \"connection_cost\": 2235.0\n },\n {\n \"office_id\": \"F1\",\n \"subscriber_id\": 19,\n \"connection_cost\": 339.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 1,\n \"connection_cost\": 2223.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 2,\n \"connection_cost\": 500.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 3,\n \"connection_cost\": 1732.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 4,\n \"connection_cost\": 1165.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 5,\n \"connection_cost\": 1817.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 6,\n \"connection_cost\": 398.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 7,\n \"connection_cost\": 232.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 8,\n \"connection_cost\": 1449.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 9,\n \"connection_cost\": 1131.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 10,\n \"connection_cost\": 877.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 11,\n \"connection_cost\": 615.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 12,\n \"connection_cost\": 1131.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 13,\n \"connection_cost\": 1055.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 14,\n \"connection_cost\": 1375.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 15,\n \"connection_cost\": 1846.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 16,\n \"connection_cost\": 210.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 17,\n \"connection_cost\": 1641.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 18,\n \"connection_cost\": 1752.0\n },\n {\n \"office_id\": \"F2\",\n \"subscriber_id\": 19,\n \"connection_cost\": 204.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 1,\n \"connection_cost\": 1193.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 2,\n \"connection_cost\": 54.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 3,\n \"connection_cost\": 701.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 4,\n \"connection_cost\": 376.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 5,\n \"connection_cost\": 837.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 6,\n \"connection_cost\": 75.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 7,\n \"connection_cost\": 203.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 8,\n \"connection_cost\": 416.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 9,\n \"connection_cost\": 637.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 10,\n \"connection_cost\": 343.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 11,\n \"connection_cost\": 425.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 12,\n \"connection_cost\": 113.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 13,\n \"connection_cost\": 115.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 14,\n \"connection_cost\": 360.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 15,\n \"connection_cost\": 839.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 16,\n \"connection_cost\": 62.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 17,\n \"connection_cost\": 840.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 18,\n \"connection_cost\": 817.0\n },\n {\n \"office_id\": \"F3\",\n \"subscriber_id\": 19,\n \"connection_cost\": 80.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 1,\n \"connection_cost\": 1357.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 2,\n \"connection_cost\": 250.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 3,\n \"connection_cost\": 930.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 4,\n \"connection_cost\": 769.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 5,\n \"connection_cost\": 1203.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 6,\n \"connection_cost\": 263.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 7,\n \"connection_cost\": 61.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 8,\n \"connection_cost\": 734.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 9,\n \"connection_cost\": 21.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 10,\n \"connection_cost\": 667.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 11,\n \"connection_cost\": 62.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 12,\n \"connection_cost\": 462.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 13,\n \"connection_cost\": 514.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 14,\n \"connection_cost\": 607.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 15,\n \"connection_cost\": 1177.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 16,\n \"connection_cost\": 181.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 17,\n \"connection_cost\": 1243.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 18,\n \"connection_cost\": 1206.0\n },\n {\n \"office_id\": \"F4\",\n \"subscriber_id\": 19,\n \"connection_cost\": 186.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 1,\n \"connection_cost\": 1775.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 2,\n \"connection_cost\": 209.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 3,\n \"connection_cost\": 1310.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 4,\n \"connection_cost\": 498.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 5,\n \"connection_cost\": 1223.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 6,\n \"connection_cost\": 74.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 7,\n \"connection_cost\": 496.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 8,\n \"connection_cost\": 1023.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 9,\n \"connection_cost\": 1206.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 10,\n \"connection_cost\": 231.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 11,\n \"connection_cost\": 839.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 12,\n \"connection_cost\": 797.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 13,\n \"connection_cost\": 607.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 14,\n \"connection_cost\": 1028.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 15,\n \"connection_cost\": 1289.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 16,\n \"connection_cost\": 36.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 17,\n \"connection_cost\": 947.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 18,\n \"connection_cost\": 1115.0\n },\n {\n \"office_id\": \"F5\",\n \"subscriber_id\": 19,\n \"connection_cost\": 54.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 1,\n \"connection_cost\": 1006.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 2,\n \"connection_cost\": 111.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 3,\n \"connection_cost\": 608.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 4,\n \"connection_cost\": 67.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 5,\n \"connection_cost\": 402.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 6,\n \"connection_cost\": 61.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 7,\n \"connection_cost\": 371.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 8,\n \"connection_cost\": 389.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 9,\n \"connection_cost\": 874.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 10,\n \"connection_cost\": 116.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 11,\n \"connection_cost\": 642.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 12,\n \"connection_cost\": 329.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 13,\n \"connection_cost\": 165.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 14,\n \"connection_cost\": 464.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 15,\n \"connection_cost\": 477.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 16,\n \"connection_cost\": 36.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 17,\n \"connection_cost\": 375.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 18,\n \"connection_cost\": 325.0\n },\n {\n \"office_id\": \"F6\",\n \"subscriber_id\": 19,\n \"connection_cost\": 54.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 1,\n \"connection_cost\": 2444.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 2,\n \"connection_cost\": 722.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 3,\n \"connection_cost\": 1975.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 4,\n \"connection_cost\": 1143.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 5,\n \"connection_cost\": 1877.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 6,\n \"connection_cost\": 445.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 7,\n \"connection_cost\": 861.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 8,\n \"connection_cost\": 1686.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 9,\n \"connection_cost\": 1711.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 10,\n \"connection_cost\": 653.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 11,\n \"connection_cost\": 1246.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 12,\n \"connection_cost\": 1433.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 13,\n \"connection_cost\": 1262.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 14,\n \"connection_cost\": 1676.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 15,\n \"connection_cost\": 1952.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 16,\n \"connection_cost\": 114.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 17,\n \"connection_cost\": 1499.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 18,\n \"connection_cost\": 1750.0\n },\n {\n \"office_id\": \"F7\",\n \"subscriber_id\": 19,\n \"connection_cost\": 97.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 1,\n \"connection_cost\": 1543.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 2,\n \"connection_cost\": 171.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 3,\n \"connection_cost\": 1061.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 4,\n \"connection_cost\": 718.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 5,\n \"connection_cost\": 1242.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 6,\n \"connection_cost\": 189.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 7,\n \"connection_cost\": 90.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 8,\n \"connection_cost\": 803.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 9,\n \"connection_cost\": 515.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 10,\n \"connection_cost\": 588.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 11,\n \"connection_cost\": 251.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 12,\n \"connection_cost\": 483.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 13,\n \"connection_cost\": 488.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 14,\n \"connection_cost\": 699.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 15,\n \"connection_cost\": 1242.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 16,\n \"connection_cost\": 128.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 17,\n \"connection_cost\": 1206.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 18,\n \"connection_cost\": 1217.0\n },\n {\n \"office_id\": \"F8\",\n \"subscriber_id\": 19,\n \"connection_cost\": 139.0\n }\n ]\n}\n\nOh, and just so you know how I’d like the answer returned, a handy little JSON sketch is what I’m expecting — nothing fancy, just the shape of the response so it’s easy to check and parse.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nPretty simple: \"selected\" lists the offices you decide to switch on (their IDs), and \"assignments\" lists, in order, which switched-on office each subscriber is assigned to (by that office’s ID). Think of it like filling out a form: one line for which offices are active, another line saying who connects to which active office.\n\nThis JSON is just a sketch of the expected shape — not the actual final plan.\n\nPlease use the exact identifiers from the instance input: no renaming and no new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 2821.0, 1022.0, 2332.0, 1619.0, 2333.0, 795.0, 913.0, 2040.0, 1813.0, 1203.0, 1280.0, 1741.0, 1619.0, 1991.0, 2386.0, 395.0, 2041.0, 2235.0, 339.0 ], [ 2223.0, 500.0, 1732.0, 1165.0, 1817.0, 398.0, 232.0, 1449.0, 1131.0, 877.0, 615.0, 1131.0, 1055.0, 1375.0, 1846.0, 210.0, 1641.0, 1752.0, 204.0 ], [ 1193.0, 54.0, 701.0, 376.0, 837.0, 75.0, 203.0, 416.0, 637.0, 343.0, 425.0, 113.0, 115.0, 360.0, 839.0, 62.0, 840.0, 817.0, 80.0 ], [ 1357.0, 250.0, 930.0, 769.0, 1203.0, 263.0, 61.0, 734.0, 21.0, 667.0, 62.0, 462.0, 514.0, 607.0, 1177.0, 181.0, 1243.0, 1206.0, 186.0 ], [ 1775.0, 209.0, 1310.0, 498.0, 1223.0, 74.0, 496.0, 1023.0, 1206.0, 231.0, 839.0, 797.0, 607.0, 1028.0, 1289.0, 36.0, 947.0, 1115.0, 54.0 ], [ 1006.0, 111.0, 608.0, 67.0, 402.0, 61.0, 371.0, 389.0, 874.0, 116.0, 642.0, 329.0, 165.0, 464.0, 477.0, 36.0, 375.0, 325.0, 54.0 ], [ 2444.0, 722.0, 1975.0, 1143.0, 1877.0, 445.0, 861.0, 1686.0, 1711.0, 653.0, 1246.0, 1433.0, 1262.0, 1676.0, 1952.0, 114.0, 1499.0, 1750.0, 97.0 ], [ 1543.0, 171.0, 1061.0, 718.0, 1242.0, 189.0, 90.0, 803.0, 515.0, 588.0, 251.0, 483.0, 488.0, 699.0, 1242.0, 128.0, 1206.0, 1217.0, 139.0 ] ], "demands": [ 13.0, 26.0, 23.0, 28.0, 28.0, 26.0, 30.0, 27.0, 10.0, 23.0, 23.0, 23.0, 22.0, 26.0, 21.0, 18.0, 24.0, 15.0, 27.0 ], "objective": 5902.0 }, "solution": { "open_facilities": [ 2, 3, 5 ], "assignments": [ 5, 2, 5, 5, 5, 5, 3, 5, 3, 5, 3, 2, 2, 2, 5, 5, 5, 5, 5 ] }, "obj": 5902.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 19, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F7", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F8", "opening_cost": 400.0, "capacity": 500.0 } ], "customers": [ { "id": 1, "demand": 13.0 }, { "id": 2, "demand": 26.0 }, { "id": 3, "demand": 23.0 }, { "id": 4, "demand": 28.0 }, { "id": 5, "demand": 28.0 }, { "id": 6, "demand": 26.0 }, { "id": 7, "demand": 30.0 }, { "id": 8, "demand": 27.0 }, { "id": 9, "demand": 10.0 }, { "id": 10, "demand": 23.0 }, { "id": 11, "demand": 23.0 }, { "id": 12, "demand": 23.0 }, { "id": 13, "demand": 22.0 }, { "id": 14, "demand": 26.0 }, { "id": 15, "demand": 21.0 }, { "id": 16, "demand": 18.0 }, { "id": 17, "demand": 24.0 }, { "id": 18, "demand": 15.0 }, { "id": 19, "demand": 27.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 2821.0 }, { "facility": "F1", "customer": 2, "cost": 1022.0 }, { "facility": "F1", "customer": 3, "cost": 2332.0 }, { "facility": "F1", "customer": 4, "cost": 1619.0 }, { "facility": "F1", "customer": 5, "cost": 2333.0 }, { "facility": "F1", "customer": 6, "cost": 795.0 }, { "facility": "F1", "customer": 7, "cost": 913.0 }, { "facility": "F1", "customer": 8, "cost": 2040.0 }, { "facility": "F1", "customer": 9, "cost": 1813.0 }, { "facility": "F1", "customer": 10, "cost": 1203.0 }, { "facility": "F1", "customer": 11, "cost": 1280.0 }, { "facility": "F1", "customer": 12, "cost": 1741.0 }, { "facility": "F1", "customer": 13, "cost": 1619.0 }, { "facility": "F1", "customer": 14, "cost": 1991.0 }, { "facility": "F1", "customer": 15, "cost": 2386.0 }, { "facility": "F1", "customer": 16, "cost": 395.0 }, { "facility": "F1", "customer": 17, "cost": 2041.0 }, { "facility": "F1", "customer": 18, "cost": 2235.0 }, { "facility": "F1", "customer": 19, "cost": 339.0 }, { "facility": "F2", "customer": 1, "cost": 2223.0 }, { "facility": "F2", "customer": 2, "cost": 500.0 }, { "facility": "F2", "customer": 3, "cost": 1732.0 }, { "facility": "F2", "customer": 4, "cost": 1165.0 }, { "facility": "F2", "customer": 5, "cost": 1817.0 }, { "facility": "F2", "customer": 6, "cost": 398.0 }, { "facility": "F2", "customer": 7, "cost": 232.0 }, { "facility": "F2", "customer": 8, "cost": 1449.0 }, { "facility": "F2", "customer": 9, "cost": 1131.0 }, { "facility": "F2", "customer": 10, "cost": 877.0 }, { "facility": "F2", "customer": 11, "cost": 615.0 }, { "facility": "F2", "customer": 12, "cost": 1131.0 }, { "facility": "F2", "customer": 13, "cost": 1055.0 }, { "facility": "F2", "customer": 14, "cost": 1375.0 }, { "facility": "F2", "customer": 15, "cost": 1846.0 }, { "facility": "F2", "customer": 16, "cost": 210.0 }, { "facility": "F2", "customer": 17, "cost": 1641.0 }, { "facility": "F2", "customer": 18, "cost": 1752.0 }, { "facility": "F2", "customer": 19, "cost": 204.0 }, { "facility": "F3", "customer": 1, "cost": 1193.0 }, { "facility": "F3", "customer": 2, "cost": 54.0 }, { "facility": "F3", "customer": 3, "cost": 701.0 }, { "facility": "F3", "customer": 4, "cost": 376.0 }, { "facility": "F3", "customer": 5, "cost": 837.0 }, { "facility": "F3", "customer": 6, "cost": 75.0 }, { "facility": "F3", "customer": 7, "cost": 203.0 }, { "facility": "F3", "customer": 8, "cost": 416.0 }, { "facility": "F3", "customer": 9, "cost": 637.0 }, { "facility": "F3", "customer": 10, "cost": 343.0 }, { "facility": "F3", "customer": 11, "cost": 425.0 }, { "facility": "F3", "customer": 12, "cost": 113.0 }, { "facility": "F3", "customer": 13, "cost": 115.0 }, { "facility": "F3", "customer": 14, "cost": 360.0 }, { "facility": "F3", "customer": 15, "cost": 839.0 }, { "facility": "F3", "customer": 16, "cost": 62.0 }, { "facility": "F3", "customer": 17, "cost": 840.0 }, { "facility": "F3", "customer": 18, "cost": 817.0 }, { "facility": "F3", "customer": 19, "cost": 80.0 }, { "facility": "F4", "customer": 1, "cost": 1357.0 }, { "facility": "F4", "customer": 2, "cost": 250.0 }, { "facility": "F4", "customer": 3, "cost": 930.0 }, { "facility": "F4", "customer": 4, "cost": 769.0 }, { "facility": "F4", "customer": 5, "cost": 1203.0 }, { "facility": "F4", "customer": 6, "cost": 263.0 }, { "facility": "F4", "customer": 7, "cost": 61.0 }, { "facility": "F4", "customer": 8, "cost": 734.0 }, { "facility": "F4", "customer": 9, "cost": 21.0 }, { "facility": "F4", "customer": 10, "cost": 667.0 }, { "facility": "F4", "customer": 11, "cost": 62.0 }, { "facility": "F4", "customer": 12, "cost": 462.0 }, { "facility": "F4", "customer": 13, "cost": 514.0 }, { "facility": "F4", "customer": 14, "cost": 607.0 }, { "facility": "F4", "customer": 15, "cost": 1177.0 }, { "facility": "F4", "customer": 16, "cost": 181.0 }, { "facility": "F4", "customer": 17, "cost": 1243.0 }, { "facility": "F4", "customer": 18, "cost": 1206.0 }, { "facility": "F4", "customer": 19, "cost": 186.0 }, { "facility": "F5", "customer": 1, "cost": 1775.0 }, { "facility": "F5", "customer": 2, "cost": 209.0 }, { "facility": "F5", "customer": 3, "cost": 1310.0 }, { "facility": "F5", "customer": 4, "cost": 498.0 }, { "facility": "F5", "customer": 5, "cost": 1223.0 }, { "facility": "F5", "customer": 6, "cost": 74.0 }, { "facility": "F5", "customer": 7, "cost": 496.0 }, { "facility": "F5", "customer": 8, "cost": 1023.0 }, { "facility": "F5", "customer": 9, "cost": 1206.0 }, { "facility": "F5", "customer": 10, "cost": 231.0 }, { "facility": "F5", "customer": 11, "cost": 839.0 }, { "facility": "F5", "customer": 12, "cost": 797.0 }, { "facility": "F5", "customer": 13, "cost": 607.0 }, { "facility": "F5", "customer": 14, "cost": 1028.0 }, { "facility": "F5", "customer": 15, "cost": 1289.0 }, { "facility": "F5", "customer": 16, "cost": 36.0 }, { "facility": "F5", "customer": 17, "cost": 947.0 }, { "facility": "F5", "customer": 18, "cost": 1115.0 }, { "facility": "F5", "customer": 19, "cost": 54.0 }, { "facility": "F6", "customer": 1, "cost": 1006.0 }, { "facility": "F6", "customer": 2, "cost": 111.0 }, { "facility": "F6", "customer": 3, "cost": 608.0 }, { "facility": "F6", "customer": 4, "cost": 67.0 }, { "facility": "F6", "customer": 5, "cost": 402.0 }, { "facility": "F6", "customer": 6, "cost": 61.0 }, { "facility": "F6", "customer": 7, "cost": 371.0 }, { "facility": "F6", "customer": 8, "cost": 389.0 }, { "facility": "F6", "customer": 9, "cost": 874.0 }, { "facility": "F6", "customer": 10, "cost": 116.0 }, { "facility": "F6", "customer": 11, "cost": 642.0 }, { "facility": "F6", "customer": 12, "cost": 329.0 }, { "facility": "F6", "customer": 13, "cost": 165.0 }, { "facility": "F6", "customer": 14, "cost": 464.0 }, { "facility": "F6", "customer": 15, "cost": 477.0 }, { "facility": "F6", "customer": 16, "cost": 36.0 }, { "facility": "F6", "customer": 17, "cost": 375.0 }, { "facility": "F6", "customer": 18, "cost": 325.0 }, { "facility": "F6", "customer": 19, "cost": 54.0 }, { "facility": "F7", "customer": 1, "cost": 2444.0 }, { "facility": "F7", "customer": 2, "cost": 722.0 }, { "facility": "F7", "customer": 3, "cost": 1975.0 }, { "facility": "F7", "customer": 4, "cost": 1143.0 }, { "facility": "F7", "customer": 5, "cost": 1877.0 }, { "facility": "F7", "customer": 6, "cost": 445.0 }, { "facility": "F7", "customer": 7, "cost": 861.0 }, { "facility": "F7", "customer": 8, "cost": 1686.0 }, { "facility": "F7", "customer": 9, "cost": 1711.0 }, { "facility": "F7", "customer": 10, "cost": 653.0 }, { "facility": "F7", "customer": 11, "cost": 1246.0 }, { "facility": "F7", "customer": 12, "cost": 1433.0 }, { "facility": "F7", "customer": 13, "cost": 1262.0 }, { "facility": "F7", "customer": 14, "cost": 1676.0 }, { "facility": "F7", "customer": 15, "cost": 1952.0 }, { "facility": "F7", "customer": 16, "cost": 114.0 }, { "facility": "F7", "customer": 17, "cost": 1499.0 }, { "facility": "F7", "customer": 18, "cost": 1750.0 }, { "facility": "F7", "customer": 19, "cost": 97.0 }, { "facility": "F8", "customer": 1, "cost": 1543.0 }, { "facility": "F8", "customer": 2, "cost": 171.0 }, { "facility": "F8", "customer": 3, "cost": 1061.0 }, { "facility": "F8", "customer": 4, "cost": 718.0 }, { "facility": "F8", "customer": 5, "cost": 1242.0 }, { "facility": "F8", "customer": 6, "cost": 189.0 }, { "facility": "F8", "customer": 7, "cost": 90.0 }, { "facility": "F8", "customer": 8, "cost": 803.0 }, { "facility": "F8", "customer": 9, "cost": 515.0 }, { "facility": "F8", "customer": 10, "cost": 588.0 }, { "facility": "F8", "customer": 11, "cost": 251.0 }, { "facility": "F8", "customer": 12, "cost": 483.0 }, { "facility": "F8", "customer": 13, "cost": 488.0 }, { "facility": "F8", "customer": 14, "cost": 699.0 }, { "facility": "F8", "customer": 15, "cost": 1242.0 }, { "facility": "F8", "customer": 16, "cost": 128.0 }, { "facility": "F8", "customer": 17, "cost": 1206.0 }, { "facility": "F8", "customer": 18, "cost": 1217.0 }, { "facility": "F8", "customer": 19, "cost": 139.0 } ], "objective": 5902.0 }, "solution_variant": { "selected": [ "F3", "F4", "F6" ], "assignments": [ "F6", "F3", "F6", "F6", "F6", "F6", "F4", "F6", "F4", "F6", "F4", "F3", "F3", "F3", "F6", "F6", "F6", "F6", "F6" ] }, "context_index": 46, "input_format": "json", "input_index_base": 1 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Many people are coordinating a distribution effort, and the basic question is which service centers to activate and how to assign each beneficiary to one active center without exceeding any center’s capacity. The sensible outcome is the one with the lowest combined expense — the total you get when you add the opening fees for the centers in use to all the individual serving costs. Numbers and specifics come right below.\n\nThey are considering 8 candidate distribution centers and 20 beneficiaries.\nCenter F1 has opening cost 400.0 and capacity 907.0.\nCenter F2 has opening cost 400.0 and capacity 1105.0.\nCenter F3 has opening cost 400.0 and capacity 898.0.\nCenter F4 has opening cost 400.0 and capacity 975.0.\nCenter F5 has opening cost 400.0 and capacity 588.0.\nCenter F6 has opening cost 400.0 and capacity 745.0.\nCenter F7 has opening cost 400.0 and capacity 972.0.\nCenter F8 has opening cost 400.0 and capacity 506.0.\nBeneficiary 0 has demand 40.0.\nBeneficiary 1 has demand 23.0.\nBeneficiary 2 has demand 10.0.\nBeneficiary 3 has demand 31.0.\nBeneficiary 4 has demand 44.0.\nBeneficiary 5 has demand 33.0.\nBeneficiary 6 has demand 17.0.\nBeneficiary 7 has demand 11.0.\nBeneficiary 8 has demand 21.0.\nBeneficiary 9 has demand 45.0.\nBeneficiary 10 has demand 22.0.\nBeneficiary 11 has demand 18.0.\nBeneficiary 12 has demand 38.0.\nBeneficiary 13 has demand 35.0.\nBeneficiary 14 has demand 42.0.\nBeneficiary 15 has demand 22.0.\nBeneficiary 16 has demand 46.0.\nBeneficiary 17 has demand 31.0.\nBeneficiary 18 has demand 49.0.\nBeneficiary 19 has demand 42.0.\nServing beneficiary 0 from center F1 incurs cost 579.0.\nServing beneficiary 1 from center F1 incurs cost 413.0.\nServing beneficiary 2 from center F1 incurs cost 186.0.\nServing beneficiary 3 from center F1 incurs cost 229.0.\nServing beneficiary 4 from center F1 incurs cost 161.0.\nServing beneficiary 5 from center F1 incurs cost 452.0.\nServing beneficiary 6 from center F1 incurs cost 393.0.\nServing beneficiary 7 from center F1 incurs cost 409.0.\nServing beneficiary 8 from center F1 incurs cost 480.0.\nServing beneficiary 9 from center F1 incurs cost 70.0.\nServing beneficiary 10 from center F1 incurs cost 439.0.\nServing beneficiary 11 from center F1 incurs cost 423.0.\nServing beneficiary 12 from center F1 incurs cost 473.0.\nServing beneficiary 13 from center F1 incurs cost 187.0.\nServing beneficiary 14 from center F1 incurs cost 162.0.\nServing beneficiary 15 from center F1 incurs cost 402.0.\nServing beneficiary 16 from center F1 incurs cost 258.0.\nServing beneficiary 17 from center F1 incurs cost 165.0.\nServing beneficiary 18 from center F1 incurs cost 64.0.\nServing beneficiary 19 from center F1 incurs cost 92.0.\nServing beneficiary 0 from center F2 incurs cost 296.0.\nServing beneficiary 1 from center F2 incurs cost 247.0.\nServing beneficiary 2 from center F2 incurs cost 540.0.\nServing beneficiary 3 from center F2 incurs cost 377.0.\nServing beneficiary 4 from center F2 incurs cost 437.0.\nServing beneficiary 5 from center F2 incurs cost 549.0.\nServing beneficiary 6 from center F2 incurs cost 219.0.\nServing beneficiary 7 from center F2 incurs cost 473.0.\nServing beneficiary 8 from center F2 incurs cost 405.0.\nServing beneficiary 9 from center F2 incurs cost 520.0.\nServing beneficiary 10 from center F2 incurs cost 506.0.\nServing beneficiary 11 from center F2 incurs cost 143.0.\nServing beneficiary 12 from center F2 incurs cost 305.0.\nServing beneficiary 13 from center F2 incurs cost 345.0.\nServing beneficiary 14 from center F2 incurs cost 442.0.\nServing beneficiary 15 from center F2 incurs cost 545.0.\nServing beneficiary 16 from center F2 incurs cost 290.0.\nServing beneficiary 17 from center F2 incurs cost 589.0.\nServing beneficiary 18 from center F2 incurs cost 487.0.\nServing beneficiary 19 from center F2 incurs cost 520.0.\nServing beneficiary 0 from center F3 incurs cost 259.0.\nServing beneficiary 1 from center F3 incurs cost 423.0.\nServing beneficiary 2 from center F3 incurs cost 469.0.\nServing beneficiary 3 from center F3 incurs cost 378.0.\nServing beneficiary 4 from center F3 incurs cost 378.0.\nServing beneficiary 5 from center F3 incurs cost 233.0.\nServing beneficiary 6 from center F3 incurs cost 118.0.\nServing beneficiary 7 from center F3 incurs cost 157.0.\nServing beneficiary 8 from center F3 incurs cost 163.0.\nServing beneficiary 9 from center F3 incurs cost 295.0.\nServing beneficiary 10 from center F3 incurs cost 195.0.\nServing beneficiary 11 from center F3 incurs cost 352.0.\nServing beneficiary 12 from center F3 incurs cost 146.0.\nServing beneficiary 13 from center F3 incurs cost 158.0.\nServing beneficiary 14 from center F3 incurs cost 383.0.\nServing beneficiary 15 from center F3 incurs cost 218.0.\nServing beneficiary 16 from center F3 incurs cost 313.0.\nServing beneficiary 17 from center F3 incurs cost 319.0.\nServing beneficiary 18 from center F3 incurs cost 353.0.\nServing beneficiary 19 from center F3 incurs cost 396.0.\nServing beneficiary 0 from center F4 incurs cost 708.0.\nServing beneficiary 1 from center F4 incurs cost 375.0.\nServing beneficiary 2 from center F4 incurs cost 17.0.\nServing beneficiary 3 from center F4 incurs cost 182.0.\nServing beneficiary 4 from center F4 incurs cost 122.0.\nServing beneficiary 5 from center F4 incurs cost 643.0.\nServing beneficiary 6 from center F4 incurs cost 515.0.\nServing beneficiary 7 from center F4 incurs cost 593.0.\nServing beneficiary 8 from center F4 incurs cost 647.0.\nServing beneficiary 9 from center F4 incurs cost 265.0.\nServing beneficiary 10 from center F4 incurs cost 625.0.\nServing beneficiary 11 from center F4 incurs cost 433.0.\nServing beneficiary 12 from center F4 incurs cost 617.0.\nServing beneficiary 13 from center F4 incurs cost 327.0.\nServing beneficiary 14 from center F4 incurs cost 117.0.\nServing beneficiary 15 from center F4 incurs cost 595.0.\nServing beneficiary 16 from center F4 incurs cost 267.0.\nServing beneficiary 17 from center F4 incurs cost 352.0.\nServing beneficiary 18 from center F4 incurs cost 141.0.\nServing beneficiary 19 from center F4 incurs cost 104.0.\nServing beneficiary 0 from center F5 incurs cost 354.0.\nServing beneficiary 1 from center F5 incurs cost 322.0.\nServing beneficiary 2 from center F5 incurs cost 344.0.\nServing beneficiary 3 from center F5 incurs cost 249.0.\nServing beneficiary 4 from center F5 incurs cost 250.0.\nServing beneficiary 5 from center F5 incurs cost 342.0.\nServing beneficiary 6 from center F5 incurs cost 164.0.\nServing beneficiary 7 from center F5 incurs cost 272.0.\nServing beneficiary 8 from center F5 incurs cost 293.0.\nServing beneficiary 9 from center F5 incurs cost 220.0.\nServing beneficiary 10 from center F5 incurs cost 310.0.\nServing beneficiary 11 from center F5 incurs cost 274.0.\nServing beneficiary 12 from center F5 incurs cost 256.0.\nServing beneficiary 13 from center F5 incurs cost 43.0.\nServing beneficiary 14 from center F5 incurs cost 255.0.\nServing beneficiary 15 from center F5 incurs cost 312.0.\nServing beneficiary 16 from center F5 incurs cost 190.0.\nServing beneficiary 17 from center F5 incurs cost 282.0.\nServing beneficiary 18 from center F5 incurs cost 238.0.\nServing beneficiary 19 from center F5 incurs cost 280.0.\nServing beneficiary 0 from center F6 incurs cost 549.0.\nServing beneficiary 1 from center F6 incurs cost 43.0.\nServing beneficiary 2 from center F6 incurs cost 332.0.\nServing beneficiary 3 from center F6 incurs cost 179.0.\nServing beneficiary 4 from center F6 incurs cost 256.0.\nServing beneficiary 5 from center F6 incurs cost 673.0.\nServing beneficiary 6 from center F6 incurs cost 389.0.\nServing beneficiary 7 from center F6 incurs cost 600.0.\nServing beneficiary 8 from center F6 incurs cost 586.0.\nServing beneficiary 9 from center F6 incurs cost 449.0.\nServing beneficiary 10 from center F6 incurs cost 638.0.\nServing beneficiary 11 from center F6 incurs cost 147.0.\nServing beneficiary 12 from center F6 incurs cost 508.0.\nServing beneficiary 13 from center F6 incurs cost 342.0.\nServing beneficiary 14 from center F6 incurs cost 259.0.\nServing beneficiary 15 from center F6 incurs cost 646.0.\nServing beneficiary 16 from center F6 incurs cost 156.0.\nServing beneficiary 17 from center F6 incurs cost 546.0.\nServing beneficiary 18 from center F6 incurs cost 348.0.\nServing beneficiary 19 from center F6 incurs cost 360.0.\nServing beneficiary 0 from center F7 incurs cost 168.0.\nServing beneficiary 1 from center F7 incurs cost 369.0.\nServing beneficiary 2 from center F7 incurs cost 525.0.\nServing beneficiary 3 from center F7 incurs cost 395.0.\nServing beneficiary 4 from center F7 incurs cost 422.0.\nServing beneficiary 5 from center F7 incurs cost 343.0.\nServing beneficiary 6 from center F7 incurs cost 30.0.\nServing beneficiary 7 from center F7 incurs cost 268.0.\nServing beneficiary 8 from center F7 incurs cost 202.0.\nServing beneficiary 9 from center F7 incurs cost 408.0.\nServing beneficiary 10 from center F7 incurs cost 300.0.\nServing beneficiary 11 from center F7 incurs cost 274.0.\nServing beneficiary 12 from center F7 incurs cost 110.0.\nServing beneficiary 13 from center F7 incurs cost 237.0.\nServing beneficiary 14 from center F7 incurs cost 428.0.\nServing beneficiary 15 from center F7 incurs cost 343.0.\nServing beneficiary 16 from center F7 incurs cost 310.0.\nServing beneficiary 17 from center F7 incurs cost 450.0.\nServing beneficiary 18 from center F7 incurs cost 429.0.\nServing beneficiary 19 from center F7 incurs cost 471.0.\nServing beneficiary 0 from center F8 incurs cost 320.0.\nServing beneficiary 1 from center F8 incurs cost 237.0.\nServing beneficiary 2 from center F8 incurs cost 382.0.\nServing beneficiary 3 from center F8 incurs cost 242.0.\nServing beneficiary 4 from center F8 incurs cost 277.0.\nServing beneficiary 5 from center F8 incurs cost 421.0.\nServing beneficiary 6 from center F8 incurs cost 135.0.\nServing beneficiary 7 from center F8 incurs cost 345.0.\nServing beneficiary 8 from center F8 incurs cost 326.0.\nServing beneficiary 9 from center F8 incurs cost 324.0.\nServing beneficiary 10 from center F8 incurs cost 383.0.\nServing beneficiary 11 from center F8 incurs cost 167.0.\nServing beneficiary 12 from center F8 incurs cost 255.0.\nServing beneficiary 13 from center F8 incurs cost 150.0.\nServing beneficiary 14 from center F8 incurs cost 283.0.\nServing beneficiary 15 from center F8 incurs cost 401.0.\nServing beneficiary 16 from center F8 incurs cost 156.0.\nServing beneficiary 17 from center F8 incurs cost 395.0.\nServing beneficiary 18 from center F8 incurs cost 304.0.\nServing beneficiary 19 from center F8 incurs cost 342.0.\nThey will select which centers to open and how to assign beneficiaries so the total of opening fees plus service costs is minimized.\n\nWhen you're ready to send back the decisions, just stick to this simple JSON shape so it's easy to read and check:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is the list of centers you'll activate. \"assignments\" is the chosen active center for each beneficiary (one entry per beneficiary, in the same order as the input). Think of it like filling out a short form: which sites are on, and for each person, which open site they're assigned to.\n\nThis is just a sketch of the expected shape, not the actual answer.\n\nPlease use the exact identifiers from the instance input — don't rename them and don't invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 907.0, 1105.0, 898.0, 975.0, 588.0, 745.0, 972.0, 506.0 ], "connection_costs": [ [ 579.0, 413.0, 186.0, 229.0, 161.0, 452.0, 393.0, 409.0, 480.0, 70.0, 439.0, 423.0, 473.0, 187.0, 162.0, 402.0, 258.0, 165.0, 64.0, 92.0 ], [ 296.0, 247.0, 540.0, 377.0, 437.0, 549.0, 219.0, 473.0, 405.0, 520.0, 506.0, 143.0, 305.0, 345.0, 442.0, 545.0, 290.0, 589.0, 487.0, 520.0 ], [ 259.0, 423.0, 469.0, 378.0, 378.0, 233.0, 118.0, 157.0, 163.0, 295.0, 195.0, 352.0, 146.0, 158.0, 383.0, 218.0, 313.0, 319.0, 353.0, 396.0 ], [ 708.0, 375.0, 17.0, 182.0, 122.0, 643.0, 515.0, 593.0, 647.0, 265.0, 625.0, 433.0, 617.0, 327.0, 117.0, 595.0, 267.0, 352.0, 141.0, 104.0 ], [ 354.0, 322.0, 344.0, 249.0, 250.0, 342.0, 164.0, 272.0, 293.0, 220.0, 310.0, 274.0, 256.0, 43.0, 255.0, 312.0, 190.0, 282.0, 238.0, 280.0 ], [ 549.0, 43.0, 332.0, 179.0, 256.0, 673.0, 389.0, 600.0, 586.0, 449.0, 638.0, 147.0, 508.0, 342.0, 259.0, 646.0, 156.0, 546.0, 348.0, 360.0 ], [ 168.0, 369.0, 525.0, 395.0, 422.0, 343.0, 30.0, 268.0, 202.0, 408.0, 300.0, 274.0, 110.0, 237.0, 428.0, 343.0, 310.0, 450.0, 429.0, 471.0 ], [ 320.0, 237.0, 382.0, 242.0, 277.0, 421.0, 135.0, 345.0, 326.0, 324.0, 383.0, 167.0, 255.0, 150.0, 283.0, 401.0, 156.0, 395.0, 304.0, 342.0 ] ], "demands": [ 40.0, 23.0, 10.0, 31.0, 44.0, 33.0, 17.0, 11.0, 21.0, 45.0, 22.0, 18.0, 38.0, 35.0, 42.0, 22.0, 46.0, 31.0, 49.0, 42.0 ], "objective": 4272.0 }, "solution": { "open_facilities": [ 0, 2, 5 ], "assignments": [ 2, 5, 0, 5, 0, 2, 2, 2, 2, 0, 2, 5, 2, 2, 0, 2, 5, 0, 0, 0 ] }, "obj": 4272.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 8, "num_customers": 20, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 907.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 1105.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 898.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 975.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 588.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 745.0 }, { "id": "F7", "opening_cost": 400.0, "capacity": 972.0 }, { "id": "F8", "opening_cost": 400.0, "capacity": 506.0 } ], "customers": [ { "id": 0, "demand": 40.0 }, { "id": 1, "demand": 23.0 }, { "id": 2, "demand": 10.0 }, { "id": 3, "demand": 31.0 }, { "id": 4, "demand": 44.0 }, { "id": 5, "demand": 33.0 }, { "id": 6, "demand": 17.0 }, { "id": 7, "demand": 11.0 }, { "id": 8, "demand": 21.0 }, { "id": 9, "demand": 45.0 }, { "id": 10, "demand": 22.0 }, { "id": 11, "demand": 18.0 }, { "id": 12, "demand": 38.0 }, { "id": 13, "demand": 35.0 }, { "id": 14, "demand": 42.0 }, { "id": 15, "demand": 22.0 }, { "id": 16, "demand": 46.0 }, { "id": 17, "demand": 31.0 }, { "id": 18, "demand": 49.0 }, { "id": 19, "demand": 42.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 579.0 }, { "facility": "F1", "customer": 1, "cost": 413.0 }, { "facility": "F1", "customer": 2, "cost": 186.0 }, { "facility": "F1", "customer": 3, "cost": 229.0 }, { "facility": "F1", "customer": 4, "cost": 161.0 }, { "facility": "F1", "customer": 5, "cost": 452.0 }, { "facility": "F1", "customer": 6, "cost": 393.0 }, { "facility": "F1", "customer": 7, "cost": 409.0 }, { "facility": "F1", "customer": 8, "cost": 480.0 }, { "facility": "F1", "customer": 9, "cost": 70.0 }, { "facility": "F1", "customer": 10, "cost": 439.0 }, { "facility": "F1", "customer": 11, "cost": 423.0 }, { "facility": "F1", "customer": 12, "cost": 473.0 }, { "facility": "F1", "customer": 13, "cost": 187.0 }, { "facility": "F1", "customer": 14, "cost": 162.0 }, { "facility": "F1", "customer": 15, "cost": 402.0 }, { "facility": "F1", "customer": 16, "cost": 258.0 }, { "facility": "F1", "customer": 17, "cost": 165.0 }, { "facility": "F1", "customer": 18, "cost": 64.0 }, { "facility": "F1", "customer": 19, "cost": 92.0 }, { "facility": "F2", "customer": 0, "cost": 296.0 }, { "facility": "F2", "customer": 1, "cost": 247.0 }, { "facility": "F2", "customer": 2, "cost": 540.0 }, { "facility": "F2", "customer": 3, "cost": 377.0 }, { "facility": "F2", "customer": 4, "cost": 437.0 }, { "facility": "F2", "customer": 5, "cost": 549.0 }, { "facility": "F2", "customer": 6, "cost": 219.0 }, { "facility": "F2", "customer": 7, "cost": 473.0 }, { "facility": "F2", "customer": 8, "cost": 405.0 }, { "facility": "F2", "customer": 9, "cost": 520.0 }, { "facility": "F2", "customer": 10, "cost": 506.0 }, { "facility": "F2", "customer": 11, "cost": 143.0 }, { "facility": "F2", "customer": 12, "cost": 305.0 }, { "facility": "F2", "customer": 13, "cost": 345.0 }, { "facility": "F2", "customer": 14, "cost": 442.0 }, { "facility": "F2", "customer": 15, "cost": 545.0 }, { "facility": "F2", "customer": 16, "cost": 290.0 }, { "facility": "F2", "customer": 17, "cost": 589.0 }, { "facility": "F2", "customer": 18, "cost": 487.0 }, { "facility": "F2", "customer": 19, "cost": 520.0 }, { "facility": "F3", "customer": 0, "cost": 259.0 }, { "facility": "F3", "customer": 1, "cost": 423.0 }, { "facility": "F3", "customer": 2, "cost": 469.0 }, { "facility": "F3", "customer": 3, "cost": 378.0 }, { "facility": "F3", "customer": 4, "cost": 378.0 }, { "facility": "F3", "customer": 5, "cost": 233.0 }, { "facility": "F3", "customer": 6, "cost": 118.0 }, { "facility": "F3", "customer": 7, "cost": 157.0 }, { "facility": "F3", "customer": 8, "cost": 163.0 }, { "facility": "F3", "customer": 9, "cost": 295.0 }, { "facility": "F3", "customer": 10, "cost": 195.0 }, { "facility": "F3", "customer": 11, "cost": 352.0 }, { "facility": "F3", "customer": 12, "cost": 146.0 }, { "facility": "F3", "customer": 13, "cost": 158.0 }, { "facility": "F3", "customer": 14, "cost": 383.0 }, { "facility": "F3", "customer": 15, "cost": 218.0 }, { "facility": "F3", "customer": 16, "cost": 313.0 }, { "facility": "F3", "customer": 17, "cost": 319.0 }, { "facility": "F3", "customer": 18, "cost": 353.0 }, { "facility": "F3", "customer": 19, "cost": 396.0 }, { "facility": "F4", "customer": 0, "cost": 708.0 }, { "facility": "F4", "customer": 1, "cost": 375.0 }, { "facility": "F4", "customer": 2, "cost": 17.0 }, { "facility": "F4", "customer": 3, "cost": 182.0 }, { "facility": "F4", "customer": 4, "cost": 122.0 }, { "facility": "F4", "customer": 5, "cost": 643.0 }, { "facility": "F4", "customer": 6, "cost": 515.0 }, { "facility": "F4", "customer": 7, "cost": 593.0 }, { "facility": "F4", "customer": 8, "cost": 647.0 }, { "facility": "F4", "customer": 9, "cost": 265.0 }, { "facility": "F4", "customer": 10, "cost": 625.0 }, { "facility": "F4", "customer": 11, "cost": 433.0 }, { "facility": "F4", "customer": 12, "cost": 617.0 }, { "facility": "F4", "customer": 13, "cost": 327.0 }, { "facility": "F4", "customer": 14, "cost": 117.0 }, { "facility": "F4", "customer": 15, "cost": 595.0 }, { "facility": "F4", "customer": 16, "cost": 267.0 }, { "facility": "F4", "customer": 17, "cost": 352.0 }, { "facility": "F4", "customer": 18, "cost": 141.0 }, { "facility": "F4", "customer": 19, "cost": 104.0 }, { "facility": "F5", "customer": 0, "cost": 354.0 }, { "facility": "F5", "customer": 1, "cost": 322.0 }, { "facility": "F5", "customer": 2, "cost": 344.0 }, { "facility": "F5", "customer": 3, "cost": 249.0 }, { "facility": "F5", "customer": 4, "cost": 250.0 }, { "facility": "F5", "customer": 5, "cost": 342.0 }, { "facility": "F5", "customer": 6, "cost": 164.0 }, { "facility": "F5", "customer": 7, "cost": 272.0 }, { "facility": "F5", "customer": 8, "cost": 293.0 }, { "facility": "F5", "customer": 9, "cost": 220.0 }, { "facility": "F5", "customer": 10, "cost": 310.0 }, { "facility": "F5", "customer": 11, "cost": 274.0 }, { "facility": "F5", "customer": 12, "cost": 256.0 }, { "facility": "F5", "customer": 13, "cost": 43.0 }, { "facility": "F5", "customer": 14, "cost": 255.0 }, { "facility": "F5", "customer": 15, "cost": 312.0 }, { "facility": "F5", "customer": 16, "cost": 190.0 }, { "facility": "F5", "customer": 17, "cost": 282.0 }, { "facility": "F5", "customer": 18, "cost": 238.0 }, { "facility": "F5", "customer": 19, "cost": 280.0 }, { "facility": "F6", "customer": 0, "cost": 549.0 }, { "facility": "F6", "customer": 1, "cost": 43.0 }, { "facility": "F6", "customer": 2, "cost": 332.0 }, { "facility": "F6", "customer": 3, "cost": 179.0 }, { "facility": "F6", "customer": 4, "cost": 256.0 }, { "facility": "F6", "customer": 5, "cost": 673.0 }, { "facility": "F6", "customer": 6, "cost": 389.0 }, { "facility": "F6", "customer": 7, "cost": 600.0 }, { "facility": "F6", "customer": 8, "cost": 586.0 }, { "facility": "F6", "customer": 9, "cost": 449.0 }, { "facility": "F6", "customer": 10, "cost": 638.0 }, { "facility": "F6", "customer": 11, "cost": 147.0 }, { "facility": "F6", "customer": 12, "cost": 508.0 }, { "facility": "F6", "customer": 13, "cost": 342.0 }, { "facility": "F6", "customer": 14, "cost": 259.0 }, { "facility": "F6", "customer": 15, "cost": 646.0 }, { "facility": "F6", "customer": 16, "cost": 156.0 }, { "facility": "F6", "customer": 17, "cost": 546.0 }, { "facility": "F6", "customer": 18, "cost": 348.0 }, { "facility": "F6", "customer": 19, "cost": 360.0 }, { "facility": "F7", "customer": 0, "cost": 168.0 }, { "facility": "F7", "customer": 1, "cost": 369.0 }, { "facility": "F7", "customer": 2, "cost": 525.0 }, { "facility": "F7", "customer": 3, "cost": 395.0 }, { "facility": "F7", "customer": 4, "cost": 422.0 }, { "facility": "F7", "customer": 5, "cost": 343.0 }, { "facility": "F7", "customer": 6, "cost": 30.0 }, { "facility": "F7", "customer": 7, "cost": 268.0 }, { "facility": "F7", "customer": 8, "cost": 202.0 }, { "facility": "F7", "customer": 9, "cost": 408.0 }, { "facility": "F7", "customer": 10, "cost": 300.0 }, { "facility": "F7", "customer": 11, "cost": 274.0 }, { "facility": "F7", "customer": 12, "cost": 110.0 }, { "facility": "F7", "customer": 13, "cost": 237.0 }, { "facility": "F7", "customer": 14, "cost": 428.0 }, { "facility": "F7", "customer": 15, "cost": 343.0 }, { "facility": "F7", "customer": 16, "cost": 310.0 }, { "facility": "F7", "customer": 17, "cost": 450.0 }, { "facility": "F7", "customer": 18, "cost": 429.0 }, { "facility": "F7", "customer": 19, "cost": 471.0 }, { "facility": "F8", "customer": 0, "cost": 320.0 }, { "facility": "F8", "customer": 1, "cost": 237.0 }, { "facility": "F8", "customer": 2, "cost": 382.0 }, { "facility": "F8", "customer": 3, "cost": 242.0 }, { "facility": "F8", "customer": 4, "cost": 277.0 }, { "facility": "F8", "customer": 5, "cost": 421.0 }, { "facility": "F8", "customer": 6, "cost": 135.0 }, { "facility": "F8", "customer": 7, "cost": 345.0 }, { "facility": "F8", "customer": 8, "cost": 326.0 }, { "facility": "F8", "customer": 9, "cost": 324.0 }, { "facility": "F8", "customer": 10, "cost": 383.0 }, { "facility": "F8", "customer": 11, "cost": 167.0 }, { "facility": "F8", "customer": 12, "cost": 255.0 }, { "facility": "F8", "customer": 13, "cost": 150.0 }, { "facility": "F8", "customer": 14, "cost": 283.0 }, { "facility": "F8", "customer": 15, "cost": 401.0 }, { "facility": "F8", "customer": 16, "cost": 156.0 }, { "facility": "F8", "customer": 17, "cost": 395.0 }, { "facility": "F8", "customer": 18, "cost": 304.0 }, { "facility": "F8", "customer": 19, "cost": 342.0 } ], "objective": 4272.0 }, "solution_variant": { "selected": [ "F1", "F3", "F6" ], "assignments": [ "F3", "F6", "F1", "F6", "F1", "F3", "F3", "F3", "F3", "F1", "F3", "F6", "F3", "F3", "F1", "F3", "F6", "F1", "F1", "F1" ] }, "context_index": 47, "input_format": "nl", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "At the dorm office the decision is to keep some laundry rooms open and close others, then assign each dormitory to exactly one of the rooms that remain open. Each machine room has a finite capacity, so assignments must fit within those limits. The way to judge plans is straightforward: total cost — tally up the operating costs for the chosen laundry rooms plus the travel or usage cost for every dorm’s assignment, and prefer the arrangement with the lowest combined total. No dorm can be left out or sent to more than one place. The particular figures are shown below.\n\n{\n \"num_laundry_rooms\": 9,\n \"num_dormitories\": 20,\n \"laundry_rooms\": [\n {\n \"laundry_room_id\": \"F1\",\n \"operating_cost\": 400.0,\n \"laundry_capacity\": 500.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"operating_cost\": 400.0,\n \"laundry_capacity\": 500.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"operating_cost\": 400.0,\n \"laundry_capacity\": 500.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"operating_cost\": 400.0,\n \"laundry_capacity\": 500.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"operating_cost\": 400.0,\n \"laundry_capacity\": 500.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"operating_cost\": 400.0,\n \"laundry_capacity\": 500.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"operating_cost\": 400.0,\n \"laundry_capacity\": 500.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"operating_cost\": 400.0,\n \"laundry_capacity\": 500.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"operating_cost\": 400.0,\n \"laundry_capacity\": 500.0\n }\n ],\n \"dorms\": [\n {\n \"dorm_id\": 1,\n \"dorm_demand\": 21.0\n },\n {\n \"dorm_id\": 2,\n \"dorm_demand\": 25.0\n },\n {\n \"dorm_id\": 3,\n \"dorm_demand\": 20.0\n },\n {\n \"dorm_id\": 4,\n \"dorm_demand\": 12.0\n },\n {\n \"dorm_id\": 5,\n \"dorm_demand\": 24.0\n },\n {\n \"dorm_id\": 6,\n \"dorm_demand\": 23.0\n },\n {\n \"dorm_id\": 7,\n \"dorm_demand\": 17.0\n },\n {\n \"dorm_id\": 8,\n \"dorm_demand\": 26.0\n },\n {\n \"dorm_id\": 9,\n \"dorm_demand\": 17.0\n },\n {\n \"dorm_id\": 10,\n \"dorm_demand\": 18.0\n },\n {\n \"dorm_id\": 11,\n \"dorm_demand\": 23.0\n },\n {\n \"dorm_id\": 12,\n \"dorm_demand\": 17.0\n },\n {\n \"dorm_id\": 13,\n \"dorm_demand\": 18.0\n },\n {\n \"dorm_id\": 14,\n \"dorm_demand\": 17.0\n },\n {\n \"dorm_id\": 15,\n \"dorm_demand\": 16.0\n },\n {\n \"dorm_id\": 16,\n \"dorm_demand\": 20.0\n },\n {\n \"dorm_id\": 17,\n \"dorm_demand\": 15.0\n },\n {\n \"dorm_id\": 18,\n \"dorm_demand\": 22.0\n },\n {\n \"dorm_id\": 19,\n \"dorm_demand\": 25.0\n },\n {\n \"dorm_id\": 20,\n \"dorm_demand\": 22.0\n }\n ],\n \"assignments\": [\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 1,\n \"assignment_cost\": 858.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 2,\n \"assignment_cost\": 668.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 3,\n \"assignment_cost\": 255.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 4,\n \"assignment_cost\": 83.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 5,\n \"assignment_cost\": 49.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 6,\n \"assignment_cost\": 71.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 7,\n \"assignment_cost\": 232.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 8,\n \"assignment_cost\": 83.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 9,\n \"assignment_cost\": 386.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 10,\n \"assignment_cost\": 92.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 11,\n \"assignment_cost\": 65.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 12,\n \"assignment_cost\": 186.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 13,\n \"assignment_cost\": 772.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 14,\n \"assignment_cost\": 399.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 15,\n \"assignment_cost\": 32.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 16,\n \"assignment_cost\": 50.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 17,\n \"assignment_cost\": 245.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 18,\n \"assignment_cost\": 872.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 19,\n \"assignment_cost\": 661.0\n },\n {\n \"laundry_room_id\": \"F1\",\n \"dorm_id\": 20,\n \"assignment_cost\": 68.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 1,\n \"assignment_cost\": 1168.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 2,\n \"assignment_cost\": 1168.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 3,\n \"assignment_cost\": 488.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 4,\n \"assignment_cost\": 241.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 5,\n \"assignment_cost\": 52.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 6,\n \"assignment_cost\": 339.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 7,\n \"assignment_cost\": 484.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 8,\n \"assignment_cost\": 161.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 9,\n \"assignment_cost\": 1088.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 10,\n \"assignment_cost\": 686.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 11,\n \"assignment_cost\": 47.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 12,\n \"assignment_cost\": 419.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 13,\n \"assignment_cost\": 1419.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 14,\n \"assignment_cost\": 858.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 15,\n \"assignment_cost\": 88.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 16,\n \"assignment_cost\": 150.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 17,\n \"assignment_cost\": 362.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 18,\n \"assignment_cost\": 1152.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 19,\n \"assignment_cost\": 1130.0\n },\n {\n \"laundry_room_id\": \"F2\",\n \"dorm_id\": 20,\n \"assignment_cost\": 460.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 1,\n \"assignment_cost\": 647.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 2,\n \"assignment_cost\": 389.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 3,\n \"assignment_cost\": 132.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 4,\n \"assignment_cost\": 30.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 5,\n \"assignment_cost\": 65.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 6,\n \"assignment_cost\": 53.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 7,\n \"assignment_cost\": 402.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 8,\n \"assignment_cost\": 54.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 9,\n \"assignment_cost\": 63.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 10,\n \"assignment_cost\": 71.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 11,\n \"assignment_cost\": 129.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 12,\n \"assignment_cost\": 80.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 13,\n \"assignment_cost\": 441.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 14,\n \"assignment_cost\": 171.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 15,\n \"assignment_cost\": 61.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 16,\n \"assignment_cost\": 45.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 17,\n \"assignment_cost\": 162.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 18,\n \"assignment_cost\": 675.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 19,\n \"assignment_cost\": 396.0\n },\n {\n \"laundry_room_id\": \"F3\",\n \"dorm_id\": 20,\n \"assignment_cost\": 206.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 1,\n \"assignment_cost\": 1597.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 2,\n \"assignment_cost\": 1973.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 3,\n \"assignment_cost\": 1048.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 4,\n \"assignment_cost\": 900.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 5,\n \"assignment_cost\": 232.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 6,\n \"assignment_cost\": 1337.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 7,\n \"assignment_cost\": 1733.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 8,\n \"assignment_cost\": 579.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 9,\n \"assignment_cost\": 2185.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 10,\n \"assignment_cost\": 1814.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 11,\n \"assignment_cost\": 927.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 12,\n \"assignment_cost\": 1064.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 13,\n \"assignment_cost\": 2392.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 14,\n \"assignment_cost\": 1700.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 15,\n \"assignment_cost\": 969.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 16,\n \"assignment_cost\": 919.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 17,\n \"assignment_cost\": 547.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 18,\n \"assignment_cost\": 1518.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 19,\n \"assignment_cost\": 1891.0\n },\n {\n \"laundry_room_id\": \"F4\",\n \"dorm_id\": 20,\n \"assignment_cost\": 1689.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 1,\n \"assignment_cost\": 217.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 2,\n \"assignment_cost\": 934.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 3,\n \"assignment_cost\": 302.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 4,\n \"assignment_cost\": 427.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 5,\n \"assignment_cost\": 311.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 6,\n \"assignment_cost\": 834.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 7,\n \"assignment_cost\": 1444.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 8,\n \"assignment_cost\": 309.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 9,\n \"assignment_cost\": 1452.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 10,\n \"assignment_cost\": 1222.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 11,\n \"assignment_cost\": 749.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 12,\n \"assignment_cost\": 401.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 13,\n \"assignment_cost\": 1448.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 14,\n \"assignment_cost\": 813.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 15,\n \"assignment_cost\": 671.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 16,\n \"assignment_cost\": 567.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 17,\n \"assignment_cost\": 43.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 18,\n \"assignment_cost\": 175.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 19,\n \"assignment_cost\": 824.0\n },\n {\n \"laundry_room_id\": \"F5\",\n \"dorm_id\": 20,\n \"assignment_cost\": 1270.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 1,\n \"assignment_cost\": 758.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 2,\n \"assignment_cost\": 1300.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 3,\n \"assignment_cost\": 447.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 4,\n \"assignment_cost\": 517.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 5,\n \"assignment_cost\": 307.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 6,\n \"assignment_cost\": 979.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 7,\n \"assignment_cost\": 1555.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 8,\n \"assignment_cost\": 335.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 9,\n \"assignment_cost\": 1711.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 10,\n \"assignment_cost\": 1421.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 11,\n \"assignment_cost\": 805.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 12,\n \"assignment_cost\": 542.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 13,\n \"assignment_cost\": 1792.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 14,\n \"assignment_cost\": 1101.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 15,\n \"assignment_cost\": 749.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 16,\n \"assignment_cost\": 646.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 17,\n \"assignment_cost\": 33.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 18,\n \"assignment_cost\": 679.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 19,\n \"assignment_cost\": 1198.0\n },\n {\n \"laundry_room_id\": \"F6\",\n \"dorm_id\": 20,\n \"assignment_cost\": 1414.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 1,\n \"assignment_cost\": 554.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 2,\n \"assignment_cost\": 516.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 3,\n \"assignment_cost\": 48.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 4,\n \"assignment_cost\": 62.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 5,\n \"assignment_cost\": 124.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 6,\n \"assignment_cost\": 298.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 7,\n \"assignment_cost\": 903.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 8,\n \"assignment_cost\": 75.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 9,\n \"assignment_cost\": 858.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 10,\n \"assignment_cost\": 625.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 11,\n \"assignment_cost\": 343.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 12,\n \"assignment_cost\": 37.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 13,\n \"assignment_cost\": 944.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 14,\n \"assignment_cost\": 242.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 15,\n \"assignment_cost\": 243.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 16,\n \"assignment_cost\": 164.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 17,\n \"assignment_cost\": 87.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 18,\n \"assignment_cost\": 571.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 19,\n \"assignment_cost\": 453.0\n },\n {\n \"laundry_room_id\": \"F7\",\n \"dorm_id\": 20,\n \"assignment_cost\": 704.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 1,\n \"assignment_cost\": 791.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 2,\n \"assignment_cost\": 630.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 3,\n \"assignment_cost\": 193.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 4,\n \"assignment_cost\": 45.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 5,\n \"assignment_cost\": 58.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 6,\n \"assignment_cost\": 46.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 7,\n \"assignment_cost\": 457.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 8,\n \"assignment_cost\": 61.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 9,\n \"assignment_cost\": 497.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 10,\n \"assignment_cost\": 128.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 11,\n \"assignment_cost\": 116.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 12,\n \"assignment_cost\": 128.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 13,\n \"assignment_cost\": 817.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 14,\n \"assignment_cost\": 343.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 15,\n \"assignment_cost\": 49.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 16,\n \"assignment_cost\": 40.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 17,\n \"assignment_cost\": 198.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 18,\n \"assignment_cost\": 804.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 19,\n \"assignment_cost\": 615.0\n },\n {\n \"laundry_room_id\": \"F8\",\n \"dorm_id\": 20,\n \"assignment_cost\": 244.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 1,\n \"assignment_cost\": 930.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 2,\n \"assignment_cost\": 885.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 3,\n \"assignment_cost\": 274.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 4,\n \"assignment_cost\": 73.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 5,\n \"assignment_cost\": 55.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 6,\n \"assignment_cost\": 67.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 7,\n \"assignment_cost\": 601.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 8,\n \"assignment_cost\": 71.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 9,\n \"assignment_cost\": 870.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 10,\n \"assignment_cost\": 484.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 11,\n \"assignment_cost\": 117.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 12,\n \"assignment_cost\": 201.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 13,\n \"assignment_cost\": 1157.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 14,\n \"assignment_cost\": 575.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 15,\n \"assignment_cost\": 43.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 16,\n \"assignment_cost\": 41.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 17,\n \"assignment_cost\": 235.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 18,\n \"assignment_cost\": 927.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 19,\n \"assignment_cost\": 849.0\n },\n {\n \"laundry_room_id\": \"F9\",\n \"dorm_id\": 20,\n \"assignment_cost\": 425.0\n }\n ]\n}\n\nIf you want to send back a plan, just stick to this simple JSON shape so I can read it easily.\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of laundry rooms you decide to keep running, and \"assignments\" as, for each dorm in the same order they were given, which open room that dorm will use. This is just a sketch of the expected shape — not the actual answer.\n\nPlease make sure to use the exact identifiers from the instance input (do not rename them or invent new ones).\n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”\".", "instance": { "opening_costs": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 858.0, 668.0, 255.0, 83.0, 49.0, 71.0, 232.0, 83.0, 386.0, 92.0, 65.0, 186.0, 772.0, 399.0, 32.0, 50.0, 245.0, 872.0, 661.0, 68.0 ], [ 1168.0, 1168.0, 488.0, 241.0, 52.0, 339.0, 484.0, 161.0, 1088.0, 686.0, 47.0, 419.0, 1419.0, 858.0, 88.0, 150.0, 362.0, 1152.0, 1130.0, 460.0 ], [ 647.0, 389.0, 132.0, 30.0, 65.0, 53.0, 402.0, 54.0, 63.0, 71.0, 129.0, 80.0, 441.0, 171.0, 61.0, 45.0, 162.0, 675.0, 396.0, 206.0 ], [ 1597.0, 1973.0, 1048.0, 900.0, 232.0, 1337.0, 1733.0, 579.0, 2185.0, 1814.0, 927.0, 1064.0, 2392.0, 1700.0, 969.0, 919.0, 547.0, 1518.0, 1891.0, 1689.0 ], [ 217.0, 934.0, 302.0, 427.0, 311.0, 834.0, 1444.0, 309.0, 1452.0, 1222.0, 749.0, 401.0, 1448.0, 813.0, 671.0, 567.0, 43.0, 175.0, 824.0, 1270.0 ], [ 758.0, 1300.0, 447.0, 517.0, 307.0, 979.0, 1555.0, 335.0, 1711.0, 1421.0, 805.0, 542.0, 1792.0, 1101.0, 749.0, 646.0, 33.0, 679.0, 1198.0, 1414.0 ], [ 554.0, 516.0, 48.0, 62.0, 124.0, 298.0, 903.0, 75.0, 858.0, 625.0, 343.0, 37.0, 944.0, 242.0, 243.0, 164.0, 87.0, 571.0, 453.0, 704.0 ], [ 791.0, 630.0, 193.0, 45.0, 58.0, 46.0, 457.0, 61.0, 497.0, 128.0, 116.0, 128.0, 817.0, 343.0, 49.0, 40.0, 198.0, 804.0, 615.0, 244.0 ], [ 930.0, 885.0, 274.0, 73.0, 55.0, 67.0, 601.0, 71.0, 870.0, 484.0, 117.0, 201.0, 1157.0, 575.0, 43.0, 41.0, 235.0, 927.0, 849.0, 425.0 ] ], "demands": [ 21.0, 25.0, 20.0, 12.0, 24.0, 23.0, 17.0, 26.0, 17.0, 18.0, 23.0, 17.0, 18.0, 17.0, 16.0, 20.0, 15.0, 22.0, 25.0, 22.0 ], "objective": 4006.0 }, "solution": { "open_facilities": [ 0, 2, 4 ], "assignments": [ 4, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 4, 4, 2, 0 ] }, "obj": 4006.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 9, "num_customers": 20, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F7", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F8", "opening_cost": 400.0, "capacity": 500.0 }, { "id": "F9", "opening_cost": 400.0, "capacity": 500.0 } ], "customers": [ { "id": 1, "demand": 21.0 }, { "id": 2, "demand": 25.0 }, { "id": 3, "demand": 20.0 }, { "id": 4, "demand": 12.0 }, { "id": 5, "demand": 24.0 }, { "id": 6, "demand": 23.0 }, { "id": 7, "demand": 17.0 }, { "id": 8, "demand": 26.0 }, { "id": 9, "demand": 17.0 }, { "id": 10, "demand": 18.0 }, { "id": 11, "demand": 23.0 }, { "id": 12, "demand": 17.0 }, { "id": 13, "demand": 18.0 }, { "id": 14, "demand": 17.0 }, { "id": 15, "demand": 16.0 }, { "id": 16, "demand": 20.0 }, { "id": 17, "demand": 15.0 }, { "id": 18, "demand": 22.0 }, { "id": 19, "demand": 25.0 }, { "id": 20, "demand": 22.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 858.0 }, { "facility": "F1", "customer": 2, "cost": 668.0 }, { "facility": "F1", "customer": 3, "cost": 255.0 }, { "facility": "F1", "customer": 4, "cost": 83.0 }, { "facility": "F1", "customer": 5, "cost": 49.0 }, { "facility": "F1", "customer": 6, "cost": 71.0 }, { "facility": "F1", "customer": 7, "cost": 232.0 }, { "facility": "F1", "customer": 8, "cost": 83.0 }, { "facility": "F1", "customer": 9, "cost": 386.0 }, { "facility": "F1", "customer": 10, "cost": 92.0 }, { "facility": "F1", "customer": 11, "cost": 65.0 }, { "facility": "F1", "customer": 12, "cost": 186.0 }, { "facility": "F1", "customer": 13, "cost": 772.0 }, { "facility": "F1", "customer": 14, "cost": 399.0 }, { "facility": "F1", "customer": 15, "cost": 32.0 }, { "facility": "F1", "customer": 16, "cost": 50.0 }, { "facility": "F1", "customer": 17, "cost": 245.0 }, { "facility": "F1", "customer": 18, "cost": 872.0 }, { "facility": "F1", "customer": 19, "cost": 661.0 }, { "facility": "F1", "customer": 20, "cost": 68.0 }, { "facility": "F2", "customer": 1, "cost": 1168.0 }, { "facility": "F2", "customer": 2, "cost": 1168.0 }, { "facility": "F2", "customer": 3, "cost": 488.0 }, { "facility": "F2", "customer": 4, "cost": 241.0 }, { "facility": "F2", "customer": 5, "cost": 52.0 }, { "facility": "F2", "customer": 6, "cost": 339.0 }, { "facility": "F2", "customer": 7, "cost": 484.0 }, { "facility": "F2", "customer": 8, "cost": 161.0 }, { "facility": "F2", "customer": 9, "cost": 1088.0 }, { "facility": "F2", "customer": 10, "cost": 686.0 }, { "facility": "F2", "customer": 11, "cost": 47.0 }, { "facility": "F2", "customer": 12, "cost": 419.0 }, { "facility": "F2", "customer": 13, "cost": 1419.0 }, { "facility": "F2", "customer": 14, "cost": 858.0 }, { "facility": "F2", "customer": 15, "cost": 88.0 }, { "facility": "F2", "customer": 16, "cost": 150.0 }, { "facility": "F2", "customer": 17, "cost": 362.0 }, { "facility": "F2", "customer": 18, "cost": 1152.0 }, { "facility": "F2", "customer": 19, "cost": 1130.0 }, { "facility": "F2", "customer": 20, "cost": 460.0 }, { "facility": "F3", "customer": 1, "cost": 647.0 }, { "facility": "F3", "customer": 2, "cost": 389.0 }, { "facility": "F3", "customer": 3, "cost": 132.0 }, { "facility": "F3", "customer": 4, "cost": 30.0 }, { "facility": "F3", "customer": 5, "cost": 65.0 }, { "facility": "F3", "customer": 6, "cost": 53.0 }, { "facility": "F3", "customer": 7, "cost": 402.0 }, { "facility": "F3", "customer": 8, "cost": 54.0 }, { "facility": "F3", "customer": 9, "cost": 63.0 }, { "facility": "F3", "customer": 10, "cost": 71.0 }, { "facility": "F3", "customer": 11, "cost": 129.0 }, { "facility": "F3", "customer": 12, "cost": 80.0 }, { "facility": "F3", "customer": 13, "cost": 441.0 }, { "facility": "F3", "customer": 14, "cost": 171.0 }, { "facility": "F3", "customer": 15, "cost": 61.0 }, { "facility": "F3", "customer": 16, "cost": 45.0 }, { "facility": "F3", "customer": 17, "cost": 162.0 }, { "facility": "F3", "customer": 18, "cost": 675.0 }, { "facility": "F3", "customer": 19, "cost": 396.0 }, { "facility": "F3", "customer": 20, "cost": 206.0 }, { "facility": "F4", "customer": 1, "cost": 1597.0 }, { "facility": "F4", "customer": 2, "cost": 1973.0 }, { "facility": "F4", "customer": 3, "cost": 1048.0 }, { "facility": "F4", "customer": 4, "cost": 900.0 }, { "facility": "F4", "customer": 5, "cost": 232.0 }, { "facility": "F4", "customer": 6, "cost": 1337.0 }, { "facility": "F4", "customer": 7, "cost": 1733.0 }, { "facility": "F4", "customer": 8, "cost": 579.0 }, { "facility": "F4", "customer": 9, "cost": 2185.0 }, { "facility": "F4", "customer": 10, "cost": 1814.0 }, { "facility": "F4", "customer": 11, "cost": 927.0 }, { "facility": "F4", "customer": 12, "cost": 1064.0 }, { "facility": "F4", "customer": 13, "cost": 2392.0 }, { "facility": "F4", "customer": 14, "cost": 1700.0 }, { "facility": "F4", "customer": 15, "cost": 969.0 }, { "facility": "F4", "customer": 16, "cost": 919.0 }, { "facility": "F4", "customer": 17, "cost": 547.0 }, { "facility": "F4", "customer": 18, "cost": 1518.0 }, { "facility": "F4", "customer": 19, "cost": 1891.0 }, { "facility": "F4", "customer": 20, "cost": 1689.0 }, { "facility": "F5", "customer": 1, "cost": 217.0 }, { "facility": "F5", "customer": 2, "cost": 934.0 }, { "facility": "F5", "customer": 3, "cost": 302.0 }, { "facility": "F5", "customer": 4, "cost": 427.0 }, { "facility": "F5", "customer": 5, "cost": 311.0 }, { "facility": "F5", "customer": 6, "cost": 834.0 }, { "facility": "F5", "customer": 7, "cost": 1444.0 }, { "facility": "F5", "customer": 8, "cost": 309.0 }, { "facility": "F5", "customer": 9, "cost": 1452.0 }, { "facility": "F5", "customer": 10, "cost": 1222.0 }, { "facility": "F5", "customer": 11, "cost": 749.0 }, { "facility": "F5", "customer": 12, "cost": 401.0 }, { "facility": "F5", "customer": 13, "cost": 1448.0 }, { "facility": "F5", "customer": 14, "cost": 813.0 }, { "facility": "F5", "customer": 15, "cost": 671.0 }, { "facility": "F5", "customer": 16, "cost": 567.0 }, { "facility": "F5", "customer": 17, "cost": 43.0 }, { "facility": "F5", "customer": 18, "cost": 175.0 }, { "facility": "F5", "customer": 19, "cost": 824.0 }, { "facility": "F5", "customer": 20, "cost": 1270.0 }, { "facility": "F6", "customer": 1, "cost": 758.0 }, { "facility": "F6", "customer": 2, "cost": 1300.0 }, { "facility": "F6", "customer": 3, "cost": 447.0 }, { "facility": "F6", "customer": 4, "cost": 517.0 }, { "facility": "F6", "customer": 5, "cost": 307.0 }, { "facility": "F6", "customer": 6, "cost": 979.0 }, { "facility": "F6", "customer": 7, "cost": 1555.0 }, { "facility": "F6", "customer": 8, "cost": 335.0 }, { "facility": "F6", "customer": 9, "cost": 1711.0 }, { "facility": "F6", "customer": 10, "cost": 1421.0 }, { "facility": "F6", "customer": 11, "cost": 805.0 }, { "facility": "F6", "customer": 12, "cost": 542.0 }, { "facility": "F6", "customer": 13, "cost": 1792.0 }, { "facility": "F6", "customer": 14, "cost": 1101.0 }, { "facility": "F6", "customer": 15, "cost": 749.0 }, { "facility": "F6", "customer": 16, "cost": 646.0 }, { "facility": "F6", "customer": 17, "cost": 33.0 }, { "facility": "F6", "customer": 18, "cost": 679.0 }, { "facility": "F6", "customer": 19, "cost": 1198.0 }, { "facility": "F6", "customer": 20, "cost": 1414.0 }, { "facility": "F7", "customer": 1, "cost": 554.0 }, { "facility": "F7", "customer": 2, "cost": 516.0 }, { "facility": "F7", "customer": 3, "cost": 48.0 }, { "facility": "F7", "customer": 4, "cost": 62.0 }, { "facility": "F7", "customer": 5, "cost": 124.0 }, { "facility": "F7", "customer": 6, "cost": 298.0 }, { "facility": "F7", "customer": 7, "cost": 903.0 }, { "facility": "F7", "customer": 8, "cost": 75.0 }, { "facility": "F7", "customer": 9, "cost": 858.0 }, { "facility": "F7", "customer": 10, "cost": 625.0 }, { "facility": "F7", "customer": 11, "cost": 343.0 }, { "facility": "F7", "customer": 12, "cost": 37.0 }, { "facility": "F7", "customer": 13, "cost": 944.0 }, { "facility": "F7", "customer": 14, "cost": 242.0 }, { "facility": "F7", "customer": 15, "cost": 243.0 }, { "facility": "F7", "customer": 16, "cost": 164.0 }, { "facility": "F7", "customer": 17, "cost": 87.0 }, { "facility": "F7", "customer": 18, "cost": 571.0 }, { "facility": "F7", "customer": 19, "cost": 453.0 }, { "facility": "F7", "customer": 20, "cost": 704.0 }, { "facility": "F8", "customer": 1, "cost": 791.0 }, { "facility": "F8", "customer": 2, "cost": 630.0 }, { "facility": "F8", "customer": 3, "cost": 193.0 }, { "facility": "F8", "customer": 4, "cost": 45.0 }, { "facility": "F8", "customer": 5, "cost": 58.0 }, { "facility": "F8", "customer": 6, "cost": 46.0 }, { "facility": "F8", "customer": 7, "cost": 457.0 }, { "facility": "F8", "customer": 8, "cost": 61.0 }, { "facility": "F8", "customer": 9, "cost": 497.0 }, { "facility": "F8", "customer": 10, "cost": 128.0 }, { "facility": "F8", "customer": 11, "cost": 116.0 }, { "facility": "F8", "customer": 12, "cost": 128.0 }, { "facility": "F8", "customer": 13, "cost": 817.0 }, { "facility": "F8", "customer": 14, "cost": 343.0 }, { "facility": "F8", "customer": 15, "cost": 49.0 }, { "facility": "F8", "customer": 16, "cost": 40.0 }, { "facility": "F8", "customer": 17, "cost": 198.0 }, { "facility": "F8", "customer": 18, "cost": 804.0 }, { "facility": "F8", "customer": 19, "cost": 615.0 }, { "facility": "F8", "customer": 20, "cost": 244.0 }, { "facility": "F9", "customer": 1, "cost": 930.0 }, { "facility": "F9", "customer": 2, "cost": 885.0 }, { "facility": "F9", "customer": 3, "cost": 274.0 }, { "facility": "F9", "customer": 4, "cost": 73.0 }, { "facility": "F9", "customer": 5, "cost": 55.0 }, { "facility": "F9", "customer": 6, "cost": 67.0 }, { "facility": "F9", "customer": 7, "cost": 601.0 }, { "facility": "F9", "customer": 8, "cost": 71.0 }, { "facility": "F9", "customer": 9, "cost": 870.0 }, { "facility": "F9", "customer": 10, "cost": 484.0 }, { "facility": "F9", "customer": 11, "cost": 117.0 }, { "facility": "F9", "customer": 12, "cost": 201.0 }, { "facility": "F9", "customer": 13, "cost": 1157.0 }, { "facility": "F9", "customer": 14, "cost": 575.0 }, { "facility": "F9", "customer": 15, "cost": 43.0 }, { "facility": "F9", "customer": 16, "cost": 41.0 }, { "facility": "F9", "customer": 17, "cost": 235.0 }, { "facility": "F9", "customer": 18, "cost": 927.0 }, { "facility": "F9", "customer": 19, "cost": 849.0 }, { "facility": "F9", "customer": 20, "cost": 425.0 } ], "objective": 4006.0 }, "solution_variant": { "selected": [ "F1", "F3", "F5" ], "assignments": [ "F5", "F3", "F3", "F3", "F1", "F3", "F1", "F3", "F3", "F3", "F1", "F3", "F3", "F3", "F1", "F3", "F5", "F5", "F3", "F1" ] }, "context_index": 48, "input_format": "json", "input_index_base": 1 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "We’re playing the role of a planning team deciding which local library sites to activate and how to send each neighborhood to a single branch. Opening a site costs money and each one can only handle so many people; sending a neighborhood to a branch adds a travel cost. The score for any arrangement is simply the sum of the opening costs and all the travel costs, and the aim is to keep that sum as small as we can while making sure every neighborhood is served by exactly one open branch and no branch is overloaded. The specific numbers will be listed below.\n\n# num_branches=7\n# num_neighborhoods=18\n# BRANCHS\nbranch_id,branch_opening_cost,branch_capacity\nF1,300.0,256.0\nF2,300.0,404.0\nF3,300.0,259.0\nF4,300.0,490.0\nF5,300.0,410.0\nF6,300.0,213.0\nF7,300.0,564.0\n# NEIGHBORHOODS\nneighborhood_id,neighborhood_patrons\n0,11.0\n1,28.0\n2,18.0\n3,12.0\n4,28.0\n5,19.0\n6,29.0\n7,12.0\n8,29.0\n9,13.0\n10,26.0\n11,23.0\n12,24.0\n13,16.0\n14,13.0\n15,11.0\n16,27.0\n17,16.0\n# TRAVELS\nbranch_id,neighborhood_id,travel_cost\nF1,0,231.0\nF1,1,1017.0\nF1,2,58.0\nF1,3,660.0\nF1,4,726.0\nF1,5,720.0\nF1,6,58.0\nF1,7,463.0\nF1,8,391.0\nF1,9,36.0\nF1,10,463.0\nF1,11,298.0\nF1,12,48.0\nF1,13,298.0\nF1,14,282.0\nF1,15,201.0\nF1,16,64.0\nF1,17,1401.0\nF2,0,30.0\nF2,1,1671.0\nF2,2,499.0\nF2,3,699.0\nF2,4,674.0\nF2,5,1105.0\nF2,6,178.0\nF2,7,542.0\nF2,8,138.0\nF2,9,292.0\nF2,10,422.0\nF2,11,805.0\nF2,12,718.0\nF2,13,864.0\nF2,14,374.0\nF2,15,22.0\nF2,16,190.0\nF2,17,1987.0\nF3,0,368.0\nF3,1,1223.0\nF3,2,273.0\nF3,3,936.0\nF3,4,986.0\nF3,5,1037.0\nF3,6,72.0\nF3,7,732.0\nF3,8,558.0\nF3,9,29.0\nF3,10,706.0\nF3,11,231.0\nF3,12,365.0\nF3,13,613.0\nF3,14,525.0\nF3,15,339.0\nF3,16,54.0\nF3,17,1661.0\nF4,0,521.0\nF4,1,1334.0\nF4,2,492.0\nF4,3,1154.0\nF4,4,1199.0\nF4,5,1254.0\nF4,6,135.0\nF4,7,949.0\nF4,8,727.0\nF4,9,104.0\nF4,10,915.0\nF4,11,85.0\nF4,12,584.0\nF4,13,826.0\nF4,14,737.0\nF4,15,496.0\nF4,16,72.0\nF4,17,1807.0\nF5,0,372.0\nF5,1,1591.0\nF5,2,466.0\nF5,3,1066.0\nF5,4,1090.0\nF5,5,1277.0\nF5,6,59.0\nF5,7,864.0\nF5,8,579.0\nF5,9,40.0\nF5,10,804.0\nF5,11,531.0\nF5,12,653.0\nF5,13,891.0\nF5,14,642.0\nF5,15,347.0\nF5,16,62.0\nF5,17,2002.0\nF6,0,674.0\nF6,1,1877.0\nF6,2,851.0\nF6,3,1453.0\nF6,4,1467.0\nF6,5,1663.0\nF6,6,223.0\nF6,7,1253.0\nF6,8,898.0\nF6,9,288.0\nF6,10,1184.0\nF6,11,653.0\nF6,12,1011.0\nF6,13,1260.0\nF6,14,1031.0\nF6,15,661.0\nF6,16,97.0\nF6,17,2328.0\nF7,0,277.0\nF7,1,644.0\nF7,2,104.0\nF7,3,656.0\nF7,4,736.0\nF7,5,609.0\nF7,6,64.0\nF7,7,473.0\nF7,8,436.0\nF7,9,26.0\nF7,10,489.0\nF7,11,149.0\nF7,12,94.0\nF7,13,213.0\nF7,14,314.0\nF7,15,247.0\nF7,16,55.0\nF7,17,1079.0\n\nAlso, when you send back a plan, use this simple JSON layout so everything’s easy to read and check:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\n\"selected\" is just the list of library sites we choose to open. \"assignments\" lists, in the same order as the neighborhoods appear in the instance, which open site each neighborhood goes to. Think of it like a short form: which branches we flip on, and for each neighborhood which branch it uses.\n\nThis JSON is only a sketch of the shape I need — not the filled-in answer yet. Please make sure to use the exact identifiers from the instance input; do not rename or invent new labels. \n- For example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 256.0, 404.0, 259.0, 490.0, 410.0, 213.0, 564.0 ], "connection_costs": [ [ 231.0, 1017.0, 58.0, 660.0, 726.0, 720.0, 58.0, 463.0, 391.0, 36.0, 463.0, 298.0, 48.0, 298.0, 282.0, 201.0, 64.0, 1401.0 ], [ 30.0, 1671.0, 499.0, 699.0, 674.0, 1105.0, 178.0, 542.0, 138.0, 292.0, 422.0, 805.0, 718.0, 864.0, 374.0, 22.0, 190.0, 1987.0 ], [ 368.0, 1223.0, 273.0, 936.0, 986.0, 1037.0, 72.0, 732.0, 558.0, 29.0, 706.0, 231.0, 365.0, 613.0, 525.0, 339.0, 54.0, 1661.0 ], [ 521.0, 1334.0, 492.0, 1154.0, 1199.0, 1254.0, 135.0, 949.0, 727.0, 104.0, 915.0, 85.0, 584.0, 826.0, 737.0, 496.0, 72.0, 1807.0 ], [ 372.0, 1591.0, 466.0, 1066.0, 1090.0, 1277.0, 59.0, 864.0, 579.0, 40.0, 804.0, 531.0, 653.0, 891.0, 642.0, 347.0, 62.0, 2002.0 ], [ 674.0, 1877.0, 851.0, 1453.0, 1467.0, 1663.0, 223.0, 1253.0, 898.0, 288.0, 1184.0, 653.0, 1011.0, 1260.0, 1031.0, 661.0, 97.0, 2328.0 ], [ 277.0, 644.0, 104.0, 656.0, 736.0, 609.0, 64.0, 473.0, 436.0, 26.0, 489.0, 149.0, 94.0, 213.0, 314.0, 247.0, 55.0, 1079.0 ] ], "demands": [ 11.0, 28.0, 18.0, 12.0, 28.0, 19.0, 29.0, 12.0, 29.0, 13.0, 26.0, 23.0, 24.0, 16.0, 13.0, 11.0, 27.0, 16.0 ], "objective": 6366.0 }, "solution": { "open_facilities": [ 1, 6 ], "assignments": [ 1, 6, 6, 6, 1, 6, 6, 6, 1, 6, 1, 6, 6, 6, 6, 1, 6, 6 ] }, "obj": 6366.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 18, "facilities": [ { "id": "F1", "opening_cost": 300.0, "capacity": 256.0 }, { "id": "F2", "opening_cost": 300.0, "capacity": 404.0 }, { "id": "F3", "opening_cost": 300.0, "capacity": 259.0 }, { "id": "F4", "opening_cost": 300.0, "capacity": 490.0 }, { "id": "F5", "opening_cost": 300.0, "capacity": 410.0 }, { "id": "F6", "opening_cost": 300.0, "capacity": 213.0 }, { "id": "F7", "opening_cost": 300.0, "capacity": 564.0 } ], "customers": [ { "id": 0, "demand": 11.0 }, { "id": 1, "demand": 28.0 }, { "id": 2, "demand": 18.0 }, { "id": 3, "demand": 12.0 }, { "id": 4, "demand": 28.0 }, { "id": 5, "demand": 19.0 }, { "id": 6, "demand": 29.0 }, { "id": 7, "demand": 12.0 }, { "id": 8, "demand": 29.0 }, { "id": 9, "demand": 13.0 }, { "id": 10, "demand": 26.0 }, { "id": 11, "demand": 23.0 }, { "id": 12, "demand": 24.0 }, { "id": 13, "demand": 16.0 }, { "id": 14, "demand": 13.0 }, { "id": 15, "demand": 11.0 }, { "id": 16, "demand": 27.0 }, { "id": 17, "demand": 16.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 231.0 }, { "facility": "F1", "customer": 1, "cost": 1017.0 }, { "facility": "F1", "customer": 2, "cost": 58.0 }, { "facility": "F1", "customer": 3, "cost": 660.0 }, { "facility": "F1", "customer": 4, "cost": 726.0 }, { "facility": "F1", "customer": 5, "cost": 720.0 }, { "facility": "F1", "customer": 6, "cost": 58.0 }, { "facility": "F1", "customer": 7, "cost": 463.0 }, { "facility": "F1", "customer": 8, "cost": 391.0 }, { "facility": "F1", "customer": 9, "cost": 36.0 }, { "facility": "F1", "customer": 10, "cost": 463.0 }, { "facility": "F1", "customer": 11, "cost": 298.0 }, { "facility": "F1", "customer": 12, "cost": 48.0 }, { "facility": "F1", "customer": 13, "cost": 298.0 }, { "facility": "F1", "customer": 14, "cost": 282.0 }, { "facility": "F1", "customer": 15, "cost": 201.0 }, { "facility": "F1", "customer": 16, "cost": 64.0 }, { "facility": "F1", "customer": 17, "cost": 1401.0 }, { "facility": "F2", "customer": 0, "cost": 30.0 }, { "facility": "F2", "customer": 1, "cost": 1671.0 }, { "facility": "F2", "customer": 2, "cost": 499.0 }, { "facility": "F2", "customer": 3, "cost": 699.0 }, { "facility": "F2", "customer": 4, "cost": 674.0 }, { "facility": "F2", "customer": 5, "cost": 1105.0 }, { "facility": "F2", "customer": 6, "cost": 178.0 }, { "facility": "F2", "customer": 7, "cost": 542.0 }, { "facility": "F2", "customer": 8, "cost": 138.0 }, { "facility": "F2", "customer": 9, "cost": 292.0 }, { "facility": "F2", "customer": 10, "cost": 422.0 }, { "facility": "F2", "customer": 11, "cost": 805.0 }, { "facility": "F2", "customer": 12, "cost": 718.0 }, { "facility": "F2", "customer": 13, "cost": 864.0 }, { "facility": "F2", "customer": 14, "cost": 374.0 }, { "facility": "F2", "customer": 15, "cost": 22.0 }, { "facility": "F2", "customer": 16, "cost": 190.0 }, { "facility": "F2", "customer": 17, "cost": 1987.0 }, { "facility": "F3", "customer": 0, "cost": 368.0 }, { "facility": "F3", "customer": 1, "cost": 1223.0 }, { "facility": "F3", "customer": 2, "cost": 273.0 }, { "facility": "F3", "customer": 3, "cost": 936.0 }, { "facility": "F3", "customer": 4, "cost": 986.0 }, { "facility": "F3", "customer": 5, "cost": 1037.0 }, { "facility": "F3", "customer": 6, "cost": 72.0 }, { "facility": "F3", "customer": 7, "cost": 732.0 }, { "facility": "F3", "customer": 8, "cost": 558.0 }, { "facility": "F3", "customer": 9, "cost": 29.0 }, { "facility": "F3", "customer": 10, "cost": 706.0 }, { "facility": "F3", "customer": 11, "cost": 231.0 }, { "facility": "F3", "customer": 12, "cost": 365.0 }, { "facility": "F3", "customer": 13, "cost": 613.0 }, { "facility": "F3", "customer": 14, "cost": 525.0 }, { "facility": "F3", "customer": 15, "cost": 339.0 }, { "facility": "F3", "customer": 16, "cost": 54.0 }, { "facility": "F3", "customer": 17, "cost": 1661.0 }, { "facility": "F4", "customer": 0, "cost": 521.0 }, { "facility": "F4", "customer": 1, "cost": 1334.0 }, { "facility": "F4", "customer": 2, "cost": 492.0 }, { "facility": "F4", "customer": 3, "cost": 1154.0 }, { "facility": "F4", "customer": 4, "cost": 1199.0 }, { "facility": "F4", "customer": 5, "cost": 1254.0 }, { "facility": "F4", "customer": 6, "cost": 135.0 }, { "facility": "F4", "customer": 7, "cost": 949.0 }, { "facility": "F4", "customer": 8, "cost": 727.0 }, { "facility": "F4", "customer": 9, "cost": 104.0 }, { "facility": "F4", "customer": 10, "cost": 915.0 }, { "facility": "F4", "customer": 11, "cost": 85.0 }, { "facility": "F4", "customer": 12, "cost": 584.0 }, { "facility": "F4", "customer": 13, "cost": 826.0 }, { "facility": "F4", "customer": 14, "cost": 737.0 }, { "facility": "F4", "customer": 15, "cost": 496.0 }, { "facility": "F4", "customer": 16, "cost": 72.0 }, { "facility": "F4", "customer": 17, "cost": 1807.0 }, { "facility": "F5", "customer": 0, "cost": 372.0 }, { "facility": "F5", "customer": 1, "cost": 1591.0 }, { "facility": "F5", "customer": 2, "cost": 466.0 }, { "facility": "F5", "customer": 3, "cost": 1066.0 }, { "facility": "F5", "customer": 4, "cost": 1090.0 }, { "facility": "F5", "customer": 5, "cost": 1277.0 }, { "facility": "F5", "customer": 6, "cost": 59.0 }, { "facility": "F5", "customer": 7, "cost": 864.0 }, { "facility": "F5", "customer": 8, "cost": 579.0 }, { "facility": "F5", "customer": 9, "cost": 40.0 }, { "facility": "F5", "customer": 10, "cost": 804.0 }, { "facility": "F5", "customer": 11, "cost": 531.0 }, { "facility": "F5", "customer": 12, "cost": 653.0 }, { "facility": "F5", "customer": 13, "cost": 891.0 }, { "facility": "F5", "customer": 14, "cost": 642.0 }, { "facility": "F5", "customer": 15, "cost": 347.0 }, { "facility": "F5", "customer": 16, "cost": 62.0 }, { "facility": "F5", "customer": 17, "cost": 2002.0 }, { "facility": "F6", "customer": 0, "cost": 674.0 }, { "facility": "F6", "customer": 1, "cost": 1877.0 }, { "facility": "F6", "customer": 2, "cost": 851.0 }, { "facility": "F6", "customer": 3, "cost": 1453.0 }, { "facility": "F6", "customer": 4, "cost": 1467.0 }, { "facility": "F6", "customer": 5, "cost": 1663.0 }, { "facility": "F6", "customer": 6, "cost": 223.0 }, { "facility": "F6", "customer": 7, "cost": 1253.0 }, { "facility": "F6", "customer": 8, "cost": 898.0 }, { "facility": "F6", "customer": 9, "cost": 288.0 }, { "facility": "F6", "customer": 10, "cost": 1184.0 }, { "facility": "F6", "customer": 11, "cost": 653.0 }, { "facility": "F6", "customer": 12, "cost": 1011.0 }, { "facility": "F6", "customer": 13, "cost": 1260.0 }, { "facility": "F6", "customer": 14, "cost": 1031.0 }, { "facility": "F6", "customer": 15, "cost": 661.0 }, { "facility": "F6", "customer": 16, "cost": 97.0 }, { "facility": "F6", "customer": 17, "cost": 2328.0 }, { "facility": "F7", "customer": 0, "cost": 277.0 }, { "facility": "F7", "customer": 1, "cost": 644.0 }, { "facility": "F7", "customer": 2, "cost": 104.0 }, { "facility": "F7", "customer": 3, "cost": 656.0 }, { "facility": "F7", "customer": 4, "cost": 736.0 }, { "facility": "F7", "customer": 5, "cost": 609.0 }, { "facility": "F7", "customer": 6, "cost": 64.0 }, { "facility": "F7", "customer": 7, "cost": 473.0 }, { "facility": "F7", "customer": 8, "cost": 436.0 }, { "facility": "F7", "customer": 9, "cost": 26.0 }, { "facility": "F7", "customer": 10, "cost": 489.0 }, { "facility": "F7", "customer": 11, "cost": 149.0 }, { "facility": "F7", "customer": 12, "cost": 94.0 }, { "facility": "F7", "customer": 13, "cost": 213.0 }, { "facility": "F7", "customer": 14, "cost": 314.0 }, { "facility": "F7", "customer": 15, "cost": 247.0 }, { "facility": "F7", "customer": 16, "cost": 55.0 }, { "facility": "F7", "customer": 17, "cost": 1079.0 } ], "objective": 6366.0 }, "solution_variant": { "selected": [ "F2", "F7" ], "assignments": [ "F2", "F7", "F7", "F7", "F2", "F7", "F7", "F7", "F2", "F7", "F2", "F7", "F7", "F7", "F7", "F2", "F7", "F7" ] }, "context_index": 49, "input_format": "csv", "input_index_base": 0 }, { "task_name": "CFLP", "problem_type": "CFLP", "instruction": "Picture this: a grocery chain choosing which branches to run for the season and then lining up every household to a single running branch. Each branch that’s kept open comes with an opening expense, and serving each household from a branch adds a travel or delivery cost — so the sensible thing is to pick stores and assignments that make the total bill (opening fees plus all travel costs) as small as possible. At the same time, every household must be assigned to one branch only, and no branch can exceed its stocking capacity. The exact store choices and household details appear below.\n\nThere are 7 stores and 19 households in this instance.\n\n**Stores**\n| store_id | store_opening_cost | stocking_capacity |\n|---|---|---|\n| F1 | 600.0 | 500.0 |\n| F2 | 600.0 | 500.0 |\n| F3 | 600.0 | 500.0 |\n| F4 | 600.0 | 500.0 |\n| F5 | 600.0 | 500.0 |\n| F6 | 600.0 | 500.0 |\n| F7 | 600.0 | 500.0 |\n\n**Households**\n| household_id | household_demand |\n|---|---|\n| A | 16.0 |\n| B | 31.0 |\n| C | 11.0 |\n| D | 25.0 |\n| E | 14.0 |\n| F | 25.0 |\n| G | 37.0 |\n| H | 17.0 |\n| I | 19.0 |\n| J | 38.0 |\n| K | 45.0 |\n| L | 26.0 |\n| M | 27.0 |\n| N | 14.0 |\n| O | 14.0 |\n| P | 45.0 |\n| Q | 35.0 |\n| R | 44.0 |\n| S | 17.0 |\n\n**Travel Cost**\n| store_id | household_id | travel_cost |\n|---|---|---|\n| F1 | A | 456.0 |\n| F1 | B | 494.0 |\n| F1 | C | 367.0 |\n| F1 | D | 599.0 |\n| F1 | E | 160.0 |\n| F1 | F | 584.0 |\n| F1 | G | 543.0 |\n| F1 | H | 726.0 |\n| F1 | I | 552.0 |\n| F1 | J | 390.0 |\n| F1 | K | 563.0 |\n| F1 | L | 644.0 |\n| F1 | M | 156.0 |\n| F1 | N | 269.0 |\n| F1 | O | 131.0 |\n| F1 | P | 308.0 |\n| F1 | Q | 251.0 |\n| F1 | R | 637.0 |\n| F1 | S | 336.0 |\n| F2 | A | 271.0 |\n| F2 | B | 769.0 |\n| F2 | C | 271.0 |\n| F2 | D | 196.0 |\n| F2 | E | 453.0 |\n| F2 | F | 90.0 |\n| F2 | G | 142.0 |\n| F2 | H | 422.0 |\n| F2 | I | 389.0 |\n| F2 | J | 492.0 |\n| F2 | K | 503.0 |\n| F2 | L | 249.0 |\n| F2 | M | 475.0 |\n| F2 | N | 589.0 |\n| F2 | O | 476.0 |\n| F2 | P | 300.0 |\n| F2 | Q | 351.0 |\n| F2 | R | 292.0 |\n| F2 | S | 696.0 |\n| F3 | A | 246.0 |\n| F3 | B | 480.0 |\n| F3 | C | 229.0 |\n| F3 | D | 382.0 |\n| F3 | E | 149.0 |\n| F3 | F | 399.0 |\n| F3 | G | 326.0 |\n| F3 | H | 527.0 |\n| F3 | I | 363.0 |\n| F3 | J | 262.0 |\n| F3 | K | 406.0 |\n| F3 | L | 429.0 |\n| F3 | M | 89.0 |\n| F3 | N | 248.0 |\n| F3 | O | 150.0 |\n| F3 | P | 92.0 |\n| F3 | Q | 36.0 |\n| F3 | R | 426.0 |\n| F3 | S | 356.0 |\n| F4 | A | 433.0 |\n| F4 | B | 92.0 |\n| F4 | C | 668.0 |\n| F4 | D | 562.0 |\n| F4 | E | 572.0 |\n| F4 | F | 761.0 |\n| F4 | G | 571.0 |\n| F4 | H | 505.0 |\n| F4 | I | 363.0 |\n| F4 | J | 215.0 |\n| F4 | K | 263.0 |\n| F4 | L | 560.0 |\n| F4 | M | 404.0 |\n| F4 | N | 237.0 |\n| F4 | O | 556.0 |\n| F4 | P | 472.0 |\n| F4 | Q | 463.0 |\n| F4 | R | 517.0 |\n| F4 | S | 196.0 |\n| F5 | A | 110.0 |\n| F5 | B | 608.0 |\n| F5 | C | 268.0 |\n| F5 | D | 120.0 |\n| F5 | E | 383.0 |\n| F5 | F | 228.0 |\n| F5 | G | 53.0 |\n| F5 | H | 327.0 |\n| F5 | I | 242.0 |\n| F5 | J | 331.0 |\n| F5 | K | 351.0 |\n| F5 | L | 178.0 |\n| F5 | M | 352.0 |\n| F5 | N | 439.0 |\n| F5 | O | 399.0 |\n| F5 | P | 182.0 |\n| F5 | Q | 239.0 |\n| F5 | R | 198.0 |\n| F5 | S | 542.0 |\n| F6 | A | 402.0 |\n| F6 | B | 115.0 |\n| F6 | C | 591.0 |\n| F6 | D | 547.0 |\n| F6 | E | 474.0 |\n| F6 | F | 711.0 |\n| F6 | G | 541.0 |\n| F6 | H | 536.0 |\n| F6 | I | 371.0 |\n| F6 | J | 177.0 |\n| F6 | K | 297.0 |\n| F6 | L | 557.0 |\n| F6 | M | 307.0 |\n| F6 | N | 132.0 |\n| F6 | O | 457.0 |\n| F6 | P | 403.0 |\n| F6 | Q | 383.0 |\n| F6 | R | 520.0 |\n| F6 | S | 95.0 |\n| F7 | A | 300.0 |\n| F7 | B | 208.0 |\n| F7 | C | 548.0 |\n| F7 | D | 433.0 |\n| F7 | E | 479.0 |\n| F7 | F | 629.0 |\n| F7 | G | 438.0 |\n| F7 | H | 404.0 |\n| F7 | I | 243.0 |\n| F7 | J | 87.0 |\n| F7 | K | 166.0 |\n| F7 | L | 435.0 |\n| F7 | M | 316.0 |\n| F7 | N | 190.0 |\n| F7 | O | 469.0 |\n| F7 | P | 350.0 |\n| F7 | Q | 349.0 |\n| F7 | R | 395.0 |\n| F7 | S | 218.0 |\n\nAlso, when you send back your pick and the household line-up, please follow this simple JSON layout so it's easy to read and check:\n\n{\n \"solution\": {\n \"selected\": [, , ...],\n \"assignments\": [, , ...]\n }\n}\n\nThink of \"selected\" as the list of branches you decide to keep open, and \"assignments\" as the list that, in order, tells which open branch each household is assigned to (one entry per household). Super informal sketch — it's just the shape I need, not the real answer itself.\n\nPlease use the exact identifiers from the instance input — no renaming, no made-up labels. \n- for example: \"Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.\"", "instance": { "opening_costs": [ 600.0, 600.0, 600.0, 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 456.0, 494.0, 367.0, 599.0, 160.0, 584.0, 543.0, 726.0, 552.0, 390.0, 563.0, 644.0, 156.0, 269.0, 131.0, 308.0, 251.0, 637.0, 336.0 ], [ 271.0, 769.0, 271.0, 196.0, 453.0, 90.0, 142.0, 422.0, 389.0, 492.0, 503.0, 249.0, 475.0, 589.0, 476.0, 300.0, 351.0, 292.0, 696.0 ], [ 246.0, 480.0, 229.0, 382.0, 149.0, 399.0, 326.0, 527.0, 363.0, 262.0, 406.0, 429.0, 89.0, 248.0, 150.0, 92.0, 36.0, 426.0, 356.0 ], [ 433.0, 92.0, 668.0, 562.0, 572.0, 761.0, 571.0, 505.0, 363.0, 215.0, 263.0, 560.0, 404.0, 237.0, 556.0, 472.0, 463.0, 517.0, 196.0 ], [ 110.0, 608.0, 268.0, 120.0, 383.0, 228.0, 53.0, 327.0, 242.0, 331.0, 351.0, 178.0, 352.0, 439.0, 399.0, 182.0, 239.0, 198.0, 542.0 ], [ 402.0, 115.0, 591.0, 547.0, 474.0, 711.0, 541.0, 536.0, 371.0, 177.0, 297.0, 557.0, 307.0, 132.0, 457.0, 403.0, 383.0, 520.0, 95.0 ], [ 300.0, 208.0, 548.0, 433.0, 479.0, 629.0, 438.0, 404.0, 243.0, 87.0, 166.0, 435.0, 316.0, 190.0, 469.0, 350.0, 349.0, 395.0, 218.0 ] ], "demands": [ 16.0, 31.0, 11.0, 25.0, 14.0, 25.0, 37.0, 17.0, 19.0, 38.0, 45.0, 26.0, 27.0, 14.0, 14.0, 45.0, 35.0, 44.0, 17.0 ], "objective": 4817.0 }, "solution": { "open_facilities": [ 2, 4, 5 ], "assignments": [ 4, 5, 2, 4, 2, 4, 4, 4, 4, 5, 5, 4, 2, 5, 2, 2, 2, 4, 5 ] }, "obj": 4817.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 19, "facilities": [ { "id": "F1", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F2", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F3", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F4", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F5", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F6", "opening_cost": 600.0, "capacity": 500.0 }, { "id": "F7", "opening_cost": 600.0, "capacity": 500.0 } ], "customers": [ { "id": "A", "demand": 16.0 }, { "id": "B", "demand": 31.0 }, { "id": "C", "demand": 11.0 }, { "id": "D", "demand": 25.0 }, { "id": "E", "demand": 14.0 }, { "id": "F", "demand": 25.0 }, { "id": "G", "demand": 37.0 }, { "id": "H", "demand": 17.0 }, { "id": "I", "demand": 19.0 }, { "id": "J", "demand": 38.0 }, { "id": "K", "demand": 45.0 }, { "id": "L", "demand": 26.0 }, { "id": "M", "demand": 27.0 }, { "id": "N", "demand": 14.0 }, { "id": "O", "demand": 14.0 }, { "id": "P", "demand": 45.0 }, { "id": "Q", "demand": 35.0 }, { "id": "R", "demand": 44.0 }, { "id": "S", "demand": 17.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 456.0 }, { "facility": "F1", "customer": "B", "cost": 494.0 }, { "facility": "F1", "customer": "C", "cost": 367.0 }, { "facility": "F1", "customer": "D", "cost": 599.0 }, { "facility": "F1", "customer": "E", "cost": 160.0 }, { "facility": "F1", "customer": "F", "cost": 584.0 }, { "facility": "F1", "customer": "G", "cost": 543.0 }, { "facility": "F1", "customer": "H", "cost": 726.0 }, { "facility": "F1", "customer": "I", "cost": 552.0 }, { "facility": "F1", "customer": "J", "cost": 390.0 }, { "facility": "F1", "customer": "K", "cost": 563.0 }, { "facility": "F1", "customer": "L", "cost": 644.0 }, { "facility": "F1", "customer": "M", "cost": 156.0 }, { "facility": "F1", "customer": "N", "cost": 269.0 }, { "facility": "F1", "customer": "O", "cost": 131.0 }, { "facility": "F1", "customer": "P", "cost": 308.0 }, { "facility": "F1", "customer": "Q", "cost": 251.0 }, { "facility": "F1", "customer": "R", "cost": 637.0 }, { "facility": "F1", "customer": "S", "cost": 336.0 }, { "facility": "F2", "customer": "A", "cost": 271.0 }, { "facility": "F2", "customer": "B", "cost": 769.0 }, { "facility": "F2", "customer": "C", "cost": 271.0 }, { "facility": "F2", "customer": "D", "cost": 196.0 }, { "facility": "F2", "customer": "E", "cost": 453.0 }, { "facility": "F2", "customer": "F", "cost": 90.0 }, { "facility": "F2", "customer": "G", "cost": 142.0 }, { "facility": "F2", "customer": "H", "cost": 422.0 }, { "facility": "F2", "customer": "I", "cost": 389.0 }, { "facility": "F2", "customer": "J", "cost": 492.0 }, { "facility": "F2", "customer": "K", "cost": 503.0 }, { "facility": "F2", "customer": "L", "cost": 249.0 }, { "facility": "F2", "customer": "M", "cost": 475.0 }, { "facility": "F2", "customer": "N", "cost": 589.0 }, { "facility": "F2", "customer": "O", "cost": 476.0 }, { "facility": "F2", "customer": "P", "cost": 300.0 }, { "facility": "F2", "customer": "Q", "cost": 351.0 }, { "facility": "F2", "customer": "R", "cost": 292.0 }, { "facility": "F2", "customer": "S", "cost": 696.0 }, { "facility": "F3", "customer": "A", "cost": 246.0 }, { "facility": "F3", "customer": "B", "cost": 480.0 }, { "facility": "F3", "customer": "C", "cost": 229.0 }, { "facility": "F3", "customer": "D", "cost": 382.0 }, { "facility": "F3", "customer": "E", "cost": 149.0 }, { "facility": "F3", "customer": "F", "cost": 399.0 }, { "facility": "F3", "customer": "G", "cost": 326.0 }, { "facility": "F3", "customer": "H", "cost": 527.0 }, { "facility": "F3", "customer": "I", "cost": 363.0 }, { "facility": "F3", "customer": "J", "cost": 262.0 }, { "facility": "F3", "customer": "K", "cost": 406.0 }, { "facility": "F3", "customer": "L", "cost": 429.0 }, { "facility": "F3", "customer": "M", "cost": 89.0 }, { "facility": "F3", "customer": "N", "cost": 248.0 }, { "facility": "F3", "customer": "O", "cost": 150.0 }, { "facility": "F3", "customer": "P", "cost": 92.0 }, { "facility": "F3", "customer": "Q", "cost": 36.0 }, { "facility": "F3", "customer": "R", "cost": 426.0 }, { "facility": "F3", "customer": "S", "cost": 356.0 }, { "facility": "F4", "customer": "A", "cost": 433.0 }, { "facility": "F4", "customer": "B", "cost": 92.0 }, { "facility": "F4", "customer": "C", "cost": 668.0 }, { "facility": "F4", "customer": "D", "cost": 562.0 }, { "facility": "F4", "customer": "E", "cost": 572.0 }, { "facility": "F4", "customer": "F", "cost": 761.0 }, { "facility": "F4", "customer": "G", "cost": 571.0 }, { "facility": "F4", "customer": "H", "cost": 505.0 }, { "facility": "F4", "customer": "I", "cost": 363.0 }, { "facility": "F4", "customer": "J", "cost": 215.0 }, { "facility": "F4", "customer": "K", "cost": 263.0 }, { "facility": "F4", "customer": "L", "cost": 560.0 }, { "facility": "F4", "customer": "M", "cost": 404.0 }, { "facility": "F4", "customer": "N", "cost": 237.0 }, { "facility": "F4", "customer": "O", "cost": 556.0 }, { "facility": "F4", "customer": "P", "cost": 472.0 }, { "facility": "F4", "customer": "Q", "cost": 463.0 }, { "facility": "F4", "customer": "R", "cost": 517.0 }, { "facility": "F4", "customer": "S", "cost": 196.0 }, { "facility": "F5", "customer": "A", "cost": 110.0 }, { "facility": "F5", "customer": "B", "cost": 608.0 }, { "facility": "F5", "customer": "C", "cost": 268.0 }, { "facility": "F5", "customer": "D", "cost": 120.0 }, { "facility": "F5", "customer": "E", "cost": 383.0 }, { "facility": "F5", "customer": "F", "cost": 228.0 }, { "facility": "F5", "customer": "G", "cost": 53.0 }, { "facility": "F5", "customer": "H", "cost": 327.0 }, { "facility": "F5", "customer": "I", "cost": 242.0 }, { "facility": "F5", "customer": "J", "cost": 331.0 }, { "facility": "F5", "customer": "K", "cost": 351.0 }, { "facility": "F5", "customer": "L", "cost": 178.0 }, { "facility": "F5", "customer": "M", "cost": 352.0 }, { "facility": "F5", "customer": "N", "cost": 439.0 }, { "facility": "F5", "customer": "O", "cost": 399.0 }, { "facility": "F5", "customer": "P", "cost": 182.0 }, { "facility": "F5", "customer": "Q", "cost": 239.0 }, { "facility": "F5", "customer": "R", "cost": 198.0 }, { "facility": "F5", "customer": "S", "cost": 542.0 }, { "facility": "F6", "customer": "A", "cost": 402.0 }, { "facility": "F6", "customer": "B", "cost": 115.0 }, { "facility": "F6", "customer": "C", "cost": 591.0 }, { "facility": "F6", "customer": "D", "cost": 547.0 }, { "facility": "F6", "customer": "E", "cost": 474.0 }, { "facility": "F6", "customer": "F", "cost": 711.0 }, { "facility": "F6", "customer": "G", "cost": 541.0 }, { "facility": "F6", "customer": "H", "cost": 536.0 }, { "facility": "F6", "customer": "I", "cost": 371.0 }, { "facility": "F6", "customer": "J", "cost": 177.0 }, { "facility": "F6", "customer": "K", "cost": 297.0 }, { "facility": "F6", "customer": "L", "cost": 557.0 }, { "facility": "F6", "customer": "M", "cost": 307.0 }, { "facility": "F6", "customer": "N", "cost": 132.0 }, { "facility": "F6", "customer": "O", "cost": 457.0 }, { "facility": "F6", "customer": "P", "cost": 403.0 }, { "facility": "F6", "customer": "Q", "cost": 383.0 }, { "facility": "F6", 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