[ { "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\nThere are 6 candidate transfer stations and 13 city blocks; the following lines list their parameters and pairwise haul costs.\nTransfer station F1 has startup cost 400.0 and handling capacity 300.0.\nTransfer station F2 has startup cost 400.0 and handling capacity 300.0.\nTransfer station F3 has startup cost 400.0 and handling capacity 300.0.\nTransfer station F4 has startup cost 400.0 and handling capacity 300.0.\nTransfer station F5 has startup cost 400.0 and handling capacity 300.0.\nTransfer station F6 has startup cost 400.0 and handling capacity 300.0.\nBlock 0 generates 25.0 units of waste.\nBlock 1 generates 28.0 units of waste.\nBlock 2 generates 19.0 units of waste.\nBlock 3 generates 11.0 units of waste.\nBlock 4 generates 12.0 units of waste.\nBlock 5 generates 14.0 units of waste.\nBlock 6 generates 24.0 units of waste.\nBlock 7 generates 24.0 units of waste.\nBlock 8 generates 18.0 units of waste.\nBlock 9 generates 13.0 units of waste.\nBlock 10 generates 16.0 units of waste.\nBlock 11 generates 18.0 units of waste.\nBlock 12 generates 25.0 units of waste.\nHaul cost from station F1 to block 0 is 71.0.\nHaul cost from station F1 to block 1 is 81.0.\nHaul cost from station F1 to block 2 is 197.0.\nHaul cost from station F1 to block 3 is 22.0.\nHaul cost from station F1 to block 4 is 43.0.\nHaul cost from station F1 to block 5 is 145.0.\nHaul cost from station F1 to block 6 is 339.0.\nHaul cost from station F1 to block 7 is 49.0.\nHaul cost from station F1 to block 8 is 46.0.\nHaul cost from station F1 to block 9 is 151.0.\nHaul cost from station F1 to block 10 is 81.0.\nHaul cost from station F1 to block 11 is 146.0.\nHaul cost from station F1 to block 12 is 239.0.\nHaul cost from station F2 to block 0 is 1087.0.\nHaul cost from station F2 to block 1 is 260.0.\nHaul cost from station F2 to block 2 is 1185.0.\nHaul cost from station F2 to block 3 is 1542.0.\nHaul cost from station F2 to block 4 is 269.0.\nHaul cost from station F2 to block 5 is 1287.0.\nHaul cost from station F2 to block 6 is 438.0.\nHaul cost from station F2 to block 7 is 671.0.\nHaul cost from station F2 to block 8 is 1086.0.\nHaul cost from station F2 to block 9 is 475.0.\nHaul cost from station F2 to block 10 is 1305.0.\nHaul cost from station F2 to block 11 is 1944.0.\nHaul cost from station F2 to block 12 is 1284.0.\nHaul cost from station F3 to block 0 is 285.0.\nHaul cost from station F3 to block 1 is 56.0.\nHaul cost from station F3 to block 2 is 131.0.\nHaul cost from station F3 to block 3 is 448.0.\nHaul cost from station F3 to block 4 is 99.0.\nHaul cost from station F3 to block 5 is 112.0.\nHaul cost from station F3 to block 6 is 261.0.\nHaul cost from station F3 to block 7 is 87.0.\nHaul cost from station F3 to block 8 is 242.0.\nHaul cost from station F3 to block 9 is 79.0.\nHaul cost from station F3 to block 10 is 415.0.\nHaul cost from station F3 to block 11 is 769.0.\nHaul cost from station F3 to block 12 is 203.0.\nHaul cost from station F4 to block 0 is 1241.0.\nHaul cost from station F4 to block 1 is 439.0.\nHaul cost from station F4 to block 2 is 1167.0.\nHaul cost from station F4 to block 3 is 1631.0.\nHaul cost from station F4 to block 4 is 472.0.\nHaul cost from station F4 to block 5 is 1297.0.\nHaul cost from station F4 to block 6 is 48.0.\nHaul cost from station F4 to block 7 is 825.0.\nHaul cost from station F4 to block 8 is 1229.0.\nHaul cost from station F4 to block 9 is 458.0.\nHaul cost from station F4 to block 10 is 1453.0.\nHaul cost from station F4 to block 11 is 1986.0.\nHaul cost from station F4 to block 12 is 1255.0.\nHaul cost from station F5 to block 0 is 110.0.\nHaul cost from station F5 to block 1 is 78.0.\nHaul cost from station F5 to block 2 is 269.0.\nHaul cost from station F5 to block 3 is 180.0.\nHaul cost from station F5 to block 4 is 51.0.\nHaul cost from station F5 to block 5 is 228.0.\nHaul cost from station F5 to block 6 is 353.0.\nHaul cost from station F5 to block 7 is 48.0.\nHaul cost from station F5 to block 8 is 72.0.\nHaul cost from station F5 to block 9 is 162.0.\nHaul cost from station F5 to block 10 is 178.0.\nHaul cost from station F5 to block 11 is 602.0.\nHaul cost from station F5 to block 12 is 334.0.\nHaul cost from station F6 to block 0 is 1136.0.\nHaul cost from station F6 to block 1 is 330.0.\nHaul cost from station F6 to block 2 is 1105.0.\nHaul cost from station F6 to block 3 is 1541.0.\nHaul cost from station F6 to block 4 is 380.0.\nHaul cost from station F6 to block 5 is 1228.0.\nHaul cost from station F6 to block 6 is 192.0.\nHaul cost from station F6 to block 7 is 718.0.\nHaul cost from station F6 to block 8 is 1126.0.\nHaul cost from station F6 to block 9 is 374.0.\nHaul cost from station F6 to block 10 is 1350.0.\nHaul cost from station F6 to block 11 is 1911.0.\nHaul cost from station F6 to block 12 is 1198.0.\nUse these figures to pick the set of stations to open and assign each block so the total startup plus hauling cost is minimized.\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 ], "capacities": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "connection_costs": [ [ 71.0, 81.0, 197.0, 22.0, 43.0, 145.0, 339.0, 49.0, 46.0, 151.0, 81.0, 146.0, 239.0 ], [ 1087.0, 260.0, 1185.0, 1542.0, 269.0, 1287.0, 438.0, 671.0, 1086.0, 475.0, 1305.0, 1944.0, 1284.0 ], [ 285.0, 56.0, 131.0, 448.0, 99.0, 112.0, 261.0, 87.0, 242.0, 79.0, 415.0, 769.0, 203.0 ], [ 1241.0, 439.0, 1167.0, 1631.0, 472.0, 1297.0, 48.0, 825.0, 1229.0, 458.0, 1453.0, 1986.0, 1255.0 ], [ 110.0, 78.0, 269.0, 180.0, 51.0, 228.0, 353.0, 48.0, 72.0, 162.0, 178.0, 602.0, 334.0 ], [ 1136.0, 330.0, 1105.0, 1541.0, 380.0, 1228.0, 192.0, 718.0, 1126.0, 374.0, 1350.0, 1911.0, 1198.0 ] ], "demands": [ 25.0, 28.0, 19.0, 11.0, 12.0, 14.0, 24.0, 24.0, 18.0, 13.0, 16.0, 18.0, 25.0 ], "objective": 2010.0 }, "solution": { "open_facilities": [ 0 ], "assignments": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] }, "obj": 2010.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 6, "num_customers": 13, "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 } ], "customers": [ { "id": 0, "demand": 25.0 }, { "id": 1, "demand": 28.0 }, { "id": 2, "demand": 19.0 }, { "id": 3, "demand": 11.0 }, { "id": 4, "demand": 12.0 }, { "id": 5, "demand": 14.0 }, { "id": 6, "demand": 24.0 }, { "id": 7, "demand": 24.0 }, { "id": 8, "demand": 18.0 }, { "id": 9, "demand": 13.0 }, { "id": 10, "demand": 16.0 }, { "id": 11, "demand": 18.0 }, { "id": 12, "demand": 25.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 71.0 }, { "facility": "F1", "customer": 1, "cost": 81.0 }, { "facility": "F1", "customer": 2, "cost": 197.0 }, { "facility": "F1", "customer": 3, "cost": 22.0 }, { "facility": "F1", "customer": 4, "cost": 43.0 }, { "facility": "F1", "customer": 5, "cost": 145.0 }, { "facility": "F1", "customer": 6, "cost": 339.0 }, { "facility": "F1", "customer": 7, "cost": 49.0 }, { "facility": "F1", "customer": 8, "cost": 46.0 }, { "facility": "F1", "customer": 9, "cost": 151.0 }, { "facility": "F1", "customer": 10, "cost": 81.0 }, { "facility": "F1", "customer": 11, "cost": 146.0 }, { "facility": "F1", "customer": 12, "cost": 239.0 }, { "facility": "F2", "customer": 0, "cost": 1087.0 }, { "facility": "F2", "customer": 1, "cost": 260.0 }, { "facility": "F2", "customer": 2, "cost": 1185.0 }, { "facility": "F2", "customer": 3, "cost": 1542.0 }, { "facility": "F2", "customer": 4, "cost": 269.0 }, { "facility": "F2", "customer": 5, "cost": 1287.0 }, { "facility": "F2", "customer": 6, "cost": 438.0 }, { "facility": "F2", "customer": 7, "cost": 671.0 }, { "facility": "F2", "customer": 8, "cost": 1086.0 }, { "facility": "F2", "customer": 9, "cost": 475.0 }, { "facility": "F2", "customer": 10, "cost": 1305.0 }, { "facility": "F2", "customer": 11, "cost": 1944.0 }, { "facility": "F2", "customer": 12, "cost": 1284.0 }, { "facility": "F3", "customer": 0, "cost": 285.0 }, { "facility": "F3", "customer": 1, "cost": 56.0 }, { "facility": "F3", "customer": 2, "cost": 131.0 }, { "facility": "F3", "customer": 3, "cost": 448.0 }, { "facility": "F3", "customer": 4, "cost": 99.0 }, { "facility": "F3", "customer": 5, "cost": 112.0 }, { "facility": "F3", "customer": 6, "cost": 261.0 }, { "facility": "F3", "customer": 7, "cost": 87.0 }, { "facility": "F3", "customer": 8, "cost": 242.0 }, { "facility": "F3", "customer": 9, "cost": 79.0 }, { "facility": "F3", "customer": 10, "cost": 415.0 }, { "facility": "F3", "customer": 11, "cost": 769.0 }, { "facility": "F3", "customer": 12, "cost": 203.0 }, { "facility": "F4", "customer": 0, "cost": 1241.0 }, { "facility": "F4", "customer": 1, "cost": 439.0 }, { "facility": "F4", "customer": 2, "cost": 1167.0 }, { "facility": "F4", "customer": 3, "cost": 1631.0 }, { "facility": "F4", "customer": 4, "cost": 472.0 }, { "facility": "F4", "customer": 5, "cost": 1297.0 }, { "facility": "F4", "customer": 6, "cost": 48.0 }, { "facility": "F4", "customer": 7, "cost": 825.0 }, { "facility": "F4", "customer": 8, "cost": 1229.0 }, { "facility": "F4", "customer": 9, "cost": 458.0 }, { "facility": "F4", "customer": 10, "cost": 1453.0 }, { "facility": "F4", "customer": 11, "cost": 1986.0 }, { "facility": "F4", "customer": 12, "cost": 1255.0 }, { "facility": "F5", "customer": 0, "cost": 110.0 }, { "facility": "F5", "customer": 1, "cost": 78.0 }, { "facility": "F5", "customer": 2, "cost": 269.0 }, { "facility": "F5", "customer": 3, "cost": 180.0 }, { "facility": "F5", "customer": 4, "cost": 51.0 }, { "facility": "F5", "customer": 5, "cost": 228.0 }, { "facility": "F5", "customer": 6, "cost": 353.0 }, { "facility": "F5", "customer": 7, "cost": 48.0 }, { "facility": "F5", "customer": 8, "cost": 72.0 }, { "facility": "F5", "customer": 9, "cost": 162.0 }, { "facility": "F5", "customer": 10, "cost": 178.0 }, { "facility": "F5", "customer": 11, "cost": 602.0 }, { "facility": "F5", "customer": 12, "cost": 334.0 }, { "facility": "F6", "customer": 0, "cost": 1136.0 }, { "facility": "F6", "customer": 1, "cost": 330.0 }, { "facility": "F6", "customer": 2, "cost": 1105.0 }, { "facility": "F6", "customer": 3, "cost": 1541.0 }, { "facility": "F6", "customer": 4, "cost": 380.0 }, { "facility": "F6", "customer": 5, "cost": 1228.0 }, { "facility": "F6", "customer": 6, "cost": 192.0 }, { "facility": "F6", "customer": 7, "cost": 718.0 }, { "facility": "F6", "customer": 8, "cost": 1126.0 }, { "facility": "F6", "customer": 9, "cost": 374.0 }, { "facility": "F6", "customer": 10, "cost": 1350.0 }, { "facility": "F6", "customer": 11, "cost": 1911.0 }, { "facility": "F6", "customer": 12, "cost": 1198.0 } ], "objective": 2010.0 }, "solution_variant": { "selected": [ "F1" ], "assignments": [ "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1" ] }, "context_index": 1, "input_format": "nl", "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 4 depots and 10 stores in this instance.\n\n**Depots**\n| depot_id | activation_fee | handling_capacity |\n|---|---|---|\n| F1 | 300.0 | 384.0 |\n| F2 | 300.0 | 494.0 |\n| F3 | 300.0 | 427.0 |\n| F4 | 300.0 | 430.0 |\n\n**Stores**\n| store_id | store_demand |\n|---|---|\n| A | 12.0 |\n| B | 20.0 |\n| C | 18.0 |\n| D | 19.0 |\n| E | 26.0 |\n| F | 13.0 |\n| G | 28.0 |\n| H | 20.0 |\n| I | 23.0 |\n| J | 19.0 |\n\n**Delivery Cost**\n| depot_id | store_id | delivery_cost |\n|---|---|---|\n| F1 | A | 127.0 |\n| F1 | B | 43.0 |\n| F1 | C | 390.0 |\n| F1 | D | 755.0 |\n| F1 | E | 201.0 |\n| F1 | F | 574.0 |\n| F1 | G | 67.0 |\n| F1 | H | 546.0 |\n| F1 | I | 293.0 |\n| F1 | J | 133.0 |\n| F2 | A | 261.0 |\n| F2 | B | 159.0 |\n| F2 | C | 822.0 |\n| F2 | D | 1486.0 |\n| F2 | E | 475.0 |\n| F2 | F | 1086.0 |\n| F2 | G | 666.0 |\n| F2 | H | 653.0 |\n| F2 | I | 474.0 |\n| F2 | J | 302.0 |\n| F3 | A | 257.0 |\n| F3 | B | 132.0 |\n| F3 | C | 56.0 |\n| F3 | D | 323.0 |\n| F3 | E | 372.0 |\n| F3 | F | 778.0 |\n| F3 | G | 243.0 |\n| F3 | H | 299.0 |\n| F3 | I | 86.0 |\n| F3 | J | 274.0 |\n| F4 | A | 865.0 |\n| F4 | B | 1048.0 |\n| F4 | C | 1665.0 |\n| F4 | D | 2409.0 |\n| F4 | E | 1236.0 |\n| F4 | F | 1896.0 |\n| F4 | G | 1612.0 |\n| F4 | H | 1048.0 |\n| F4 | I | 1176.0 |\n| F4 | J | 990.0 |\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": [ 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 384.0, 494.0, 427.0, 430.0 ], "connection_costs": [ [ 127.0, 43.0, 390.0, 755.0, 201.0, 574.0, 67.0, 546.0, 293.0, 133.0 ], [ 261.0, 159.0, 822.0, 1486.0, 475.0, 1086.0, 666.0, 653.0, 474.0, 302.0 ], [ 257.0, 132.0, 56.0, 323.0, 372.0, 778.0, 243.0, 299.0, 86.0, 274.0 ], [ 865.0, 1048.0, 1665.0, 2409.0, 1236.0, 1896.0, 1612.0, 1048.0, 1176.0, 990.0 ] ], "demands": [ 12.0, 20.0, 18.0, 19.0, 26.0, 13.0, 28.0, 20.0, 23.0, 19.0 ], "objective": 2509.0 }, "solution": { "open_facilities": [ 0, 2 ], "assignments": [ 0, 0, 2, 2, 0, 0, 0, 2, 2, 0 ] }, "obj": 2509.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 4, "num_customers": 10, "facilities": [ { "id": "F1", "opening_cost": 300.0, "capacity": 384.0 }, { "id": "F2", "opening_cost": 300.0, "capacity": 494.0 }, { "id": "F3", "opening_cost": 300.0, "capacity": 427.0 }, { "id": "F4", "opening_cost": 300.0, "capacity": 430.0 } ], "customers": [ { "id": "A", "demand": 12.0 }, { "id": "B", "demand": 20.0 }, { "id": "C", "demand": 18.0 }, { "id": "D", "demand": 19.0 }, { "id": "E", "demand": 26.0 }, { "id": "F", "demand": 13.0 }, { "id": "G", "demand": 28.0 }, { "id": "H", "demand": 20.0 }, { "id": "I", "demand": 23.0 }, { "id": "J", "demand": 19.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 127.0 }, { "facility": "F1", "customer": "B", "cost": 43.0 }, { "facility": "F1", "customer": "C", "cost": 390.0 }, { "facility": "F1", "customer": "D", "cost": 755.0 }, { "facility": "F1", "customer": "E", "cost": 201.0 }, { "facility": "F1", "customer": "F", "cost": 574.0 }, { "facility": "F1", "customer": "G", "cost": 67.0 }, { "facility": "F1", "customer": "H", "cost": 546.0 }, { "facility": "F1", "customer": "I", "cost": 293.0 }, { "facility": "F1", "customer": "J", "cost": 133.0 }, { "facility": "F2", "customer": "A", "cost": 261.0 }, { "facility": "F2", "customer": "B", "cost": 159.0 }, { "facility": "F2", "customer": "C", "cost": 822.0 }, { "facility": "F2", "customer": "D", "cost": 1486.0 }, { "facility": "F2", "customer": "E", "cost": 475.0 }, { "facility": "F2", "customer": "F", "cost": 1086.0 }, { "facility": "F2", "customer": "G", "cost": 666.0 }, { "facility": "F2", "customer": "H", "cost": 653.0 }, { "facility": "F2", "customer": "I", "cost": 474.0 }, { "facility": "F2", "customer": "J", "cost": 302.0 }, { "facility": "F3", "customer": "A", "cost": 257.0 }, { "facility": "F3", "customer": "B", "cost": 132.0 }, { "facility": "F3", "customer": "C", "cost": 56.0 }, { "facility": "F3", "customer": "D", "cost": 323.0 }, { "facility": "F3", "customer": "E", "cost": 372.0 }, { "facility": "F3", "customer": "F", "cost": 778.0 }, { "facility": "F3", "customer": "G", "cost": 243.0 }, { "facility": "F3", "customer": "H", "cost": 299.0 }, { "facility": "F3", "customer": "I", "cost": 86.0 }, { "facility": "F3", "customer": "J", "cost": 274.0 }, { "facility": "F4", "customer": "A", "cost": 865.0 }, { "facility": "F4", "customer": "B", "cost": 1048.0 }, { "facility": "F4", "customer": "C", "cost": 1665.0 }, { "facility": "F4", "customer": "D", "cost": 2409.0 }, { "facility": "F4", "customer": "E", "cost": 1236.0 }, { "facility": "F4", "customer": "F", "cost": 1896.0 }, { "facility": "F4", "customer": "G", "cost": 1612.0 }, { "facility": "F4", "customer": "H", "cost": 1048.0 }, { "facility": "F4", "customer": "I", "cost": 1176.0 }, { "facility": "F4", "customer": "J", "cost": 990.0 } ], "objective": 2509.0 }, "solution_variant": { "selected": [ "F1", "F3" ], "assignments": [ "F1", "F1", "F3", "F3", "F1", "F1", "F1", "F3", "F3", "F1" ] }, "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\n# num_kitchens=4\n# num_schools=11\n# KITCHENS\nkitchen_id,staffing_cost,production_capacity\nF1,400.0,1382.0\nF2,400.0,1335.0\nF3,400.0,1105.0\nF4,400.0,1331.0\n# SCHOOLS\nschool_id,meal_demand\n0,11.0\n1,36.0\n2,42.0\n3,42.0\n4,38.0\n5,17.0\n6,31.0\n7,43.0\n8,45.0\n9,27.0\n10,34.0\n# DELIVERYS\nkitchen_id,school_id,delivery_cost\nF1,0,262.0\nF1,1,569.0\nF1,2,487.0\nF1,3,652.0\nF1,4,501.0\nF1,5,734.0\nF1,6,364.0\nF1,7,520.0\nF1,8,200.0\nF1,9,190.0\nF1,10,224.0\nF2,0,686.0\nF2,1,501.0\nF2,2,342.0\nF2,3,274.0\nF2,4,299.0\nF2,5,114.0\nF2,6,502.0\nF2,7,282.0\nF2,8,600.0\nF2,9,635.0\nF2,10,577.0\nF3,0,474.0\nF3,1,566.0\nF3,2,163.0\nF3,3,23.0\nF3,4,205.0\nF3,5,144.0\nF3,6,456.0\nF3,7,182.0\nF3,8,466.0\nF3,9,461.0\nF3,10,429.0\nF4,0,544.0\nF4,1,258.0\nF4,2,256.0\nF4,3,338.0\nF4,4,161.0\nF4,5,269.0\nF4,6,247.0\nF4,7,169.0\nF4,8,387.0\nF4,9,452.0\nF4,10,378.0\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": [ 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 1382.0, 1335.0, 1105.0, 1331.0 ], "connection_costs": [ [ 262.0, 569.0, 487.0, 652.0, 501.0, 734.0, 364.0, 520.0, 200.0, 190.0, 224.0 ], [ 686.0, 501.0, 342.0, 274.0, 299.0, 114.0, 502.0, 282.0, 600.0, 635.0, 577.0 ], [ 474.0, 566.0, 163.0, 23.0, 205.0, 144.0, 456.0, 182.0, 466.0, 461.0, 429.0 ], [ 544.0, 258.0, 256.0, 338.0, 161.0, 269.0, 247.0, 169.0, 387.0, 452.0, 378.0 ] ], "demands": [ 11.0, 36.0, 42.0, 42.0, 38.0, 17.0, 31.0, 43.0, 45.0, 27.0, 34.0 ], "objective": 3241.0 }, "solution": { "open_facilities": [ 0, 2, 3 ], "assignments": [ 0, 3, 2, 2, 3, 2, 3, 3, 0, 0, 0 ] }, "obj": 3241.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 4, "num_customers": 11, "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": 1105.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 1331.0 } ], "customers": [ { "id": 0, "demand": 11.0 }, { "id": 1, "demand": 36.0 }, { "id": 2, "demand": 42.0 }, { "id": 3, "demand": 42.0 }, { "id": 4, "demand": 38.0 }, { "id": 5, "demand": 17.0 }, { "id": 6, "demand": 31.0 }, { "id": 7, "demand": 43.0 }, { "id": 8, "demand": 45.0 }, { "id": 9, "demand": 27.0 }, { "id": 10, "demand": 34.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 262.0 }, { "facility": "F1", "customer": 1, "cost": 569.0 }, { "facility": "F1", "customer": 2, "cost": 487.0 }, { "facility": "F1", "customer": 3, "cost": 652.0 }, { "facility": "F1", "customer": 4, "cost": 501.0 }, { "facility": "F1", "customer": 5, "cost": 734.0 }, { "facility": "F1", "customer": 6, "cost": 364.0 }, { "facility": "F1", "customer": 7, "cost": 520.0 }, { "facility": "F1", "customer": 8, "cost": 200.0 }, { "facility": "F1", "customer": 9, "cost": 190.0 }, { "facility": "F1", "customer": 10, "cost": 224.0 }, { "facility": "F2", "customer": 0, "cost": 686.0 }, { "facility": "F2", "customer": 1, "cost": 501.0 }, { "facility": "F2", "customer": 2, "cost": 342.0 }, { "facility": "F2", "customer": 3, "cost": 274.0 }, { "facility": "F2", "customer": 4, "cost": 299.0 }, { "facility": "F2", "customer": 5, "cost": 114.0 }, { "facility": "F2", "customer": 6, "cost": 502.0 }, { "facility": "F2", "customer": 7, "cost": 282.0 }, { "facility": "F2", "customer": 8, "cost": 600.0 }, { "facility": "F2", "customer": 9, "cost": 635.0 }, { "facility": "F2", "customer": 10, "cost": 577.0 }, { "facility": "F3", "customer": 0, "cost": 474.0 }, { "facility": "F3", "customer": 1, "cost": 566.0 }, { "facility": "F3", "customer": 2, "cost": 163.0 }, { "facility": "F3", "customer": 3, "cost": 23.0 }, { "facility": "F3", "customer": 4, "cost": 205.0 }, { "facility": "F3", "customer": 5, "cost": 144.0 }, { "facility": "F3", "customer": 6, "cost": 456.0 }, { "facility": "F3", "customer": 7, "cost": 182.0 }, { "facility": "F3", "customer": 8, "cost": 466.0 }, { "facility": "F3", "customer": 9, "cost": 461.0 }, { "facility": "F3", "customer": 10, "cost": 429.0 }, { "facility": "F4", "customer": 0, "cost": 544.0 }, { "facility": "F4", "customer": 1, "cost": 258.0 }, { "facility": "F4", "customer": 2, "cost": 256.0 }, { "facility": "F4", "customer": 3, "cost": 338.0 }, { "facility": "F4", "customer": 4, "cost": 161.0 }, { "facility": "F4", "customer": 5, "cost": 269.0 }, { "facility": "F4", "customer": 6, "cost": 247.0 }, { "facility": "F4", "customer": 7, "cost": 169.0 }, { "facility": "F4", "customer": 8, "cost": 387.0 }, { "facility": "F4", "customer": 9, "cost": 452.0 }, { "facility": "F4", "customer": 10, "cost": 378.0 } ], "objective": 3241.0 }, "solution_variant": { "selected": [ "F1", "F3", "F4" ], "assignments": [ "F1", "F4", "F3", "F3", "F4", "F3", "F4", "F4", "F1", "F1", "F1" ] }, "context_index": 3, "input_format": "csv", "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\n{\n \"num_clinics\": 5,\n \"num_neighborhoods\": 10,\n \"clinics\": [\n {\n \"clinic_id\": \"F1\",\n \"clinic_opening_cost\": 300.0,\n \"clinic_capacity\": 500.0\n },\n {\n \"clinic_id\": \"F2\",\n \"clinic_opening_cost\": 300.0,\n \"clinic_capacity\": 500.0\n },\n {\n \"clinic_id\": \"F3\",\n \"clinic_opening_cost\": 300.0,\n \"clinic_capacity\": 500.0\n },\n {\n \"clinic_id\": \"F4\",\n \"clinic_opening_cost\": 300.0,\n \"clinic_capacity\": 500.0\n },\n {\n \"clinic_id\": \"F5\",\n \"clinic_opening_cost\": 300.0,\n \"clinic_capacity\": 500.0\n }\n ],\n \"neighborhoods\": [\n {\n \"neighborhood_id\": 1,\n \"neighborhood_patient_count\": 12.0\n },\n {\n \"neighborhood_id\": 2,\n \"neighborhood_patient_count\": 26.0\n },\n {\n \"neighborhood_id\": 3,\n \"neighborhood_patient_count\": 25.0\n },\n {\n \"neighborhood_id\": 4,\n \"neighborhood_patient_count\": 29.0\n },\n {\n \"neighborhood_id\": 5,\n \"neighborhood_patient_count\": 14.0\n },\n {\n \"neighborhood_id\": 6,\n \"neighborhood_patient_count\": 14.0\n },\n {\n \"neighborhood_id\": 7,\n \"neighborhood_patient_count\": 13.0\n },\n {\n \"neighborhood_id\": 8,\n \"neighborhood_patient_count\": 23.0\n },\n {\n \"neighborhood_id\": 9,\n \"neighborhood_patient_count\": 18.0\n },\n {\n \"neighborhood_id\": 10,\n \"neighborhood_patient_count\": 27.0\n }\n ],\n \"assignment_travels\": [\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 1,\n \"assignment_travel_cost\": 34.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 2,\n \"assignment_travel_cost\": 180.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 3,\n \"assignment_travel_cost\": 558.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 4,\n \"assignment_travel_cost\": 91.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 5,\n \"assignment_travel_cost\": 525.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 6,\n \"assignment_travel_cost\": 368.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 7,\n \"assignment_travel_cost\": 125.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 8,\n \"assignment_travel_cost\": 136.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 9,\n \"assignment_travel_cost\": 1262.0\n },\n {\n \"clinic_id\": \"F1\",\n \"neighborhood_id\": 10,\n \"assignment_travel_cost\": 691.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 1,\n \"assignment_travel_cost\": 60.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 2,\n \"assignment_travel_cost\": 54.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 3,\n \"assignment_travel_cost\": 147.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 4,\n \"assignment_travel_cost\": 264.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 5,\n \"assignment_travel_cost\": 84.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 6,\n \"assignment_travel_cost\": 41.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 7,\n \"assignment_travel_cost\": 50.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 8,\n \"assignment_travel_cost\": 385.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 9,\n \"assignment_travel_cost\": 101.0\n },\n {\n \"clinic_id\": \"F2\",\n \"neighborhood_id\": 10,\n \"assignment_travel_cost\": 189.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 1,\n \"assignment_travel_cost\": 60.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 2,\n \"assignment_travel_cost\": 250.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 3,\n \"assignment_travel_cost\": 619.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 4,\n \"assignment_travel_cost\": 61.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 5,\n \"assignment_travel_cost\": 598.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 6,\n \"assignment_travel_cost\": 458.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 7,\n \"assignment_travel_cost\": 153.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 8,\n \"assignment_travel_cost\": 62.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 9,\n \"assignment_travel_cost\": 1306.0\n },\n {\n \"clinic_id\": \"F3\",\n \"neighborhood_id\": 10,\n \"assignment_travel_cost\": 732.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 1,\n \"assignment_travel_cost\": 341.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 2,\n \"assignment_travel_cost\": 410.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 3,\n \"assignment_travel_cost\": 1407.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 4,\n \"assignment_travel_cost\": 727.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 5,\n \"assignment_travel_cost\": 1295.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 6,\n \"assignment_travel_cost\": 464.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 7,\n \"assignment_travel_cost\": 27.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 8,\n \"assignment_travel_cost\": 1033.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 9,\n \"assignment_travel_cost\": 1860.0\n },\n {\n \"clinic_id\": \"F4\",\n \"neighborhood_id\": 10,\n \"assignment_travel_cost\": 1566.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 1,\n \"assignment_travel_cost\": 172.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 2,\n \"assignment_travel_cost\": 150.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 3,\n \"assignment_travel_cost\": 885.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 4,\n \"assignment_travel_cost\": 500.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 5,\n \"assignment_travel_cost\": 770.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 6,\n \"assignment_travel_cost\": 79.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 7,\n \"assignment_travel_cost\": 30.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 8,\n \"assignment_travel_cost\": 741.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 9,\n \"assignment_travel_cost\": 1287.0\n },\n {\n \"clinic_id\": \"F5\",\n \"neighborhood_id\": 10,\n \"assignment_travel_cost\": 1034.0\n }\n ]\n}\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 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 34.0, 180.0, 558.0, 91.0, 525.0, 368.0, 125.0, 136.0, 1262.0, 691.0 ], [ 60.0, 54.0, 147.0, 264.0, 84.0, 41.0, 50.0, 385.0, 101.0, 189.0 ], [ 60.0, 250.0, 619.0, 61.0, 598.0, 458.0, 153.0, 62.0, 1306.0, 732.0 ], [ 341.0, 410.0, 1407.0, 727.0, 1295.0, 464.0, 27.0, 1033.0, 1860.0, 1566.0 ], [ 172.0, 150.0, 885.0, 500.0, 770.0, 79.0, 30.0, 741.0, 1287.0, 1034.0 ] ], "demands": [ 12.0, 26.0, 25.0, 29.0, 14.0, 14.0, 13.0, 23.0, 18.0, 27.0 ], "objective": 1449.0 }, "solution": { "open_facilities": [ 1, 2 ], "assignments": [ 1, 1, 1, 2, 1, 1, 1, 2, 1, 1 ] }, "obj": 1449.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 10, "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 } ], "customers": [ { "id": 1, "demand": 12.0 }, { "id": 2, "demand": 26.0 }, { "id": 3, "demand": 25.0 }, { "id": 4, "demand": 29.0 }, { "id": 5, "demand": 14.0 }, { "id": 6, "demand": 14.0 }, { "id": 7, "demand": 13.0 }, { "id": 8, "demand": 23.0 }, { "id": 9, "demand": 18.0 }, { "id": 10, "demand": 27.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 34.0 }, { "facility": "F1", "customer": 2, "cost": 180.0 }, { "facility": "F1", "customer": 3, "cost": 558.0 }, { "facility": "F1", "customer": 4, "cost": 91.0 }, { "facility": "F1", "customer": 5, "cost": 525.0 }, { "facility": "F1", "customer": 6, "cost": 368.0 }, { "facility": "F1", "customer": 7, "cost": 125.0 }, { "facility": "F1", "customer": 8, "cost": 136.0 }, { "facility": "F1", "customer": 9, "cost": 1262.0 }, { "facility": "F1", "customer": 10, "cost": 691.0 }, { "facility": "F2", "customer": 1, "cost": 60.0 }, { "facility": "F2", "customer": 2, "cost": 54.0 }, { "facility": "F2", "customer": 3, "cost": 147.0 }, { "facility": "F2", "customer": 4, "cost": 264.0 }, { "facility": "F2", "customer": 5, "cost": 84.0 }, { "facility": "F2", "customer": 6, "cost": 41.0 }, { "facility": "F2", "customer": 7, "cost": 50.0 }, { "facility": "F2", "customer": 8, "cost": 385.0 }, { "facility": "F2", "customer": 9, "cost": 101.0 }, { "facility": "F2", "customer": 10, "cost": 189.0 }, { "facility": "F3", "customer": 1, "cost": 60.0 }, { "facility": "F3", "customer": 2, "cost": 250.0 }, { "facility": "F3", "customer": 3, "cost": 619.0 }, { "facility": "F3", "customer": 4, "cost": 61.0 }, { "facility": "F3", "customer": 5, "cost": 598.0 }, { "facility": "F3", "customer": 6, "cost": 458.0 }, { "facility": "F3", "customer": 7, "cost": 153.0 }, { "facility": "F3", "customer": 8, "cost": 62.0 }, { "facility": "F3", "customer": 9, "cost": 1306.0 }, { "facility": "F3", "customer": 10, "cost": 732.0 }, { "facility": "F4", "customer": 1, "cost": 341.0 }, { "facility": "F4", "customer": 2, "cost": 410.0 }, { "facility": "F4", "customer": 3, "cost": 1407.0 }, { "facility": "F4", "customer": 4, "cost": 727.0 }, { "facility": "F4", "customer": 5, "cost": 1295.0 }, { "facility": "F4", "customer": 6, "cost": 464.0 }, { "facility": "F4", "customer": 7, "cost": 27.0 }, { "facility": "F4", "customer": 8, "cost": 1033.0 }, { "facility": "F4", "customer": 9, "cost": 1860.0 }, { "facility": "F4", "customer": 10, "cost": 1566.0 }, { "facility": "F5", "customer": 1, "cost": 172.0 }, { "facility": "F5", "customer": 2, "cost": 150.0 }, { "facility": "F5", "customer": 3, "cost": 885.0 }, { "facility": "F5", "customer": 4, "cost": 500.0 }, { "facility": "F5", "customer": 5, "cost": 770.0 }, { "facility": "F5", "customer": 6, "cost": 79.0 }, { "facility": "F5", "customer": 7, "cost": 30.0 }, { "facility": "F5", "customer": 8, "cost": 741.0 }, { "facility": "F5", "customer": 9, "cost": 1287.0 }, { "facility": "F5", "customer": 10, "cost": 1034.0 } ], "objective": 1449.0 }, "solution_variant": { "selected": [ "F2", "F3" ], "assignments": [ "F2", "F2", "F2", "F3", "F2", "F2", "F2", "F3", "F2", "F2" ] }, "context_index": 4, "input_format": "json", "input_index_base": 1 }, { "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\n{\n \"num_stalls\": 5,\n \"num_vendor_areas\": 13,\n \"stalls\": [\n {\n \"stall_id\": \"F1\",\n \"stall_setup_cost\": 213.0,\n \"stall_capacity\": 700.0\n },\n {\n \"stall_id\": \"F2\",\n \"stall_setup_cost\": 295.0,\n \"stall_capacity\": 700.0\n },\n {\n \"stall_id\": \"F3\",\n \"stall_setup_cost\": 289.0,\n \"stall_capacity\": 700.0\n },\n {\n \"stall_id\": \"F4\",\n \"stall_setup_cost\": 573.0,\n \"stall_capacity\": 700.0\n },\n {\n \"stall_id\": \"F5\",\n \"stall_setup_cost\": 450.0,\n \"stall_capacity\": 700.0\n }\n ],\n \"vendor_areas\": [\n {\n \"vendor_area_id\": 0,\n \"vendor_crowd_size\": 28.0\n },\n {\n \"vendor_area_id\": 1,\n \"vendor_crowd_size\": 17.0\n },\n {\n \"vendor_area_id\": 2,\n \"vendor_crowd_size\": 14.0\n },\n {\n \"vendor_area_id\": 3,\n \"vendor_crowd_size\": 19.0\n },\n {\n \"vendor_area_id\": 4,\n \"vendor_crowd_size\": 19.0\n },\n {\n \"vendor_area_id\": 5,\n \"vendor_crowd_size\": 16.0\n },\n {\n \"vendor_area_id\": 6,\n \"vendor_crowd_size\": 27.0\n },\n {\n \"vendor_area_id\": 7,\n \"vendor_crowd_size\": 25.0\n },\n {\n \"vendor_area_id\": 8,\n \"vendor_crowd_size\": 20.0\n },\n {\n \"vendor_area_id\": 9,\n \"vendor_crowd_size\": 16.0\n },\n {\n \"vendor_area_id\": 10,\n \"vendor_crowd_size\": 23.0\n },\n {\n \"vendor_area_id\": 11,\n \"vendor_crowd_size\": 25.0\n },\n {\n \"vendor_area_id\": 12,\n \"vendor_crowd_size\": 22.0\n }\n ],\n \"servings\": [\n {\n \"stall_id\": \"F1\",\n \"vendor_area_id\": 0,\n \"serving_cost\": 647.0\n },\n {\n \"stall_id\": \"F1\",\n \"vendor_area_id\": 1,\n \"serving_cost\": 1664.0\n },\n {\n \"stall_id\": \"F1\",\n \"vendor_area_id\": 2,\n \"serving_cost\": 1297.0\n },\n {\n \"stall_id\": \"F1\",\n \"vendor_area_id\": 3,\n \"serving_cost\": 1042.0\n },\n {\n \"stall_id\": \"F1\",\n \"vendor_area_id\": 4,\n \"serving_cost\": 1964.0\n },\n {\n \"stall_id\": \"F1\",\n \"vendor_area_id\": 5,\n \"serving_cost\": 960.0\n },\n {\n \"stall_id\": \"F1\",\n \"vendor_area_id\": 6,\n \"serving_cost\": 1518.0\n },\n {\n \"stall_id\": \"F1\",\n \"vendor_area_id\": 7,\n \"serving_cost\": 627.0\n },\n {\n \"stall_id\": \"F1\",\n \"vendor_area_id\": 8,\n \"serving_cost\": 1120.0\n },\n {\n \"stall_id\": \"F1\",\n \"vendor_area_id\": 9,\n \"serving_cost\": 2069.0\n },\n {\n \"stall_id\": \"F1\",\n \"vendor_area_id\": 10,\n \"serving_cost\": 1030.0\n },\n {\n \"stall_id\": \"F1\",\n \"vendor_area_id\": 11,\n \"serving_cost\": 1255.0\n },\n {\n \"stall_id\": \"F1\",\n \"vendor_area_id\": 12,\n \"serving_cost\": 1523.0\n },\n {\n \"stall_id\": \"F2\",\n \"vendor_area_id\": 0,\n \"serving_cost\": 1511.0\n },\n {\n \"stall_id\": \"F2\",\n \"vendor_area_id\": 1,\n \"serving_cost\": 1733.0\n },\n {\n \"stall_id\": \"F2\",\n \"vendor_area_id\": 2,\n \"serving_cost\": 1876.0\n },\n {\n \"stall_id\": \"F2\",\n \"vendor_area_id\": 3,\n \"serving_cost\": 1338.0\n },\n {\n \"stall_id\": \"F2\",\n \"vendor_area_id\": 4,\n \"serving_cost\": 2409.0\n },\n {\n \"stall_id\": \"F2\",\n \"vendor_area_id\": 5,\n \"serving_cost\": 1416.0\n },\n {\n \"stall_id\": \"F2\",\n \"vendor_area_id\": 6,\n \"serving_cost\": 2142.0\n },\n {\n \"stall_id\": \"F2\",\n \"vendor_area_id\": 7,\n \"serving_cost\": 1345.0\n },\n {\n \"stall_id\": \"F2\",\n \"vendor_area_id\": 8,\n \"serving_cost\": 1048.0\n },\n {\n \"stall_id\": \"F2\",\n \"vendor_area_id\": 9,\n \"serving_cost\": 2527.0\n },\n {\n \"stall_id\": \"F2\",\n \"vendor_area_id\": 10,\n \"serving_cost\": 1176.0\n },\n {\n \"stall_id\": \"F2\",\n \"vendor_area_id\": 11,\n \"serving_cost\": 1891.0\n },\n {\n \"stall_id\": \"F2\",\n \"vendor_area_id\": 12,\n \"serving_cost\": 1689.0\n },\n {\n \"stall_id\": \"F3\",\n \"vendor_area_id\": 0,\n \"serving_cost\": 1307.0\n },\n {\n \"stall_id\": \"F3\",\n \"vendor_area_id\": 1,\n \"serving_cost\": 811.0\n },\n {\n \"stall_id\": \"F3\",\n \"vendor_area_id\": 2,\n \"serving_cost\": 1389.0\n },\n {\n \"stall_id\": \"F3\",\n \"vendor_area_id\": 3,\n \"serving_cost\": 727.0\n },\n {\n \"stall_id\": \"F3\",\n \"vendor_area_id\": 4,\n \"serving_cost\": 1740.0\n },\n {\n \"stall_id\": \"F3\",\n \"vendor_area_id\": 5,\n \"serving_cost\": 926.0\n },\n {\n \"stall_id\": \"F3\",\n \"vendor_area_id\": 6,\n \"serving_cost\": 1659.0\n },\n {\n \"stall_id\": \"F3\",\n \"vendor_area_id\": 7,\n \"serving_cost\": 1069.0\n },\n {\n \"stall_id\": \"F3\",\n \"vendor_area_id\": 8,\n \"serving_cost\": 113.0\n },\n {\n \"stall_id\": \"F3\",\n \"vendor_area_id\": 9,\n \"serving_cost\": 1857.0\n },\n {\n \"stall_id\": \"F3\",\n \"vendor_area_id\": 10,\n \"serving_cost\": 463.0\n },\n {\n \"stall_id\": \"F3\",\n \"vendor_area_id\": 11,\n \"serving_cost\": 1452.0\n },\n {\n \"stall_id\": \"F3\",\n \"vendor_area_id\": 12,\n \"serving_cost\": 857.0\n },\n {\n \"stall_id\": \"F4\",\n \"vendor_area_id\": 0,\n \"serving_cost\": 56.0\n },\n {\n \"stall_id\": \"F4\",\n \"vendor_area_id\": 1,\n \"serving_cost\": 1302.0\n },\n {\n \"stall_id\": \"F4\",\n \"vendor_area_id\": 2,\n \"serving_cost\": 598.0\n },\n {\n \"stall_id\": \"F4\",\n \"vendor_area_id\": 3,\n \"serving_cost\": 625.0\n },\n {\n \"stall_id\": \"F4\",\n \"vendor_area_id\": 4,\n \"serving_cost\": 1278.0\n },\n {\n \"stall_id\": \"F4\",\n \"vendor_area_id\": 5,\n \"serving_cost\": 463.0\n },\n {\n \"stall_id\": \"F4\",\n \"vendor_area_id\": 6,\n \"serving_cost\": 732.0\n },\n {\n \"stall_id\": \"F4\",\n \"vendor_area_id\": 7,\n \"serving_cost\": 130.0\n },\n {\n \"stall_id\": \"F4\",\n \"vendor_area_id\": 8,\n \"serving_cost\": 906.0\n },\n {\n \"stall_id\": \"F4\",\n \"vendor_area_id\": 9,\n \"serving_cost\": 1360.0\n },\n {\n \"stall_id\": \"F4\",\n \"vendor_area_id\": 10,\n \"serving_cost\": 703.0\n },\n {\n \"stall_id\": \"F4\",\n \"vendor_area_id\": 11,\n \"serving_cost\": 516.0\n },\n {\n \"stall_id\": \"F4\",\n \"vendor_area_id\": 12,\n \"serving_cost\": 1108.0\n },\n {\n \"stall_id\": \"F5\",\n \"vendor_area_id\": 0,\n \"serving_cost\": 309.0\n },\n {\n \"stall_id\": \"F5\",\n \"vendor_area_id\": 1,\n \"serving_cost\": 1253.0\n },\n {\n \"stall_id\": \"F5\",\n \"vendor_area_id\": 2,\n \"serving_cost\": 722.0\n },\n {\n \"stall_id\": \"F5\",\n \"vendor_area_id\": 3,\n \"serving_cost\": 579.0\n },\n {\n \"stall_id\": \"F5\",\n \"vendor_area_id\": 4,\n \"serving_cost\": 1400.0\n },\n {\n \"stall_id\": \"F5\",\n \"vendor_area_id\": 5,\n \"serving_cost\": 440.0\n },\n {\n \"stall_id\": \"F5\",\n \"vendor_area_id\": 6,\n \"serving_cost\": 942.0\n },\n {\n \"stall_id\": \"F5\",\n \"vendor_area_id\": 7,\n \"serving_cost\": 50.0\n },\n {\n \"stall_id\": \"F5\",\n \"vendor_area_id\": 8,\n \"serving_cost\": 827.0\n },\n {\n \"stall_id\": \"F5\",\n \"vendor_area_id\": 9,\n \"serving_cost\": 1501.0\n },\n {\n \"stall_id\": \"F5\",\n \"vendor_area_id\": 10,\n \"serving_cost\": 636.0\n },\n {\n \"stall_id\": \"F5\",\n \"vendor_area_id\": 11,\n \"serving_cost\": 678.0\n },\n {\n \"stall_id\": \"F5\",\n \"vendor_area_id\": 12,\n \"serving_cost\": 1073.0\n }\n ]\n}\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": [ 213.0, 295.0, 289.0, 573.0, 450.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 647.0, 1664.0, 1297.0, 1042.0, 1964.0, 960.0, 1518.0, 627.0, 1120.0, 2069.0, 1030.0, 1255.0, 1523.0 ], [ 1511.0, 1733.0, 1876.0, 1338.0, 2409.0, 1416.0, 2142.0, 1345.0, 1048.0, 2527.0, 1176.0, 1891.0, 1689.0 ], [ 1307.0, 811.0, 1389.0, 727.0, 1740.0, 926.0, 1659.0, 1069.0, 113.0, 1857.0, 463.0, 1452.0, 857.0 ], [ 56.0, 1302.0, 598.0, 625.0, 1278.0, 463.0, 732.0, 130.0, 906.0, 1360.0, 703.0, 516.0, 1108.0 ], [ 309.0, 1253.0, 722.0, 579.0, 1400.0, 440.0, 942.0, 50.0, 827.0, 1501.0, 636.0, 678.0, 1073.0 ] ], "demands": [ 28.0, 17.0, 14.0, 19.0, 19.0, 16.0, 27.0, 25.0, 20.0, 16.0, 23.0, 25.0, 22.0 ], "objective": 8864.0 }, "solution": { "open_facilities": [ 2, 3 ], "assignments": [ 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 2 ] }, "obj": 8864.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 13, "facilities": [ { "id": "F1", "opening_cost": 213.0, "capacity": 700.0 }, { "id": "F2", "opening_cost": 295.0, "capacity": 700.0 }, { "id": "F3", "opening_cost": 289.0, "capacity": 700.0 }, { "id": "F4", "opening_cost": 573.0, "capacity": 700.0 }, { "id": "F5", "opening_cost": 450.0, "capacity": 700.0 } ], "customers": [ { "id": 0, "demand": 28.0 }, { "id": 1, "demand": 17.0 }, { "id": 2, "demand": 14.0 }, { "id": 3, "demand": 19.0 }, { "id": 4, "demand": 19.0 }, { "id": 5, "demand": 16.0 }, { "id": 6, "demand": 27.0 }, { "id": 7, "demand": 25.0 }, { "id": 8, "demand": 20.0 }, { "id": 9, "demand": 16.0 }, { "id": 10, "demand": 23.0 }, { "id": 11, "demand": 25.0 }, { "id": 12, "demand": 22.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 647.0 }, { "facility": "F1", "customer": 1, "cost": 1664.0 }, { "facility": "F1", "customer": 2, "cost": 1297.0 }, { "facility": "F1", "customer": 3, "cost": 1042.0 }, { "facility": "F1", "customer": 4, "cost": 1964.0 }, { "facility": "F1", "customer": 5, "cost": 960.0 }, { "facility": "F1", "customer": 6, "cost": 1518.0 }, { "facility": "F1", "customer": 7, "cost": 627.0 }, { "facility": "F1", "customer": 8, "cost": 1120.0 }, { "facility": "F1", "customer": 9, "cost": 2069.0 }, { "facility": "F1", "customer": 10, "cost": 1030.0 }, { "facility": "F1", "customer": 11, "cost": 1255.0 }, { "facility": "F1", "customer": 12, "cost": 1523.0 }, { "facility": "F2", "customer": 0, "cost": 1511.0 }, { "facility": "F2", "customer": 1, "cost": 1733.0 }, { "facility": "F2", "customer": 2, "cost": 1876.0 }, { "facility": "F2", "customer": 3, "cost": 1338.0 }, { "facility": "F2", "customer": 4, "cost": 2409.0 }, { "facility": "F2", "customer": 5, "cost": 1416.0 }, { "facility": "F2", "customer": 6, "cost": 2142.0 }, { "facility": "F2", "customer": 7, "cost": 1345.0 }, { "facility": "F2", "customer": 8, "cost": 1048.0 }, { "facility": "F2", "customer": 9, "cost": 2527.0 }, { "facility": "F2", "customer": 10, "cost": 1176.0 }, { "facility": "F2", "customer": 11, "cost": 1891.0 }, { "facility": "F2", "customer": 12, "cost": 1689.0 }, { "facility": "F3", "customer": 0, "cost": 1307.0 }, { "facility": "F3", "customer": 1, "cost": 811.0 }, { "facility": "F3", "customer": 2, "cost": 1389.0 }, { "facility": "F3", "customer": 3, "cost": 727.0 }, { "facility": "F3", "customer": 4, "cost": 1740.0 }, { "facility": "F3", "customer": 5, "cost": 926.0 }, { "facility": "F3", "customer": 6, "cost": 1659.0 }, { "facility": "F3", "customer": 7, "cost": 1069.0 }, { "facility": "F3", "customer": 8, "cost": 113.0 }, { "facility": "F3", "customer": 9, "cost": 1857.0 }, { "facility": "F3", "customer": 10, "cost": 463.0 }, { "facility": "F3", "customer": 11, "cost": 1452.0 }, { "facility": "F3", "customer": 12, "cost": 857.0 }, { "facility": "F4", "customer": 0, "cost": 56.0 }, { "facility": "F4", "customer": 1, "cost": 1302.0 }, { "facility": "F4", "customer": 2, "cost": 598.0 }, { "facility": "F4", "customer": 3, "cost": 625.0 }, { "facility": "F4", "customer": 4, "cost": 1278.0 }, { "facility": "F4", "customer": 5, "cost": 463.0 }, { "facility": "F4", "customer": 6, "cost": 732.0 }, { "facility": "F4", "customer": 7, "cost": 130.0 }, { "facility": "F4", "customer": 8, "cost": 906.0 }, { "facility": "F4", "customer": 9, "cost": 1360.0 }, { "facility": "F4", "customer": 10, "cost": 703.0 }, { "facility": "F4", "customer": 11, "cost": 516.0 }, { "facility": "F4", "customer": 12, "cost": 1108.0 }, { "facility": "F5", "customer": 0, "cost": 309.0 }, { "facility": "F5", "customer": 1, "cost": 1253.0 }, { "facility": "F5", "customer": 2, "cost": 722.0 }, { "facility": "F5", "customer": 3, "cost": 579.0 }, { "facility": "F5", "customer": 4, "cost": 1400.0 }, { "facility": "F5", "customer": 5, "cost": 440.0 }, { "facility": "F5", "customer": 6, "cost": 942.0 }, { "facility": "F5", "customer": 7, "cost": 50.0 }, { "facility": "F5", "customer": 8, "cost": 827.0 }, { "facility": "F5", "customer": 9, "cost": 1501.0 }, { "facility": "F5", "customer": 10, "cost": 636.0 }, { "facility": "F5", "customer": 11, "cost": 678.0 }, { "facility": "F5", "customer": 12, "cost": 1073.0 } ], "objective": 8864.0 }, "solution_variant": { "selected": [ "F3", "F4" ], "assignments": [ "F4", "F3", "F4", "F4", "F4", "F4", "F4", "F4", "F3", "F4", "F3", "F4", "F3" ] }, "context_index": 5, "input_format": "json", "input_index_base": 0 }, { "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{\n \"num_data_centers\": 5,\n \"num_applications\": 12,\n \"data_centers\": [\n {\n \"data_center_id\": \"F1\",\n \"activation_cost\": 400.0,\n \"bandwidth_capacity\": 700.0\n },\n {\n \"data_center_id\": \"F2\",\n \"activation_cost\": 400.0,\n \"bandwidth_capacity\": 700.0\n },\n {\n \"data_center_id\": \"F3\",\n \"activation_cost\": 400.0,\n \"bandwidth_capacity\": 700.0\n },\n {\n \"data_center_id\": \"F4\",\n \"activation_cost\": 400.0,\n \"bandwidth_capacity\": 700.0\n },\n {\n \"data_center_id\": \"F5\",\n \"activation_cost\": 400.0,\n \"bandwidth_capacity\": 700.0\n }\n ],\n \"applications\": [\n {\n \"application_id\": 0,\n \"bandwidth_demand\": 14.0\n },\n {\n \"application_id\": 1,\n \"bandwidth_demand\": 20.0\n },\n {\n \"application_id\": 2,\n \"bandwidth_demand\": 24.0\n },\n {\n \"application_id\": 3,\n \"bandwidth_demand\": 11.0\n },\n {\n \"application_id\": 4,\n \"bandwidth_demand\": 19.0\n },\n {\n \"application_id\": 5,\n \"bandwidth_demand\": 13.0\n },\n {\n \"application_id\": 6,\n \"bandwidth_demand\": 26.0\n },\n {\n \"application_id\": 7,\n \"bandwidth_demand\": 24.0\n },\n {\n \"application_id\": 8,\n \"bandwidth_demand\": 10.0\n },\n {\n \"application_id\": 9,\n \"bandwidth_demand\": 16.0\n },\n {\n \"application_id\": 10,\n \"bandwidth_demand\": 18.0\n },\n {\n \"application_id\": 11,\n \"bandwidth_demand\": 23.0\n }\n ],\n \"routings\": [\n {\n \"data_center_id\": \"F1\",\n \"application_id\": 0,\n \"routing_cost\": 349.0\n },\n {\n \"data_center_id\": \"F1\",\n \"application_id\": 1,\n \"routing_cost\": 165.0\n },\n {\n \"data_center_id\": \"F1\",\n \"application_id\": 2,\n \"routing_cost\": 122.0\n },\n {\n \"data_center_id\": \"F1\",\n \"application_id\": 3,\n \"routing_cost\": 22.0\n },\n {\n \"data_center_id\": \"F1\",\n \"application_id\": 4,\n \"routing_cost\": 39.0\n },\n {\n \"data_center_id\": \"F1\",\n \"application_id\": 5,\n \"routing_cost\": 42.0\n },\n {\n \"data_center_id\": \"F1\",\n \"application_id\": 6,\n \"routing_cost\": 283.0\n },\n {\n \"data_center_id\": \"F1\",\n \"application_id\": 7,\n \"routing_cost\": 49.0\n },\n {\n \"data_center_id\": \"F1\",\n \"application_id\": 8,\n \"routing_cost\": 65.0\n },\n {\n \"data_center_id\": \"F1\",\n \"application_id\": 9,\n \"routing_cost\": 316.0\n },\n {\n \"data_center_id\": \"F1\",\n \"application_id\": 10,\n \"routing_cost\": 36.0\n },\n {\n \"data_center_id\": \"F1\",\n \"application_id\": 11,\n \"routing_cost\": 114.0\n },\n {\n \"data_center_id\": \"F2\",\n \"application_id\": 0,\n \"routing_cost\": 89.0\n },\n {\n \"data_center_id\": \"F2\",\n \"application_id\": 1,\n \"routing_cost\": 728.0\n },\n {\n \"data_center_id\": \"F2\",\n \"application_id\": 2,\n \"routing_cost\": 366.0\n },\n {\n \"data_center_id\": \"F2\",\n \"application_id\": 3,\n \"routing_cost\": 923.0\n },\n {\n \"data_center_id\": \"F2\",\n \"application_id\": 4,\n \"routing_cost\": 1216.0\n },\n {\n \"data_center_id\": \"F2\",\n \"application_id\": 5,\n \"routing_cost\": 125.0\n },\n {\n \"data_center_id\": \"F2\",\n \"application_id\": 6,\n \"routing_cost\": 53.0\n },\n {\n \"data_center_id\": \"F2\",\n \"application_id\": 7,\n \"routing_cost\": 349.0\n },\n {\n \"data_center_id\": \"F2\",\n \"application_id\": 8,\n \"routing_cost\": 48.0\n },\n {\n \"data_center_id\": \"F2\",\n \"application_id\": 9,\n \"routing_cost\": 1076.0\n },\n {\n \"data_center_id\": \"F2\",\n \"application_id\": 10,\n \"routing_cost\": 417.0\n },\n {\n \"data_center_id\": \"F2\",\n \"application_id\": 11,\n \"routing_cost\": 611.0\n },\n {\n \"data_center_id\": \"F3\",\n \"application_id\": 0,\n \"routing_cost\": 226.0\n },\n {\n \"data_center_id\": \"F3\",\n \"application_id\": 1,\n \"routing_cost\": 1039.0\n },\n {\n \"data_center_id\": \"F3\",\n \"application_id\": 2,\n \"routing_cost\": 473.0\n },\n {\n \"data_center_id\": \"F3\",\n \"application_id\": 3,\n \"routing_cost\": 1541.0\n },\n {\n \"data_center_id\": \"F3\",\n \"application_id\": 4,\n \"routing_cost\": 1880.0\n },\n {\n \"data_center_id\": \"F3\",\n \"application_id\": 5,\n \"routing_cost\": 151.0\n },\n {\n \"data_center_id\": \"F3\",\n \"application_id\": 6,\n \"routing_cost\": 422.0\n },\n {\n \"data_center_id\": \"F3\",\n \"application_id\": 7,\n \"routing_cost\": 718.0\n },\n {\n \"data_center_id\": \"F3\",\n \"application_id\": 8,\n \"routing_cost\": 133.0\n },\n {\n \"data_center_id\": \"F3\",\n \"application_id\": 9,\n \"routing_cost\": 1443.0\n },\n {\n \"data_center_id\": \"F3\",\n \"application_id\": 10,\n \"routing_cost\": 808.0\n },\n {\n \"data_center_id\": \"F3\",\n \"application_id\": 11,\n \"routing_cost\": 921.0\n },\n {\n \"data_center_id\": \"F4\",\n \"application_id\": 0,\n \"routing_cost\": 300.0\n },\n {\n \"data_center_id\": \"F4\",\n \"application_id\": 1,\n \"routing_cost\": 217.0\n },\n {\n \"data_center_id\": \"F4\",\n \"application_id\": 2,\n \"routing_cost\": 146.0\n },\n {\n \"data_center_id\": \"F4\",\n \"application_id\": 3,\n \"routing_cost\": 51.0\n },\n {\n \"data_center_id\": \"F4\",\n \"application_id\": 4,\n \"routing_cost\": 128.0\n },\n {\n \"data_center_id\": \"F4\",\n \"application_id\": 5,\n \"routing_cost\": 50.0\n },\n {\n \"data_center_id\": \"F4\",\n \"application_id\": 6,\n \"routing_cost\": 232.0\n },\n {\n \"data_center_id\": \"F4\",\n \"application_id\": 7,\n \"routing_cost\": 50.0\n },\n {\n \"data_center_id\": \"F4\",\n \"application_id\": 8,\n \"routing_cost\": 46.0\n },\n {\n \"data_center_id\": \"F4\",\n \"application_id\": 9,\n \"routing_cost\": 394.0\n },\n {\n \"data_center_id\": \"F4\",\n \"application_id\": 10,\n \"routing_cost\": 45.0\n },\n {\n \"data_center_id\": \"F4\",\n \"application_id\": 11,\n \"routing_cost\": 154.0\n },\n {\n \"data_center_id\": \"F5\",\n \"application_id\": 0,\n \"routing_cost\": 511.0\n },\n {\n \"data_center_id\": \"F5\",\n \"application_id\": 1,\n \"routing_cost\": 182.0\n },\n {\n \"data_center_id\": \"F5\",\n \"application_id\": 2,\n \"routing_cost\": 104.0\n },\n {\n \"data_center_id\": \"F5\",\n \"application_id\": 3,\n \"routing_cost\": 617.0\n },\n {\n \"data_center_id\": \"F5\",\n \"application_id\": 4,\n \"routing_cost\": 960.0\n },\n {\n \"data_center_id\": \"F5\",\n \"application_id\": 5,\n \"routing_cost\": 35.0\n },\n {\n \"data_center_id\": \"F5\",\n \"application_id\": 6,\n \"routing_cost\": 489.0\n },\n {\n \"data_center_id\": \"F5\",\n \"application_id\": 7,\n \"routing_cost\": 94.0\n },\n {\n \"data_center_id\": \"F5\",\n \"application_id\": 8,\n \"routing_cost\": 127.0\n },\n {\n \"data_center_id\": \"F5\",\n \"application_id\": 9,\n \"routing_cost\": 469.0\n },\n {\n \"data_center_id\": \"F5\",\n \"application_id\": 10,\n \"routing_cost\": 64.0\n },\n {\n \"data_center_id\": \"F5\",\n \"application_id\": 11,\n \"routing_cost\": 105.0\n }\n ]\n}\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": [ 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 349.0, 165.0, 122.0, 22.0, 39.0, 42.0, 283.0, 49.0, 65.0, 316.0, 36.0, 114.0 ], [ 89.0, 728.0, 366.0, 923.0, 1216.0, 125.0, 53.0, 349.0, 48.0, 1076.0, 417.0, 611.0 ], [ 226.0, 1039.0, 473.0, 1541.0, 1880.0, 151.0, 422.0, 718.0, 133.0, 1443.0, 808.0, 921.0 ], [ 300.0, 217.0, 146.0, 51.0, 128.0, 50.0, 232.0, 50.0, 46.0, 394.0, 45.0, 154.0 ], [ 511.0, 182.0, 104.0, 617.0, 960.0, 35.0, 489.0, 94.0, 127.0, 469.0, 64.0, 105.0 ] ], "demands": [ 14.0, 20.0, 24.0, 11.0, 19.0, 13.0, 26.0, 24.0, 10.0, 16.0, 18.0, 23.0 ], "objective": 1895.0 }, "solution": { "open_facilities": [ 0, 1 ], "assignments": [ 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0 ] }, "obj": 1895.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 12, "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 } ], "customers": [ { "id": 0, "demand": 14.0 }, { "id": 1, "demand": 20.0 }, { "id": 2, "demand": 24.0 }, { "id": 3, "demand": 11.0 }, { "id": 4, "demand": 19.0 }, { "id": 5, "demand": 13.0 }, { "id": 6, "demand": 26.0 }, { "id": 7, "demand": 24.0 }, { "id": 8, "demand": 10.0 }, { "id": 9, "demand": 16.0 }, { "id": 10, "demand": 18.0 }, { "id": 11, "demand": 23.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 349.0 }, { "facility": "F1", "customer": 1, "cost": 165.0 }, { "facility": "F1", "customer": 2, "cost": 122.0 }, { "facility": "F1", "customer": 3, "cost": 22.0 }, { "facility": "F1", "customer": 4, "cost": 39.0 }, { "facility": "F1", "customer": 5, "cost": 42.0 }, { "facility": "F1", "customer": 6, "cost": 283.0 }, { "facility": "F1", "customer": 7, "cost": 49.0 }, { "facility": "F1", "customer": 8, "cost": 65.0 }, { "facility": "F1", "customer": 9, "cost": 316.0 }, { "facility": "F1", "customer": 10, "cost": 36.0 }, { "facility": "F1", "customer": 11, "cost": 114.0 }, { "facility": "F2", "customer": 0, "cost": 89.0 }, { "facility": "F2", "customer": 1, "cost": 728.0 }, { "facility": "F2", "customer": 2, "cost": 366.0 }, { "facility": "F2", "customer": 3, "cost": 923.0 }, { "facility": "F2", "customer": 4, "cost": 1216.0 }, { "facility": "F2", "customer": 5, "cost": 125.0 }, { "facility": "F2", "customer": 6, "cost": 53.0 }, { "facility": "F2", "customer": 7, "cost": 349.0 }, { "facility": "F2", "customer": 8, "cost": 48.0 }, { "facility": "F2", "customer": 9, "cost": 1076.0 }, { "facility": "F2", "customer": 10, "cost": 417.0 }, { "facility": "F2", "customer": 11, "cost": 611.0 }, { "facility": "F3", "customer": 0, "cost": 226.0 }, { "facility": "F3", "customer": 1, "cost": 1039.0 }, { "facility": "F3", "customer": 2, "cost": 473.0 }, { "facility": "F3", "customer": 3, "cost": 1541.0 }, { "facility": "F3", "customer": 4, "cost": 1880.0 }, { "facility": "F3", "customer": 5, "cost": 151.0 }, { "facility": "F3", "customer": 6, "cost": 422.0 }, { "facility": "F3", "customer": 7, "cost": 718.0 }, { "facility": "F3", "customer": 8, "cost": 133.0 }, { "facility": "F3", "customer": 9, "cost": 1443.0 }, { "facility": "F3", "customer": 10, "cost": 808.0 }, { "facility": "F3", "customer": 11, "cost": 921.0 }, { "facility": "F4", "customer": 0, "cost": 300.0 }, { "facility": "F4", "customer": 1, "cost": 217.0 }, { "facility": "F4", "customer": 2, "cost": 146.0 }, { "facility": "F4", "customer": 3, "cost": 51.0 }, { "facility": "F4", "customer": 4, "cost": 128.0 }, { "facility": "F4", "customer": 5, "cost": 50.0 }, { "facility": "F4", "customer": 6, "cost": 232.0 }, { "facility": "F4", "customer": 7, "cost": 50.0 }, { "facility": "F4", "customer": 8, "cost": 46.0 }, { "facility": "F4", "customer": 9, "cost": 394.0 }, { "facility": "F4", "customer": 10, "cost": 45.0 }, { "facility": "F4", "customer": 11, "cost": 154.0 }, { "facility": "F5", "customer": 0, "cost": 511.0 }, { "facility": "F5", "customer": 1, "cost": 182.0 }, { "facility": "F5", "customer": 2, "cost": 104.0 }, { "facility": "F5", "customer": 3, "cost": 617.0 }, { "facility": "F5", "customer": 4, "cost": 960.0 }, { "facility": "F5", "customer": 5, "cost": 35.0 }, { "facility": "F5", "customer": 6, "cost": 489.0 }, { "facility": "F5", "customer": 7, "cost": 94.0 }, { "facility": "F5", "customer": 8, "cost": 127.0 }, { "facility": "F5", "customer": 9, "cost": 469.0 }, { "facility": "F5", "customer": 10, "cost": 64.0 }, { "facility": "F5", "customer": 11, "cost": 105.0 } ], "objective": 1895.0 }, "solution_variant": { "selected": [ "F1", "F2" ], "assignments": [ "F2", "F1", "F1", "F1", "F1", "F1", "F2", "F1", "F2", "F1", "F1", "F1" ] }, "context_index": 6, "input_format": "json", "input_index_base": 0 }, { "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 4 candidate vans and 11 neighborhoods to consider.\nVan F1 has deployment cost 600.0 and book capacity 700.0.\nVan F2 has deployment cost 600.0 and book capacity 700.0.\nVan F3 has deployment cost 600.0 and book capacity 700.0.\nVan F4 has deployment cost 600.0 and book capacity 700.0.\nNeighborhood 0 requires 11.0 books.\nNeighborhood 1 requires 26.0 books.\nNeighborhood 2 requires 20.0 books.\nNeighborhood 3 requires 12.0 books.\nNeighborhood 4 requires 20.0 books.\nNeighborhood 5 requires 19.0 books.\nNeighborhood 6 requires 20.0 books.\nNeighborhood 7 requires 26.0 books.\nNeighborhood 8 requires 16.0 books.\nNeighborhood 9 requires 14.0 books.\nNeighborhood 10 requires 13.0 books.\nAssigning neighborhood 0 to van F1 incurs delivery effort 183.0.\nAssigning neighborhood 1 to van F1 incurs delivery effort 62.0.\nAssigning neighborhood 2 to van F1 incurs delivery effort 87.0.\nAssigning neighborhood 3 to van F1 incurs delivery effort 24.0.\nAssigning neighborhood 4 to van F1 incurs delivery effort 165.0.\nAssigning neighborhood 5 to van F1 incurs delivery effort 248.0.\nAssigning neighborhood 6 to van F1 incurs delivery effort 77.0.\nAssigning neighborhood 7 to van F1 incurs delivery effort 313.0.\nAssigning neighborhood 8 to van F1 incurs delivery effort 49.0.\nAssigning neighborhood 9 to van F1 incurs delivery effort 28.0.\nAssigning neighborhood 10 to van F1 incurs delivery effort 42.0.\nAssigning neighborhood 0 to van F2 incurs delivery effort 30.0.\nAssigning neighborhood 1 to van F2 incurs delivery effort 391.0.\nAssigning neighborhood 2 to van F2 incurs delivery effort 447.0.\nAssigning neighborhood 3 to van F2 incurs delivery effort 517.0.\nAssigning neighborhood 4 to van F2 incurs delivery effort 1039.0.\nAssigning neighborhood 5 to van F2 incurs delivery effort 1382.0.\nAssigning neighborhood 6 to van F2 incurs delivery effort 132.0.\nAssigning neighborhood 7 to van F2 incurs delivery effort 201.0.\nAssigning neighborhood 8 to van F2 incurs delivery effort 864.0.\nAssigning neighborhood 9 to van F2 incurs delivery effort 305.0.\nAssigning neighborhood 10 to van F2 incurs delivery effort 780.0.\nAssigning neighborhood 0 to van F3 incurs delivery effort 445.0.\nAssigning neighborhood 1 to van F3 incurs delivery effort 275.0.\nAssigning neighborhood 2 to van F3 incurs delivery effort 421.0.\nAssigning neighborhood 3 to van F3 incurs delivery effort 194.0.\nAssigning neighborhood 4 to van F3 incurs delivery effort 57.0.\nAssigning neighborhood 5 to van F3 incurs delivery effort 103.0.\nAssigning neighborhood 6 to van F3 incurs delivery effort 272.0.\nAssigning neighborhood 7 to van F3 incurs delivery effort 687.0.\nAssigning neighborhood 8 to van F3 incurs delivery effort 489.0.\nAssigning neighborhood 9 to van F3 incurs delivery effort 124.0.\nAssigning neighborhood 10 to van F3 incurs delivery effort 162.0.\nAssigning neighborhood 0 to van F4 incurs delivery effort 329.0.\nAssigning neighborhood 1 to van F4 incurs delivery effort 150.0.\nAssigning neighborhood 2 to van F4 incurs delivery effort 274.0.\nAssigning neighborhood 3 to van F4 incurs delivery effort 73.0.\nAssigning neighborhood 4 to van F4 incurs delivery effort 148.0.\nAssigning neighborhood 5 to van F4 incurs delivery effort 398.0.\nAssigning neighborhood 6 to van F4 incurs delivery effort 166.0.\nAssigning neighborhood 7 to van F4 incurs delivery effort 547.0.\nAssigning neighborhood 8 to van F4 incurs delivery effort 342.0.\nAssigning neighborhood 9 to van F4 incurs delivery effort 49.0.\nAssigning neighborhood 10 to van F4 incurs delivery effort 37.0.\nUse these 4 vans and 11 neighborhood figures to find the assignment that minimizes total deployment fees plus delivery effort.\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 ], "capacities": [ 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 183.0, 62.0, 87.0, 24.0, 165.0, 248.0, 77.0, 313.0, 49.0, 28.0, 42.0 ], [ 30.0, 391.0, 447.0, 517.0, 1039.0, 1382.0, 132.0, 201.0, 864.0, 305.0, 780.0 ], [ 445.0, 275.0, 421.0, 194.0, 57.0, 103.0, 272.0, 687.0, 489.0, 124.0, 162.0 ], [ 329.0, 150.0, 274.0, 73.0, 148.0, 398.0, 166.0, 547.0, 342.0, 49.0, 37.0 ] ], "demands": [ 11.0, 26.0, 20.0, 12.0, 20.0, 19.0, 20.0, 26.0, 16.0, 14.0, 13.0 ], "objective": 1878.0 }, "solution": { "open_facilities": [ 0 ], "assignments": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] }, "obj": 1878.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 4, "num_customers": 11, "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 } ], "customers": [ { "id": 0, "demand": 11.0 }, { "id": 1, "demand": 26.0 }, { "id": 2, "demand": 20.0 }, { "id": 3, "demand": 12.0 }, { "id": 4, "demand": 20.0 }, { "id": 5, "demand": 19.0 }, { "id": 6, "demand": 20.0 }, { "id": 7, "demand": 26.0 }, { "id": 8, "demand": 16.0 }, { "id": 9, "demand": 14.0 }, { "id": 10, "demand": 13.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 183.0 }, { "facility": "F1", "customer": 1, "cost": 62.0 }, { "facility": "F1", "customer": 2, "cost": 87.0 }, { "facility": "F1", "customer": 3, "cost": 24.0 }, { "facility": "F1", "customer": 4, "cost": 165.0 }, { "facility": "F1", "customer": 5, "cost": 248.0 }, { "facility": "F1", "customer": 6, "cost": 77.0 }, { "facility": "F1", "customer": 7, "cost": 313.0 }, { "facility": "F1", "customer": 8, "cost": 49.0 }, { "facility": "F1", "customer": 9, "cost": 28.0 }, { "facility": "F1", "customer": 10, "cost": 42.0 }, { "facility": "F2", "customer": 0, "cost": 30.0 }, { "facility": "F2", "customer": 1, "cost": 391.0 }, { "facility": "F2", "customer": 2, "cost": 447.0 }, { "facility": "F2", "customer": 3, "cost": 517.0 }, { "facility": "F2", "customer": 4, "cost": 1039.0 }, { "facility": "F2", "customer": 5, "cost": 1382.0 }, { "facility": "F2", "customer": 6, "cost": 132.0 }, { "facility": "F2", "customer": 7, "cost": 201.0 }, { "facility": "F2", "customer": 8, "cost": 864.0 }, { "facility": "F2", "customer": 9, "cost": 305.0 }, { "facility": "F2", "customer": 10, "cost": 780.0 }, { "facility": "F3", "customer": 0, "cost": 445.0 }, { "facility": "F3", "customer": 1, "cost": 275.0 }, { "facility": "F3", "customer": 2, "cost": 421.0 }, { "facility": "F3", "customer": 3, "cost": 194.0 }, { "facility": "F3", "customer": 4, "cost": 57.0 }, { "facility": "F3", "customer": 5, "cost": 103.0 }, { "facility": "F3", "customer": 6, "cost": 272.0 }, { "facility": "F3", "customer": 7, "cost": 687.0 }, { "facility": "F3", "customer": 8, "cost": 489.0 }, { "facility": "F3", "customer": 9, "cost": 124.0 }, { "facility": "F3", "customer": 10, "cost": 162.0 }, { "facility": "F4", "customer": 0, "cost": 329.0 }, { "facility": "F4", "customer": 1, "cost": 150.0 }, { "facility": "F4", "customer": 2, "cost": 274.0 }, { "facility": "F4", "customer": 3, "cost": 73.0 }, { "facility": "F4", "customer": 4, "cost": 148.0 }, { "facility": "F4", "customer": 5, "cost": 398.0 }, { "facility": "F4", "customer": 6, "cost": 166.0 }, { "facility": "F4", "customer": 7, "cost": 547.0 }, { "facility": "F4", "customer": 8, "cost": 342.0 }, { "facility": "F4", "customer": 9, "cost": 49.0 }, { "facility": "F4", "customer": 10, "cost": 37.0 } ], "objective": 1878.0 }, "solution_variant": { "selected": [ "F1" ], "assignments": [ "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1" ] }, "context_index": 7, "input_format": "nl", "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\nThere are 4 hubs and 10 sites in this instance.\n\n**Hubs**\n| hub_id | setup_cost | hub_capacity |\n|---|---|---|\n| F1 | 300.0 | 700.0 |\n| F2 | 300.0 | 700.0 |\n| F3 | 300.0 | 700.0 |\n| F4 | 300.0 | 700.0 |\n\n**Sites**\n| site_id | site_demand |\n|---|---|\n| 1 | 24.0 |\n| 2 | 25.0 |\n| 3 | 15.0 |\n| 4 | 13.0 |\n| 5 | 14.0 |\n| 6 | 19.0 |\n| 7 | 17.0 |\n| 8 | 18.0 |\n| 9 | 17.0 |\n| 10 | 19.0 |\n\n**Shipment Cost**\n| hub_id | site_id | shipment_cost |\n|---|---|---|\n| F1 | 1 | 228.0 |\n| F1 | 2 | 389.0 |\n| F1 | 3 | 43.0 |\n| F1 | 4 | 26.0 |\n| F1 | 5 | 30.0 |\n| F1 | 6 | 38.0 |\n| F1 | 7 | 171.0 |\n| F1 | 8 | 37.0 |\n| F1 | 9 | 266.0 |\n| F1 | 10 | 274.0 |\n| F2 | 1 | 818.0 |\n| F2 | 2 | 120.0 |\n| F2 | 3 | 200.0 |\n| F2 | 4 | 99.0 |\n| F2 | 5 | 172.0 |\n| F2 | 6 | 273.0 |\n| F2 | 7 | 146.0 |\n| F2 | 8 | 87.0 |\n| F2 | 9 | 691.0 |\n| F2 | 10 | 70.0 |\n| F3 | 1 | 1276.0 |\n| F3 | 2 | 619.0 |\n| F3 | 3 | 414.0 |\n| F3 | 4 | 242.0 |\n| F3 | 5 | 458.0 |\n| F3 | 6 | 625.0 |\n| F3 | 7 | 573.0 |\n| F3 | 8 | 181.0 |\n| F3 | 9 | 1040.0 |\n| F3 | 10 | 56.0 |\n| F4 | 1 | 1148.0 |\n| F4 | 2 | 1197.0 |\n| F4 | 3 | 40.0 |\n| F4 | 4 | 29.0 |\n| F4 | 5 | 249.0 |\n| F4 | 6 | 467.0 |\n| F4 | 7 | 894.0 |\n| F4 | 8 | 36.0 |\n| F4 | 9 | 644.0 |\n| F4 | 10 | 516.0 |\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": [ 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 228.0, 389.0, 43.0, 26.0, 30.0, 38.0, 171.0, 37.0, 266.0, 274.0 ], [ 818.0, 120.0, 200.0, 99.0, 172.0, 273.0, 146.0, 87.0, 691.0, 70.0 ], [ 1276.0, 619.0, 414.0, 242.0, 458.0, 625.0, 573.0, 181.0, 1040.0, 56.0 ], [ 1148.0, 1197.0, 40.0, 29.0, 249.0, 467.0, 894.0, 36.0, 644.0, 516.0 ] ], "demands": [ 24.0, 25.0, 15.0, 13.0, 14.0, 19.0, 17.0, 18.0, 17.0, 19.0 ], "objective": 1604.0 }, "solution": { "open_facilities": [ 0, 1 ], "assignments": [ 0, 1, 0, 0, 0, 0, 1, 0, 0, 1 ] }, "obj": 1604.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 4, "num_customers": 10, "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 } ], "customers": [ { "id": 1, "demand": 24.0 }, { "id": 2, "demand": 25.0 }, { "id": 3, "demand": 15.0 }, { "id": 4, "demand": 13.0 }, { "id": 5, "demand": 14.0 }, { "id": 6, "demand": 19.0 }, { "id": 7, "demand": 17.0 }, { "id": 8, "demand": 18.0 }, { "id": 9, "demand": 17.0 }, { "id": 10, "demand": 19.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 228.0 }, { "facility": "F1", "customer": 2, "cost": 389.0 }, { "facility": "F1", "customer": 3, "cost": 43.0 }, { "facility": "F1", "customer": 4, "cost": 26.0 }, { "facility": "F1", "customer": 5, "cost": 30.0 }, { "facility": "F1", "customer": 6, "cost": 38.0 }, { "facility": "F1", "customer": 7, "cost": 171.0 }, { "facility": "F1", "customer": 8, "cost": 37.0 }, { "facility": "F1", "customer": 9, "cost": 266.0 }, { "facility": "F1", "customer": 10, "cost": 274.0 }, { "facility": "F2", "customer": 1, "cost": 818.0 }, { "facility": "F2", "customer": 2, "cost": 120.0 }, { "facility": "F2", "customer": 3, "cost": 200.0 }, { "facility": "F2", "customer": 4, "cost": 99.0 }, { "facility": "F2", "customer": 5, "cost": 172.0 }, { "facility": "F2", "customer": 6, "cost": 273.0 }, { "facility": "F2", "customer": 7, "cost": 146.0 }, { "facility": "F2", "customer": 8, "cost": 87.0 }, { "facility": "F2", "customer": 9, "cost": 691.0 }, { "facility": "F2", "customer": 10, "cost": 70.0 }, { "facility": "F3", "customer": 1, "cost": 1276.0 }, { "facility": "F3", "customer": 2, "cost": 619.0 }, { "facility": "F3", "customer": 3, "cost": 414.0 }, { "facility": "F3", "customer": 4, "cost": 242.0 }, { "facility": "F3", "customer": 5, "cost": 458.0 }, { "facility": "F3", "customer": 6, "cost": 625.0 }, { "facility": "F3", "customer": 7, "cost": 573.0 }, { "facility": "F3", "customer": 8, "cost": 181.0 }, { "facility": "F3", "customer": 9, "cost": 1040.0 }, { "facility": "F3", "customer": 10, "cost": 56.0 }, { "facility": "F4", "customer": 1, "cost": 1148.0 }, { "facility": "F4", "customer": 2, "cost": 1197.0 }, { "facility": "F4", "customer": 3, "cost": 40.0 }, { "facility": "F4", "customer": 4, "cost": 29.0 }, { "facility": "F4", "customer": 5, "cost": 249.0 }, { "facility": "F4", "customer": 6, "cost": 467.0 }, { "facility": "F4", "customer": 7, "cost": 894.0 }, { "facility": "F4", "customer": 8, "cost": 36.0 }, { "facility": "F4", "customer": 9, "cost": 644.0 }, { "facility": "F4", "customer": 10, "cost": 516.0 } ], "objective": 1604.0 }, "solution_variant": { "selected": [ "F1", "F2" ], "assignments": [ "F1", "F2", "F1", "F1", "F1", "F1", "F2", "F1", "F1", "F2" ] }, "context_index": 8, "input_format": "markdown_table", "input_index_base": 1 }, { "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\": 4,\n \"num_customers\": 9,\n \"teams\": [\n {\n \"team_id\": \"F1\",\n \"activation_fee\": 400.0,\n \"workload_capacity\": 300.0\n },\n {\n \"team_id\": \"F2\",\n \"activation_fee\": 400.0,\n \"workload_capacity\": 300.0\n },\n {\n \"team_id\": \"F3\",\n \"activation_fee\": 400.0,\n \"workload_capacity\": 300.0\n },\n {\n \"team_id\": \"F4\",\n \"activation_fee\": 400.0,\n \"workload_capacity\": 300.0\n }\n ],\n \"requests\": [\n {\n \"request_id\": 1,\n \"installation_demand\": 21.0\n },\n {\n \"request_id\": 2,\n \"installation_demand\": 28.0\n },\n {\n \"request_id\": 3,\n \"installation_demand\": 12.0\n },\n {\n \"request_id\": 4,\n \"installation_demand\": 13.0\n },\n {\n \"request_id\": 5,\n \"installation_demand\": 13.0\n },\n {\n \"request_id\": 6,\n \"installation_demand\": 12.0\n },\n {\n \"request_id\": 7,\n \"installation_demand\": 19.0\n },\n {\n \"request_id\": 8,\n \"installation_demand\": 17.0\n },\n {\n \"request_id\": 9,\n \"installation_demand\": 12.0\n }\n ],\n \"travel_and_services\": [\n {\n \"team_id\": \"F1\",\n \"request_id\": 1,\n \"travel_and_service_cost\": 647.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 2,\n \"travel_and_service_cost\": 324.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 3,\n \"travel_and_service_cost\": 481.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 4,\n \"travel_and_service_cost\": 242.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 5,\n \"travel_and_service_cost\": 27.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 6,\n \"travel_and_service_cost\": 333.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 7,\n \"travel_and_service_cost\": 38.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 8,\n \"travel_and_service_cost\": 171.0\n },\n {\n \"team_id\": \"F1\",\n \"request_id\": 9,\n \"travel_and_service_cost\": 31.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 1,\n \"travel_and_service_cost\": 217.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 2,\n \"travel_and_service_cost\": 341.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 3,\n \"travel_and_service_cost\": 232.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 4,\n \"travel_and_service_cost\": 1237.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 5,\n \"travel_and_service_cost\": 904.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 6,\n \"travel_and_service_cost\": 203.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 7,\n \"travel_and_service_cost\": 776.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 8,\n \"travel_and_service_cost\": 813.0\n },\n {\n \"team_id\": \"F2\",\n \"request_id\": 9,\n \"travel_and_service_cost\": 1039.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 1,\n \"travel_and_service_cost\": 273.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 2,\n \"travel_and_service_cost\": 66.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 3,\n \"travel_and_service_cost\": 131.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 4,\n \"travel_and_service_cost\": 712.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 5,\n \"travel_and_service_cost\": 341.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 6,\n \"travel_and_service_cost\": 57.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 7,\n \"travel_and_service_cost\": 273.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 8,\n \"travel_and_service_cost\": 146.0\n },\n {\n \"team_id\": \"F3\",\n \"request_id\": 9,\n \"travel_and_service_cost\": 429.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 1,\n \"travel_and_service_cost\": 820.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 2,\n \"travel_and_service_cost\": 474.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 3,\n \"travel_and_service_cost\": 656.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 4,\n \"travel_and_service_cost\": 399.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 5,\n \"travel_and_service_cost\": 26.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 6,\n \"travel_and_service_cost\": 473.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 7,\n \"travel_and_service_cost\": 42.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 8,\n \"travel_and_service_cost\": 421.0\n },\n {\n \"team_id\": \"F4\",\n \"request_id\": 9,\n \"travel_and_service_cost\": 180.0\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": [ 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 300.0, 300.0, 300.0, 300.0 ], "connection_costs": [ [ 647.0, 324.0, 481.0, 242.0, 27.0, 333.0, 38.0, 171.0, 31.0 ], [ 217.0, 341.0, 232.0, 1237.0, 904.0, 203.0, 776.0, 813.0, 1039.0 ], [ 273.0, 66.0, 131.0, 712.0, 341.0, 57.0, 273.0, 146.0, 429.0 ], [ 820.0, 474.0, 656.0, 399.0, 26.0, 473.0, 42.0, 421.0, 180.0 ] ], "demands": [ 21.0, 28.0, 12.0, 13.0, 13.0, 12.0, 19.0, 17.0, 12.0 ], "objective": 1811.0 }, "solution": { "open_facilities": [ 0, 2 ], "assignments": [ 2, 2, 2, 0, 0, 2, 0, 2, 0 ] }, "obj": 1811.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 4, "num_customers": 9, "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 } ], "customers": [ { "id": 1, "demand": 21.0 }, { "id": 2, "demand": 28.0 }, { "id": 3, "demand": 12.0 }, { "id": 4, "demand": 13.0 }, { "id": 5, "demand": 13.0 }, { "id": 6, "demand": 12.0 }, { "id": 7, "demand": 19.0 }, { "id": 8, "demand": 17.0 }, { "id": 9, "demand": 12.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 647.0 }, { "facility": "F1", "customer": 2, "cost": 324.0 }, { "facility": "F1", "customer": 3, "cost": 481.0 }, { "facility": "F1", "customer": 4, "cost": 242.0 }, { "facility": "F1", "customer": 5, "cost": 27.0 }, { "facility": "F1", "customer": 6, "cost": 333.0 }, { "facility": "F1", "customer": 7, "cost": 38.0 }, { "facility": "F1", "customer": 8, "cost": 171.0 }, { "facility": "F1", "customer": 9, "cost": 31.0 }, { "facility": "F2", "customer": 1, "cost": 217.0 }, { "facility": "F2", "customer": 2, "cost": 341.0 }, { "facility": "F2", "customer": 3, "cost": 232.0 }, { "facility": "F2", "customer": 4, "cost": 1237.0 }, { "facility": "F2", "customer": 5, "cost": 904.0 }, { "facility": "F2", "customer": 6, "cost": 203.0 }, { "facility": "F2", "customer": 7, "cost": 776.0 }, { "facility": "F2", "customer": 8, "cost": 813.0 }, { "facility": "F2", "customer": 9, "cost": 1039.0 }, { "facility": "F3", "customer": 1, "cost": 273.0 }, { "facility": "F3", "customer": 2, "cost": 66.0 }, { "facility": "F3", "customer": 3, "cost": 131.0 }, { "facility": "F3", "customer": 4, "cost": 712.0 }, { "facility": "F3", "customer": 5, "cost": 341.0 }, { "facility": "F3", "customer": 6, "cost": 57.0 }, { "facility": "F3", "customer": 7, "cost": 273.0 }, { "facility": "F3", "customer": 8, "cost": 146.0 }, { "facility": "F3", "customer": 9, "cost": 429.0 }, { "facility": "F4", "customer": 1, "cost": 820.0 }, { "facility": "F4", "customer": 2, "cost": 474.0 }, { "facility": "F4", "customer": 3, "cost": 656.0 }, { "facility": "F4", "customer": 4, "cost": 399.0 }, { "facility": "F4", "customer": 5, "cost": 26.0 }, { "facility": "F4", "customer": 6, "cost": 473.0 }, { "facility": "F4", "customer": 7, "cost": 42.0 }, { "facility": "F4", "customer": 8, "cost": 421.0 }, { "facility": "F4", "customer": 9, "cost": 180.0 } ], "objective": 1811.0 }, "solution_variant": { "selected": [ "F1", "F3" ], "assignments": [ "F3", "F3", "F3", "F1", "F1", "F3", "F1", "F3", "F1" ] }, "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 6 candidate towers and 13 service areas.\nTower F1 has commissioning cost 400.0 and user capacity 300.0.\nTower F2 has commissioning cost 400.0 and user capacity 300.0.\nTower F3 has commissioning cost 400.0 and user capacity 300.0.\nTower F4 has commissioning cost 400.0 and user capacity 300.0.\nTower F5 has commissioning cost 400.0 and user capacity 300.0.\nTower F6 has commissioning cost 400.0 and user capacity 300.0.\nService area 1 has 28.0 users.\nService area 2 has 23.0 users.\nService area 3 has 18.0 users.\nService area 4 has 12.0 users.\nService area 5 has 20.0 users.\nService area 6 has 29.0 users.\nService area 7 has 22.0 users.\nService area 8 has 27.0 users.\nService area 9 has 23.0 users.\nService area 10 has 11.0 users.\nService area 11 has 11.0 users.\nService area 12 has 29.0 users.\nService area 13 has 11.0 users.\nAssigning service area 1 to tower F1 incurs a connection penalty of 83.0.\nAssigning service area 2 to tower F1 incurs a connection penalty of 120.0.\nAssigning service area 3 to tower F1 incurs a connection penalty of 42.0.\nAssigning service area 4 to tower F1 incurs a connection penalty of 282.0.\nAssigning service area 5 to tower F1 incurs a connection penalty of 477.0.\nAssigning service area 6 to tower F1 incurs a connection penalty of 231.0.\nAssigning service area 7 to tower F1 incurs a connection penalty of 832.0.\nAssigning service area 8 to tower F1 incurs a connection penalty of 383.0.\nAssigning service area 9 to tower F1 incurs a connection penalty of 46.0.\nAssigning service area 10 to tower F1 incurs a connection penalty of 335.0.\nAssigning service area 11 to tower F1 incurs a connection penalty of 97.0.\nAssigning service area 12 to tower F1 incurs a connection penalty of 475.0.\nAssigning service area 13 to tower F1 incurs a connection penalty of 606.0.\nAssigning service area 1 to tower F2 incurs a connection penalty of 517.0.\nAssigning service area 2 to tower F2 incurs a connection penalty of 364.0.\nAssigning service area 3 to tower F2 incurs a connection penalty of 161.0.\nAssigning service area 4 to tower F2 incurs a connection penalty of 691.0.\nAssigning service area 5 to tower F2 incurs a connection penalty of 142.0.\nAssigning service area 6 to tower F2 incurs a connection penalty of 495.0.\nAssigning service area 7 to tower F2 incurs a connection penalty of 729.0.\nAssigning service area 8 to tower F2 incurs a connection penalty of 781.0.\nAssigning service area 9 to tower F2 incurs a connection penalty of 342.0.\nAssigning service area 10 to tower F2 incurs a connection penalty of 720.0.\nAssigning service area 11 to tower F2 incurs a connection penalty of 303.0.\nAssigning service area 12 to tower F2 incurs a connection penalty of 875.0.\nAssigning service area 13 to tower F2 incurs a connection penalty of 501.0.\nAssigning service area 1 to tower F3 incurs a connection penalty of 213.0.\nAssigning service area 2 to tower F3 incurs a connection penalty of 193.0.\nAssigning service area 3 to tower F3 incurs a connection penalty of 44.0.\nAssigning service area 4 to tower F3 incurs a connection penalty of 412.0.\nAssigning service area 5 to tower F3 incurs a connection penalty of 340.0.\nAssigning service area 6 to tower F3 incurs a connection penalty of 315.0.\nAssigning service area 7 to tower F3 incurs a connection penalty of 611.0.\nAssigning service area 8 to tower F3 incurs a connection penalty of 447.0.\nAssigning service area 9 to tower F3 incurs a connection penalty of 105.0.\nAssigning service area 10 to tower F3 incurs a connection penalty of 459.0.\nAssigning service area 11 to tower F3 incurs a connection penalty of 158.0.\nAssigning service area 12 to tower F3 incurs a connection penalty of 604.0.\nAssigning service area 13 to tower F3 incurs a connection penalty of 356.0.\nAssigning service area 1 to tower F4 incurs a connection penalty of 389.0.\nAssigning service area 2 to tower F4 incurs a connection penalty of 46.0.\nAssigning service area 3 to tower F4 incurs a connection penalty of 208.0.\nAssigning service area 4 to tower F4 incurs a connection penalty of 33.0.\nAssigning service area 5 to tower F4 incurs a connection penalty of 750.0.\nAssigning service area 6 to tower F4 incurs a connection penalty of 91.0.\nAssigning service area 7 to tower F4 incurs a connection penalty of 1286.0.\nAssigning service area 8 to tower F4 incurs a connection penalty of 691.0.\nAssigning service area 9 to tower F4 incurs a connection penalty of 288.0.\nAssigning service area 10 to tower F4 incurs a connection penalty of 86.0.\nAssigning service area 11 to tower F4 incurs a connection penalty of 24.0.\nAssigning service area 12 to tower F4 incurs a connection penalty of 200.0.\nAssigning service area 13 to tower F4 incurs a connection penalty of 1077.0.\nAssigning service area 1 to tower F5 incurs a connection penalty of 84.0.\nAssigning service area 2 to tower F5 incurs a connection penalty of 70.0.\nAssigning service area 3 to tower F5 incurs a connection penalty of 78.0.\nAssigning service area 4 to tower F5 incurs a connection penalty of 131.0.\nAssigning service area 5 to tower F5 incurs a connection penalty of 561.0.\nAssigning service area 6 to tower F5 incurs a connection penalty of 155.0.\nAssigning service area 7 to tower F5 incurs a connection penalty of 829.0.\nAssigning service area 8 to tower F5 incurs a connection penalty of 220.0.\nAssigning service area 9 to tower F5 incurs a connection penalty of 79.0.\nAssigning service area 10 to tower F5 incurs a connection penalty of 191.0.\nAssigning service area 11 to tower F5 incurs a connection penalty of 53.0.\nAssigning service area 12 to tower F5 incurs a connection penalty of 311.0.\nAssigning service area 13 to tower F5 incurs a connection penalty of 640.0.\nAssigning service area 1 to tower F6 incurs a connection penalty of 526.0.\nAssigning service area 2 to tower F6 incurs a connection penalty of 305.0.\nAssigning service area 3 to tower F6 incurs a connection penalty of 104.0.\nAssigning service area 4 to tower F6 incurs a connection penalty of 656.0.\nAssigning service area 5 to tower F6 incurs a connection penalty of 289.0.\nAssigning service area 6 to tower F6 incurs a connection penalty of 436.0.\nAssigning service area 7 to tower F6 incurs a connection penalty of 1051.0.\nAssigning service area 8 to tower F6 incurs a connection penalty of 873.0.\nAssigning service area 9 to tower F6 incurs a connection penalty of 305.0.\nAssigning service area 10 to tower F6 incurs a connection penalty of 673.0.\nAssigning service area 11 to tower F6 incurs a connection penalty of 247.0.\nAssigning service area 12 to tower F6 incurs a connection penalty of 831.0.\nAssigning service area 13 to tower F6 incurs a connection penalty of 787.0.\nUse these numbers to decide which towers to commission and how to assign each area so the total bill (commissioning costs plus connection penalties) is minimized.\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": [ 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 ], "connection_costs": [ [ 83.0, 120.0, 42.0, 282.0, 477.0, 231.0, 832.0, 383.0, 46.0, 335.0, 97.0, 475.0, 606.0 ], [ 517.0, 364.0, 161.0, 691.0, 142.0, 495.0, 729.0, 781.0, 342.0, 720.0, 303.0, 875.0, 501.0 ], [ 213.0, 193.0, 44.0, 412.0, 340.0, 315.0, 611.0, 447.0, 105.0, 459.0, 158.0, 604.0, 356.0 ], [ 389.0, 46.0, 208.0, 33.0, 750.0, 91.0, 1286.0, 691.0, 288.0, 86.0, 24.0, 200.0, 1077.0 ], [ 84.0, 70.0, 78.0, 131.0, 561.0, 155.0, 829.0, 220.0, 79.0, 191.0, 53.0, 311.0, 640.0 ], [ 526.0, 305.0, 104.0, 656.0, 289.0, 436.0, 1051.0, 873.0, 305.0, 673.0, 247.0, 831.0, 787.0 ] ], "demands": [ 28.0, 23.0, 18.0, 12.0, 20.0, 29.0, 22.0, 27.0, 23.0, 11.0, 11.0, 29.0, 11.0 ], "objective": 3396.0 }, "solution": { "open_facilities": [ 2, 3 ], "assignments": [ 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 3, 3, 2 ] }, "obj": 3396.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 6, "num_customers": 13, "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 } ], "customers": [ { "id": 1, "demand": 28.0 }, { "id": 2, "demand": 23.0 }, { "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": 27.0 }, { "id": 9, "demand": 23.0 }, { "id": 10, "demand": 11.0 }, { "id": 11, "demand": 11.0 }, { "id": 12, "demand": 29.0 }, { "id": 13, "demand": 11.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 83.0 }, { "facility": "F1", "customer": 2, "cost": 120.0 }, { "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": 383.0 }, { "facility": "F1", "customer": 9, "cost": 46.0 }, { "facility": "F1", "customer": 10, "cost": 335.0 }, { "facility": "F1", "customer": 11, "cost": 97.0 }, { "facility": "F1", "customer": 12, "cost": 475.0 }, { "facility": "F1", "customer": 13, "cost": 606.0 }, { "facility": "F2", "customer": 1, "cost": 517.0 }, { "facility": "F2", "customer": 2, "cost": 364.0 }, { "facility": "F2", "customer": 3, "cost": 161.0 }, { "facility": "F2", "customer": 4, "cost": 691.0 }, { "facility": "F2", "customer": 5, "cost": 142.0 }, { "facility": "F2", "customer": 6, "cost": 495.0 }, { "facility": "F2", "customer": 7, "cost": 729.0 }, { "facility": "F2", "customer": 8, "cost": 781.0 }, { "facility": "F2", "customer": 9, "cost": 342.0 }, { "facility": "F2", "customer": 10, "cost": 720.0 }, { "facility": "F2", "customer": 11, "cost": 303.0 }, { "facility": "F2", "customer": 12, "cost": 875.0 }, { "facility": "F2", "customer": 13, "cost": 501.0 }, { "facility": "F3", "customer": 1, "cost": 213.0 }, { "facility": "F3", "customer": 2, "cost": 193.0 }, { "facility": "F3", "customer": 3, "cost": 44.0 }, { "facility": "F3", "customer": 4, "cost": 412.0 }, { "facility": "F3", "customer": 5, "cost": 340.0 }, { "facility": "F3", "customer": 6, "cost": 315.0 }, { "facility": "F3", "customer": 7, "cost": 611.0 }, { "facility": "F3", "customer": 8, "cost": 447.0 }, { "facility": "F3", "customer": 9, "cost": 105.0 }, { "facility": "F3", "customer": 10, "cost": 459.0 }, { "facility": "F3", "customer": 11, "cost": 158.0 }, { "facility": "F3", "customer": 12, "cost": 604.0 }, { "facility": "F3", "customer": 13, "cost": 356.0 }, { "facility": "F4", "customer": 1, "cost": 389.0 }, { "facility": "F4", "customer": 2, "cost": 46.0 }, { "facility": "F4", "customer": 3, "cost": 208.0 }, { "facility": "F4", "customer": 4, "cost": 33.0 }, { "facility": "F4", "customer": 5, "cost": 750.0 }, { "facility": "F4", "customer": 6, "cost": 91.0 }, { "facility": "F4", "customer": 7, "cost": 1286.0 }, { "facility": "F4", "customer": 8, "cost": 691.0 }, { "facility": "F4", "customer": 9, "cost": 288.0 }, { "facility": "F4", "customer": 10, "cost": 86.0 }, { "facility": "F4", "customer": 11, "cost": 24.0 }, { "facility": "F4", "customer": 12, "cost": 200.0 }, { "facility": "F4", "customer": 13, "cost": 1077.0 }, { "facility": "F5", "customer": 1, "cost": 84.0 }, { "facility": "F5", "customer": 2, "cost": 70.0 }, { "facility": "F5", "customer": 3, "cost": 78.0 }, { "facility": "F5", "customer": 4, "cost": 131.0 }, { "facility": "F5", "customer": 5, "cost": 561.0 }, { "facility": "F5", "customer": 6, "cost": 155.0 }, { "facility": "F5", "customer": 7, "cost": 829.0 }, { "facility": "F5", "customer": 8, "cost": 220.0 }, { "facility": "F5", "customer": 9, "cost": 79.0 }, { "facility": "F5", "customer": 10, "cost": 191.0 }, { "facility": "F5", "customer": 11, "cost": 53.0 }, { "facility": "F5", "customer": 12, "cost": 311.0 }, { "facility": "F5", "customer": 13, "cost": 640.0 }, { "facility": "F6", "customer": 1, "cost": 526.0 }, { "facility": "F6", "customer": 2, "cost": 305.0 }, { "facility": "F6", "customer": 3, "cost": 104.0 }, { "facility": "F6", "customer": 4, "cost": 656.0 }, { "facility": "F6", "customer": 5, "cost": 289.0 }, { "facility": "F6", "customer": 6, "cost": 436.0 }, { "facility": "F6", "customer": 7, "cost": 1051.0 }, { "facility": "F6", "customer": 8, "cost": 873.0 }, { "facility": "F6", "customer": 9, "cost": 305.0 }, { "facility": "F6", "customer": 10, "cost": 673.0 }, { "facility": "F6", "customer": 11, "cost": 247.0 }, { "facility": "F6", "customer": 12, "cost": 831.0 }, { "facility": "F6", "customer": 13, "cost": 787.0 } ], "objective": 3396.0 }, "solution_variant": { "selected": [ "F3", "F4" ], "assignments": [ "F3", "F4", "F3", "F4", "F3", "F4", "F3", "F3", "F3", "F4", "F4", "F4", "F3" ] }, "context_index": 10, "input_format": "nl", "input_index_base": 1 }, { "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\nThere are 4 clinics and 9 neighborhoods in this instance.\n\n**Clinics**\n| clinic_id | clinic_opening_cost | clinic_daily_throughput |\n|---|---|---|\n| F1 | 296.0 | 504.0 |\n| F2 | 310.0 | 580.0 |\n| F3 | 329.0 | 456.0 |\n| F4 | 179.0 | 549.0 |\n\n**Neighborhoods**\n| neighborhood_id | neighborhood_demand |\n|---|---|\n| 0 | 31.0 |\n| 1 | 14.0 |\n| 2 | 40.0 |\n| 3 | 26.0 |\n| 4 | 22.0 |\n| 5 | 37.0 |\n| 6 | 19.0 |\n| 7 | 10.0 |\n| 8 | 37.0 |\n\n**Transport Cost**\n| clinic_id | neighborhood_id | transport_cost |\n|---|---|---|\n| F1 | 0 | 329.0 |\n| F1 | 1 | 376.0 |\n| F1 | 2 | 335.0 |\n| F1 | 3 | 337.0 |\n| F1 | 4 | 467.0 |\n| F1 | 5 | 243.0 |\n| F1 | 6 | 411.0 |\n| F1 | 7 | 364.0 |\n| F1 | 8 | 156.0 |\n| F2 | 0 | 564.0 |\n| F2 | 1 | 582.0 |\n| F2 | 2 | 294.0 |\n| F2 | 3 | 532.0 |\n| F2 | 4 | 524.0 |\n| F2 | 5 | 9.0 |\n| F2 | 6 | 651.0 |\n| F2 | 7 | 200.0 |\n| F2 | 8 | 141.0 |\n| F3 | 0 | 387.0 |\n| F3 | 1 | 643.0 |\n| F3 | 2 | 200.0 |\n| F3 | 3 | 237.0 |\n| F3 | 4 | 124.0 |\n| F3 | 5 | 425.0 |\n| F3 | 6 | 519.0 |\n| F3 | 7 | 626.0 |\n| F3 | 8 | 297.0 |\n| F4 | 0 | 742.0 |\n| F4 | 1 | 700.0 |\n| F4 | 2 | 458.0 |\n| F4 | 3 | 724.0 |\n| F4 | 4 | 702.0 |\n| F4 | 5 | 197.0 |\n| F4 | 6 | 817.0 |\n| F4 | 7 | 113.0 |\n| F4 | 8 | 334.0 |\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": [ 296.0, 310.0, 329.0, 179.0 ], "capacities": [ 504.0, 580.0, 456.0, 549.0 ], "connection_costs": [ [ 329.0, 376.0, 335.0, 337.0, 467.0, 243.0, 411.0, 364.0, 156.0 ], [ 564.0, 582.0, 294.0, 532.0, 524.0, 9.0, 651.0, 200.0, 141.0 ], [ 387.0, 643.0, 200.0, 237.0, 124.0, 425.0, 519.0, 626.0, 297.0 ], [ 742.0, 700.0, 458.0, 724.0, 702.0, 197.0, 817.0, 113.0, 334.0 ] ], "demands": [ 31.0, 14.0, 40.0, 26.0, 22.0, 37.0, 19.0, 10.0, 37.0 ], "objective": 2947.0 }, "solution": { "open_facilities": [ 0, 2, 3 ], "assignments": [ 0, 0, 2, 2, 2, 3, 0, 3, 0 ] }, "obj": 2947.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 4, "num_customers": 9, "facilities": [ { "id": "F1", "opening_cost": 296.0, "capacity": 504.0 }, { "id": "F2", "opening_cost": 310.0, "capacity": 580.0 }, { "id": "F3", "opening_cost": 329.0, "capacity": 456.0 }, { "id": "F4", "opening_cost": 179.0, "capacity": 549.0 } ], "customers": [ { "id": 0, "demand": 31.0 }, { "id": 1, "demand": 14.0 }, { "id": 2, "demand": 40.0 }, { "id": 3, "demand": 26.0 }, { "id": 4, "demand": 22.0 }, { "id": 5, "demand": 37.0 }, { "id": 6, "demand": 19.0 }, { "id": 7, "demand": 10.0 }, { "id": 8, "demand": 37.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 329.0 }, { "facility": "F1", "customer": 1, "cost": 376.0 }, { "facility": "F1", "customer": 2, "cost": 335.0 }, { "facility": "F1", "customer": 3, "cost": 337.0 }, { "facility": "F1", "customer": 4, "cost": 467.0 }, { "facility": "F1", "customer": 5, "cost": 243.0 }, { "facility": "F1", "customer": 6, "cost": 411.0 }, { "facility": "F1", "customer": 7, "cost": 364.0 }, { "facility": "F1", "customer": 8, "cost": 156.0 }, { "facility": "F2", "customer": 0, "cost": 564.0 }, { "facility": "F2", "customer": 1, "cost": 582.0 }, { "facility": "F2", "customer": 2, "cost": 294.0 }, { "facility": "F2", "customer": 3, "cost": 532.0 }, { "facility": "F2", "customer": 4, "cost": 524.0 }, { "facility": "F2", "customer": 5, "cost": 9.0 }, { "facility": "F2", "customer": 6, "cost": 651.0 }, { "facility": "F2", "customer": 7, "cost": 200.0 }, { "facility": "F2", "customer": 8, "cost": 141.0 }, { "facility": "F3", "customer": 0, "cost": 387.0 }, { "facility": "F3", "customer": 1, "cost": 643.0 }, { "facility": "F3", "customer": 2, "cost": 200.0 }, { "facility": "F3", "customer": 3, "cost": 237.0 }, { "facility": "F3", "customer": 4, "cost": 124.0 }, { "facility": "F3", "customer": 5, "cost": 425.0 }, { "facility": "F3", "customer": 6, "cost": 519.0 }, { "facility": "F3", "customer": 7, "cost": 626.0 }, { "facility": "F3", "customer": 8, "cost": 297.0 }, { "facility": "F4", "customer": 0, "cost": 742.0 }, { "facility": "F4", "customer": 1, "cost": 700.0 }, { "facility": "F4", "customer": 2, "cost": 458.0 }, { "facility": "F4", "customer": 3, "cost": 724.0 }, { "facility": "F4", "customer": 4, "cost": 702.0 }, { "facility": "F4", "customer": 5, "cost": 197.0 }, { "facility": "F4", "customer": 6, "cost": 817.0 }, { "facility": "F4", "customer": 7, "cost": 113.0 }, { "facility": "F4", "customer": 8, "cost": 334.0 } ], "objective": 2947.0 }, "solution_variant": { "selected": [ "F1", "F3", "F4" ], "assignments": [ "F1", "F1", "F3", "F3", "F3", "F4", "F1", "F4", "F1" ] }, "context_index": 11, "input_format": "markdown_table", "input_index_base": 0 }, { "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\nBelow are the 5 candidate trailers and the 12 events to consider.\nTrailer F1 has a deployment cost of 400.0 and a meal capacity of 1183.0.\nTrailer F2 has a deployment cost of 400.0 and a meal capacity of 907.0.\nTrailer F3 has a deployment cost of 400.0 and a meal capacity of 1362.0.\nTrailer F4 has a deployment cost of 400.0 and a meal capacity of 975.0.\nTrailer F5 has a deployment cost of 400.0 and a meal capacity of 1331.0.\nEvent 0 requires 40.0 meals and must be served entirely by a single deployed trailer.\nEvent 1 requires 22.0 meals and must be served entirely by a single deployed trailer.\nEvent 2 requires 28.0 meals and must be served entirely by a single deployed trailer.\nEvent 3 requires 33.0 meals and must be served entirely by a single deployed trailer.\nEvent 4 requires 25.0 meals and must be served entirely by a single deployed trailer.\nEvent 5 requires 11.0 meals and must be served entirely by a single deployed trailer.\nEvent 6 requires 39.0 meals and must be served entirely by a single deployed trailer.\nEvent 7 requires 12.0 meals and must be served entirely by a single deployed trailer.\nEvent 8 requires 42.0 meals and must be served entirely by a single deployed trailer.\nEvent 9 requires 27.0 meals and must be served entirely by a single deployed trailer.\nEvent 10 requires 13.0 meals and must be served entirely by a single deployed trailer.\nEvent 11 requires 13.0 meals and must be served entirely by a single deployed trailer.\nIf trailer F1 serves event 0, the delivery fee incurred is 580.0.\nIf trailer F1 serves event 1, the delivery fee incurred is 232.0.\nIf trailer F1 serves event 2, the delivery fee incurred is 524.0.\nIf trailer F1 serves event 3, the delivery fee incurred is 400.0.\nIf trailer F1 serves event 4, the delivery fee incurred is 584.0.\nIf trailer F1 serves event 5, the delivery fee incurred is 286.0.\nIf trailer F1 serves event 6, the delivery fee incurred is 719.0.\nIf trailer F1 serves event 7, the delivery fee incurred is 231.0.\nIf trailer F1 serves event 8, the delivery fee incurred is 579.0.\nIf trailer F1 serves event 9, the delivery fee incurred is 156.0.\nIf trailer F1 serves event 10, the delivery fee incurred is 175.0.\nIf trailer F1 serves event 11, the delivery fee incurred is 451.0.\nIf trailer F2 serves event 0, the delivery fee incurred is 579.0.\nIf trailer F2 serves event 1, the delivery fee incurred is 320.0.\nIf trailer F2 serves event 2, the delivery fee incurred is 458.0.\nIf trailer F2 serves event 3, the delivery fee incurred is 99.0.\nIf trailer F2 serves event 4, the delivery fee incurred is 620.0.\nIf trailer F2 serves event 5, the delivery fee incurred is 409.0.\nIf trailer F2 serves event 6, the delivery fee incurred is 453.0.\nIf trailer F2 serves event 7, the delivery fee incurred is 100.0.\nIf trailer F2 serves event 8, the delivery fee incurred is 294.0.\nIf trailer F2 serves event 9, the delivery fee incurred is 208.0.\nIf trailer F2 serves event 10, the delivery fee incurred is 420.0.\nIf trailer F2 serves event 11, the delivery fee incurred is 362.0.\nIf trailer F3 serves event 0, the delivery fee incurred is 544.0.\nIf trailer F3 serves event 1, the delivery fee incurred is 230.0.\nIf trailer F3 serves event 2, the delivery fee incurred is 447.0.\nIf trailer F3 serves event 3, the delivery fee incurred is 220.0.\nIf trailer F3 serves event 4, the delivery fee incurred is 572.0.\nIf trailer F3 serves event 5, the delivery fee incurred is 318.0.\nIf trailer F3 serves event 6, the delivery fee incurred is 547.0.\nIf trailer F3 serves event 7, the delivery fee incurred is 50.0.\nIf trailer F3 serves event 8, the delivery fee incurred is 399.0.\nIf trailer F3 serves event 9, the delivery fee incurred is 97.0.\nIf trailer F3 serves event 10, the delivery fee incurred is 298.0.\nIf trailer F3 serves event 11, the delivery fee incurred is 356.0.\nIf trailer F4 serves event 0, the delivery fee incurred is 708.0.\nIf trailer F4 serves event 1, the delivery fee incurred is 506.0.\nIf trailer F4 serves event 2, the delivery fee incurred is 572.0.\nIf trailer F4 serves event 3, the delivery fee incurred is 106.0.\nIf trailer F4 serves event 4, the delivery fee incurred is 761.0.\nIf trailer F4 serves event 5, the delivery fee incurred is 593.0.\nIf trailer F4 serves event 6, the delivery fee incurred is 396.0.\nIf trailer F4 serves event 7, the delivery fee incurred is 296.0.\nIf trailer F4 serves event 8, the delivery fee incurred is 244.0.\nIf trailer F4 serves event 9, the delivery fee incurred is 404.0.\nIf trailer F4 serves event 10, the delivery fee incurred is 616.0.\nIf trailer F4 serves event 11, the delivery fee incurred is 480.0.\nIf trailer F5 serves event 0, the delivery fee incurred is 510.0.\nIf trailer F5 serves event 1, the delivery fee incurred is 423.0.\nIf trailer F5 serves event 2, the delivery fee incurred is 367.0.\nIf trailer F5 serves event 3, the delivery fee incurred is 260.0.\nIf trailer F5 serves event 4, the delivery fee incurred is 573.0.\nIf trailer F5 serves event 5, the delivery fee incurred is 491.0.\nIf trailer F5 serves event 6, the delivery fee incurred is 195.0.\nIf trailer F5 serves event 7, the delivery fee incurred is 306.0.\nIf trailer F5 serves event 8, the delivery fee incurred is 51.0.\nIf trailer F5 serves event 9, the delivery fee incurred is 384.0.\nIf trailer F5 serves event 10, the delivery fee incurred is 575.0.\nIf trailer F5 serves event 11, the delivery fee incurred is 291.0.\nUse these entries to choose which trailers to deploy and which trailer will serve each event so all demands are met without exceeding capacities at minimum total cost.\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": [ 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 1183.0, 907.0, 1362.0, 975.0, 1331.0 ], "connection_costs": [ [ 580.0, 232.0, 524.0, 400.0, 584.0, 286.0, 719.0, 231.0, 579.0, 156.0, 175.0, 451.0 ], [ 579.0, 320.0, 458.0, 99.0, 620.0, 409.0, 453.0, 100.0, 294.0, 208.0, 420.0, 362.0 ], [ 544.0, 230.0, 447.0, 220.0, 572.0, 318.0, 547.0, 50.0, 399.0, 97.0, 298.0, 356.0 ], [ 708.0, 506.0, 572.0, 106.0, 761.0, 593.0, 396.0, 296.0, 244.0, 404.0, 616.0, 480.0 ], [ 510.0, 423.0, 367.0, 260.0, 573.0, 491.0, 195.0, 306.0, 51.0, 384.0, 575.0, 291.0 ] ], "demands": [ 40.0, 22.0, 28.0, 33.0, 25.0, 11.0, 39.0, 12.0, 42.0, 27.0, 13.0, 13.0 ], "objective": 3999.0 }, "solution": { "open_facilities": [ 2, 4 ], "assignments": [ 4, 2, 4, 2, 2, 2, 4, 2, 4, 2, 2, 4 ] }, "obj": 3999.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 12, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 1183.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 907.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 1362.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 975.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 1331.0 } ], "customers": [ { "id": 0, "demand": 40.0 }, { "id": 1, "demand": 22.0 }, { "id": 2, "demand": 28.0 }, { "id": 3, "demand": 33.0 }, { "id": 4, "demand": 25.0 }, { "id": 5, "demand": 11.0 }, { "id": 6, "demand": 39.0 }, { "id": 7, "demand": 12.0 }, { "id": 8, "demand": 42.0 }, { "id": 9, "demand": 27.0 }, { "id": 10, "demand": 13.0 }, { "id": 11, "demand": 13.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 580.0 }, { "facility": "F1", "customer": 1, "cost": 232.0 }, { "facility": "F1", "customer": 2, "cost": 524.0 }, { "facility": "F1", "customer": 3, "cost": 400.0 }, { "facility": "F1", "customer": 4, "cost": 584.0 }, { "facility": "F1", "customer": 5, "cost": 286.0 }, { "facility": "F1", "customer": 6, "cost": 719.0 }, { "facility": "F1", "customer": 7, "cost": 231.0 }, { "facility": "F1", "customer": 8, "cost": 579.0 }, { "facility": "F1", "customer": 9, "cost": 156.0 }, { "facility": "F1", "customer": 10, "cost": 175.0 }, { "facility": "F1", "customer": 11, "cost": 451.0 }, { "facility": "F2", "customer": 0, "cost": 579.0 }, { "facility": "F2", "customer": 1, "cost": 320.0 }, { "facility": "F2", "customer": 2, "cost": 458.0 }, { "facility": "F2", "customer": 3, "cost": 99.0 }, { "facility": "F2", "customer": 4, "cost": 620.0 }, { "facility": "F2", "customer": 5, "cost": 409.0 }, { "facility": "F2", "customer": 6, "cost": 453.0 }, { "facility": "F2", "customer": 7, "cost": 100.0 }, { "facility": "F2", "customer": 8, "cost": 294.0 }, { "facility": "F2", "customer": 9, "cost": 208.0 }, { "facility": "F2", "customer": 10, "cost": 420.0 }, { "facility": "F2", "customer": 11, "cost": 362.0 }, { "facility": "F3", "customer": 0, "cost": 544.0 }, { "facility": "F3", "customer": 1, "cost": 230.0 }, { "facility": "F3", "customer": 2, "cost": 447.0 }, { "facility": "F3", "customer": 3, "cost": 220.0 }, { "facility": "F3", "customer": 4, "cost": 572.0 }, { "facility": "F3", "customer": 5, "cost": 318.0 }, { "facility": "F3", "customer": 6, "cost": 547.0 }, { "facility": "F3", "customer": 7, "cost": 50.0 }, { "facility": "F3", "customer": 8, "cost": 399.0 }, { "facility": "F3", "customer": 9, "cost": 97.0 }, { "facility": "F3", "customer": 10, "cost": 298.0 }, { "facility": "F3", "customer": 11, "cost": 356.0 }, { "facility": "F4", "customer": 0, "cost": 708.0 }, { "facility": "F4", "customer": 1, "cost": 506.0 }, { "facility": "F4", "customer": 2, "cost": 572.0 }, { "facility": "F4", "customer": 3, "cost": 106.0 }, { "facility": "F4", "customer": 4, "cost": 761.0 }, { "facility": "F4", "customer": 5, "cost": 593.0 }, { "facility": "F4", "customer": 6, "cost": 396.0 }, { "facility": "F4", "customer": 7, "cost": 296.0 }, { "facility": "F4", "customer": 8, "cost": 244.0 }, { "facility": "F4", "customer": 9, "cost": 404.0 }, { "facility": "F4", "customer": 10, "cost": 616.0 }, { "facility": "F4", "customer": 11, "cost": 480.0 }, { "facility": "F5", "customer": 0, "cost": 510.0 }, { "facility": "F5", "customer": 1, "cost": 423.0 }, { "facility": "F5", "customer": 2, "cost": 367.0 }, { "facility": "F5", "customer": 3, "cost": 260.0 }, { "facility": "F5", "customer": 4, "cost": 573.0 }, { "facility": "F5", "customer": 5, "cost": 491.0 }, { "facility": "F5", "customer": 6, "cost": 195.0 }, { "facility": "F5", "customer": 7, "cost": 306.0 }, { "facility": "F5", "customer": 8, "cost": 51.0 }, { "facility": "F5", "customer": 9, "cost": 384.0 }, { "facility": "F5", "customer": 10, "cost": 575.0 }, { "facility": "F5", "customer": 11, "cost": 291.0 } ], "objective": 3999.0 }, "solution_variant": { "selected": [ "F3", "F5" ], "assignments": [ "F5", "F3", "F5", "F3", "F3", "F3", "F5", "F3", "F5", "F3", "F3", "F5" ] }, "context_index": 12, "input_format": "nl", "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=5\n# num_commuter_zones=11\n# HUBS\nhub_id,activation_cost,dock_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\n# ZONES\nzone_id,rider_demand\n1,24.0\n2,28.0\n3,12.0\n4,23.0\n5,29.0\n6,19.0\n7,23.0\n8,20.0\n9,27.0\n10,23.0\n11,27.0\n# REDISTRIBUTIONS\nhub_id,zone_id,redistribution_cost\nF1,1,267.0\nF1,2,392.0\nF1,3,660.0\nF1,4,315.0\nF1,5,391.0\nF1,6,1285.0\nF1,7,621.0\nF1,8,536.0\nF1,9,64.0\nF1,10,310.0\nF1,11,800.0\nF2,1,508.0\nF2,2,312.0\nF2,3,1016.0\nF2,4,339.0\nF2,5,667.0\nF2,6,1349.0\nF2,7,946.0\nF2,8,150.0\nF2,9,70.0\nF2,10,147.0\nF2,11,1157.0\nF3,1,102.0\nF3,2,409.0\nF3,3,131.0\nF3,4,336.0\nF3,5,155.0\nF3,6,765.0\nF3,7,236.0\nF3,8,631.0\nF3,9,104.0\nF3,10,382.0\nF3,11,166.0\nF4,1,48.0\nF4,2,769.0\nF4,3,55.0\nF4,4,689.0\nF4,5,61.0\nF4,6,1278.0\nF4,7,62.0\nF4,8,906.0\nF4,9,186.0\nF4,10,703.0\nF4,11,149.0\nF5,1,403.0\nF5,2,498.0\nF5,3,936.0\nF5,4,459.0\nF5,5,558.0\nF5,6,1542.0\nF5,7,839.0\nF5,8,471.0\nF5,9,54.0\nF5,10,323.0\nF5,11,1094.0\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": [ 300.0, 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 267.0, 392.0, 660.0, 315.0, 391.0, 1285.0, 621.0, 536.0, 64.0, 310.0, 800.0 ], [ 508.0, 312.0, 1016.0, 339.0, 667.0, 1349.0, 946.0, 150.0, 70.0, 147.0, 1157.0 ], [ 102.0, 409.0, 131.0, 336.0, 155.0, 765.0, 236.0, 631.0, 104.0, 382.0, 166.0 ], [ 48.0, 769.0, 55.0, 689.0, 61.0, 1278.0, 62.0, 906.0, 186.0, 703.0, 149.0 ], [ 403.0, 498.0, 936.0, 459.0, 558.0, 1542.0, 839.0, 471.0, 54.0, 323.0, 1094.0 ] ], "demands": [ 24.0, 28.0, 12.0, 23.0, 29.0, 19.0, 23.0, 20.0, 27.0, 23.0, 27.0 ], "objective": 3055.0 }, "solution": { "open_facilities": [ 1, 2, 3 ], "assignments": [ 3, 1, 3, 2, 3, 2, 3, 1, 1, 1, 3 ] }, "obj": 3055.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 11, "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 } ], "customers": [ { "id": 1, "demand": 24.0 }, { "id": 2, "demand": 28.0 }, { "id": 3, "demand": 12.0 }, { "id": 4, "demand": 23.0 }, { "id": 5, "demand": 29.0 }, { "id": 6, "demand": 19.0 }, { "id": 7, "demand": 23.0 }, { "id": 8, "demand": 20.0 }, { "id": 9, "demand": 27.0 }, { "id": 10, "demand": 23.0 }, { "id": 11, "demand": 27.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 267.0 }, { "facility": "F1", "customer": 2, "cost": 392.0 }, { "facility": "F1", "customer": 3, "cost": 660.0 }, { "facility": "F1", "customer": 4, "cost": 315.0 }, { "facility": "F1", "customer": 5, "cost": 391.0 }, { "facility": "F1", "customer": 6, "cost": 1285.0 }, { "facility": "F1", "customer": 7, "cost": 621.0 }, { "facility": "F1", "customer": 8, "cost": 536.0 }, { "facility": "F1", "customer": 9, "cost": 64.0 }, { "facility": "F1", "customer": 10, "cost": 310.0 }, { "facility": "F1", "customer": 11, "cost": 800.0 }, { "facility": "F2", "customer": 1, "cost": 508.0 }, { "facility": "F2", "customer": 2, "cost": 312.0 }, { "facility": "F2", "customer": 3, "cost": 1016.0 }, { "facility": "F2", "customer": 4, "cost": 339.0 }, { "facility": "F2", "customer": 5, "cost": 667.0 }, { "facility": "F2", "customer": 6, "cost": 1349.0 }, { "facility": "F2", "customer": 7, "cost": 946.0 }, { "facility": "F2", "customer": 8, "cost": 150.0 }, { "facility": "F2", "customer": 9, "cost": 70.0 }, { "facility": "F2", "customer": 10, "cost": 147.0 }, { "facility": "F2", "customer": 11, "cost": 1157.0 }, { "facility": "F3", "customer": 1, "cost": 102.0 }, { "facility": "F3", "customer": 2, "cost": 409.0 }, { "facility": "F3", "customer": 3, "cost": 131.0 }, { "facility": "F3", "customer": 4, "cost": 336.0 }, { "facility": "F3", "customer": 5, "cost": 155.0 }, { "facility": "F3", "customer": 6, "cost": 765.0 }, { "facility": "F3", "customer": 7, "cost": 236.0 }, { "facility": "F3", "customer": 8, "cost": 631.0 }, { "facility": "F3", "customer": 9, "cost": 104.0 }, { "facility": "F3", "customer": 10, "cost": 382.0 }, { "facility": "F3", "customer": 11, "cost": 166.0 }, { "facility": "F4", "customer": 1, "cost": 48.0 }, { "facility": "F4", "customer": 2, "cost": 769.0 }, { "facility": "F4", "customer": 3, "cost": 55.0 }, { "facility": "F4", "customer": 4, "cost": 689.0 }, { "facility": "F4", "customer": 5, "cost": 61.0 }, { "facility": "F4", "customer": 6, "cost": 1278.0 }, { "facility": "F4", "customer": 7, "cost": 62.0 }, { "facility": "F4", "customer": 8, "cost": 906.0 }, { "facility": "F4", "customer": 9, "cost": 186.0 }, { "facility": "F4", "customer": 10, "cost": 703.0 }, { "facility": "F4", "customer": 11, "cost": 149.0 }, { "facility": "F5", "customer": 1, "cost": 403.0 }, { "facility": "F5", "customer": 2, "cost": 498.0 }, { "facility": "F5", "customer": 3, "cost": 936.0 }, { "facility": "F5", "customer": 4, "cost": 459.0 }, { "facility": "F5", "customer": 5, "cost": 558.0 }, { "facility": "F5", "customer": 6, "cost": 1542.0 }, { "facility": "F5", "customer": 7, "cost": 839.0 }, { "facility": "F5", "customer": 8, "cost": 471.0 }, { "facility": "F5", "customer": 9, "cost": 54.0 }, { "facility": "F5", "customer": 10, "cost": 323.0 }, { "facility": "F5", "customer": 11, "cost": 1094.0 } ], "objective": 3055.0 }, "solution_variant": { "selected": [ "F2", "F3", "F4" ], "assignments": [ "F4", "F2", "F4", "F3", "F4", "F3", "F4", "F2", "F2", "F2", "F4" ] }, "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{\n \"num_packing_facilities\": 4,\n \"num_farms\": 11,\n \"packing_facilitys\": [\n {\n \"packing_facility_id\": \"F1\",\n \"facility_opening_cost\": 600.0,\n \"throughput_capacity\": 500.0\n },\n {\n \"packing_facility_id\": \"F2\",\n \"facility_opening_cost\": 600.0,\n \"throughput_capacity\": 500.0\n },\n {\n \"packing_facility_id\": \"F3\",\n \"facility_opening_cost\": 600.0,\n \"throughput_capacity\": 500.0\n },\n {\n \"packing_facility_id\": \"F4\",\n \"facility_opening_cost\": 600.0,\n \"throughput_capacity\": 500.0\n }\n ],\n \"farms\": [\n {\n \"farm_id\": 1,\n \"farm_production\": 11.0\n },\n {\n \"farm_id\": 2,\n \"farm_production\": 28.0\n },\n {\n \"farm_id\": 3,\n \"farm_production\": 44.0\n },\n {\n \"farm_id\": 4,\n \"farm_production\": 45.0\n },\n {\n \"farm_id\": 5,\n \"farm_production\": 41.0\n },\n {\n \"farm_id\": 6,\n \"farm_production\": 27.0\n },\n {\n \"farm_id\": 7,\n \"farm_production\": 33.0\n },\n {\n \"farm_id\": 8,\n \"farm_production\": 14.0\n },\n {\n \"farm_id\": 9,\n \"farm_production\": 49.0\n },\n {\n \"farm_id\": 10,\n \"farm_production\": 45.0\n },\n {\n \"farm_id\": 11,\n \"farm_production\": 18.0\n }\n ],\n \"transports\": [\n {\n \"packing_facility_id\": \"F1\",\n \"farm_id\": 1,\n \"transport_cost\": 182.0\n },\n {\n \"packing_facility_id\": \"F1\",\n \"farm_id\": 2,\n \"transport_cost\": 245.0\n },\n {\n \"packing_facility_id\": \"F1\",\n \"farm_id\": 3,\n \"transport_cost\": 94.0\n },\n {\n \"packing_facility_id\": \"F1\",\n \"farm_id\": 4,\n \"transport_cost\": 387.0\n },\n {\n \"packing_facility_id\": \"F1\",\n \"farm_id\": 5,\n \"transport_cost\": 365.0\n },\n {\n \"packing_facility_id\": \"F1\",\n \"farm_id\": 6,\n \"transport_cost\": 208.0\n },\n {\n \"packing_facility_id\": \"F1\",\n \"farm_id\": 7,\n \"transport_cost\": 413.0\n },\n {\n \"packing_facility_id\": \"F1\",\n \"farm_id\": 8,\n \"transport_cost\": 88.0\n },\n {\n \"packing_facility_id\": \"F1\",\n \"farm_id\": 9,\n \"transport_cost\": 567.0\n },\n {\n \"packing_facility_id\": \"F1\",\n \"farm_id\": 10,\n \"transport_cost\": 116.0\n },\n {\n \"packing_facility_id\": \"F1\",\n \"farm_id\": 11,\n \"transport_cost\": 63.0\n },\n {\n \"packing_facility_id\": \"F2\",\n \"farm_id\": 1,\n \"transport_cost\": 514.0\n },\n {\n \"packing_facility_id\": \"F2\",\n \"farm_id\": 2,\n \"transport_cost\": 627.0\n },\n {\n \"packing_facility_id\": \"F2\",\n \"farm_id\": 3,\n \"transport_cost\": 555.0\n },\n {\n \"packing_facility_id\": \"F2\",\n \"farm_id\": 4,\n \"transport_cost\": 231.0\n },\n {\n \"packing_facility_id\": \"F2\",\n \"farm_id\": 5,\n \"transport_cost\": 628.0\n },\n {\n \"packing_facility_id\": \"F2\",\n \"farm_id\": 6,\n \"transport_cost\": 532.0\n },\n {\n \"packing_facility_id\": \"F2\",\n \"farm_id\": 7,\n \"transport_cost\": 281.0\n },\n {\n \"packing_facility_id\": \"F2\",\n \"farm_id\": 8,\n \"transport_cost\": 568.0\n },\n {\n \"packing_facility_id\": \"F2\",\n \"farm_id\": 9,\n \"transport_cost\": 560.0\n },\n {\n \"packing_facility_id\": \"F2\",\n \"farm_id\": 10,\n \"transport_cost\": 722.0\n },\n {\n \"packing_facility_id\": \"F2\",\n \"farm_id\": 11,\n \"transport_cost\": 615.0\n },\n {\n \"packing_facility_id\": \"F3\",\n \"farm_id\": 1,\n \"transport_cost\": 542.0\n },\n {\n \"packing_facility_id\": \"F3\",\n \"farm_id\": 2,\n \"transport_cost\": 161.0\n },\n {\n \"packing_facility_id\": \"F3\",\n \"farm_id\": 3,\n \"transport_cost\": 326.0\n },\n {\n \"packing_facility_id\": \"F3\",\n \"farm_id\": 4,\n \"transport_cost\": 549.0\n },\n {\n \"packing_facility_id\": \"F3\",\n \"farm_id\": 5,\n \"transport_cost\": 49.0\n },\n {\n \"packing_facility_id\": \"F3\",\n \"farm_id\": 6,\n \"transport_cost\": 224.0\n },\n {\n \"packing_facility_id\": \"F3\",\n \"farm_id\": 7,\n \"transport_cost\": 641.0\n },\n {\n \"packing_facility_id\": \"F3\",\n \"farm_id\": 8,\n \"transport_cost\": 475.0\n },\n {\n \"packing_facility_id\": \"F3\",\n \"farm_id\": 9,\n \"transport_cost\": 251.0\n },\n {\n \"packing_facility_id\": \"F3\",\n \"farm_id\": 10,\n \"transport_cost\": 417.0\n },\n {\n \"packing_facility_id\": \"F3\",\n \"farm_id\": 11,\n \"transport_cost\": 468.0\n },\n {\n \"packing_facility_id\": \"F4\",\n \"farm_id\": 1,\n \"transport_cost\": 442.0\n },\n {\n \"packing_facility_id\": \"F4\",\n \"farm_id\": 2,\n \"transport_cost\": 456.0\n },\n {\n \"packing_facility_id\": \"F4\",\n \"farm_id\": 3,\n \"transport_cost\": 413.0\n },\n {\n \"packing_facility_id\": \"F4\",\n \"farm_id\": 4,\n \"transport_cost\": 194.0\n },\n {\n \"packing_facility_id\": \"F4\",\n \"farm_id\": 5,\n \"transport_cost\": 445.0\n },\n {\n \"packing_facility_id\": \"F4\",\n \"farm_id\": 6,\n \"transport_cost\": 366.0\n },\n {\n \"packing_facility_id\": \"F4\",\n \"farm_id\": 7,\n \"transport_cost\": 298.0\n },\n {\n \"packing_facility_id\": \"F4\",\n \"farm_id\": 8,\n \"transport_cost\": 467.0\n },\n {\n \"packing_facility_id\": \"F4\",\n \"farm_id\": 9,\n \"transport_cost\": 387.0\n },\n {\n \"packing_facility_id\": \"F4\",\n \"farm_id\": 10,\n \"transport_cost\": 591.0\n },\n {\n \"packing_facility_id\": \"F4\",\n \"farm_id\": 11,\n \"transport_cost\": 508.0\n }\n ]\n}\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": [ 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 182.0, 245.0, 94.0, 387.0, 365.0, 208.0, 413.0, 88.0, 567.0, 116.0, 63.0 ], [ 514.0, 627.0, 555.0, 231.0, 628.0, 532.0, 281.0, 568.0, 560.0, 722.0, 615.0 ], [ 542.0, 161.0, 326.0, 549.0, 49.0, 224.0, 641.0, 475.0, 251.0, 417.0, 468.0 ], [ 442.0, 456.0, 413.0, 194.0, 445.0, 366.0, 298.0, 467.0, 387.0, 591.0, 508.0 ] ], "demands": [ 11.0, 28.0, 44.0, 45.0, 41.0, 27.0, 33.0, 14.0, 49.0, 45.0, 18.0 ], "objective": 3212.0 }, "solution": { "open_facilities": [ 0, 2 ], "assignments": [ 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0 ] }, "obj": 3212.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 4, "num_customers": 11, "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 } ], "customers": [ { "id": 1, "demand": 11.0 }, { "id": 2, "demand": 28.0 }, { "id": 3, "demand": 44.0 }, { "id": 4, "demand": 45.0 }, { "id": 5, "demand": 41.0 }, { "id": 6, "demand": 27.0 }, { "id": 7, "demand": 33.0 }, { "id": 8, "demand": 14.0 }, { "id": 9, "demand": 49.0 }, { "id": 10, "demand": 45.0 }, { "id": 11, "demand": 18.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 182.0 }, { "facility": "F1", "customer": 2, "cost": 245.0 }, { "facility": "F1", "customer": 3, "cost": 94.0 }, { "facility": "F1", "customer": 4, "cost": 387.0 }, { "facility": "F1", "customer": 5, "cost": 365.0 }, { "facility": "F1", "customer": 6, "cost": 208.0 }, { "facility": "F1", "customer": 7, "cost": 413.0 }, { "facility": "F1", "customer": 8, "cost": 88.0 }, { "facility": "F1", "customer": 9, "cost": 567.0 }, { "facility": "F1", "customer": 10, "cost": 116.0 }, { "facility": "F1", "customer": 11, "cost": 63.0 }, { "facility": "F2", "customer": 1, "cost": 514.0 }, { "facility": "F2", "customer": 2, "cost": 627.0 }, { "facility": "F2", "customer": 3, "cost": 555.0 }, { "facility": "F2", "customer": 4, "cost": 231.0 }, { "facility": "F2", "customer": 5, "cost": 628.0 }, { "facility": "F2", "customer": 6, "cost": 532.0 }, { "facility": "F2", "customer": 7, "cost": 281.0 }, { "facility": "F2", "customer": 8, "cost": 568.0 }, { "facility": "F2", "customer": 9, "cost": 560.0 }, { "facility": "F2", "customer": 10, "cost": 722.0 }, { "facility": "F2", "customer": 11, "cost": 615.0 }, { "facility": "F3", "customer": 1, "cost": 542.0 }, { "facility": "F3", "customer": 2, "cost": 161.0 }, { "facility": "F3", "customer": 3, "cost": 326.0 }, { "facility": "F3", "customer": 4, "cost": 549.0 }, { "facility": "F3", "customer": 5, "cost": 49.0 }, { "facility": "F3", "customer": 6, "cost": 224.0 }, { "facility": "F3", "customer": 7, "cost": 641.0 }, { "facility": "F3", "customer": 8, "cost": 475.0 }, { "facility": "F3", "customer": 9, "cost": 251.0 }, { "facility": "F3", "customer": 10, "cost": 417.0 }, { "facility": "F3", "customer": 11, "cost": 468.0 }, { "facility": "F4", "customer": 1, "cost": 442.0 }, { "facility": "F4", "customer": 2, "cost": 456.0 }, { "facility": "F4", "customer": 3, "cost": 413.0 }, { "facility": "F4", "customer": 4, "cost": 194.0 }, { "facility": "F4", "customer": 5, "cost": 445.0 }, { "facility": "F4", "customer": 6, "cost": 366.0 }, { "facility": "F4", "customer": 7, "cost": 298.0 }, { "facility": "F4", "customer": 8, "cost": 467.0 }, { "facility": "F4", "customer": 9, "cost": 387.0 }, { "facility": "F4", "customer": 10, "cost": 591.0 }, { "facility": "F4", "customer": 11, "cost": 508.0 } ], "objective": 3212.0 }, "solution_variant": { "selected": [ "F1", "F3" ], "assignments": [ "F1", "F3", "F1", "F1", "F3", "F1", "F1", "F1", "F3", "F1", "F1" ] }, "context_index": 14, "input_format": "json", "input_index_base": 1 }, { "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 14 makers in this instance.\n\n**Booths**\n| booth_id | booth_rental_fee | booth_space_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**Makers**\n| maker_id | maker_space_requirement |\n|---|---|\n| 0 | 30.0 |\n| 1 | 49.0 |\n| 2 | 36.0 |\n| 3 | 39.0 |\n| 4 | 34.0 |\n| 5 | 48.0 |\n| 6 | 37.0 |\n| 7 | 45.0 |\n| 8 | 20.0 |\n| 9 | 35.0 |\n| 10 | 22.0 |\n| 11 | 45.0 |\n| 12 | 42.0 |\n| 13 | 13.0 |\n\n**Setup Transfer Cost**\n| booth_id | maker_id | setup_transfer_cost |\n|---|---|---|\n| F1 | 0 | 128.0 |\n| F1 | 1 | 480.0 |\n| F1 | 2 | 569.0 |\n| F1 | 3 | 93.0 |\n| F1 | 4 | 359.0 |\n| F1 | 5 | 735.0 |\n| F1 | 6 | 502.0 |\n| F1 | 7 | 341.0 |\n| F1 | 8 | 653.0 |\n| F1 | 9 | 373.0 |\n| F1 | 10 | 117.0 |\n| F1 | 11 | 200.0 |\n| F1 | 12 | 404.0 |\n| F1 | 13 | 500.0 |\n| F2 | 0 | 581.0 |\n| F2 | 1 | 586.0 |\n| F2 | 2 | 696.0 |\n| F2 | 3 | 432.0 |\n| F2 | 4 | 255.0 |\n| F2 | 5 | 377.0 |\n| F2 | 6 | 142.0 |\n| F2 | 7 | 555.0 |\n| F2 | 8 | 751.0 |\n| F2 | 9 | 393.0 |\n| F2 | 10 | 400.0 |\n| F2 | 11 | 403.0 |\n| F2 | 12 | 564.0 |\n| F2 | 13 | 224.0 |\n| F3 | 0 | 263.0 |\n| F3 | 1 | 479.0 |\n| F3 | 2 | 586.0 |\n| F3 | 3 | 104.0 |\n| F3 | 4 | 239.0 |\n| F3 | 5 | 605.0 |\n| F3 | 6 | 351.0 |\n| F3 | 7 | 369.0 |\n| F3 | 8 | 665.0 |\n| F3 | 9 | 314.0 |\n| F3 | 10 | 57.0 |\n| F3 | 11 | 168.0 |\n| F3 | 12 | 416.0 |\n| F3 | 13 | 368.0 |\n| F4 | 0 | 364.0 |\n| F4 | 1 | 235.0 |\n| F4 | 2 | 347.0 |\n| F4 | 3 | 297.0 |\n| F4 | 4 | 106.0 |\n| F4 | 5 | 375.0 |\n| F4 | 6 | 236.0 |\n| F4 | 7 | 220.0 |\n| F4 | 8 | 410.0 |\n| F4 | 9 | 43.0 |\n| F4 | 10 | 312.0 |\n| F4 | 11 | 184.0 |\n| F4 | 12 | 215.0 |\n| F4 | 13 | 178.0 |\n| F5 | 0 | 153.0 |\n| F5 | 1 | 281.0 |\n| F5 | 2 | 377.0 |\n| F5 | 3 | 145.0 |\n| F5 | 4 | 236.0 |\n| F5 | 5 | 585.0 |\n| F5 | 6 | 400.0 |\n| F5 | 7 | 151.0 |\n| F5 | 8 | 460.0 |\n| F5 | 9 | 187.0 |\n| F5 | 10 | 189.0 |\n| F5 | 11 | 68.0 |\n| F5 | 12 | 208.0 |\n| F5 | 13 | 369.0 |\n| F6 | 0 | 533.0 |\n| F6 | 1 | 196.0 |\n| F6 | 2 | 258.0 |\n| F6 | 3 | 505.0 |\n| F6 | 4 | 308.0 |\n| F6 | 5 | 321.0 |\n| F6 | 6 | 360.0 |\n| F6 | 7 | 305.0 |\n| F6 | 8 | 278.0 |\n| F6 | 9 | 214.0 |\n| F6 | 10 | 526.0 |\n| F6 | 11 | 387.0 |\n| F6 | 12 | 250.0 |\n| F6 | 13 | 278.0 |\n| F7 | 0 | 643.0 |\n| F7 | 1 | 676.0 |\n| F7 | 2 | 787.0 |\n| F7 | 3 | 487.0 |\n| F7 | 4 | 342.0 |\n| F7 | 5 | 445.0 |\n| F7 | 6 | 233.0 |\n| F7 | 7 | 639.0 |\n| F7 | 8 | 843.0 |\n| F7 | 9 | 482.0 |\n| F7 | 10 | 448.0 |\n| F7 | 11 | 475.0 |\n| F7 | 12 | 652.0 |\n| F7 | 13 | 315.0 |\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": [ 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": [ [ 128.0, 480.0, 569.0, 93.0, 359.0, 735.0, 502.0, 341.0, 653.0, 373.0, 117.0, 200.0, 404.0, 500.0 ], [ 581.0, 586.0, 696.0, 432.0, 255.0, 377.0, 142.0, 555.0, 751.0, 393.0, 400.0, 403.0, 564.0, 224.0 ], [ 263.0, 479.0, 586.0, 104.0, 239.0, 605.0, 351.0, 369.0, 665.0, 314.0, 57.0, 168.0, 416.0, 368.0 ], [ 364.0, 235.0, 347.0, 297.0, 106.0, 375.0, 236.0, 220.0, 410.0, 43.0, 312.0, 184.0, 215.0, 178.0 ], [ 153.0, 281.0, 377.0, 145.0, 236.0, 585.0, 400.0, 151.0, 460.0, 187.0, 189.0, 68.0, 208.0, 369.0 ], [ 533.0, 196.0, 258.0, 505.0, 308.0, 321.0, 360.0, 305.0, 278.0, 214.0, 526.0, 387.0, 250.0, 278.0 ], [ 643.0, 676.0, 787.0, 487.0, 342.0, 445.0, 233.0, 639.0, 843.0, 482.0, 448.0, 475.0, 652.0, 315.0 ] ], "demands": [ 30.0, 49.0, 36.0, 39.0, 34.0, 48.0, 37.0, 45.0, 20.0, 35.0, 22.0, 45.0, 42.0, 13.0 ], "objective": 4044.0 }, "solution": { "open_facilities": [ 3, 4 ], "assignments": [ 4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 4, 4, 4, 3 ] }, "obj": 4044.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 7, "num_customers": 14, "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": 0, "demand": 30.0 }, { "id": 1, "demand": 49.0 }, { "id": 2, "demand": 36.0 }, { "id": 3, "demand": 39.0 }, { "id": 4, "demand": 34.0 }, { "id": 5, "demand": 48.0 }, { "id": 6, "demand": 37.0 }, { "id": 7, "demand": 45.0 }, { "id": 8, "demand": 20.0 }, { "id": 9, "demand": 35.0 }, { "id": 10, "demand": 22.0 }, { "id": 11, "demand": 45.0 }, { "id": 12, "demand": 42.0 }, { "id": 13, "demand": 13.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 128.0 }, { "facility": "F1", "customer": 1, "cost": 480.0 }, { "facility": "F1", "customer": 2, "cost": 569.0 }, { "facility": "F1", "customer": 3, "cost": 93.0 }, { "facility": "F1", "customer": 4, "cost": 359.0 }, { "facility": "F1", "customer": 5, "cost": 735.0 }, { "facility": "F1", "customer": 6, "cost": 502.0 }, { "facility": "F1", "customer": 7, "cost": 341.0 }, { "facility": "F1", "customer": 8, "cost": 653.0 }, { "facility": "F1", "customer": 9, "cost": 373.0 }, { "facility": "F1", "customer": 10, "cost": 117.0 }, { "facility": "F1", "customer": 11, "cost": 200.0 }, { "facility": "F1", "customer": 12, "cost": 404.0 }, { "facility": "F1", "customer": 13, "cost": 500.0 }, { "facility": "F2", "customer": 0, "cost": 581.0 }, { "facility": "F2", "customer": 1, "cost": 586.0 }, { "facility": "F2", "customer": 2, "cost": 696.0 }, { "facility": "F2", "customer": 3, "cost": 432.0 }, { "facility": "F2", "customer": 4, "cost": 255.0 }, { "facility": "F2", "customer": 5, "cost": 377.0 }, { "facility": "F2", "customer": 6, "cost": 142.0 }, { "facility": "F2", "customer": 7, "cost": 555.0 }, { "facility": "F2", "customer": 8, "cost": 751.0 }, { "facility": "F2", "customer": 9, "cost": 393.0 }, { "facility": "F2", "customer": 10, "cost": 400.0 }, { "facility": "F2", "customer": 11, "cost": 403.0 }, { "facility": "F2", "customer": 12, "cost": 564.0 }, { "facility": "F2", "customer": 13, "cost": 224.0 }, { "facility": "F3", "customer": 0, "cost": 263.0 }, { "facility": "F3", "customer": 1, "cost": 479.0 }, { "facility": "F3", "customer": 2, "cost": 586.0 }, { "facility": "F3", "customer": 3, "cost": 104.0 }, { "facility": "F3", "customer": 4, "cost": 239.0 }, { "facility": "F3", "customer": 5, "cost": 605.0 }, { "facility": "F3", "customer": 6, "cost": 351.0 }, { "facility": "F3", "customer": 7, "cost": 369.0 }, { "facility": "F3", "customer": 8, "cost": 665.0 }, { "facility": "F3", "customer": 9, "cost": 314.0 }, { "facility": "F3", "customer": 10, "cost": 57.0 }, { "facility": "F3", "customer": 11, "cost": 168.0 }, { "facility": "F3", "customer": 12, "cost": 416.0 }, { "facility": "F3", "customer": 13, "cost": 368.0 }, { "facility": "F4", "customer": 0, "cost": 364.0 }, { "facility": "F4", "customer": 1, "cost": 235.0 }, { "facility": "F4", "customer": 2, "cost": 347.0 }, { "facility": "F4", "customer": 3, "cost": 297.0 }, { "facility": "F4", "customer": 4, "cost": 106.0 }, { "facility": "F4", "customer": 5, "cost": 375.0 }, { "facility": "F4", "customer": 6, "cost": 236.0 }, { "facility": "F4", "customer": 7, "cost": 220.0 }, { "facility": "F4", "customer": 8, "cost": 410.0 }, { "facility": "F4", "customer": 9, "cost": 43.0 }, { "facility": "F4", "customer": 10, "cost": 312.0 }, { "facility": "F4", "customer": 11, "cost": 184.0 }, { "facility": "F4", "customer": 12, "cost": 215.0 }, { "facility": "F4", "customer": 13, "cost": 178.0 }, { "facility": "F5", "customer": 0, "cost": 153.0 }, { "facility": "F5", "customer": 1, "cost": 281.0 }, { "facility": "F5", "customer": 2, "cost": 377.0 }, { "facility": "F5", "customer": 3, "cost": 145.0 }, { "facility": "F5", "customer": 4, "cost": 236.0 }, { "facility": "F5", "customer": 5, "cost": 585.0 }, { "facility": "F5", "customer": 6, "cost": 400.0 }, { "facility": "F5", "customer": 7, "cost": 151.0 }, { "facility": "F5", "customer": 8, "cost": 460.0 }, { "facility": "F5", "customer": 9, "cost": 187.0 }, { "facility": "F5", "customer": 10, "cost": 189.0 }, { "facility": "F5", "customer": 11, "cost": 68.0 }, { "facility": "F5", "customer": 12, "cost": 208.0 }, { "facility": "F5", "customer": 13, "cost": 369.0 }, { "facility": "F6", "customer": 0, "cost": 533.0 }, { "facility": "F6", "customer": 1, "cost": 196.0 }, { "facility": "F6", "customer": 2, "cost": 258.0 }, { "facility": "F6", "customer": 3, "cost": 505.0 }, { "facility": "F6", "customer": 4, "cost": 308.0 }, { "facility": "F6", "customer": 5, "cost": 321.0 }, { "facility": "F6", "customer": 6, "cost": 360.0 }, { "facility": "F6", "customer": 7, "cost": 305.0 }, { "facility": "F6", "customer": 8, "cost": 278.0 }, { "facility": "F6", "customer": 9, "cost": 214.0 }, { "facility": "F6", "customer": 10, "cost": 526.0 }, { "facility": "F6", "customer": 11, "cost": 387.0 }, { "facility": "F6", "customer": 12, "cost": 250.0 }, { "facility": "F6", "customer": 13, "cost": 278.0 }, { "facility": "F7", "customer": 0, "cost": 643.0 }, { "facility": "F7", "customer": 1, "cost": 676.0 }, { "facility": "F7", "customer": 2, "cost": 787.0 }, { "facility": "F7", "customer": 3, "cost": 487.0 }, { "facility": "F7", "customer": 4, "cost": 342.0 }, { "facility": "F7", "customer": 5, "cost": 445.0 }, { "facility": "F7", "customer": 6, "cost": 233.0 }, { "facility": "F7", "customer": 7, "cost": 639.0 }, { "facility": "F7", "customer": 8, "cost": 843.0 }, { "facility": "F7", "customer": 9, "cost": 482.0 }, { "facility": "F7", "customer": 10, "cost": 448.0 }, { "facility": "F7", "customer": 11, "cost": 475.0 }, { "facility": "F7", "customer": 12, "cost": 652.0 }, { "facility": "F7", "customer": 13, "cost": 315.0 } ], "objective": 4044.0 }, "solution_variant": { "selected": [ "F4", "F5" ], "assignments": [ "F5", "F4", "F4", "F5", "F4", "F4", "F4", "F5", "F4", "F4", "F5", "F5", "F5", "F4" ] }, "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{\n \"num_staging_areas\": 4,\n \"num_communities\": 9,\n \"staging_areas\": [\n {\n \"staging_area_id\": \"F1\",\n \"staffing_cost\": 400.0,\n \"staging_capacity\": 1500.0\n },\n {\n \"staging_area_id\": \"F2\",\n \"staffing_cost\": 400.0,\n \"staging_capacity\": 1500.0\n },\n {\n \"staging_area_id\": \"F3\",\n \"staffing_cost\": 400.0,\n \"staging_capacity\": 1500.0\n },\n {\n \"staging_area_id\": \"F4\",\n \"staffing_cost\": 400.0,\n \"staging_capacity\": 1500.0\n }\n ],\n \"communitys\": [\n {\n \"community_id\": 1,\n \"beneficiary_demand\": 14.0\n },\n {\n \"community_id\": 2,\n \"beneficiary_demand\": 11.0\n },\n {\n \"community_id\": 3,\n \"beneficiary_demand\": 34.0\n },\n {\n \"community_id\": 4,\n \"beneficiary_demand\": 26.0\n },\n {\n \"community_id\": 5,\n \"beneficiary_demand\": 33.0\n },\n {\n \"community_id\": 6,\n \"beneficiary_demand\": 49.0\n },\n {\n \"community_id\": 7,\n \"beneficiary_demand\": 18.0\n },\n {\n \"community_id\": 8,\n \"beneficiary_demand\": 42.0\n },\n {\n \"community_id\": 9,\n \"beneficiary_demand\": 17.0\n }\n ],\n \"distributions\": [\n {\n \"staging_area_id\": \"F1\",\n \"community_id\": 1,\n \"distribution_cost\": 265.0\n },\n {\n \"staging_area_id\": \"F1\",\n \"community_id\": 2,\n \"distribution_cost\": 413.0\n },\n {\n \"staging_area_id\": \"F1\",\n \"community_id\": 3,\n \"distribution_cost\": 206.0\n },\n {\n \"staging_area_id\": \"F1\",\n \"community_id\": 4,\n \"distribution_cost\": 364.0\n },\n {\n \"staging_area_id\": \"F1\",\n \"community_id\": 5,\n \"distribution_cost\": 258.0\n },\n {\n \"staging_area_id\": \"F1\",\n \"community_id\": 6,\n \"distribution_cost\": 106.0\n },\n {\n \"staging_area_id\": \"F1\",\n \"community_id\": 7,\n \"distribution_cost\": 207.0\n },\n {\n \"staging_area_id\": \"F1\",\n \"community_id\": 8,\n \"distribution_cost\": 178.0\n },\n {\n \"staging_area_id\": \"F1\",\n \"community_id\": 9,\n \"distribution_cost\": 257.0\n },\n {\n \"staging_area_id\": \"F2\",\n \"community_id\": 1,\n \"distribution_cost\": 504.0\n },\n {\n \"staging_area_id\": \"F2\",\n \"community_id\": 2,\n \"distribution_cost\": 367.0\n },\n {\n \"staging_area_id\": \"F2\",\n \"community_id\": 3,\n \"distribution_cost\": 382.0\n },\n {\n \"staging_area_id\": \"F2\",\n \"community_id\": 4,\n \"distribution_cost\": 644.0\n },\n {\n \"staging_area_id\": \"F2\",\n \"community_id\": 5,\n \"distribution_cost\": 599.0\n },\n {\n \"staging_area_id\": \"F2\",\n \"community_id\": 6,\n \"distribution_cost\": 389.0\n },\n {\n \"staging_area_id\": \"F2\",\n \"community_id\": 7,\n \"distribution_cost\": 225.0\n },\n {\n \"staging_area_id\": \"F2\",\n \"community_id\": 8,\n \"distribution_cost\": 405.0\n },\n {\n \"staging_area_id\": \"F2\",\n \"community_id\": 9,\n \"distribution_cost\": 336.0\n },\n {\n \"staging_area_id\": \"F3\",\n \"community_id\": 1,\n \"distribution_cost\": 617.0\n },\n {\n \"staging_area_id\": \"F3\",\n \"community_id\": 2,\n \"distribution_cost\": 94.0\n },\n {\n \"staging_area_id\": \"F3\",\n \"community_id\": 3,\n \"distribution_cost\": 239.0\n },\n {\n \"staging_area_id\": \"F3\",\n \"community_id\": 4,\n \"distribution_cost\": 482.0\n },\n {\n \"staging_area_id\": \"F3\",\n \"community_id\": 5,\n \"distribution_cost\": 625.0\n },\n {\n \"staging_area_id\": \"F3\",\n \"community_id\": 6,\n \"distribution_cost\": 460.0\n },\n {\n \"staging_area_id\": \"F3\",\n \"community_id\": 7,\n \"distribution_cost\": 391.0\n },\n {\n \"staging_area_id\": \"F3\",\n \"community_id\": 8,\n \"distribution_cost\": 514.0\n },\n {\n \"staging_area_id\": \"F3\",\n \"community_id\": 9,\n \"distribution_cost\": 512.0\n },\n {\n \"staging_area_id\": \"F4\",\n \"community_id\": 1,\n \"distribution_cost\": 453.0\n },\n {\n \"staging_area_id\": \"F4\",\n \"community_id\": 2,\n \"distribution_cost\": 229.0\n },\n {\n \"staging_area_id\": \"F4\",\n \"community_id\": 3,\n \"distribution_cost\": 166.0\n },\n {\n \"staging_area_id\": \"F4\",\n \"community_id\": 4,\n \"distribution_cost\": 429.0\n },\n {\n \"staging_area_id\": \"F4\",\n \"community_id\": 5,\n \"distribution_cost\": 473.0\n },\n {\n \"staging_area_id\": \"F4\",\n \"community_id\": 6,\n \"distribution_cost\": 297.0\n },\n {\n \"staging_area_id\": \"F4\",\n \"community_id\": 7,\n \"distribution_cost\": 241.0\n },\n {\n \"staging_area_id\": \"F4\",\n \"community_id\": 8,\n \"distribution_cost\": 350.0\n },\n {\n \"staging_area_id\": \"F4\",\n \"community_id\": 9,\n \"distribution_cost\": 356.0\n }\n ]\n}\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": [ 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 1500.0, 1500.0, 1500.0, 1500.0 ], "connection_costs": [ [ 265.0, 413.0, 206.0, 364.0, 258.0, 106.0, 207.0, 178.0, 257.0 ], [ 504.0, 367.0, 382.0, 644.0, 599.0, 389.0, 225.0, 405.0, 336.0 ], [ 617.0, 94.0, 239.0, 482.0, 625.0, 460.0, 391.0, 514.0, 512.0 ], [ 453.0, 229.0, 166.0, 429.0, 473.0, 297.0, 241.0, 350.0, 356.0 ] ], "demands": [ 14.0, 11.0, 34.0, 26.0, 33.0, 49.0, 18.0, 42.0, 17.0 ], "objective": 2654.0 }, "solution": { "open_facilities": [ 0 ], "assignments": [ 0, 0, 0, 0, 0, 0, 0, 0, 0 ] }, "obj": 2654.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 4, "num_customers": 9, "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 } ], "customers": [ { "id": 1, "demand": 14.0 }, { "id": 2, "demand": 11.0 }, { "id": 3, "demand": 34.0 }, { "id": 4, "demand": 26.0 }, { "id": 5, "demand": 33.0 }, { "id": 6, "demand": 49.0 }, { "id": 7, "demand": 18.0 }, { "id": 8, "demand": 42.0 }, { "id": 9, "demand": 17.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 265.0 }, { "facility": "F1", "customer": 2, "cost": 413.0 }, { "facility": "F1", "customer": 3, "cost": 206.0 }, { "facility": "F1", "customer": 4, "cost": 364.0 }, { "facility": "F1", "customer": 5, "cost": 258.0 }, { "facility": "F1", "customer": 6, "cost": 106.0 }, { "facility": "F1", "customer": 7, "cost": 207.0 }, { "facility": "F1", "customer": 8, "cost": 178.0 }, { "facility": "F1", "customer": 9, "cost": 257.0 }, { "facility": "F2", "customer": 1, "cost": 504.0 }, { "facility": "F2", "customer": 2, "cost": 367.0 }, { "facility": "F2", "customer": 3, "cost": 382.0 }, { "facility": "F2", "customer": 4, "cost": 644.0 }, { "facility": "F2", "customer": 5, "cost": 599.0 }, { "facility": "F2", "customer": 6, "cost": 389.0 }, { "facility": "F2", "customer": 7, "cost": 225.0 }, { "facility": "F2", "customer": 8, "cost": 405.0 }, { "facility": "F2", "customer": 9, "cost": 336.0 }, { "facility": "F3", "customer": 1, "cost": 617.0 }, { "facility": "F3", "customer": 2, "cost": 94.0 }, { "facility": "F3", "customer": 3, "cost": 239.0 }, { "facility": "F3", "customer": 4, "cost": 482.0 }, { "facility": "F3", "customer": 5, "cost": 625.0 }, { "facility": "F3", "customer": 6, "cost": 460.0 }, { "facility": "F3", "customer": 7, "cost": 391.0 }, { "facility": "F3", "customer": 8, "cost": 514.0 }, { "facility": "F3", "customer": 9, "cost": 512.0 }, { "facility": "F4", "customer": 1, "cost": 453.0 }, { "facility": "F4", "customer": 2, "cost": 229.0 }, { "facility": "F4", "customer": 3, "cost": 166.0 }, { "facility": "F4", "customer": 4, "cost": 429.0 }, { "facility": "F4", "customer": 5, "cost": 473.0 }, { "facility": "F4", "customer": 6, "cost": 297.0 }, { "facility": "F4", "customer": 7, "cost": 241.0 }, { "facility": "F4", "customer": 8, "cost": 350.0 }, { "facility": "F4", "customer": 9, "cost": 356.0 } ], "objective": 2654.0 }, "solution_variant": { "selected": [ "F1" ], "assignments": [ "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1" ] }, "context_index": 16, "input_format": "json", "input_index_base": 1 }, { "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\nThere are 4 warehouses and 10 shops in this instance.\n\n**Warehouses**\n| warehouse_id | warehouse_fixed_cost | warehouse_capacity |\n|---|---|---|\n| F1 | 400.0 | 1500.0 |\n| F2 | 400.0 | 1500.0 |\n| F3 | 400.0 | 1500.0 |\n| F4 | 400.0 | 1500.0 |\n\n**Shops**\n| shop_id | shop_demand |\n|---|---|\n| 0 | 40.0 |\n| 1 | 17.0 |\n| 2 | 36.0 |\n| 3 | 11.0 |\n| 4 | 47.0 |\n| 5 | 25.0 |\n| 6 | 17.0 |\n| 7 | 31.0 |\n| 8 | 45.0 |\n| 9 | 40.0 |\n\n**Shipping Cost**\n| warehouse_id | shop_id | shipping_cost |\n|---|---|---|\n| F1 | 0 | 20.0 |\n| F1 | 1 | 43.0 |\n| F1 | 2 | 696.0 |\n| F1 | 3 | 319.0 |\n| F1 | 4 | 335.0 |\n| F1 | 5 | 148.0 |\n| F1 | 6 | 422.0 |\n| F1 | 7 | 172.0 |\n| F1 | 8 | 604.0 |\n| F1 | 9 | 104.0 |\n| F2 | 0 | 373.0 |\n| F2 | 1 | 332.0 |\n| F2 | 2 | 467.0 |\n| F2 | 3 | 483.0 |\n| F2 | 4 | 495.0 |\n| F2 | 5 | 212.0 |\n| F2 | 6 | 99.0 |\n| F2 | 7 | 289.0 |\n| F2 | 8 | 591.0 |\n| F2 | 9 | 400.0 |\n| F3 | 0 | 354.0 |\n| F3 | 1 | 309.0 |\n| F3 | 2 | 347.0 |\n| F3 | 3 | 272.0 |\n| F3 | 4 | 279.0 |\n| F3 | 5 | 251.0 |\n| F3 | 6 | 360.0 |\n| F3 | 7 | 184.0 |\n| F3 | 8 | 333.0 |\n| F3 | 9 | 318.0 |\n| F4 | 0 | 549.0 |\n| F4 | 1 | 506.0 |\n| F4 | 2 | 373.0 |\n| F4 | 3 | 600.0 |\n| F4 | 4 | 609.0 |\n| F4 | 5 | 388.0 |\n| F4 | 6 | 181.0 |\n| F4 | 7 | 437.0 |\n| F4 | 8 | 614.0 |\n| F4 | 9 | 564.0 |\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 ], "capacities": [ 1500.0, 1500.0, 1500.0, 1500.0 ], "connection_costs": [ [ 20.0, 43.0, 696.0, 319.0, 335.0, 148.0, 422.0, 172.0, 604.0, 104.0 ], [ 373.0, 332.0, 467.0, 483.0, 495.0, 212.0, 99.0, 289.0, 591.0, 400.0 ], [ 354.0, 309.0, 347.0, 272.0, 279.0, 251.0, 360.0, 184.0, 333.0, 318.0 ], [ 549.0, 506.0, 373.0, 600.0, 609.0, 388.0, 181.0, 437.0, 614.0, 564.0 ] ], "demands": [ 40.0, 17.0, 36.0, 11.0, 47.0, 25.0, 17.0, 31.0, 45.0, 40.0 ], "objective": 2878.0 }, "solution": { "open_facilities": [ 0, 2 ], "assignments": [ 0, 0, 2, 2, 2, 0, 2, 0, 2, 0 ] }, "obj": 2878.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 4, "num_customers": 10, "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 } ], "customers": [ { "id": 0, "demand": 40.0 }, { "id": 1, "demand": 17.0 }, { "id": 2, "demand": 36.0 }, { "id": 3, "demand": 11.0 }, { "id": 4, "demand": 47.0 }, { "id": 5, "demand": 25.0 }, { "id": 6, "demand": 17.0 }, { "id": 7, "demand": 31.0 }, { "id": 8, "demand": 45.0 }, { "id": 9, "demand": 40.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 20.0 }, { "facility": "F1", "customer": 1, "cost": 43.0 }, { "facility": "F1", "customer": 2, "cost": 696.0 }, { "facility": "F1", "customer": 3, "cost": 319.0 }, { "facility": "F1", "customer": 4, "cost": 335.0 }, { "facility": "F1", "customer": 5, "cost": 148.0 }, { "facility": "F1", "customer": 6, "cost": 422.0 }, { "facility": "F1", "customer": 7, "cost": 172.0 }, { "facility": "F1", "customer": 8, "cost": 604.0 }, { "facility": "F1", "customer": 9, "cost": 104.0 }, { "facility": "F2", "customer": 0, "cost": 373.0 }, { "facility": "F2", "customer": 1, "cost": 332.0 }, { "facility": "F2", "customer": 2, "cost": 467.0 }, { "facility": "F2", "customer": 3, "cost": 483.0 }, { "facility": "F2", "customer": 4, "cost": 495.0 }, { "facility": "F2", "customer": 5, "cost": 212.0 }, { "facility": "F2", "customer": 6, "cost": 99.0 }, { "facility": "F2", "customer": 7, "cost": 289.0 }, { "facility": "F2", "customer": 8, "cost": 591.0 }, { "facility": "F2", "customer": 9, "cost": 400.0 }, { "facility": "F3", "customer": 0, "cost": 354.0 }, { "facility": "F3", "customer": 1, "cost": 309.0 }, { "facility": "F3", "customer": 2, "cost": 347.0 }, { "facility": "F3", "customer": 3, "cost": 272.0 }, { "facility": "F3", "customer": 4, "cost": 279.0 }, { "facility": "F3", "customer": 5, "cost": 251.0 }, { "facility": "F3", "customer": 6, "cost": 360.0 }, { "facility": "F3", "customer": 7, "cost": 184.0 }, { "facility": "F3", "customer": 8, "cost": 333.0 }, { "facility": "F3", "customer": 9, "cost": 318.0 }, { "facility": "F4", "customer": 0, "cost": 549.0 }, { "facility": "F4", "customer": 1, "cost": 506.0 }, { "facility": "F4", "customer": 2, "cost": 373.0 }, { "facility": "F4", "customer": 3, "cost": 600.0 }, { "facility": "F4", "customer": 4, "cost": 609.0 }, { "facility": "F4", "customer": 5, "cost": 388.0 }, { "facility": "F4", "customer": 6, "cost": 181.0 }, { "facility": "F4", "customer": 7, "cost": 437.0 }, { "facility": "F4", "customer": 8, "cost": 614.0 }, { "facility": "F4", "customer": 9, "cost": 564.0 } ], "objective": 2878.0 }, "solution_variant": { "selected": [ "F1", "F3" ], "assignments": [ "F1", "F1", "F3", "F3", "F3", "F1", "F3", "F1", "F3", "F1" ] }, "context_index": 17, "input_format": "markdown_table", "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\nThere are 4 hub id for connections and 10 fault id for connections in this instance.\n\n**Hub Id For Connections**\n| hub_id_for_connection | hub_startup_cost | hub_capacity_fixes |\n|---|---|---|\n| F1 | 400.0 | 500.0 |\n| F2 | 400.0 | 500.0 |\n| F3 | 400.0 | 500.0 |\n| F4 | 400.0 | 500.0 |\n\n**Fault Id For Connections**\n| fault_id_for_connection | fault_demand |\n|---|---|\n| 1 | 45.0 |\n| 2 | 24.0 |\n| 3 | 50.0 |\n| 4 | 11.0 |\n| 5 | 42.0 |\n| 6 | 32.0 |\n| 7 | 38.0 |\n| 8 | 27.0 |\n| 9 | 34.0 |\n| 10 | 23.0 |\n\n**Travel Service Cost**\n| hub_id_for_connection | fault_id_for_connection | travel_service_cost |\n|---|---|---|\n| F1 | 1 | 207.0 |\n| F1 | 2 | 349.0 |\n| F1 | 3 | 334.0 |\n| F1 | 4 | 345.0 |\n| F1 | 5 | 237.0 |\n| F1 | 6 | 277.0 |\n| F1 | 7 | 49.0 |\n| F1 | 8 | 300.0 |\n| F1 | 9 | 220.0 |\n| F1 | 10 | 48.0 |\n| F2 | 1 | 328.0 |\n| F2 | 2 | 535.0 |\n| F2 | 3 | 433.0 |\n| F2 | 4 | 318.0 |\n| F2 | 5 | 388.0 |\n| F2 | 6 | 195.0 |\n| F2 | 7 | 210.0 |\n| F2 | 8 | 270.0 |\n| F2 | 9 | 204.0 |\n| F2 | 10 | 238.0 |\n| F3 | 1 | 321.0 |\n| F3 | 2 | 649.0 |\n| F3 | 3 | 369.0 |\n| F3 | 4 | 153.0 |\n| F3 | 5 | 400.0 |\n| F3 | 6 | 49.0 |\n| F3 | 7 | 359.0 |\n| F3 | 8 | 124.0 |\n| F3 | 9 | 133.0 |\n| F3 | 10 | 354.0 |\n| F4 | 1 | 102.0 |\n| F4 | 2 | 278.0 |\n| F4 | 3 | 206.0 |\n| F4 | 4 | 345.0 |\n| F4 | 5 | 68.0 |\n| F4 | 6 | 346.0 |\n| F4 | 7 | 202.0 |\n| F4 | 8 | 317.0 |\n| F4 | 9 | 263.0 |\n| F4 | 10 | 143.0 |\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": [ 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 207.0, 349.0, 334.0, 345.0, 237.0, 277.0, 49.0, 300.0, 220.0, 48.0 ], [ 328.0, 535.0, 433.0, 318.0, 388.0, 195.0, 210.0, 270.0, 204.0, 238.0 ], [ 321.0, 649.0, 369.0, 153.0, 400.0, 49.0, 359.0, 124.0, 133.0, 354.0 ], [ 102.0, 278.0, 206.0, 345.0, 68.0, 346.0, 202.0, 317.0, 263.0, 143.0 ] ], "demands": [ 45.0, 24.0, 50.0, 11.0, 42.0, 32.0, 38.0, 27.0, 34.0, 23.0 ], "objective": 2258.0 }, "solution": { "open_facilities": [ 2, 3 ], "assignments": [ 3, 3, 3, 2, 3, 2, 3, 2, 2, 3 ] }, "obj": 2258.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 4, "num_customers": 10, "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 } ], "customers": [ { "id": 1, "demand": 45.0 }, { "id": 2, "demand": 24.0 }, { "id": 3, "demand": 50.0 }, { "id": 4, "demand": 11.0 }, { "id": 5, "demand": 42.0 }, { "id": 6, "demand": 32.0 }, { "id": 7, "demand": 38.0 }, { "id": 8, "demand": 27.0 }, { "id": 9, "demand": 34.0 }, { "id": 10, "demand": 23.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 207.0 }, { "facility": "F1", "customer": 2, "cost": 349.0 }, { "facility": "F1", "customer": 3, "cost": 334.0 }, { "facility": "F1", "customer": 4, "cost": 345.0 }, { "facility": "F1", "customer": 5, "cost": 237.0 }, { "facility": "F1", "customer": 6, "cost": 277.0 }, { "facility": "F1", "customer": 7, "cost": 49.0 }, { "facility": "F1", "customer": 8, "cost": 300.0 }, { "facility": "F1", "customer": 9, "cost": 220.0 }, { "facility": "F1", "customer": 10, "cost": 48.0 }, { "facility": "F2", "customer": 1, "cost": 328.0 }, { "facility": "F2", "customer": 2, "cost": 535.0 }, { "facility": "F2", "customer": 3, "cost": 433.0 }, { "facility": "F2", "customer": 4, "cost": 318.0 }, { "facility": "F2", "customer": 5, "cost": 388.0 }, { "facility": "F2", "customer": 6, "cost": 195.0 }, { "facility": "F2", "customer": 7, "cost": 210.0 }, { "facility": "F2", "customer": 8, "cost": 270.0 }, { "facility": "F2", "customer": 9, "cost": 204.0 }, { "facility": "F2", "customer": 10, "cost": 238.0 }, { "facility": "F3", "customer": 1, "cost": 321.0 }, { "facility": "F3", "customer": 2, "cost": 649.0 }, { "facility": "F3", "customer": 3, "cost": 369.0 }, { "facility": "F3", "customer": 4, "cost": 153.0 }, { "facility": "F3", "customer": 5, "cost": 400.0 }, { "facility": "F3", "customer": 6, "cost": 49.0 }, { "facility": "F3", "customer": 7, "cost": 359.0 }, { "facility": "F3", "customer": 8, "cost": 124.0 }, { "facility": "F3", "customer": 9, "cost": 133.0 }, { "facility": "F3", "customer": 10, "cost": 354.0 }, { "facility": "F4", "customer": 1, "cost": 102.0 }, { "facility": "F4", "customer": 2, "cost": 278.0 }, { "facility": "F4", "customer": 3, "cost": 206.0 }, { "facility": "F4", "customer": 4, "cost": 345.0 }, { "facility": "F4", "customer": 5, "cost": 68.0 }, { "facility": "F4", "customer": 6, "cost": 346.0 }, { "facility": "F4", "customer": 7, "cost": 202.0 }, { "facility": "F4", "customer": 8, "cost": 317.0 }, { "facility": "F4", "customer": 9, "cost": 263.0 }, { "facility": "F4", "customer": 10, "cost": 143.0 } ], "objective": 2258.0 }, "solution_variant": { "selected": [ "F3", "F4" ], "assignments": [ "F4", "F4", "F4", "F3", "F4", "F3", "F4", "F3", "F3", "F4" ] }, "context_index": 18, "input_format": "markdown_table", "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\nThere are 5 distribution points and 12 recipient areas in this instance.\n\n**Distribution Points**\n| distribution_point_id | staffing_cost | distribution_capacity |\n|---|---|---|\n| F1 | 400.0 | 614.0 |\n| F2 | 400.0 | 1335.0 |\n| F3 | 400.0 | 1067.0 |\n| F4 | 400.0 | 1103.0 |\n| F5 | 400.0 | 620.0 |\n\n**Recipient Areas**\n| recipient_area_id | area_demand |\n|---|---|\n| 0 | 44.0 |\n| 1 | 22.0 |\n| 2 | 43.0 |\n| 3 | 26.0 |\n| 4 | 31.0 |\n| 5 | 42.0 |\n| 6 | 47.0 |\n| 7 | 45.0 |\n| 8 | 45.0 |\n| 9 | 24.0 |\n| 10 | 15.0 |\n| 11 | 36.0 |\n\n**Delivery Cost**\n| distribution_point_id | recipient_area_id | delivery_cost |\n|---|---|---|\n| F1 | 0 | 633.0 |\n| F1 | 1 | 365.0 |\n| F1 | 2 | 254.0 |\n| F1 | 3 | 341.0 |\n| F1 | 4 | 448.0 |\n| F1 | 5 | 111.0 |\n| F1 | 6 | 383.0 |\n| F1 | 7 | 261.0 |\n| F1 | 8 | 329.0 |\n| F1 | 9 | 192.0 |\n| F1 | 10 | 301.0 |\n| F1 | 11 | 613.0 |\n| F2 | 0 | 610.0 |\n| F2 | 1 | 617.0 |\n| F2 | 2 | 521.0 |\n| F2 | 3 | 671.0 |\n| F2 | 4 | 178.0 |\n| F2 | 5 | 274.0 |\n| F2 | 6 | 673.0 |\n| F2 | 7 | 607.0 |\n| F2 | 8 | 32.0 |\n| F2 | 9 | 189.0 |\n| F2 | 10 | 61.0 |\n| F2 | 11 | 837.0 |\n| F3 | 0 | 37.0 |\n| F3 | 1 | 502.0 |\n| F3 | 2 | 524.0 |\n| F3 | 3 | 680.0 |\n| F3 | 4 | 481.0 |\n| F3 | 5 | 697.0 |\n| F3 | 6 | 587.0 |\n| F3 | 7 | 877.0 |\n| F3 | 8 | 625.0 |\n| F3 | 9 | 683.0 |\n| F3 | 10 | 620.0 |\n| F3 | 11 | 521.0 |\n| F4 | 0 | 662.0 |\n| F4 | 1 | 242.0 |\n| F4 | 2 | 176.0 |\n| F4 | 3 | 126.0 |\n| F4 | 4 | 628.0 |\n| F4 | 5 | 338.0 |\n| F4 | 6 | 209.0 |\n| F4 | 7 | 205.0 |\n| F4 | 8 | 545.0 |\n| F4 | 9 | 419.0 |\n| F4 | 10 | 517.0 |\n| F4 | 11 | 464.0 |\n| F5 | 0 | 825.0 |\n| F5 | 1 | 424.0 |\n| F5 | 2 | 349.0 |\n| F5 | 3 | 284.0 |\n| F5 | 4 | 705.0 |\n| F5 | 5 | 336.0 |\n| F5 | 6 | 385.0 |\n| F5 | 7 | 24.0 |\n| F5 | 8 | 577.0 |\n| F5 | 9 | 424.0 |\n| F5 | 10 | 550.0 |\n| F5 | 11 | 641.0 |\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": [ 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 614.0, 1335.0, 1067.0, 1103.0, 620.0 ], "connection_costs": [ [ 633.0, 365.0, 254.0, 341.0, 448.0, 111.0, 383.0, 261.0, 329.0, 192.0, 301.0, 613.0 ], [ 610.0, 617.0, 521.0, 671.0, 178.0, 274.0, 673.0, 607.0, 32.0, 189.0, 61.0, 837.0 ], [ 37.0, 502.0, 524.0, 680.0, 481.0, 697.0, 587.0, 877.0, 625.0, 683.0, 620.0, 521.0 ], [ 662.0, 242.0, 176.0, 126.0, 628.0, 338.0, 209.0, 205.0, 545.0, 419.0, 517.0, 464.0 ], [ 825.0, 424.0, 349.0, 284.0, 705.0, 336.0, 385.0, 24.0, 577.0, 424.0, 550.0, 641.0 ] ], "demands": [ 44.0, 22.0, 43.0, 26.0, 31.0, 42.0, 47.0, 45.0, 45.0, 24.0, 15.0, 36.0 ], "objective": 3393.0 }, "solution": { "open_facilities": [ 1, 2, 3 ], "assignments": [ 2, 3, 3, 3, 1, 1, 3, 3, 1, 1, 1, 3 ] }, "obj": 3393.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 12, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 614.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 1335.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 1067.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 1103.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 620.0 } ], "customers": [ { "id": 0, "demand": 44.0 }, { "id": 1, "demand": 22.0 }, { "id": 2, "demand": 43.0 }, { "id": 3, "demand": 26.0 }, { "id": 4, "demand": 31.0 }, { "id": 5, "demand": 42.0 }, { "id": 6, "demand": 47.0 }, { "id": 7, "demand": 45.0 }, { "id": 8, "demand": 45.0 }, { "id": 9, "demand": 24.0 }, { "id": 10, "demand": 15.0 }, { "id": 11, "demand": 36.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 633.0 }, { "facility": "F1", "customer": 1, "cost": 365.0 }, { "facility": "F1", "customer": 2, "cost": 254.0 }, { "facility": "F1", "customer": 3, "cost": 341.0 }, { "facility": "F1", "customer": 4, "cost": 448.0 }, { "facility": "F1", "customer": 5, "cost": 111.0 }, { "facility": "F1", "customer": 6, "cost": 383.0 }, { "facility": "F1", "customer": 7, "cost": 261.0 }, { "facility": "F1", "customer": 8, "cost": 329.0 }, { "facility": "F1", "customer": 9, "cost": 192.0 }, { "facility": "F1", "customer": 10, "cost": 301.0 }, { "facility": "F1", "customer": 11, "cost": 613.0 }, { "facility": "F2", "customer": 0, "cost": 610.0 }, { "facility": "F2", "customer": 1, "cost": 617.0 }, { "facility": "F2", "customer": 2, "cost": 521.0 }, { "facility": "F2", "customer": 3, "cost": 671.0 }, { "facility": "F2", "customer": 4, "cost": 178.0 }, { "facility": "F2", "customer": 5, "cost": 274.0 }, { "facility": "F2", "customer": 6, "cost": 673.0 }, { "facility": "F2", "customer": 7, "cost": 607.0 }, { "facility": "F2", "customer": 8, "cost": 32.0 }, { "facility": "F2", "customer": 9, "cost": 189.0 }, { "facility": "F2", "customer": 10, "cost": 61.0 }, { "facility": "F2", "customer": 11, "cost": 837.0 }, { "facility": "F3", "customer": 0, "cost": 37.0 }, { "facility": "F3", "customer": 1, "cost": 502.0 }, { "facility": "F3", "customer": 2, "cost": 524.0 }, { "facility": "F3", "customer": 3, "cost": 680.0 }, { "facility": "F3", "customer": 4, "cost": 481.0 }, { "facility": "F3", "customer": 5, "cost": 697.0 }, { "facility": "F3", "customer": 6, "cost": 587.0 }, { "facility": "F3", "customer": 7, "cost": 877.0 }, { "facility": "F3", "customer": 8, "cost": 625.0 }, { "facility": "F3", "customer": 9, "cost": 683.0 }, { "facility": "F3", "customer": 10, "cost": 620.0 }, { "facility": "F3", "customer": 11, "cost": 521.0 }, { "facility": "F4", "customer": 0, "cost": 662.0 }, { "facility": "F4", "customer": 1, "cost": 242.0 }, { "facility": "F4", "customer": 2, "cost": 176.0 }, { "facility": "F4", "customer": 3, "cost": 126.0 }, { "facility": "F4", "customer": 4, "cost": 628.0 }, { "facility": "F4", "customer": 5, "cost": 338.0 }, { "facility": "F4", "customer": 6, "cost": 209.0 }, { "facility": "F4", "customer": 7, "cost": 205.0 }, { "facility": "F4", "customer": 8, "cost": 545.0 }, { "facility": "F4", "customer": 9, "cost": 419.0 }, { "facility": "F4", "customer": 10, "cost": 517.0 }, { "facility": "F4", "customer": 11, "cost": 464.0 }, { "facility": "F5", "customer": 0, "cost": 825.0 }, { "facility": "F5", "customer": 1, "cost": 424.0 }, { "facility": "F5", "customer": 2, "cost": 349.0 }, { "facility": "F5", "customer": 3, "cost": 284.0 }, { "facility": "F5", "customer": 4, "cost": 705.0 }, { "facility": "F5", "customer": 5, "cost": 336.0 }, { "facility": "F5", "customer": 6, "cost": 385.0 }, { "facility": "F5", "customer": 7, "cost": 24.0 }, { "facility": "F5", "customer": 8, "cost": 577.0 }, { "facility": "F5", "customer": 9, "cost": 424.0 }, { "facility": "F5", "customer": 10, "cost": 550.0 }, { "facility": "F5", "customer": 11, "cost": 641.0 } ], "objective": 3393.0 }, "solution_variant": { "selected": [ "F2", "F3", "F4" ], "assignments": [ "F3", "F4", "F4", "F4", "F2", "F2", "F4", "F4", "F2", "F2", "F2", "F4" ] }, "context_index": 19, "input_format": "markdown_table", "input_index_base": 0 }, { "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# num_repair_hubs=5\n# num_returned_devices=11\n# HUBS\nhub_id,hub_running_cost,hub_capacity\nF1,600.0,500.0\nF2,600.0,500.0\nF3,600.0,500.0\nF4,600.0,500.0\nF5,600.0,500.0\n# DEVICES\ndevice_id,device_demand\nA,17.0\nB,13.0\nC,13.0\nD,24.0\nE,25.0\nF,22.0\nG,19.0\nH,23.0\nI,13.0\nJ,10.0\nK,27.0\n# DEVICE_TRANSFERS\nhub_id,device_id,device_transfer_cost\nF1,A,1566.0\nF1,B,2821.0\nF1,C,1840.0\nF1,D,721.0\nF1,E,2163.0\nF1,F,1166.0\nF1,G,2617.0\nF1,H,1280.0\nF1,I,1953.0\nF1,J,771.0\nF1,K,1906.0\nF2,A,1292.0\nF2,B,2629.0\nF2,C,1569.0\nF2,D,436.0\nF2,E,2026.0\nF2,F,889.0\nF2,G,2409.0\nF2,H,1262.0\nF2,I,1896.0\nF2,J,651.0\nF2,K,1738.0\nF3,A,280.0\nF3,B,173.0\nF3,C,353.0\nF3,D,146.0\nF3,E,227.0\nF3,F,196.0\nF3,G,128.0\nF3,H,385.0\nF3,I,527.0\nF3,J,46.0\nF3,K,79.0\nF4,A,507.0\nF4,B,1775.0\nF4,C,756.0\nF4,D,108.0\nF4,E,1278.0\nF4,F,216.0\nF4,G,1542.0\nF4,H,839.0\nF4,I,1322.0\nF4,J,211.0\nF4,K,944.0\nF5,A,1017.0\nF5,B,2444.0\nF5,C,1295.0\nF5,D,141.0\nF5,E,1904.0\nF5,F,613.0\nF5,G,2210.0\nF5,H,1246.0\nF5,I,1842.0\nF5,J,595.0\nF5,K,1590.0\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": [ 600.0, 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 1566.0, 2821.0, 1840.0, 721.0, 2163.0, 1166.0, 2617.0, 1280.0, 1953.0, 771.0, 1906.0 ], [ 1292.0, 2629.0, 1569.0, 436.0, 2026.0, 889.0, 2409.0, 1262.0, 1896.0, 651.0, 1738.0 ], [ 280.0, 173.0, 353.0, 146.0, 227.0, 196.0, 128.0, 385.0, 527.0, 46.0, 79.0 ], [ 507.0, 1775.0, 756.0, 108.0, 1278.0, 216.0, 1542.0, 839.0, 1322.0, 211.0, 944.0 ], [ 1017.0, 2444.0, 1295.0, 141.0, 1904.0, 613.0, 2210.0, 1246.0, 1842.0, 595.0, 1590.0 ] ], "demands": [ 17.0, 13.0, 13.0, 24.0, 25.0, 22.0, 19.0, 23.0, 13.0, 10.0, 27.0 ], "objective": 3140.0 }, "solution": { "open_facilities": [ 2 ], "assignments": [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ] }, "obj": 3140.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 11, "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 } ], "customers": [ { "id": "A", "demand": 17.0 }, { "id": "B", "demand": 13.0 }, { "id": "C", "demand": 13.0 }, { "id": "D", "demand": 24.0 }, { "id": "E", "demand": 25.0 }, { "id": "F", "demand": 22.0 }, { "id": "G", "demand": 19.0 }, { "id": "H", "demand": 23.0 }, { "id": "I", "demand": 13.0 }, { "id": "J", "demand": 10.0 }, { "id": "K", "demand": 27.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 1566.0 }, { "facility": "F1", "customer": "B", "cost": 2821.0 }, { "facility": "F1", "customer": "C", "cost": 1840.0 }, { "facility": "F1", "customer": "D", "cost": 721.0 }, { "facility": "F1", "customer": "E", "cost": 2163.0 }, { "facility": "F1", "customer": "F", "cost": 1166.0 }, { "facility": "F1", "customer": "G", "cost": 2617.0 }, { "facility": "F1", "customer": "H", "cost": 1280.0 }, { "facility": "F1", "customer": "I", "cost": 1953.0 }, { "facility": "F1", "customer": "J", "cost": 771.0 }, { "facility": "F1", "customer": "K", "cost": 1906.0 }, { "facility": "F2", "customer": "A", "cost": 1292.0 }, { "facility": "F2", "customer": "B", "cost": 2629.0 }, { "facility": "F2", "customer": "C", "cost": 1569.0 }, { "facility": "F2", "customer": "D", "cost": 436.0 }, { "facility": "F2", "customer": "E", "cost": 2026.0 }, { "facility": "F2", "customer": "F", "cost": 889.0 }, { "facility": "F2", "customer": "G", "cost": 2409.0 }, { "facility": "F2", "customer": "H", "cost": 1262.0 }, { "facility": "F2", "customer": "I", "cost": 1896.0 }, { "facility": "F2", "customer": "J", "cost": 651.0 }, { "facility": "F2", "customer": "K", "cost": 1738.0 }, { "facility": "F3", "customer": "A", "cost": 280.0 }, { "facility": "F3", "customer": "B", "cost": 173.0 }, { "facility": "F3", "customer": "C", "cost": 353.0 }, { "facility": "F3", "customer": "D", "cost": 146.0 }, { "facility": "F3", "customer": "E", "cost": 227.0 }, { "facility": "F3", "customer": "F", "cost": 196.0 }, { "facility": "F3", "customer": "G", "cost": 128.0 }, { "facility": "F3", "customer": "H", "cost": 385.0 }, { "facility": "F3", "customer": "I", "cost": 527.0 }, { "facility": "F3", "customer": "J", "cost": 46.0 }, { "facility": "F3", "customer": "K", "cost": 79.0 }, { "facility": "F4", "customer": "A", "cost": 507.0 }, { "facility": "F4", "customer": "B", "cost": 1775.0 }, { "facility": "F4", "customer": "C", "cost": 756.0 }, { "facility": "F4", "customer": "D", "cost": 108.0 }, { "facility": "F4", "customer": "E", "cost": 1278.0 }, { "facility": "F4", "customer": "F", "cost": 216.0 }, { "facility": "F4", "customer": "G", "cost": 1542.0 }, { "facility": "F4", "customer": "H", "cost": 839.0 }, { "facility": "F4", "customer": "I", "cost": 1322.0 }, { "facility": "F4", "customer": "J", "cost": 211.0 }, { "facility": "F4", "customer": "K", "cost": 944.0 }, { "facility": "F5", "customer": "A", "cost": 1017.0 }, { "facility": "F5", "customer": "B", "cost": 2444.0 }, { "facility": "F5", "customer": "C", "cost": 1295.0 }, { "facility": "F5", "customer": "D", "cost": 141.0 }, { "facility": "F5", "customer": "E", "cost": 1904.0 }, { "facility": "F5", "customer": "F", "cost": 613.0 }, { "facility": "F5", "customer": "G", "cost": 2210.0 }, { "facility": "F5", "customer": "H", "cost": 1246.0 }, { "facility": "F5", "customer": "I", "cost": 1842.0 }, { "facility": "F5", "customer": "J", "cost": 595.0 }, { "facility": "F5", "customer": "K", "cost": 1590.0 } ], "objective": 3140.0 }, "solution_variant": { "selected": [ "F3" ], "assignments": [ "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3" ] }, "context_index": 20, "input_format": "csv", "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 5 candidate centers and 12 households in the data below.\nCenter F1 has activation cost 600.0 and capacity 500.0.\nCenter F2 has activation cost 600.0 and capacity 500.0.\nCenter F3 has activation cost 600.0 and capacity 500.0.\nCenter F4 has activation cost 600.0 and capacity 500.0.\nCenter F5 has activation cost 600.0 and capacity 500.0.\nHousehold 1 has demand 14.0.\nHousehold 2 has demand 12.0.\nHousehold 3 has demand 23.0.\nHousehold 4 has demand 12.0.\nHousehold 5 has demand 18.0.\nHousehold 6 has demand 23.0.\nHousehold 7 has demand 17.0.\nHousehold 8 has demand 13.0.\nHousehold 9 has demand 23.0.\nHousehold 10 has demand 10.0.\nHousehold 11 has demand 29.0.\nHousehold 12 has demand 23.0.\nServing household 1 from center F1 incurs delivery cost 457.0.\nServing household 2 from center F1 incurs delivery cost 261.0.\nServing household 3 from center F1 incurs delivery cost 1201.0.\nServing household 4 from center F1 incurs delivery cost 105.0.\nServing household 5 from center F1 incurs delivery cost 898.0.\nServing household 6 from center F1 incurs delivery cost 620.0.\nServing household 7 from center F1 incurs delivery cost 114.0.\nServing household 8 from center F1 incurs delivery cost 547.0.\nServing household 9 from center F1 incurs delivery cost 1116.0.\nServing household 10 from center F1 incurs delivery cost 63.0.\nServing household 11 from center F1 incurs delivery cost 85.0.\nServing household 12 from center F1 incurs delivery cost 474.0.\nServing household 1 from center F2 incurs delivery cost 100.0.\nServing household 2 from center F2 incurs delivery cost 133.0.\nServing household 3 from center F2 incurs delivery cost 1633.0.\nServing household 4 from center F2 incurs delivery cost 472.0.\nServing household 5 from center F2 incurs delivery cost 1451.0.\nServing household 6 from center F2 incurs delivery cost 342.0.\nServing household 7 from center F2 incurs delivery cost 648.0.\nServing household 8 from center F2 incurs delivery cost 1109.0.\nServing household 9 from center F2 incurs delivery cost 1391.0.\nServing household 10 from center F2 incurs delivery cost 233.0.\nServing household 11 from center F2 incurs delivery cost 217.0.\nServing household 12 from center F2 incurs delivery cost 1030.0.\nServing household 1 from center F3 incurs delivery cost 1030.0.\nServing household 2 from center F3 incurs delivery cost 865.0.\nServing household 3 from center F3 incurs delivery cost 2147.0.\nServing household 4 from center F3 incurs delivery cost 478.0.\nServing household 5 from center F3 incurs delivery cost 1765.0.\nServing household 6 from center F3 incurs delivery cost 1262.0.\nServing household 7 from center F3 incurs delivery cost 1064.0.\nServing household 8 from center F3 incurs delivery cost 1422.0.\nServing household 9 from center F3 incurs delivery cost 2054.0.\nServing household 10 from center F3 incurs delivery cost 651.0.\nServing household 11 from center F3 incurs delivery cost 64.0.\nServing household 12 from center F3 incurs delivery cost 1176.0.\nServing household 1 from center F4 incurs delivery cost 385.0.\nServing household 2 from center F4 incurs delivery cost 232.0.\nServing household 3 from center F4 incurs delivery cost 1732.0.\nServing household 4 from center F4 incurs delivery cost 430.0.\nServing household 5 from center F4 incurs delivery cost 1488.0.\nServing household 6 from center F4 incurs delivery cost 615.0.\nServing household 7 from center F4 incurs delivery cost 680.0.\nServing household 8 from center F4 incurs delivery cost 1138.0.\nServing household 9 from center F4 incurs delivery cost 1540.0.\nServing household 10 from center F4 incurs delivery cost 212.0.\nServing household 11 from center F4 incurs delivery cost 182.0.\nServing household 12 from center F4 incurs delivery cost 1020.0.\nServing household 1 from center F5 incurs delivery cost 158.0.\nServing household 2 from center F5 incurs delivery cost 43.0.\nServing household 3 from center F5 incurs delivery cost 1061.0.\nServing household 4 from center F5 incurs delivery cost 241.0.\nServing household 5 from center F5 incurs delivery cost 943.0.\nServing household 6 from center F5 incurs delivery cost 251.0.\nServing household 7 from center F5 incurs delivery cost 220.0.\nServing household 8 from center F5 incurs delivery cost 630.0.\nServing household 9 from center F5 incurs delivery cost 820.0.\nServing household 10 from center F5 incurs delivery cost 36.0.\nServing household 11 from center F5 incurs delivery cost 137.0.\nServing household 12 from center F5 incurs delivery cost 636.0.\nThe team will use these figures to identify a plan that minimizes total activation plus delivery cost.\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": [ 600.0, 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 457.0, 261.0, 1201.0, 105.0, 898.0, 620.0, 114.0, 547.0, 1116.0, 63.0, 85.0, 474.0 ], [ 100.0, 133.0, 1633.0, 472.0, 1451.0, 342.0, 648.0, 1109.0, 1391.0, 233.0, 217.0, 1030.0 ], [ 1030.0, 865.0, 2147.0, 478.0, 1765.0, 1262.0, 1064.0, 1422.0, 2054.0, 651.0, 64.0, 1176.0 ], [ 385.0, 232.0, 1732.0, 430.0, 1488.0, 615.0, 680.0, 1138.0, 1540.0, 212.0, 182.0, 1020.0 ], [ 158.0, 43.0, 1061.0, 241.0, 943.0, 251.0, 220.0, 630.0, 820.0, 36.0, 137.0, 636.0 ] ], "demands": [ 14.0, 12.0, 23.0, 12.0, 18.0, 23.0, 17.0, 13.0, 23.0, 10.0, 29.0, 23.0 ], "objective": 5776.0 }, "solution": { "open_facilities": [ 4 ], "assignments": [ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ] }, "obj": 5776.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 12, "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 } ], "customers": [ { "id": 1, "demand": 14.0 }, { "id": 2, "demand": 12.0 }, { "id": 3, "demand": 23.0 }, { "id": 4, "demand": 12.0 }, { "id": 5, "demand": 18.0 }, { "id": 6, "demand": 23.0 }, { "id": 7, "demand": 17.0 }, { "id": 8, "demand": 13.0 }, { "id": 9, "demand": 23.0 }, { "id": 10, "demand": 10.0 }, { "id": 11, "demand": 29.0 }, { "id": 12, "demand": 23.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 457.0 }, { "facility": "F1", "customer": 2, "cost": 261.0 }, { "facility": "F1", "customer": 3, "cost": 1201.0 }, { "facility": "F1", "customer": 4, "cost": 105.0 }, { "facility": "F1", "customer": 5, "cost": 898.0 }, { "facility": "F1", "customer": 6, "cost": 620.0 }, { "facility": "F1", "customer": 7, "cost": 114.0 }, { "facility": "F1", "customer": 8, "cost": 547.0 }, { "facility": "F1", "customer": 9, "cost": 1116.0 }, { "facility": "F1", "customer": 10, "cost": 63.0 }, { "facility": "F1", "customer": 11, "cost": 85.0 }, { "facility": "F1", "customer": 12, "cost": 474.0 }, { "facility": "F2", "customer": 1, "cost": 100.0 }, { "facility": "F2", "customer": 2, "cost": 133.0 }, { "facility": "F2", "customer": 3, "cost": 1633.0 }, { "facility": "F2", "customer": 4, "cost": 472.0 }, { "facility": "F2", "customer": 5, "cost": 1451.0 }, { "facility": "F2", "customer": 6, "cost": 342.0 }, { "facility": "F2", "customer": 7, "cost": 648.0 }, { "facility": "F2", "customer": 8, "cost": 1109.0 }, { "facility": "F2", "customer": 9, "cost": 1391.0 }, { "facility": "F2", "customer": 10, "cost": 233.0 }, { "facility": "F2", "customer": 11, "cost": 217.0 }, { "facility": "F2", "customer": 12, "cost": 1030.0 }, { "facility": "F3", "customer": 1, "cost": 1030.0 }, { "facility": "F3", "customer": 2, "cost": 865.0 }, { "facility": "F3", "customer": 3, "cost": 2147.0 }, { "facility": "F3", "customer": 4, "cost": 478.0 }, { "facility": "F3", "customer": 5, "cost": 1765.0 }, { "facility": "F3", "customer": 6, "cost": 1262.0 }, { "facility": "F3", "customer": 7, "cost": 1064.0 }, { "facility": "F3", "customer": 8, "cost": 1422.0 }, { "facility": "F3", "customer": 9, "cost": 2054.0 }, { "facility": "F3", "customer": 10, "cost": 651.0 }, { "facility": "F3", "customer": 11, "cost": 64.0 }, { "facility": "F3", "customer": 12, "cost": 1176.0 }, { "facility": "F4", "customer": 1, "cost": 385.0 }, { "facility": "F4", "customer": 2, "cost": 232.0 }, { "facility": "F4", "customer": 3, "cost": 1732.0 }, { "facility": "F4", "customer": 4, "cost": 430.0 }, { "facility": "F4", "customer": 5, "cost": 1488.0 }, { "facility": "F4", "customer": 6, "cost": 615.0 }, { "facility": "F4", "customer": 7, "cost": 680.0 }, { "facility": "F4", "customer": 8, "cost": 1138.0 }, { "facility": "F4", "customer": 9, "cost": 1540.0 }, { "facility": "F4", "customer": 10, "cost": 212.0 }, { "facility": "F4", "customer": 11, "cost": 182.0 }, { "facility": "F4", "customer": 12, "cost": 1020.0 }, { "facility": "F5", "customer": 1, "cost": 158.0 }, { "facility": "F5", "customer": 2, "cost": 43.0 }, { "facility": "F5", "customer": 3, "cost": 1061.0 }, { "facility": "F5", "customer": 4, "cost": 241.0 }, { "facility": "F5", "customer": 5, "cost": 943.0 }, { "facility": "F5", "customer": 6, "cost": 251.0 }, { "facility": "F5", "customer": 7, "cost": 220.0 }, { "facility": "F5", "customer": 8, "cost": 630.0 }, { "facility": "F5", "customer": 9, "cost": 820.0 }, { "facility": "F5", "customer": 10, "cost": 36.0 }, { "facility": "F5", "customer": 11, "cost": 137.0 }, { "facility": "F5", "customer": 12, "cost": 636.0 } ], "objective": 5776.0 }, "solution_variant": { "selected": [ "F5" ], "assignments": [ "F5", "F5", "F5", "F5", "F5", "F5", "F5", "F5", "F5", "F5", "F5", "F5" ] }, "context_index": 21, "input_format": "nl", "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\n{\n \"num_candidate_stations\": 5,\n \"num_attendee_groups\": 12,\n \"stations\": [\n {\n \"station_id\": \"F1\",\n \"setup_fee\": 300.0,\n \"max_capacity\": 500.0\n },\n {\n \"station_id\": \"F2\",\n \"setup_fee\": 300.0,\n \"max_capacity\": 500.0\n },\n {\n \"station_id\": \"F3\",\n \"setup_fee\": 300.0,\n \"max_capacity\": 500.0\n },\n {\n \"station_id\": \"F4\",\n \"setup_fee\": 300.0,\n \"max_capacity\": 500.0\n },\n {\n \"station_id\": \"F5\",\n \"setup_fee\": 300.0,\n \"max_capacity\": 500.0\n }\n ],\n \"attendee_groups\": [\n {\n \"attendee_group_id\": \"A\",\n \"group_size\": 14.0\n },\n {\n \"attendee_group_id\": \"B\",\n \"group_size\": 15.0\n },\n {\n \"attendee_group_id\": \"C\",\n \"group_size\": 27.0\n },\n {\n \"attendee_group_id\": \"D\",\n \"group_size\": 10.0\n },\n {\n \"attendee_group_id\": \"E\",\n \"group_size\": 26.0\n },\n {\n \"attendee_group_id\": \"F\",\n \"group_size\": 12.0\n },\n {\n \"attendee_group_id\": \"G\",\n \"group_size\": 23.0\n },\n {\n \"attendee_group_id\": \"H\",\n \"group_size\": 21.0\n },\n {\n \"attendee_group_id\": \"I\",\n \"group_size\": 27.0\n },\n {\n \"attendee_group_id\": \"J\",\n \"group_size\": 11.0\n },\n {\n \"attendee_group_id\": \"K\",\n \"group_size\": 13.0\n },\n {\n \"attendee_group_id\": \"L\",\n \"group_size\": 27.0\n }\n ],\n \"walking_distances\": [\n {\n \"station_id\": \"F1\",\n \"attendee_group_id\": \"A\",\n \"walking_distance_cost\": 570.0\n },\n {\n \"station_id\": \"F1\",\n \"attendee_group_id\": \"B\",\n \"walking_distance_cost\": 46.0\n },\n {\n \"station_id\": \"F1\",\n \"attendee_group_id\": \"C\",\n \"walking_distance_cost\": 429.0\n },\n {\n \"station_id\": \"F1\",\n \"attendee_group_id\": \"D\",\n \"walking_distance_cost\": 938.0\n },\n {\n \"station_id\": \"F1\",\n \"attendee_group_id\": \"E\",\n \"walking_distance_cost\": 531.0\n },\n {\n \"station_id\": \"F1\",\n \"attendee_group_id\": \"F\",\n \"walking_distance_cost\": 88.0\n },\n {\n \"station_id\": \"F1\",\n \"attendee_group_id\": \"G\",\n \"walking_distance_cost\": 791.0\n },\n {\n \"station_id\": \"F1\",\n \"attendee_group_id\": \"H\",\n \"walking_distance_cost\": 374.0\n },\n {\n \"station_id\": \"F1\",\n \"attendee_group_id\": \"I\",\n \"walking_distance_cost\": 101.0\n },\n {\n \"station_id\": \"F1\",\n \"attendee_group_id\": \"J\",\n \"walking_distance_cost\": 501.0\n },\n {\n \"station_id\": \"F1\",\n \"attendee_group_id\": \"K\",\n \"walking_distance_cost\": 50.0\n },\n {\n \"station_id\": \"F1\",\n \"attendee_group_id\": \"L\",\n \"walking_distance_cost\": 461.0\n },\n {\n \"station_id\": \"F2\",\n \"attendee_group_id\": \"A\",\n \"walking_distance_cost\": 312.0\n },\n {\n \"station_id\": \"F2\",\n \"attendee_group_id\": \"B\",\n \"walking_distance_cost\": 864.0\n },\n {\n \"station_id\": \"F2\",\n \"attendee_group_id\": \"C\",\n \"walking_distance_cost\": 416.0\n },\n {\n \"station_id\": \"F2\",\n \"attendee_group_id\": \"D\",\n \"walking_distance_cost\": 637.0\n },\n {\n \"station_id\": \"F2\",\n \"attendee_group_id\": \"E\",\n \"walking_distance_cost\": 275.0\n },\n {\n \"station_id\": \"F2\",\n \"attendee_group_id\": \"F\",\n \"walking_distance_cost\": 447.0\n },\n {\n \"station_id\": \"F2\",\n \"attendee_group_id\": \"G\",\n \"walking_distance_cost\": 618.0\n },\n {\n \"station_id\": \"F2\",\n \"attendee_group_id\": \"H\",\n \"walking_distance_cost\": 839.0\n },\n {\n \"station_id\": \"F2\",\n \"attendee_group_id\": \"I\",\n \"walking_distance_cost\": 701.0\n },\n {\n \"station_id\": \"F2\",\n \"attendee_group_id\": \"J\",\n \"walking_distance_cost\": 854.0\n },\n {\n \"station_id\": \"F2\",\n \"attendee_group_id\": \"K\",\n \"walking_distance_cost\": 185.0\n },\n {\n \"station_id\": \"F2\",\n \"attendee_group_id\": \"L\",\n \"walking_distance_cost\": 273.0\n },\n {\n \"station_id\": \"F3\",\n \"attendee_group_id\": \"A\",\n \"walking_distance_cost\": 658.0\n },\n {\n \"station_id\": \"F3\",\n \"attendee_group_id\": \"B\",\n \"walking_distance_cost\": 1110.0\n },\n {\n \"station_id\": \"F3\",\n \"attendee_group_id\": \"C\",\n \"walking_distance_cost\": 1023.0\n },\n {\n \"station_id\": \"F3\",\n \"attendee_group_id\": \"D\",\n \"walking_distance_cost\": 1206.0\n },\n {\n \"station_id\": \"F3\",\n \"attendee_group_id\": \"E\",\n \"walking_distance_cost\": 626.0\n },\n {\n \"station_id\": \"F3\",\n \"attendee_group_id\": \"F\",\n \"walking_distance_cost\": 759.0\n },\n {\n \"station_id\": \"F3\",\n \"attendee_group_id\": \"G\",\n \"walking_distance_cost\": 1302.0\n },\n {\n \"station_id\": \"F3\",\n \"attendee_group_id\": \"H\",\n \"walking_distance_cost\": 1289.0\n },\n {\n \"station_id\": \"F3\",\n \"attendee_group_id\": \"I\",\n \"walking_distance_cost\": 783.0\n },\n {\n \"station_id\": \"F3\",\n \"attendee_group_id\": \"J\",\n \"walking_distance_cost\": 1368.0\n },\n {\n \"station_id\": \"F3\",\n \"attendee_group_id\": \"K\",\n \"walking_distance_cost\": 244.0\n },\n {\n \"station_id\": \"F3\",\n \"attendee_group_id\": \"L\",\n \"walking_distance_cost\": 944.0\n },\n {\n \"station_id\": \"F4\",\n \"attendee_group_id\": \"A\",\n \"walking_distance_cost\": 692.0\n },\n {\n \"station_id\": \"F4\",\n \"attendee_group_id\": \"B\",\n \"walking_distance_cost\": 1492.0\n },\n {\n \"station_id\": \"F4\",\n \"attendee_group_id\": \"C\",\n \"walking_distance_cost\": 1328.0\n },\n {\n \"station_id\": \"F4\",\n \"attendee_group_id\": \"D\",\n \"walking_distance_cost\": 1329.0\n },\n {\n \"station_id\": \"F4\",\n \"attendee_group_id\": \"E\",\n \"walking_distance_cost\": 670.0\n },\n {\n \"station_id\": \"F4\",\n \"attendee_group_id\": \"F\",\n \"walking_distance_cost\": 1126.0\n },\n {\n \"station_id\": \"F4\",\n \"attendee_group_id\": \"G\",\n \"walking_distance_cost\": 1544.0\n },\n {\n \"station_id\": \"F4\",\n \"attendee_group_id\": \"H\",\n \"walking_distance_cost\": 1646.0\n },\n {\n \"station_id\": \"F4\",\n \"attendee_group_id\": \"I\",\n \"walking_distance_cost\": 1160.0\n },\n {\n \"station_id\": \"F4\",\n \"attendee_group_id\": \"J\",\n \"walking_distance_cost\": 1712.0\n },\n {\n \"station_id\": \"F4\",\n \"attendee_group_id\": \"K\",\n \"walking_distance_cost\": 611.0\n },\n {\n \"station_id\": \"F4\",\n \"attendee_group_id\": \"L\",\n \"walking_distance_cost\": 1216.0\n },\n {\n \"station_id\": \"F5\",\n \"attendee_group_id\": \"A\",\n \"walking_distance_cost\": 158.0\n },\n {\n \"station_id\": \"F5\",\n \"attendee_group_id\": \"B\",\n \"walking_distance_cost\": 1259.0\n },\n {\n \"station_id\": \"F5\",\n \"attendee_group_id\": \"C\",\n \"walking_distance_cost\": 803.0\n },\n {\n \"station_id\": \"F5\",\n \"attendee_group_id\": \"D\",\n \"walking_distance_cost\": 515.0\n },\n {\n \"station_id\": \"F5\",\n \"attendee_group_id\": \"E\",\n \"walking_distance_cost\": 127.0\n },\n {\n \"station_id\": \"F5\",\n \"attendee_group_id\": \"F\",\n \"walking_distance_cost\": 838.0\n },\n {\n \"station_id\": \"F5\",\n \"attendee_group_id\": \"G\",\n \"walking_distance_cost\": 820.0\n },\n {\n \"station_id\": \"F5\",\n \"attendee_group_id\": \"H\",\n \"walking_distance_cost\": 1242.0\n },\n {\n \"station_id\": \"F5\",\n \"attendee_group_id\": \"I\",\n \"walking_distance_cost\": 1055.0\n },\n {\n \"station_id\": \"F5\",\n \"attendee_group_id\": \"J\",\n \"walking_distance_cost\": 1245.0\n },\n {\n \"station_id\": \"F5\",\n \"attendee_group_id\": \"K\",\n \"walking_distance_cost\": 477.0\n },\n {\n \"station_id\": \"F5\",\n \"attendee_group_id\": \"L\",\n \"walking_distance_cost\": 630.0\n }\n ]\n}\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": [ 300.0, 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 570.0, 46.0, 429.0, 938.0, 531.0, 88.0, 791.0, 374.0, 101.0, 501.0, 50.0, 461.0 ], [ 312.0, 864.0, 416.0, 637.0, 275.0, 447.0, 618.0, 839.0, 701.0, 854.0, 185.0, 273.0 ], [ 658.0, 1110.0, 1023.0, 1206.0, 626.0, 759.0, 1302.0, 1289.0, 783.0, 1368.0, 244.0, 944.0 ], [ 692.0, 1492.0, 1328.0, 1329.0, 670.0, 1126.0, 1544.0, 1646.0, 1160.0, 1712.0, 611.0, 1216.0 ], [ 158.0, 1259.0, 803.0, 515.0, 127.0, 838.0, 820.0, 1242.0, 1055.0, 1245.0, 477.0, 630.0 ] ], "demands": [ 14.0, 15.0, 27.0, 10.0, 26.0, 12.0, 23.0, 21.0, 27.0, 11.0, 13.0, 27.0 ], "objective": 4167.0 }, "solution": { "open_facilities": [ 0, 1, 4 ], "assignments": [ 4, 0, 1, 4, 4, 0, 1, 0, 0, 0, 0, 1 ] }, "obj": 4167.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 12, "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 } ], "customers": [ { "id": "A", "demand": 14.0 }, { "id": "B", "demand": 15.0 }, { "id": "C", "demand": 27.0 }, { "id": "D", "demand": 10.0 }, { "id": "E", "demand": 26.0 }, { "id": "F", "demand": 12.0 }, { "id": "G", "demand": 23.0 }, { "id": "H", "demand": 21.0 }, { "id": "I", "demand": 27.0 }, { "id": "J", "demand": 11.0 }, { "id": "K", "demand": 13.0 }, { "id": "L", "demand": 27.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 570.0 }, { "facility": "F1", "customer": "B", "cost": 46.0 }, { "facility": "F1", "customer": "C", "cost": 429.0 }, { "facility": "F1", "customer": "D", "cost": 938.0 }, { "facility": "F1", "customer": "E", "cost": 531.0 }, { "facility": "F1", "customer": "F", "cost": 88.0 }, { "facility": "F1", "customer": "G", "cost": 791.0 }, { "facility": "F1", "customer": "H", "cost": 374.0 }, { "facility": "F1", "customer": "I", "cost": 101.0 }, { "facility": "F1", "customer": "J", "cost": 501.0 }, { "facility": "F1", "customer": "K", "cost": 50.0 }, { "facility": "F1", "customer": "L", "cost": 461.0 }, { "facility": "F2", "customer": "A", "cost": 312.0 }, { "facility": "F2", "customer": "B", "cost": 864.0 }, { "facility": "F2", "customer": "C", "cost": 416.0 }, { "facility": "F2", "customer": "D", "cost": 637.0 }, { "facility": "F2", "customer": "E", "cost": 275.0 }, { "facility": "F2", "customer": "F", "cost": 447.0 }, { "facility": "F2", "customer": "G", "cost": 618.0 }, { "facility": "F2", "customer": "H", "cost": 839.0 }, { "facility": "F2", "customer": "I", "cost": 701.0 }, { "facility": "F2", "customer": "J", "cost": 854.0 }, { "facility": "F2", "customer": "K", "cost": 185.0 }, { "facility": "F2", "customer": "L", "cost": 273.0 }, { "facility": "F3", "customer": "A", "cost": 658.0 }, { "facility": "F3", "customer": "B", "cost": 1110.0 }, { "facility": "F3", "customer": "C", "cost": 1023.0 }, { "facility": "F3", "customer": "D", "cost": 1206.0 }, { "facility": "F3", "customer": "E", "cost": 626.0 }, { "facility": "F3", "customer": "F", "cost": 759.0 }, { "facility": "F3", "customer": "G", "cost": 1302.0 }, { "facility": "F3", "customer": "H", "cost": 1289.0 }, { "facility": "F3", "customer": "I", "cost": 783.0 }, { "facility": "F3", "customer": "J", "cost": 1368.0 }, { "facility": "F3", "customer": "K", "cost": 244.0 }, { "facility": "F3", "customer": "L", "cost": 944.0 }, { "facility": "F4", "customer": "A", "cost": 692.0 }, { "facility": "F4", "customer": "B", "cost": 1492.0 }, { "facility": "F4", "customer": "C", "cost": 1328.0 }, { "facility": "F4", "customer": "D", "cost": 1329.0 }, { "facility": "F4", "customer": "E", "cost": 670.0 }, { "facility": "F4", "customer": "F", "cost": 1126.0 }, { "facility": "F4", "customer": "G", "cost": 1544.0 }, { "facility": "F4", "customer": "H", "cost": 1646.0 }, { "facility": "F4", "customer": "I", "cost": 1160.0 }, { "facility": "F4", "customer": "J", "cost": 1712.0 }, { "facility": "F4", "customer": "K", "cost": 611.0 }, { "facility": "F4", "customer": "L", "cost": 1216.0 }, { "facility": "F5", "customer": "A", "cost": 158.0 }, { "facility": "F5", "customer": "B", "cost": 1259.0 }, { "facility": "F5", "customer": "C", "cost": 803.0 }, { "facility": "F5", "customer": "D", "cost": 515.0 }, { "facility": "F5", "customer": "E", "cost": 127.0 }, { "facility": "F5", "customer": "F", "cost": 838.0 }, { "facility": "F5", "customer": "G", "cost": 820.0 }, { "facility": "F5", "customer": "H", "cost": 1242.0 }, { "facility": "F5", "customer": "I", "cost": 1055.0 }, { "facility": "F5", "customer": "J", "cost": 1245.0 }, { "facility": "F5", "customer": "K", "cost": 477.0 }, { "facility": "F5", "customer": "L", "cost": 630.0 } ], "objective": 4167.0 }, "solution_variant": { "selected": [ "F1", "F2", "F5" ], "assignments": [ "F5", "F1", "F2", "F5", "F5", "F1", "F2", "F1", "F1", "F1", "F1", "F2" ] }, "context_index": 22, "input_format": "json", "input_index_base": "names" }, { "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\n# num_wings=5\n# num_students=12\n# WINGS\nwing_id,wing_opening_cost,wing_bed_capacity\nF1,600.0,500.0\nF2,600.0,500.0\nF3,600.0,500.0\nF4,600.0,500.0\nF5,600.0,500.0\n# STUDENTS\nstudent_id,student_bed_requirement\n1,28.0\n2,12.0\n3,12.0\n4,18.0\n5,27.0\n6,12.0\n7,13.0\n8,22.0\n9,18.0\n10,23.0\n11,18.0\n12,14.0\n# RELOCATION_DISTANCES\nwing_id,student_id,relocation_distance_cost\nF1,1,196.0\nF1,2,382.0\nF1,3,83.0\nF1,4,161.0\nF1,5,132.0\nF1,6,25.0\nF1,7,38.0\nF1,8,729.0\nF1,9,92.0\nF1,10,65.0\nF1,11,772.0\nF1,12,61.0\nF2,1,558.0\nF2,2,736.0\nF2,3,466.0\nF2,4,602.0\nF2,5,66.0\nF2,6,141.0\nF2,7,182.0\nF2,8,1830.0\nF2,9,1079.0\nF2,10,179.0\nF2,11,1796.0\nF2,12,430.0\nF3,1,346.0\nF3,2,493.0\nF3,3,374.0\nF3,4,466.0\nF3,5,622.0\nF3,6,105.0\nF3,7,40.0\nF3,8,1975.0\nF3,9,1309.0\nF3,10,531.0\nF3,11,1865.0\nF3,12,404.0\nF4,1,145.0\nF4,2,323.0\nF4,3,45.0\nF4,4,107.0\nF4,5,214.0\nF4,6,26.0\nF4,7,27.0\nF4,8,840.0\nF4,9,128.0\nF4,10,116.0\nF4,11,817.0\nF4,12,33.0\nF5,1,128.0\nF5,2,43.0\nF5,3,260.0\nF5,4,210.0\nF5,5,709.0\nF5,6,241.0\nF5,7,171.0\nF5,8,1478.0\nF5,9,1022.0\nF5,10,588.0\nF5,11,1289.0\nF5,12,329.0\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": [ 600.0, 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 196.0, 382.0, 83.0, 161.0, 132.0, 25.0, 38.0, 729.0, 92.0, 65.0, 772.0, 61.0 ], [ 558.0, 736.0, 466.0, 602.0, 66.0, 141.0, 182.0, 1830.0, 1079.0, 179.0, 1796.0, 430.0 ], [ 346.0, 493.0, 374.0, 466.0, 622.0, 105.0, 40.0, 1975.0, 1309.0, 531.0, 1865.0, 404.0 ], [ 145.0, 323.0, 45.0, 107.0, 214.0, 26.0, 27.0, 840.0, 128.0, 116.0, 817.0, 33.0 ], [ 128.0, 43.0, 260.0, 210.0, 709.0, 241.0, 171.0, 1478.0, 1022.0, 588.0, 1289.0, 329.0 ] ], "demands": [ 28.0, 12.0, 12.0, 18.0, 27.0, 12.0, 13.0, 22.0, 18.0, 23.0, 18.0, 14.0 ], "objective": 3336.0 }, "solution": { "open_facilities": [ 0 ], "assignments": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] }, "obj": 3336.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 12, "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 } ], "customers": [ { "id": 1, "demand": 28.0 }, { "id": 2, "demand": 12.0 }, { "id": 3, "demand": 12.0 }, { "id": 4, "demand": 18.0 }, { "id": 5, "demand": 27.0 }, { "id": 6, "demand": 12.0 }, { "id": 7, "demand": 13.0 }, { "id": 8, "demand": 22.0 }, { "id": 9, "demand": 18.0 }, { "id": 10, "demand": 23.0 }, { "id": 11, "demand": 18.0 }, { "id": 12, "demand": 14.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 196.0 }, { "facility": "F1", "customer": 2, "cost": 382.0 }, { "facility": "F1", "customer": 3, "cost": 83.0 }, { "facility": "F1", "customer": 4, "cost": 161.0 }, { "facility": "F1", "customer": 5, "cost": 132.0 }, { "facility": "F1", "customer": 6, "cost": 25.0 }, { "facility": "F1", "customer": 7, "cost": 38.0 }, { "facility": "F1", "customer": 8, "cost": 729.0 }, { "facility": "F1", "customer": 9, "cost": 92.0 }, { "facility": "F1", "customer": 10, "cost": 65.0 }, { "facility": "F1", "customer": 11, "cost": 772.0 }, { "facility": "F1", "customer": 12, "cost": 61.0 }, { "facility": "F2", "customer": 1, "cost": 558.0 }, { "facility": "F2", "customer": 2, "cost": 736.0 }, { "facility": "F2", "customer": 3, "cost": 466.0 }, { "facility": "F2", "customer": 4, "cost": 602.0 }, { "facility": "F2", "customer": 5, "cost": 66.0 }, { "facility": "F2", "customer": 6, "cost": 141.0 }, { "facility": "F2", "customer": 7, "cost": 182.0 }, { "facility": "F2", "customer": 8, "cost": 1830.0 }, { "facility": "F2", "customer": 9, "cost": 1079.0 }, { "facility": "F2", "customer": 10, "cost": 179.0 }, { "facility": "F2", "customer": 11, "cost": 1796.0 }, { "facility": "F2", "customer": 12, "cost": 430.0 }, { "facility": "F3", "customer": 1, "cost": 346.0 }, { "facility": "F3", "customer": 2, "cost": 493.0 }, { "facility": "F3", "customer": 3, "cost": 374.0 }, { "facility": "F3", "customer": 4, "cost": 466.0 }, { "facility": "F3", "customer": 5, "cost": 622.0 }, { "facility": "F3", "customer": 6, "cost": 105.0 }, { "facility": "F3", "customer": 7, "cost": 40.0 }, { "facility": "F3", "customer": 8, "cost": 1975.0 }, { "facility": "F3", "customer": 9, "cost": 1309.0 }, { "facility": "F3", "customer": 10, "cost": 531.0 }, { "facility": "F3", "customer": 11, "cost": 1865.0 }, { "facility": "F3", "customer": 12, "cost": 404.0 }, { "facility": "F4", "customer": 1, "cost": 145.0 }, { "facility": "F4", "customer": 2, "cost": 323.0 }, { "facility": "F4", "customer": 3, "cost": 45.0 }, { "facility": "F4", "customer": 4, "cost": 107.0 }, { "facility": "F4", "customer": 5, "cost": 214.0 }, { "facility": "F4", "customer": 6, "cost": 26.0 }, { "facility": "F4", "customer": 7, "cost": 27.0 }, { "facility": "F4", "customer": 8, "cost": 840.0 }, { "facility": "F4", "customer": 9, "cost": 128.0 }, { "facility": "F4", "customer": 10, "cost": 116.0 }, { "facility": "F4", "customer": 11, "cost": 817.0 }, { "facility": "F4", "customer": 12, "cost": 33.0 }, { "facility": "F5", "customer": 1, "cost": 128.0 }, { "facility": "F5", "customer": 2, "cost": 43.0 }, { "facility": "F5", "customer": 3, "cost": 260.0 }, { "facility": "F5", "customer": 4, "cost": 210.0 }, { "facility": "F5", "customer": 5, "cost": 709.0 }, { "facility": "F5", "customer": 6, "cost": 241.0 }, { "facility": "F5", "customer": 7, "cost": 171.0 }, { "facility": "F5", "customer": 8, "cost": 1478.0 }, { "facility": "F5", "customer": 9, "cost": 1022.0 }, { "facility": "F5", "customer": 10, "cost": 588.0 }, { "facility": "F5", "customer": 11, "cost": 1289.0 }, { "facility": "F5", "customer": 12, "cost": 329.0 } ], "objective": 3336.0 }, "solution_variant": { "selected": [ "F1" ], "assignments": [ "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1" ] }, "context_index": 23, "input_format": "csv", "input_index_base": 1 }, { "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=4\n# num_customers=10\n# LOCKERS\nlocker_id,activation_cost,parcel_capacity\nF1,372.0,436.0\nF2,308.0,404.0\nF3,253.0,377.0\nF4,127.0,313.0\n# CUSTOMERS\ncustomer_id,parcels_needed\n1,20.0\n2,20.0\n3,30.0\n4,20.0\n5,30.0\n6,10.0\n7,9.0\n8,16.0\n9,27.0\n10,13.0\n# TRAVELS\nlocker_id,customer_id,travel_cost\nF1,1,326.0\nF1,2,213.0\nF1,3,8.0\nF1,4,251.0\nF1,5,216.0\nF1,6,324.0\nF1,7,241.0\nF1,8,128.0\nF1,9,191.0\nF1,10,170.0\nF2,1,185.0\nF2,2,22.0\nF2,3,215.0\nF2,4,374.0\nF2,5,334.0\nF2,6,292.0\nF2,7,190.0\nF2,8,159.0\nF2,9,119.0\nF2,10,180.0\nF3,1,184.0\nF3,2,140.0\nF3,3,141.0\nF3,4,241.0\nF3,5,201.0\nF3,6,206.0\nF3,7,108.0\nF3,8,27.0\nF3,9,51.0\nF3,10,56.0\nF4,1,200.0\nF4,2,267.0\nF4,3,227.0\nF4,4,144.0\nF4,5,113.0\nF4,6,108.0\nF4,7,89.0\nF4,8,120.0\nF4,9,137.0\nF4,10,79.0\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": [ 372.0, 308.0, 253.0, 127.0 ], "capacities": [ 436.0, 404.0, 377.0, 313.0 ], "connection_costs": [ [ 326.0, 213.0, 8.0, 251.0, 216.0, 324.0, 241.0, 128.0, 191.0, 170.0 ], [ 185.0, 22.0, 215.0, 374.0, 334.0, 292.0, 190.0, 159.0, 119.0, 180.0 ], [ 184.0, 140.0, 141.0, 241.0, 201.0, 206.0, 108.0, 27.0, 51.0, 56.0 ], [ 200.0, 267.0, 227.0, 144.0, 113.0, 108.0, 89.0, 120.0, 137.0, 79.0 ] ], "demands": [ 20.0, 20.0, 30.0, 20.0, 30.0, 10.0, 9.0, 16.0, 27.0, 13.0 ], "objective": 1433.0 }, "solution": { "open_facilities": [ 2, 3 ], "assignments": [ 2, 2, 2, 3, 3, 3, 3, 2, 2, 2 ] }, "obj": 1433.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 4, "num_customers": 10, "facilities": [ { "id": "F1", "opening_cost": 372.0, "capacity": 436.0 }, { "id": "F2", "opening_cost": 308.0, "capacity": 404.0 }, { "id": "F3", "opening_cost": 253.0, "capacity": 377.0 }, { "id": "F4", "opening_cost": 127.0, "capacity": 313.0 } ], "customers": [ { "id": 1, "demand": 20.0 }, { "id": 2, "demand": 20.0 }, { "id": 3, "demand": 30.0 }, { "id": 4, "demand": 20.0 }, { "id": 5, "demand": 30.0 }, { "id": 6, "demand": 10.0 }, { "id": 7, "demand": 9.0 }, { "id": 8, "demand": 16.0 }, { "id": 9, "demand": 27.0 }, { "id": 10, "demand": 13.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 326.0 }, { "facility": "F1", "customer": 2, "cost": 213.0 }, { "facility": "F1", "customer": 3, "cost": 8.0 }, { "facility": "F1", "customer": 4, "cost": 251.0 }, { "facility": "F1", "customer": 5, "cost": 216.0 }, { "facility": "F1", "customer": 6, "cost": 324.0 }, { "facility": "F1", "customer": 7, "cost": 241.0 }, { "facility": "F1", "customer": 8, "cost": 128.0 }, { "facility": "F1", "customer": 9, "cost": 191.0 }, { "facility": "F1", "customer": 10, "cost": 170.0 }, { "facility": "F2", "customer": 1, "cost": 185.0 }, { "facility": "F2", "customer": 2, "cost": 22.0 }, { "facility": "F2", "customer": 3, "cost": 215.0 }, { "facility": "F2", "customer": 4, "cost": 374.0 }, { "facility": "F2", "customer": 5, "cost": 334.0 }, { "facility": "F2", "customer": 6, "cost": 292.0 }, { "facility": "F2", "customer": 7, "cost": 190.0 }, { "facility": "F2", "customer": 8, "cost": 159.0 }, { "facility": "F2", "customer": 9, "cost": 119.0 }, { "facility": "F2", "customer": 10, "cost": 180.0 }, { "facility": "F3", "customer": 1, "cost": 184.0 }, { "facility": "F3", "customer": 2, "cost": 140.0 }, { "facility": "F3", "customer": 3, "cost": 141.0 }, { "facility": "F3", "customer": 4, "cost": 241.0 }, { "facility": "F3", "customer": 5, "cost": 201.0 }, { "facility": "F3", "customer": 6, "cost": 206.0 }, { "facility": "F3", "customer": 7, "cost": 108.0 }, { "facility": "F3", "customer": 8, "cost": 27.0 }, { "facility": "F3", "customer": 9, "cost": 51.0 }, { "facility": "F3", "customer": 10, "cost": 56.0 }, { "facility": "F4", "customer": 1, "cost": 200.0 }, { "facility": "F4", "customer": 2, "cost": 267.0 }, { "facility": "F4", "customer": 3, "cost": 227.0 }, { "facility": "F4", "customer": 4, "cost": 144.0 }, { "facility": "F4", "customer": 5, "cost": 113.0 }, { "facility": "F4", "customer": 6, "cost": 108.0 }, { "facility": "F4", "customer": 7, "cost": 89.0 }, { "facility": "F4", "customer": 8, "cost": 120.0 }, { "facility": "F4", "customer": 9, "cost": 137.0 }, { "facility": "F4", "customer": 10, "cost": 79.0 } ], "objective": 1433.0 }, "solution_variant": { "selected": [ "F3", "F4" ], "assignments": [ "F3", "F3", "F3", "F4", "F4", "F4", "F4", "F3", "F3", "F3" ] }, "context_index": 24, "input_format": "csv", "input_index_base": 1 }, { "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\nThere are 6 shelters and 13 familys in this instance.\n\n**Shelters**\n| shelter_id | shelter_setup_cost | shelter_capacity_people |\n|---|---|---|\n| F1 | 400.0 | 1382.0 |\n| F2 | 400.0 | 567.0 |\n| F3 | 400.0 | 898.0 |\n| F4 | 400.0 | 1388.0 |\n| F5 | 400.0 | 782.0 |\n| F6 | 400.0 | 506.0 |\n\n**Familys**\n| family_id | household_size |\n|---|---|\n| 0 | 24.0 |\n| 1 | 18.0 |\n| 2 | 12.0 |\n| 3 | 26.0 |\n| 4 | 27.0 |\n| 5 | 35.0 |\n| 6 | 41.0 |\n| 7 | 36.0 |\n| 8 | 21.0 |\n| 9 | 27.0 |\n| 10 | 14.0 |\n| 11 | 44.0 |\n| 12 | 16.0 |\n\n**Transport Cost**\n| shelter_id | family_id | transport_cost |\n|---|---|---|\n| F1 | 0 | 744.0 |\n| F1 | 1 | 342.0 |\n| F1 | 2 | 14.0 |\n| F1 | 3 | 622.0 |\n| F1 | 4 | 623.0 |\n| F1 | 5 | 373.0 |\n| F1 | 6 | 269.0 |\n| F1 | 7 | 635.0 |\n| F1 | 8 | 683.0 |\n| F1 | 9 | 208.0 |\n| F1 | 10 | 372.0 |\n| F1 | 11 | 626.0 |\n| F1 | 12 | 577.0 |\n| F2 | 0 | 537.0 |\n| F2 | 1 | 445.0 |\n| F2 | 2 | 526.0 |\n| F2 | 3 | 249.0 |\n| F2 | 4 | 292.0 |\n| F2 | 5 | 393.0 |\n| F2 | 6 | 247.0 |\n| F2 | 7 | 284.0 |\n| F2 | 8 | 384.0 |\n| F2 | 9 | 475.0 |\n| F2 | 10 | 589.0 |\n| F2 | 11 | 292.0 |\n| F2 | 12 | 74.0 |\n| F3 | 0 | 465.0 |\n| F3 | 1 | 193.0 |\n| F3 | 2 | 330.0 |\n| F3 | 3 | 306.0 |\n| F3 | 4 | 307.0 |\n| F3 | 5 | 158.0 |\n| F3 | 6 | 140.0 |\n| F3 | 7 | 319.0 |\n| F3 | 8 | 374.0 |\n| F3 | 9 | 214.0 |\n| F3 | 10 | 330.0 |\n| F3 | 11 | 310.0 |\n| F3 | 12 | 300.0 |\n| F4 | 0 | 439.0 |\n| F4 | 1 | 231.0 |\n| F4 | 2 | 516.0 |\n| F4 | 3 | 557.0 |\n| F4 | 4 | 516.0 |\n| F4 | 5 | 272.0 |\n| F4 | 6 | 540.0 |\n| F4 | 7 | 538.0 |\n| F4 | 8 | 503.0 |\n| F4 | 9 | 307.0 |\n| F4 | 10 | 132.0 |\n| F4 | 11 | 520.0 |\n| F4 | 12 | 672.0 |\n| F5 | 0 | 173.0 |\n| F5 | 1 | 456.0 |\n| F5 | 2 | 754.0 |\n| F5 | 3 | 166.0 |\n| F5 | 4 | 132.0 |\n| F5 | 5 | 397.0 |\n| F5 | 6 | 540.0 |\n| F5 | 7 | 133.0 |\n| F5 | 8 | 59.0 |\n| F5 | 9 | 580.0 |\n| F5 | 10 | 566.0 |\n| F5 | 11 | 131.0 |\n| F5 | 12 | 360.0 |\n| F6 | 0 | 278.0 |\n| F6 | 1 | 213.0 |\n| F6 | 2 | 501.0 |\n| F6 | 3 | 185.0 |\n| F6 | 4 | 158.0 |\n| F6 | 5 | 150.0 |\n| F6 | 6 | 319.0 |\n| F6 | 7 | 177.0 |\n| F6 | 8 | 198.0 |\n| F6 | 9 | 326.0 |\n| F6 | 10 | 346.0 |\n| F6 | 11 | 162.0 |\n| F6 | 12 | 303.0 |\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": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 1382.0, 567.0, 898.0, 1388.0, 782.0, 506.0 ], "connection_costs": [ [ 744.0, 342.0, 14.0, 622.0, 623.0, 373.0, 269.0, 635.0, 683.0, 208.0, 372.0, 626.0, 577.0 ], [ 537.0, 445.0, 526.0, 249.0, 292.0, 393.0, 247.0, 284.0, 384.0, 475.0, 589.0, 292.0, 74.0 ], [ 465.0, 193.0, 330.0, 306.0, 307.0, 158.0, 140.0, 319.0, 374.0, 214.0, 330.0, 310.0, 300.0 ], [ 439.0, 231.0, 516.0, 557.0, 516.0, 272.0, 540.0, 538.0, 503.0, 307.0, 132.0, 520.0, 672.0 ], [ 173.0, 456.0, 754.0, 166.0, 132.0, 397.0, 540.0, 133.0, 59.0, 580.0, 566.0, 131.0, 360.0 ], [ 278.0, 213.0, 501.0, 185.0, 158.0, 150.0, 319.0, 177.0, 198.0, 326.0, 346.0, 162.0, 303.0 ] ], "demands": [ 24.0, 18.0, 12.0, 26.0, 27.0, 35.0, 41.0, 36.0, 21.0, 27.0, 14.0, 44.0, 16.0 ], "objective": 3259.0 }, "solution": { "open_facilities": [ 2, 4 ], "assignments": [ 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 2 ] }, "obj": 3259.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 6, "num_customers": 13, "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": 1388.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 782.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 506.0 } ], "customers": [ { "id": 0, "demand": 24.0 }, { "id": 1, "demand": 18.0 }, { "id": 2, "demand": 12.0 }, { "id": 3, "demand": 26.0 }, { "id": 4, "demand": 27.0 }, { "id": 5, "demand": 35.0 }, { "id": 6, "demand": 41.0 }, { "id": 7, "demand": 36.0 }, { "id": 8, "demand": 21.0 }, { "id": 9, "demand": 27.0 }, { "id": 10, "demand": 14.0 }, { "id": 11, "demand": 44.0 }, { "id": 12, "demand": 16.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 744.0 }, { "facility": "F1", "customer": 1, "cost": 342.0 }, { "facility": "F1", "customer": 2, "cost": 14.0 }, { "facility": "F1", "customer": 3, "cost": 622.0 }, { "facility": "F1", "customer": 4, "cost": 623.0 }, { "facility": "F1", "customer": 5, "cost": 373.0 }, { "facility": "F1", "customer": 6, "cost": 269.0 }, { "facility": "F1", "customer": 7, "cost": 635.0 }, { "facility": "F1", "customer": 8, "cost": 683.0 }, { "facility": "F1", "customer": 9, "cost": 208.0 }, { "facility": "F1", "customer": 10, "cost": 372.0 }, { "facility": "F1", "customer": 11, "cost": 626.0 }, { "facility": "F1", "customer": 12, "cost": 577.0 }, { "facility": "F2", "customer": 0, "cost": 537.0 }, { "facility": "F2", "customer": 1, "cost": 445.0 }, { "facility": "F2", "customer": 2, "cost": 526.0 }, { "facility": "F2", "customer": 3, "cost": 249.0 }, { "facility": "F2", "customer": 4, "cost": 292.0 }, { "facility": "F2", "customer": 5, "cost": 393.0 }, { "facility": "F2", "customer": 6, "cost": 247.0 }, { "facility": "F2", "customer": 7, "cost": 284.0 }, { "facility": "F2", "customer": 8, "cost": 384.0 }, { "facility": "F2", "customer": 9, "cost": 475.0 }, { "facility": "F2", "customer": 10, "cost": 589.0 }, { "facility": "F2", "customer": 11, "cost": 292.0 }, { "facility": "F2", "customer": 12, "cost": 74.0 }, { "facility": "F3", "customer": 0, "cost": 465.0 }, { "facility": "F3", "customer": 1, "cost": 193.0 }, { "facility": "F3", "customer": 2, "cost": 330.0 }, { "facility": "F3", "customer": 3, "cost": 306.0 }, { "facility": "F3", "customer": 4, "cost": 307.0 }, { "facility": "F3", "customer": 5, "cost": 158.0 }, { "facility": "F3", "customer": 6, "cost": 140.0 }, { "facility": "F3", "customer": 7, "cost": 319.0 }, { "facility": "F3", "customer": 8, "cost": 374.0 }, { "facility": "F3", "customer": 9, "cost": 214.0 }, { "facility": "F3", "customer": 10, "cost": 330.0 }, { "facility": "F3", "customer": 11, "cost": 310.0 }, { "facility": "F3", "customer": 12, "cost": 300.0 }, { "facility": "F4", "customer": 0, "cost": 439.0 }, { "facility": "F4", "customer": 1, "cost": 231.0 }, { "facility": "F4", "customer": 2, "cost": 516.0 }, { "facility": "F4", "customer": 3, "cost": 557.0 }, { "facility": "F4", "customer": 4, "cost": 516.0 }, { "facility": "F4", "customer": 5, "cost": 272.0 }, { "facility": "F4", "customer": 6, "cost": 540.0 }, { "facility": "F4", "customer": 7, "cost": 538.0 }, { "facility": "F4", "customer": 8, "cost": 503.0 }, { "facility": "F4", "customer": 9, "cost": 307.0 }, { "facility": "F4", "customer": 10, "cost": 132.0 }, { "facility": "F4", "customer": 11, "cost": 520.0 }, { "facility": "F4", "customer": 12, "cost": 672.0 }, { "facility": "F5", "customer": 0, "cost": 173.0 }, { "facility": "F5", "customer": 1, "cost": 456.0 }, { "facility": "F5", "customer": 2, "cost": 754.0 }, { "facility": "F5", "customer": 3, "cost": 166.0 }, { "facility": "F5", "customer": 4, "cost": 132.0 }, { "facility": "F5", "customer": 5, "cost": 397.0 }, { "facility": "F5", "customer": 6, "cost": 540.0 }, { "facility": "F5", "customer": 7, "cost": 133.0 }, { "facility": "F5", "customer": 8, "cost": 59.0 }, { "facility": "F5", "customer": 9, "cost": 580.0 }, { "facility": "F5", "customer": 10, "cost": 566.0 }, { "facility": "F5", "customer": 11, "cost": 131.0 }, { "facility": "F5", "customer": 12, "cost": 360.0 }, { "facility": "F6", "customer": 0, "cost": 278.0 }, { "facility": "F6", "customer": 1, "cost": 213.0 }, { "facility": "F6", "customer": 2, "cost": 501.0 }, { "facility": "F6", "customer": 3, "cost": 185.0 }, { "facility": "F6", "customer": 4, "cost": 158.0 }, { "facility": "F6", "customer": 5, "cost": 150.0 }, { "facility": "F6", "customer": 6, "cost": 319.0 }, { "facility": "F6", "customer": 7, "cost": 177.0 }, { "facility": "F6", "customer": 8, "cost": 198.0 }, { "facility": "F6", "customer": 9, "cost": 326.0 }, { "facility": "F6", "customer": 10, "cost": 346.0 }, { "facility": "F6", "customer": 11, "cost": 162.0 }, { "facility": "F6", "customer": 12, "cost": 303.0 } ], "objective": 3259.0 }, "solution_variant": { "selected": [ "F3", "F5" ], "assignments": [ "F5", "F3", "F3", "F5", "F5", "F3", "F3", "F5", "F5", "F3", "F3", "F5", "F3" ] }, "context_index": 25, "input_format": "markdown_table", "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 5 candidate edge servers and 14 user devices in the scenario.\nEdge server F1 can be provisioned at cost 400.0 and offers capacity 500.0.\nEdge server F2 can be provisioned at cost 400.0 and offers capacity 500.0.\nEdge server F3 can be provisioned at cost 400.0 and offers capacity 500.0.\nEdge server F4 can be provisioned at cost 400.0 and offers capacity 500.0.\nEdge server F5 can be provisioned at cost 400.0 and offers capacity 500.0.\nDevice 0 has demand 28.0.\nDevice 1 has demand 20.0.\nDevice 2 has demand 28.0.\nDevice 3 has demand 22.0.\nDevice 4 has demand 19.0.\nDevice 5 has demand 23.0.\nDevice 6 has demand 30.0.\nDevice 7 has demand 27.0.\nDevice 8 has demand 23.0.\nDevice 9 has demand 18.0.\nDevice 10 has demand 26.0.\nDevice 11 has demand 11.0.\nDevice 12 has demand 29.0.\nDevice 13 has demand 29.0.\nAssigning device 0 to edge server F1 incurs latency cost 371.0.\nAssigning device 1 to edge server F1 incurs latency cost 87.0.\nAssigning device 2 to edge server F1 incurs latency cost 506.0.\nAssigning device 3 to edge server F1 incurs latency cost 611.0.\nAssigning device 4 to edge server F1 incurs latency cost 376.0.\nAssigning device 5 to edge server F1 incurs latency cost 100.0.\nAssigning device 6 to edge server F1 incurs latency cost 255.0.\nAssigning device 7 to edge server F1 incurs latency cost 107.0.\nAssigning device 8 to edge server F1 incurs latency cost 46.0.\nAssigning device 9 to edge server F1 incurs latency cost 516.0.\nAssigning device 10 to edge server F1 incurs latency cost 190.0.\nAssigning device 11 to edge server F1 incurs latency cost 158.0.\nAssigning device 12 to edge server F1 incurs latency cost 72.0.\nAssigning device 13 to edge server F1 incurs latency cost 604.0.\nAssigning device 0 to edge server F2 incurs latency cost 1118.0.\nAssigning device 1 to edge server F2 incurs latency cost 136.0.\nAssigning device 2 to edge server F2 incurs latency cost 116.0.\nAssigning device 3 to edge server F2 incurs latency cost 1286.0.\nAssigning device 4 to edge server F2 incurs latency cost 997.0.\nAssigning device 5 to edge server F2 incurs latency cost 293.0.\nAssigning device 6 to edge server F2 incurs latency cost 68.0.\nAssigning device 7 to edge server F2 incurs latency cost 651.0.\nAssigning device 8 to edge server F2 incurs latency cost 798.0.\nAssigning device 9 to edge server F2 incurs latency cost 1070.0.\nAssigning device 10 to edge server F2 incurs latency cost 527.0.\nAssigning device 11 to edge server F2 incurs latency cost 24.0.\nAssigning device 12 to edge server F2 incurs latency cost 148.0.\nAssigning device 13 to edge server F2 incurs latency cost 200.0.\nAssigning device 0 to edge server F3 incurs latency cost 1203.0.\nAssigning device 1 to edge server F3 incurs latency cost 212.0.\nAssigning device 2 to edge server F3 incurs latency cost 56.0.\nAssigning device 3 to edge server F3 incurs latency cost 1343.0.\nAssigning device 4 to edge server F3 incurs latency cost 1092.0.\nAssigning device 5 to edge server F3 incurs latency cost 349.0.\nAssigning device 6 to edge server F3 incurs latency cost 61.0.\nAssigning device 7 to edge server F3 incurs latency cost 734.0.\nAssigning device 8 to edge server F3 incurs latency cost 879.0.\nAssigning device 9 to edge server F3 incurs latency cost 1116.0.\nAssigning device 10 to edge server F3 incurs latency cost 607.0.\nAssigning device 11 to edge server F3 incurs latency cost 26.0.\nAssigning device 12 to edge server F3 incurs latency cost 177.0.\nAssigning device 13 to edge server F3 incurs latency cost 77.0.\nAssigning device 0 to edge server F4 incurs latency cost 684.0.\nAssigning device 1 to edge server F4 incurs latency cost 421.0.\nAssigning device 2 to edge server F4 incurs latency cost 996.0.\nAssigning device 3 to edge server F4 incurs latency cost 1160.0.\nAssigning device 4 to edge server F4 incurs latency cost 103.0.\nAssigning device 5 to edge server F4 incurs latency cost 48.0.\nAssigning device 6 to edge server F4 incurs latency cost 566.0.\nAssigning device 7 to edge server F4 incurs latency cost 759.0.\nAssigning device 8 to edge server F4 incurs latency cost 739.0.\nAssigning device 9 to edge server F4 incurs latency cost 1178.0.\nAssigning device 10 to edge server F4 incurs latency cost 825.0.\nAssigning device 11 to edge server F4 incurs latency cost 416.0.\nAssigning device 12 to edge server F4 incurs latency cost 62.0.\nAssigning device 13 to edge server F4 incurs latency cost 1088.0.\nAssigning device 0 to edge server F5 incurs latency cost 1877.0.\nAssigning device 1 to edge server F5 incurs latency cost 941.0.\nAssigning device 2 to edge server F5 incurs latency cost 1467.0.\nAssigning device 3 to edge server F5 incurs latency cost 2301.0.\nAssigning device 4 to edge server F5 incurs latency cost 1376.0.\nAssigning device 5 to edge server F5 incurs latency cost 114.0.\nAssigning device 6 to edge server F5 incurs latency cost 861.0.\nAssigning device 7 to edge server F5 incurs latency cost 1686.0.\nAssigning device 8 to edge server F5 incurs latency cost 1753.0.\nAssigning device 9 to edge server F5 incurs latency cost 2217.0.\nAssigning device 10 to edge server F5 incurs latency cost 1676.0.\nAssigning device 11 to edge server F5 incurs latency cost 661.0.\nAssigning device 12 to edge server F5 incurs latency cost 68.0.\nAssigning device 13 to edge server F5 incurs latency cost 1522.0.\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": [ 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 371.0, 87.0, 506.0, 611.0, 376.0, 100.0, 255.0, 107.0, 46.0, 516.0, 190.0, 158.0, 72.0, 604.0 ], [ 1118.0, 136.0, 116.0, 1286.0, 997.0, 293.0, 68.0, 651.0, 798.0, 1070.0, 527.0, 24.0, 148.0, 200.0 ], [ 1203.0, 212.0, 56.0, 1343.0, 1092.0, 349.0, 61.0, 734.0, 879.0, 1116.0, 607.0, 26.0, 177.0, 77.0 ], [ 684.0, 421.0, 996.0, 1160.0, 103.0, 48.0, 566.0, 759.0, 739.0, 1178.0, 825.0, 416.0, 62.0, 1088.0 ], [ 1877.0, 941.0, 1467.0, 2301.0, 1376.0, 114.0, 861.0, 1686.0, 1753.0, 2217.0, 1676.0, 661.0, 68.0, 1522.0 ] ], "demands": [ 28.0, 20.0, 28.0, 22.0, 19.0, 23.0, 30.0, 27.0, 23.0, 18.0, 26.0, 11.0, 29.0, 29.0 ], "objective": 3496.0 }, "solution": { "open_facilities": [ 0, 2 ], "assignments": [ 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2 ] }, "obj": 3496.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 14, "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 } ], "customers": [ { "id": 0, "demand": 28.0 }, { "id": 1, "demand": 20.0 }, { "id": 2, "demand": 28.0 }, { "id": 3, "demand": 22.0 }, { "id": 4, "demand": 19.0 }, { "id": 5, "demand": 23.0 }, { "id": 6, "demand": 30.0 }, { "id": 7, "demand": 27.0 }, { "id": 8, "demand": 23.0 }, { "id": 9, "demand": 18.0 }, { "id": 10, "demand": 26.0 }, { "id": 11, "demand": 11.0 }, { "id": 12, "demand": 29.0 }, { "id": 13, "demand": 29.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 371.0 }, { "facility": "F1", "customer": 1, "cost": 87.0 }, { "facility": "F1", "customer": 2, "cost": 506.0 }, { "facility": "F1", "customer": 3, "cost": 611.0 }, { "facility": "F1", "customer": 4, "cost": 376.0 }, { "facility": "F1", "customer": 5, "cost": 100.0 }, { "facility": "F1", "customer": 6, "cost": 255.0 }, { "facility": "F1", "customer": 7, "cost": 107.0 }, { "facility": "F1", "customer": 8, "cost": 46.0 }, { "facility": "F1", "customer": 9, "cost": 516.0 }, { "facility": "F1", "customer": 10, "cost": 190.0 }, { "facility": "F1", "customer": 11, "cost": 158.0 }, { "facility": "F1", "customer": 12, "cost": 72.0 }, { "facility": "F1", "customer": 13, "cost": 604.0 }, { "facility": "F2", "customer": 0, "cost": 1118.0 }, { "facility": "F2", "customer": 1, "cost": 136.0 }, { "facility": "F2", "customer": 2, "cost": 116.0 }, { "facility": "F2", "customer": 3, "cost": 1286.0 }, { "facility": "F2", "customer": 4, "cost": 997.0 }, { "facility": "F2", "customer": 5, "cost": 293.0 }, { "facility": "F2", "customer": 6, "cost": 68.0 }, { "facility": "F2", "customer": 7, "cost": 651.0 }, { "facility": "F2", "customer": 8, "cost": 798.0 }, { "facility": "F2", "customer": 9, "cost": 1070.0 }, { "facility": "F2", "customer": 10, "cost": 527.0 }, { "facility": "F2", "customer": 11, "cost": 24.0 }, { "facility": "F2", "customer": 12, "cost": 148.0 }, { "facility": "F2", "customer": 13, "cost": 200.0 }, { "facility": "F3", "customer": 0, "cost": 1203.0 }, { "facility": "F3", "customer": 1, "cost": 212.0 }, { "facility": "F3", "customer": 2, "cost": 56.0 }, { "facility": "F3", "customer": 3, "cost": 1343.0 }, { "facility": "F3", "customer": 4, "cost": 1092.0 }, { "facility": "F3", "customer": 5, "cost": 349.0 }, { "facility": "F3", "customer": 6, "cost": 61.0 }, { "facility": "F3", "customer": 7, "cost": 734.0 }, { "facility": "F3", "customer": 8, "cost": 879.0 }, { "facility": "F3", "customer": 9, "cost": 1116.0 }, { "facility": "F3", "customer": 10, "cost": 607.0 }, { "facility": "F3", "customer": 11, "cost": 26.0 }, { "facility": "F3", "customer": 12, "cost": 177.0 }, { "facility": "F3", "customer": 13, "cost": 77.0 }, { "facility": "F4", "customer": 0, "cost": 684.0 }, { "facility": "F4", "customer": 1, "cost": 421.0 }, { "facility": "F4", "customer": 2, "cost": 996.0 }, { "facility": "F4", "customer": 3, "cost": 1160.0 }, { "facility": "F4", "customer": 4, "cost": 103.0 }, { "facility": "F4", "customer": 5, "cost": 48.0 }, { "facility": "F4", "customer": 6, "cost": 566.0 }, { "facility": "F4", "customer": 7, "cost": 759.0 }, { "facility": "F4", "customer": 8, "cost": 739.0 }, { "facility": "F4", "customer": 9, "cost": 1178.0 }, { "facility": "F4", "customer": 10, "cost": 825.0 }, { "facility": "F4", "customer": 11, "cost": 416.0 }, { "facility": "F4", "customer": 12, "cost": 62.0 }, { "facility": "F4", "customer": 13, "cost": 1088.0 }, { "facility": "F5", "customer": 0, "cost": 1877.0 }, { "facility": "F5", "customer": 1, "cost": 941.0 }, { "facility": "F5", "customer": 2, "cost": 1467.0 }, { "facility": "F5", "customer": 3, "cost": 2301.0 }, { "facility": "F5", "customer": 4, "cost": 1376.0 }, { "facility": "F5", "customer": 5, "cost": 114.0 }, { "facility": "F5", "customer": 6, "cost": 861.0 }, { "facility": "F5", "customer": 7, "cost": 1686.0 }, { "facility": "F5", "customer": 8, "cost": 1753.0 }, { "facility": "F5", "customer": 9, "cost": 2217.0 }, { "facility": "F5", "customer": 10, "cost": 1676.0 }, { "facility": "F5", "customer": 11, "cost": 661.0 }, { "facility": "F5", "customer": 12, "cost": 68.0 }, { "facility": "F5", "customer": 13, "cost": 1522.0 } ], "objective": 3496.0 }, "solution_variant": { "selected": [ "F1", "F3" ], "assignments": [ "F1", "F1", "F3", "F1", "F1", "F1", "F3", "F1", "F1", "F1", "F1", "F3", "F1", "F3" ] }, "context_index": 26, "input_format": "nl", "input_index_base": 0 }, { "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\n{\n \"num_stalls\": 5,\n \"num_sellers\": 12,\n \"stalls\": [\n {\n \"stall_id\": \"F1\",\n \"stall_rental_fee\": 600.0,\n \"stall_space_limit\": 700.0\n },\n {\n \"stall_id\": \"F2\",\n \"stall_rental_fee\": 600.0,\n \"stall_space_limit\": 700.0\n },\n {\n \"stall_id\": \"F3\",\n \"stall_rental_fee\": 600.0,\n \"stall_space_limit\": 700.0\n },\n {\n \"stall_id\": \"F4\",\n \"stall_rental_fee\": 600.0,\n \"stall_space_limit\": 700.0\n },\n {\n \"stall_id\": \"F5\",\n \"stall_rental_fee\": 600.0,\n \"stall_space_limit\": 700.0\n }\n ],\n \"sellers\": [\n {\n \"seller_id\": 1,\n \"seller_space_requirement\": 25.0\n },\n {\n \"seller_id\": 2,\n \"seller_space_requirement\": 24.0\n },\n {\n \"seller_id\": 3,\n \"seller_space_requirement\": 17.0\n },\n {\n \"seller_id\": 4,\n \"seller_space_requirement\": 23.0\n },\n {\n \"seller_id\": 5,\n \"seller_space_requirement\": 18.0\n },\n {\n \"seller_id\": 6,\n \"seller_space_requirement\": 17.0\n },\n {\n \"seller_id\": 7,\n \"seller_space_requirement\": 18.0\n },\n {\n \"seller_id\": 8,\n \"seller_space_requirement\": 17.0\n },\n {\n \"seller_id\": 9,\n \"seller_space_requirement\": 23.0\n },\n {\n \"seller_id\": 10,\n \"seller_space_requirement\": 18.0\n },\n {\n \"seller_id\": 11,\n \"seller_space_requirement\": 23.0\n },\n {\n \"seller_id\": 12,\n \"seller_space_requirement\": 22.0\n }\n ],\n \"setup_travels\": [\n {\n \"stall_id\": \"F1\",\n \"seller_id\": 1,\n \"setup_travel_cost\": 1087.0\n },\n {\n \"stall_id\": \"F1\",\n \"seller_id\": 2,\n \"setup_travel_cost\": 1613.0\n },\n {\n \"stall_id\": \"F1\",\n \"seller_id\": 3,\n \"setup_travel_cost\": 306.0\n },\n {\n \"stall_id\": \"F1\",\n \"seller_id\": 4,\n \"setup_travel_cost\": 993.0\n },\n {\n \"stall_id\": \"F1\",\n \"seller_id\": 5,\n \"setup_travel_cost\": 37.0\n },\n {\n \"stall_id\": \"F1\",\n \"seller_id\": 6,\n \"setup_travel_cost\": 65.0\n },\n {\n \"stall_id\": \"F1\",\n \"seller_id\": 7,\n \"setup_travel_cost\": 1086.0\n },\n {\n \"stall_id\": \"F1\",\n \"seller_id\": 8,\n \"setup_travel_cost\": 989.0\n },\n {\n \"stall_id\": \"F1\",\n \"seller_id\": 9,\n \"setup_travel_cost\": 828.0\n },\n {\n \"stall_id\": \"F1\",\n \"seller_id\": 10,\n \"setup_travel_cost\": 1944.0\n },\n {\n \"stall_id\": \"F1\",\n \"seller_id\": 11,\n \"setup_travel_cost\": 1509.0\n },\n {\n \"stall_id\": \"F1\",\n \"seller_id\": 12,\n \"setup_travel_cost\": 1335.0\n },\n {\n \"stall_id\": \"F2\",\n \"seller_id\": 1,\n \"setup_travel_cost\": 1241.0\n },\n {\n \"stall_id\": \"F2\",\n \"seller_id\": 2,\n \"setup_travel_cost\": 1776.0\n },\n {\n \"stall_id\": \"F2\",\n \"seller_id\": 3,\n \"setup_travel_cost\": 482.0\n },\n {\n \"stall_id\": \"F2\",\n \"seller_id\": 4,\n \"setup_travel_cost\": 1040.0\n },\n {\n \"stall_id\": \"F2\",\n \"seller_id\": 5,\n \"setup_travel_cost\": 59.0\n },\n {\n \"stall_id\": \"F2\",\n \"seller_id\": 6,\n \"setup_travel_cost\": 41.0\n },\n {\n \"stall_id\": \"F2\",\n \"seller_id\": 7,\n \"setup_travel_cost\": 1229.0\n },\n {\n \"stall_id\": \"F2\",\n \"seller_id\": 8,\n \"setup_travel_cost\": 1160.0\n },\n {\n \"stall_id\": \"F2\",\n \"seller_id\": 9,\n \"setup_travel_cost\": 1030.0\n },\n {\n \"stall_id\": \"F2\",\n \"seller_id\": 10,\n \"setup_travel_cost\": 1986.0\n },\n {\n \"stall_id\": \"F2\",\n \"seller_id\": 11,\n \"setup_travel_cost\": 1681.0\n },\n {\n \"stall_id\": \"F2\",\n \"seller_id\": 12,\n \"setup_travel_cost\": 1523.0\n },\n {\n \"stall_id\": \"F3\",\n \"seller_id\": 1,\n \"setup_travel_cost\": 956.0\n },\n {\n \"stall_id\": \"F3\",\n \"seller_id\": 2,\n \"setup_travel_cost\": 1480.0\n },\n {\n \"stall_id\": \"F3\",\n \"seller_id\": 3,\n \"setup_travel_cost\": 404.0\n },\n {\n \"stall_id\": \"F3\",\n \"seller_id\": 4,\n \"setup_travel_cost\": 677.0\n },\n {\n \"stall_id\": \"F3\",\n \"seller_id\": 5,\n \"setup_travel_cost\": 52.0\n },\n {\n \"stall_id\": \"F3\",\n \"seller_id\": 6,\n \"setup_travel_cost\": 35.0\n },\n {\n \"stall_id\": \"F3\",\n \"seller_id\": 7,\n \"setup_travel_cost\": 930.0\n },\n {\n \"stall_id\": \"F3\",\n \"seller_id\": 8,\n \"setup_travel_cost\": 897.0\n },\n {\n \"stall_id\": \"F3\",\n \"seller_id\": 9,\n \"setup_travel_cost\": 819.0\n },\n {\n \"stall_id\": \"F3\",\n \"seller_id\": 10,\n \"setup_travel_cost\": 1574.0\n },\n {\n \"stall_id\": \"F3\",\n \"seller_id\": 11,\n \"setup_travel_cost\": 1400.0\n },\n {\n \"stall_id\": \"F3\",\n \"seller_id\": 12,\n \"setup_travel_cost\": 1270.0\n },\n {\n \"stall_id\": \"F4\",\n \"seller_id\": 1,\n \"setup_travel_cost\": 384.0\n },\n {\n \"stall_id\": \"F4\",\n \"seller_id\": 2,\n \"setup_travel_cost\": 818.0\n },\n {\n \"stall_id\": \"F4\",\n \"seller_id\": 3,\n \"setup_travel_cost\": 221.0\n },\n {\n \"stall_id\": \"F4\",\n \"seller_id\": 4,\n \"setup_travel_cost\": 97.0\n },\n {\n \"stall_id\": \"F4\",\n \"seller_id\": 5,\n \"setup_travel_cost\": 37.0\n },\n {\n \"stall_id\": \"F4\",\n \"seller_id\": 6,\n \"setup_travel_cost\": 52.0\n },\n {\n \"stall_id\": \"F4\",\n \"seller_id\": 7,\n \"setup_travel_cost\": 341.0\n },\n {\n \"stall_id\": \"F4\",\n \"seller_id\": 8,\n \"setup_travel_cost\": 368.0\n },\n {\n \"stall_id\": \"F4\",\n \"seller_id\": 9,\n \"setup_travel_cost\": 382.0\n },\n {\n \"stall_id\": \"F4\",\n \"seller_id\": 10,\n \"setup_travel_cost\": 731.0\n },\n {\n \"stall_id\": \"F4\",\n \"seller_id\": 11,\n \"setup_travel_cost\": 771.0\n },\n {\n \"stall_id\": \"F4\",\n \"seller_id\": 12,\n \"setup_travel_cost\": 701.0\n },\n {\n \"stall_id\": \"F5\",\n \"seller_id\": 1,\n \"setup_travel_cost\": 1329.0\n },\n {\n \"stall_id\": \"F5\",\n \"seller_id\": 2,\n \"setup_travel_cost\": 1771.0\n },\n {\n \"stall_id\": \"F5\",\n \"seller_id\": 3,\n \"setup_travel_cost\": 34.0\n },\n {\n \"stall_id\": \"F5\",\n \"seller_id\": 4,\n \"setup_travel_cost\": 1433.0\n },\n {\n \"stall_id\": \"F5\",\n \"seller_id\": 5,\n \"setup_travel_cost\": 71.0\n },\n {\n \"stall_id\": \"F5\",\n \"seller_id\": 6,\n \"setup_travel_cost\": 328.0\n },\n {\n \"stall_id\": \"F5\",\n \"seller_id\": 7,\n \"setup_travel_cost\": 1358.0\n },\n {\n \"stall_id\": \"F5\",\n \"seller_id\": 8,\n \"setup_travel_cost\": 1195.0\n },\n {\n \"stall_id\": \"F5\",\n \"seller_id\": 9,\n \"setup_travel_cost\": 933.0\n },\n {\n \"stall_id\": \"F5\",\n \"seller_id\": 10,\n \"setup_travel_cost\": 2309.0\n },\n {\n \"stall_id\": \"F5\",\n \"seller_id\": 11,\n \"setup_travel_cost\": 1645.0\n },\n {\n \"stall_id\": \"F5\",\n \"seller_id\": 12,\n \"setup_travel_cost\": 1430.0\n }\n ]\n}\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 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 1087.0, 1613.0, 306.0, 993.0, 37.0, 65.0, 1086.0, 989.0, 828.0, 1944.0, 1509.0, 1335.0 ], [ 1241.0, 1776.0, 482.0, 1040.0, 59.0, 41.0, 1229.0, 1160.0, 1030.0, 1986.0, 1681.0, 1523.0 ], [ 956.0, 1480.0, 404.0, 677.0, 52.0, 35.0, 930.0, 897.0, 819.0, 1574.0, 1400.0, 1270.0 ], [ 384.0, 818.0, 221.0, 97.0, 37.0, 52.0, 341.0, 368.0, 382.0, 731.0, 771.0, 701.0 ], [ 1329.0, 1771.0, 34.0, 1433.0, 71.0, 328.0, 1358.0, 1195.0, 933.0, 2309.0, 1645.0, 1430.0 ] ], "demands": [ 25.0, 24.0, 17.0, 23.0, 18.0, 17.0, 18.0, 17.0, 23.0, 18.0, 23.0, 22.0 ], "objective": 5503.0 }, "solution": { "open_facilities": [ 3 ], "assignments": [ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ] }, "obj": 5503.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 12, "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 } ], "customers": [ { "id": 1, "demand": 25.0 }, { "id": 2, "demand": 24.0 }, { "id": 3, "demand": 17.0 }, { "id": 4, "demand": 23.0 }, { "id": 5, "demand": 18.0 }, { "id": 6, "demand": 17.0 }, { "id": 7, "demand": 18.0 }, { "id": 8, "demand": 17.0 }, { "id": 9, "demand": 23.0 }, { "id": 10, "demand": 18.0 }, { "id": 11, "demand": 23.0 }, { "id": 12, "demand": 22.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 1087.0 }, { "facility": "F1", "customer": 2, "cost": 1613.0 }, { "facility": "F1", "customer": 3, "cost": 306.0 }, { "facility": "F1", "customer": 4, "cost": 993.0 }, { "facility": "F1", "customer": 5, "cost": 37.0 }, { "facility": "F1", "customer": 6, "cost": 65.0 }, { "facility": "F1", "customer": 7, "cost": 1086.0 }, { "facility": "F1", "customer": 8, "cost": 989.0 }, { "facility": "F1", "customer": 9, "cost": 828.0 }, { "facility": "F1", "customer": 10, "cost": 1944.0 }, { "facility": "F1", "customer": 11, "cost": 1509.0 }, { "facility": "F1", "customer": 12, "cost": 1335.0 }, { "facility": "F2", "customer": 1, "cost": 1241.0 }, { "facility": "F2", "customer": 2, "cost": 1776.0 }, { "facility": "F2", "customer": 3, "cost": 482.0 }, { "facility": "F2", "customer": 4, "cost": 1040.0 }, { "facility": "F2", "customer": 5, "cost": 59.0 }, { "facility": "F2", "customer": 6, "cost": 41.0 }, { "facility": "F2", "customer": 7, "cost": 1229.0 }, { "facility": "F2", "customer": 8, "cost": 1160.0 }, { "facility": "F2", "customer": 9, "cost": 1030.0 }, { "facility": "F2", "customer": 10, "cost": 1986.0 }, { "facility": "F2", "customer": 11, "cost": 1681.0 }, { "facility": "F2", "customer": 12, "cost": 1523.0 }, { "facility": "F3", "customer": 1, "cost": 956.0 }, { "facility": "F3", "customer": 2, "cost": 1480.0 }, { "facility": "F3", "customer": 3, "cost": 404.0 }, { "facility": "F3", "customer": 4, "cost": 677.0 }, { "facility": "F3", "customer": 5, "cost": 52.0 }, { "facility": "F3", "customer": 6, "cost": 35.0 }, { "facility": "F3", "customer": 7, "cost": 930.0 }, { "facility": "F3", "customer": 8, "cost": 897.0 }, { "facility": "F3", "customer": 9, "cost": 819.0 }, { "facility": "F3", "customer": 10, "cost": 1574.0 }, { "facility": "F3", "customer": 11, "cost": 1400.0 }, { "facility": "F3", "customer": 12, "cost": 1270.0 }, { "facility": "F4", "customer": 1, "cost": 384.0 }, { "facility": "F4", "customer": 2, "cost": 818.0 }, { "facility": "F4", "customer": 3, "cost": 221.0 }, { "facility": "F4", "customer": 4, "cost": 97.0 }, { "facility": "F4", "customer": 5, "cost": 37.0 }, { "facility": "F4", "customer": 6, "cost": 52.0 }, { "facility": "F4", "customer": 7, "cost": 341.0 }, { "facility": "F4", "customer": 8, "cost": 368.0 }, { "facility": "F4", "customer": 9, "cost": 382.0 }, { "facility": "F4", "customer": 10, "cost": 731.0 }, { "facility": "F4", "customer": 11, "cost": 771.0 }, { "facility": "F4", "customer": 12, "cost": 701.0 }, { "facility": "F5", "customer": 1, "cost": 1329.0 }, { "facility": "F5", "customer": 2, "cost": 1771.0 }, { "facility": "F5", "customer": 3, "cost": 34.0 }, { "facility": "F5", "customer": 4, "cost": 1433.0 }, { "facility": "F5", "customer": 5, "cost": 71.0 }, { "facility": "F5", "customer": 6, "cost": 328.0 }, { "facility": "F5", "customer": 7, "cost": 1358.0 }, { "facility": "F5", "customer": 8, "cost": 1195.0 }, { "facility": "F5", "customer": 9, "cost": 933.0 }, { "facility": "F5", "customer": 10, "cost": 2309.0 }, { "facility": "F5", "customer": 11, "cost": 1645.0 }, { "facility": "F5", "customer": 12, "cost": 1430.0 } ], "objective": 5503.0 }, "solution_variant": { "selected": [ "F4" ], "assignments": [ "F4", "F4", "F4", "F4", "F4", "F4", "F4", "F4", "F4", "F4", "F4", "F4" ] }, "context_index": 27, "input_format": "json", "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# num_kitchens=5\n# num_student_groups=13\n# KITCHENS\nkitchen_id,kitchen_operating_cost,kitchen_capacity_students\nF1,600.0,300.0\nF2,600.0,300.0\nF3,600.0,300.0\nF4,600.0,300.0\nF5,600.0,300.0\n# STUDENT_GROUPS\nstudent_group_id,group_size\nA,28.0\nB,12.0\nC,30.0\nD,24.0\nE,20.0\nF,17.0\nG,17.0\nH,15.0\nI,12.0\nJ,25.0\nK,27.0\nL,19.0\nM,27.0\n# DISTRIBUTIONS\nkitchen_id,student_group_id,distribution_cost\nF1,A,81.0\nF1,B,24.0\nF1,C,168.0\nF1,D,595.0\nF1,E,281.0\nF1,F,80.0\nF1,G,107.0\nF1,H,126.0\nF1,I,57.0\nF1,J,245.0\nF1,K,278.0\nF1,L,40.0\nF1,M,412.0\nF2,A,78.0\nF2,B,25.0\nF2,C,165.0\nF2,D,692.0\nF2,E,340.0\nF2,F,102.0\nF2,G,104.0\nF2,H,125.0\nF2,I,120.0\nF2,J,273.0\nF2,K,401.0\nF2,L,38.0\nF2,M,486.0\nF3,A,140.0\nF3,B,258.0\nF3,C,71.0\nF3,D,274.0\nF3,E,750.0\nF3,F,485.0\nF3,G,36.0\nF3,H,30.0\nF3,I,756.0\nF3,J,64.0\nF3,K,1006.0\nF3,L,229.0\nF3,M,54.0\nF4,A,262.0\nF4,B,427.0\nF4,C,61.0\nF4,D,535.0\nF4,E,909.0\nF4,F,813.0\nF4,G,35.0\nF4,H,43.0\nF4,I,1039.0\nF4,J,250.0\nF4,K,1248.0\nF4,L,389.0\nF4,M,450.0\nF5,A,558.0\nF5,B,466.0\nF5,C,405.0\nF5,D,1637.0\nF5,E,40.0\nF5,F,1193.0\nF5,G,320.0\nF5,H,487.0\nF5,I,946.0\nF5,J,1069.0\nF5,K,754.0\nF5,L,495.0\nF5,M,1426.0\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": [ 600.0, 600.0, 600.0, 600.0, 600.0 ], "capacities": [ 300.0, 300.0, 300.0, 300.0, 300.0 ], "connection_costs": [ [ 81.0, 24.0, 168.0, 595.0, 281.0, 80.0, 107.0, 126.0, 57.0, 245.0, 278.0, 40.0, 412.0 ], [ 78.0, 25.0, 165.0, 692.0, 340.0, 102.0, 104.0, 125.0, 120.0, 273.0, 401.0, 38.0, 486.0 ], [ 140.0, 258.0, 71.0, 274.0, 750.0, 485.0, 36.0, 30.0, 756.0, 64.0, 1006.0, 229.0, 54.0 ], [ 262.0, 427.0, 61.0, 535.0, 909.0, 813.0, 35.0, 43.0, 1039.0, 250.0, 1248.0, 389.0, 450.0 ], [ 558.0, 466.0, 405.0, 1637.0, 40.0, 1193.0, 320.0, 487.0, 946.0, 1069.0, 754.0, 495.0, 1426.0 ] ], "demands": [ 28.0, 12.0, 30.0, 24.0, 20.0, 17.0, 17.0, 15.0, 12.0, 25.0, 27.0, 19.0, 27.0 ], "objective": 2570.0 }, "solution": { "open_facilities": [ 0, 2 ], "assignments": [ 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2 ] }, "obj": 2570.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 13, "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 } ], "customers": [ { "id": "A", "demand": 28.0 }, { "id": "B", "demand": 12.0 }, { "id": "C", "demand": 30.0 }, { "id": "D", "demand": 24.0 }, { "id": "E", "demand": 20.0 }, { "id": "F", "demand": 17.0 }, { "id": "G", "demand": 17.0 }, { "id": "H", "demand": 15.0 }, { "id": "I", "demand": 12.0 }, { "id": "J", "demand": 25.0 }, { "id": "K", "demand": 27.0 }, { "id": "L", "demand": 19.0 }, { "id": "M", "demand": 27.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 81.0 }, { "facility": "F1", "customer": "B", "cost": 24.0 }, { "facility": "F1", "customer": "C", "cost": 168.0 }, { "facility": "F1", "customer": "D", "cost": 595.0 }, { "facility": "F1", "customer": "E", "cost": 281.0 }, { "facility": "F1", "customer": "F", "cost": 80.0 }, { "facility": "F1", "customer": "G", "cost": 107.0 }, { "facility": "F1", "customer": "H", "cost": 126.0 }, { "facility": "F1", "customer": "I", "cost": 57.0 }, { "facility": "F1", "customer": "J", "cost": 245.0 }, { "facility": "F1", "customer": "K", "cost": 278.0 }, { "facility": "F1", "customer": "L", "cost": 40.0 }, { "facility": "F1", "customer": "M", "cost": 412.0 }, { "facility": "F2", "customer": "A", "cost": 78.0 }, { "facility": "F2", "customer": "B", "cost": 25.0 }, { "facility": "F2", "customer": "C", "cost": 165.0 }, { "facility": "F2", "customer": "D", "cost": 692.0 }, { "facility": "F2", "customer": "E", "cost": 340.0 }, { "facility": "F2", "customer": "F", "cost": 102.0 }, { "facility": "F2", "customer": "G", "cost": 104.0 }, { "facility": "F2", "customer": "H", "cost": 125.0 }, { "facility": "F2", "customer": "I", "cost": 120.0 }, { "facility": "F2", "customer": "J", "cost": 273.0 }, { "facility": "F2", "customer": "K", "cost": 401.0 }, { "facility": "F2", "customer": "L", "cost": 38.0 }, { "facility": "F2", "customer": "M", "cost": 486.0 }, { "facility": "F3", "customer": "A", "cost": 140.0 }, { "facility": "F3", "customer": "B", "cost": 258.0 }, { "facility": "F3", "customer": "C", "cost": 71.0 }, { "facility": "F3", "customer": "D", "cost": 274.0 }, { "facility": "F3", "customer": "E", "cost": 750.0 }, { "facility": "F3", "customer": "F", "cost": 485.0 }, { "facility": "F3", "customer": "G", "cost": 36.0 }, { "facility": "F3", "customer": "H", "cost": 30.0 }, { "facility": "F3", "customer": "I", "cost": 756.0 }, { "facility": "F3", "customer": "J", "cost": 64.0 }, { "facility": "F3", "customer": "K", "cost": 1006.0 }, { "facility": "F3", "customer": "L", "cost": 229.0 }, { "facility": "F3", "customer": "M", "cost": 54.0 }, { "facility": "F4", "customer": "A", "cost": 262.0 }, { "facility": "F4", "customer": "B", "cost": 427.0 }, { "facility": "F4", "customer": "C", "cost": 61.0 }, { "facility": "F4", "customer": "D", "cost": 535.0 }, { "facility": "F4", "customer": "E", "cost": 909.0 }, { "facility": "F4", "customer": "F", "cost": 813.0 }, { "facility": "F4", "customer": "G", "cost": 35.0 }, { "facility": "F4", "customer": "H", "cost": 43.0 }, { "facility": "F4", "customer": "I", "cost": 1039.0 }, { "facility": "F4", "customer": "J", "cost": 250.0 }, { "facility": "F4", "customer": "K", "cost": 1248.0 }, { "facility": "F4", "customer": "L", "cost": 389.0 }, { "facility": "F4", "customer": "M", "cost": 450.0 }, { "facility": "F5", "customer": "A", "cost": 558.0 }, { "facility": "F5", "customer": "B", "cost": 466.0 }, { "facility": "F5", "customer": "C", "cost": 405.0 }, { "facility": "F5", "customer": "D", "cost": 1637.0 }, { "facility": "F5", "customer": "E", "cost": 40.0 }, { "facility": "F5", "customer": "F", "cost": 1193.0 }, { "facility": "F5", "customer": "G", "cost": 320.0 }, { "facility": "F5", "customer": "H", "cost": 487.0 }, { "facility": "F5", "customer": "I", "cost": 946.0 }, { "facility": "F5", "customer": "J", "cost": 1069.0 }, { "facility": "F5", "customer": "K", "cost": 754.0 }, { "facility": "F5", "customer": "L", "cost": 495.0 }, { "facility": "F5", "customer": "M", "cost": 1426.0 } ], "objective": 2570.0 }, "solution_variant": { "selected": [ "F1", "F3" ], "assignments": [ "F1", "F1", "F3", "F3", "F1", "F1", "F3", "F3", "F1", "F3", "F1", "F1", "F3" ] }, "context_index": 28, "input_format": "csv", "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=5\n# num_riders=12\n# HUBS\nhub_id,staffing_cost,driver_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\n# RIDERS\nrider_id,rider_demand\nA,11.0\nB,17.0\nC,18.0\nD,21.0\nE,23.0\nF,20.0\nG,13.0\nH,17.0\nI,16.0\nJ,18.0\nK,15.0\nL,29.0\n# PICKUP_DETOURS\nhub_id,rider_id,pickup_detour_cost\nF1,A,31.0\nF1,B,813.0\nF1,C,213.0\nF1,D,162.0\nF1,E,867.0\nF1,F,136.0\nF1,G,185.0\nF1,H,1114.0\nF1,I,491.0\nF1,J,651.0\nF1,K,1116.0\nF1,L,200.0\nF2,A,690.0\nF2,B,1566.0\nF2,C,425.0\nF2,D,1642.0\nF2,E,2332.0\nF2,F,1197.0\nF2,G,665.0\nF2,H,2407.0\nF2,I,1227.0\nF2,J,1784.0\nF2,K,2235.0\nF2,L,1583.0\nF3,A,673.0\nF3,B,1292.0\nF3,C,147.0\nF3,D,1597.0\nF3,E,2147.0\nF3,F,1048.0\nF3,G,426.0\nF3,H,2185.0\nF3,I,969.0\nF3,J,1562.0\nF3,K,1990.0\nF3,L,1552.0\nF4,A,445.0\nF4,B,34.0\nF4,C,37.0\nF4,D,1084.0\nF4,E,979.0\nF4,F,421.0\nF4,G,77.0\nF4,H,810.0\nF4,I,68.0\nF4,J,384.0\nF4,K,503.0\nF4,L,1088.0\nF5,A,48.0\nF5,B,840.0\nF5,C,199.0\nF5,D,397.0\nF5,E,1061.0\nF5,F,132.0\nF5,G,171.0\nF5,H,1260.0\nF5,I,501.0\nF5,J,730.0\nF5,K,1217.0\nF5,L,404.0\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 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 31.0, 813.0, 213.0, 162.0, 867.0, 136.0, 185.0, 1114.0, 491.0, 651.0, 1116.0, 200.0 ], [ 690.0, 1566.0, 425.0, 1642.0, 2332.0, 1197.0, 665.0, 2407.0, 1227.0, 1784.0, 2235.0, 1583.0 ], [ 673.0, 1292.0, 147.0, 1597.0, 2147.0, 1048.0, 426.0, 2185.0, 969.0, 1562.0, 1990.0, 1552.0 ], [ 445.0, 34.0, 37.0, 1084.0, 979.0, 421.0, 77.0, 810.0, 68.0, 384.0, 503.0, 1088.0 ], [ 48.0, 840.0, 199.0, 397.0, 1061.0, 132.0, 171.0, 1260.0, 501.0, 730.0, 1217.0, 404.0 ] ], "demands": [ 11.0, 17.0, 18.0, 21.0, 23.0, 20.0, 13.0, 17.0, 16.0, 18.0, 15.0, 29.0 ], "objective": 4109.0 }, "solution": { "open_facilities": [ 0, 3 ], "assignments": [ 0, 3, 3, 0, 0, 0, 3, 3, 3, 3, 3, 0 ] }, "obj": 4109.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 12, "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 } ], "customers": [ { "id": "A", "demand": 11.0 }, { "id": "B", "demand": 17.0 }, { "id": "C", "demand": 18.0 }, { "id": "D", "demand": 21.0 }, { "id": "E", "demand": 23.0 }, { "id": "F", "demand": 20.0 }, { "id": "G", "demand": 13.0 }, { "id": "H", "demand": 17.0 }, { "id": "I", "demand": 16.0 }, { "id": "J", "demand": 18.0 }, { "id": "K", "demand": 15.0 }, { "id": "L", "demand": 29.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 31.0 }, { "facility": "F1", "customer": "B", "cost": 813.0 }, { "facility": "F1", "customer": "C", "cost": 213.0 }, { "facility": "F1", "customer": "D", "cost": 162.0 }, { "facility": "F1", "customer": "E", "cost": 867.0 }, { "facility": "F1", "customer": "F", "cost": 136.0 }, { "facility": "F1", "customer": "G", "cost": 185.0 }, { "facility": "F1", "customer": "H", "cost": 1114.0 }, { "facility": "F1", "customer": "I", "cost": 491.0 }, { "facility": "F1", "customer": "J", "cost": 651.0 }, { "facility": "F1", "customer": "K", "cost": 1116.0 }, { "facility": "F1", "customer": "L", "cost": 200.0 }, { "facility": "F2", "customer": "A", "cost": 690.0 }, { "facility": "F2", "customer": "B", "cost": 1566.0 }, { "facility": "F2", "customer": "C", "cost": 425.0 }, { "facility": "F2", "customer": "D", "cost": 1642.0 }, { "facility": "F2", "customer": "E", "cost": 2332.0 }, { "facility": "F2", "customer": "F", "cost": 1197.0 }, { "facility": "F2", "customer": "G", "cost": 665.0 }, { "facility": "F2", "customer": "H", "cost": 2407.0 }, { "facility": "F2", "customer": "I", "cost": 1227.0 }, { "facility": "F2", "customer": "J", "cost": 1784.0 }, { "facility": "F2", "customer": "K", "cost": 2235.0 }, { "facility": "F2", "customer": "L", "cost": 1583.0 }, { "facility": "F3", "customer": "A", "cost": 673.0 }, { "facility": "F3", "customer": "B", "cost": 1292.0 }, { "facility": "F3", "customer": "C", "cost": 147.0 }, { "facility": "F3", "customer": "D", "cost": 1597.0 }, { "facility": "F3", "customer": "E", "cost": 2147.0 }, { "facility": "F3", "customer": "F", "cost": 1048.0 }, { "facility": "F3", "customer": "G", "cost": 426.0 }, { "facility": "F3", "customer": "H", "cost": 2185.0 }, { "facility": "F3", "customer": "I", "cost": 969.0 }, { "facility": "F3", "customer": "J", "cost": 1562.0 }, { "facility": "F3", "customer": "K", "cost": 1990.0 }, { "facility": "F3", "customer": "L", "cost": 1552.0 }, { "facility": "F4", "customer": "A", "cost": 445.0 }, { "facility": "F4", "customer": "B", "cost": 34.0 }, { "facility": "F4", "customer": "C", "cost": 37.0 }, { "facility": "F4", "customer": "D", "cost": 1084.0 }, { "facility": "F4", "customer": "E", "cost": 979.0 }, { "facility": "F4", "customer": "F", "cost": 421.0 }, { "facility": "F4", "customer": "G", "cost": 77.0 }, { "facility": "F4", "customer": "H", "cost": 810.0 }, { "facility": "F4", "customer": "I", "cost": 68.0 }, { "facility": "F4", "customer": "J", "cost": 384.0 }, { "facility": "F4", "customer": "K", "cost": 503.0 }, { "facility": "F4", "customer": "L", "cost": 1088.0 }, { "facility": "F5", "customer": "A", "cost": 48.0 }, { "facility": "F5", "customer": "B", "cost": 840.0 }, { "facility": "F5", "customer": "C", "cost": 199.0 }, { "facility": "F5", "customer": "D", "cost": 397.0 }, { "facility": "F5", "customer": "E", "cost": 1061.0 }, { "facility": "F5", "customer": "F", "cost": 132.0 }, { "facility": "F5", "customer": "G", "cost": 171.0 }, { "facility": "F5", "customer": "H", "cost": 1260.0 }, { "facility": "F5", "customer": "I", "cost": 501.0 }, { "facility": "F5", "customer": "J", "cost": 730.0 }, { "facility": "F5", "customer": "K", "cost": 1217.0 }, { "facility": "F5", "customer": "L", "cost": 404.0 } ], "objective": 4109.0 }, "solution_variant": { "selected": [ "F1", "F4" ], "assignments": [ "F1", "F4", "F4", "F1", "F1", "F1", "F4", "F4", "F4", "F4", "F4", "F1" ] }, "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{\n \"num_candidate_stops\": 6,\n \"num_reader_groups\": 13,\n \"stops\": [\n {\n \"stop_id\": \"F1\",\n \"stop_operation_cost\": 213.0,\n \"circulation_capacity\": 500.0\n },\n {\n \"stop_id\": \"F2\",\n \"stop_operation_cost\": 295.0,\n \"circulation_capacity\": 500.0\n },\n {\n \"stop_id\": \"F3\",\n \"stop_operation_cost\": 379.0,\n \"circulation_capacity\": 500.0\n },\n {\n \"stop_id\": \"F4\",\n \"stop_operation_cost\": 209.0,\n \"circulation_capacity\": 500.0\n },\n {\n \"stop_id\": \"F5\",\n \"stop_operation_cost\": 405.0,\n \"circulation_capacity\": 500.0\n },\n {\n \"stop_id\": \"F6\",\n \"stop_operation_cost\": 333.0,\n \"circulation_capacity\": 500.0\n }\n ],\n \"reader_groups\": [\n {\n \"reader_group_id\": \"A\",\n \"visitor_count\": 18.0\n },\n {\n \"reader_group_id\": \"B\",\n \"visitor_count\": 23.0\n },\n {\n \"reader_group_id\": \"C\",\n \"visitor_count\": 28.0\n },\n {\n \"reader_group_id\": \"D\",\n \"visitor_count\": 12.0\n },\n {\n \"reader_group_id\": \"E\",\n \"visitor_count\": 15.0\n },\n {\n \"reader_group_id\": \"F\",\n \"visitor_count\": 22.0\n },\n {\n \"reader_group_id\": \"G\",\n \"visitor_count\": 10.0\n },\n {\n \"reader_group_id\": \"H\",\n \"visitor_count\": 13.0\n },\n {\n \"reader_group_id\": \"I\",\n \"visitor_count\": 22.0\n },\n {\n \"reader_group_id\": \"J\",\n \"visitor_count\": 25.0\n },\n {\n \"reader_group_id\": \"K\",\n \"visitor_count\": 27.0\n },\n {\n \"reader_group_id\": \"L\",\n \"visitor_count\": 19.0\n },\n {\n \"reader_group_id\": \"M\",\n \"visitor_count\": 27.0\n }\n ],\n \"travel_times\": [\n {\n \"stop_id\": \"F1\",\n \"reader_group_id\": \"A\",\n \"travel_time\": 331.0\n },\n {\n \"stop_id\": \"F1\",\n \"reader_group_id\": \"B\",\n \"travel_time\": 1633.0\n },\n {\n \"stop_id\": \"F1\",\n \"reader_group_id\": \"C\",\n \"travel_time\": 1770.0\n },\n {\n \"stop_id\": \"F1\",\n \"reader_group_id\": \"D\",\n \"travel_time\": 974.0\n },\n {\n \"stop_id\": \"F1\",\n \"reader_group_id\": \"E\",\n \"travel_time\": 621.0\n },\n {\n \"stop_id\": \"F1\",\n \"reader_group_id\": \"F\",\n \"travel_time\": 1089.0\n },\n {\n \"stop_id\": \"F1\",\n \"reader_group_id\": \"G\",\n \"travel_time\": 891.0\n },\n {\n \"stop_id\": \"F1\",\n \"reader_group_id\": \"H\",\n \"travel_time\": 1032.0\n },\n {\n \"stop_id\": \"F1\",\n \"reader_group_id\": \"I\",\n \"travel_time\": 1000.0\n },\n {\n \"stop_id\": \"F1\",\n \"reader_group_id\": \"J\",\n \"travel_time\": 627.0\n },\n {\n \"stop_id\": \"F1\",\n \"reader_group_id\": \"K\",\n \"travel_time\": 246.0\n },\n {\n \"stop_id\": \"F1\",\n \"reader_group_id\": \"L\",\n \"travel_time\": 586.0\n },\n {\n \"stop_id\": \"F1\",\n \"reader_group_id\": \"M\",\n \"travel_time\": 930.0\n },\n {\n \"stop_id\": \"F2\",\n \"reader_group_id\": \"A\",\n \"travel_time\": 147.0\n },\n {\n \"stop_id\": \"F2\",\n \"reader_group_id\": \"B\",\n \"travel_time\": 2147.0\n },\n {\n \"stop_id\": \"F2\",\n \"reader_group_id\": \"C\",\n \"travel_time\": 2102.0\n },\n {\n \"stop_id\": \"F2\",\n \"reader_group_id\": \"D\",\n \"travel_time\": 1489.0\n },\n {\n \"stop_id\": \"F2\",\n \"reader_group_id\": \"E\",\n \"travel_time\": 684.0\n },\n {\n \"stop_id\": \"F2\",\n \"reader_group_id\": \"F\",\n \"travel_time\": 1959.0\n },\n {\n \"stop_id\": \"F2\",\n \"reader_group_id\": \"G\",\n \"travel_time\": 1760.0\n },\n {\n \"stop_id\": \"F2\",\n \"reader_group_id\": \"H\",\n \"travel_time\": 1896.0\n },\n {\n \"stop_id\": \"F2\",\n \"reader_group_id\": \"I\",\n \"travel_time\": 1427.0\n },\n {\n \"stop_id\": \"F2\",\n \"reader_group_id\": \"J\",\n \"travel_time\": 1345.0\n },\n {\n \"stop_id\": \"F2\",\n \"reader_group_id\": \"K\",\n \"travel_time\": 54.0\n },\n {\n \"stop_id\": \"F2\",\n \"reader_group_id\": \"L\",\n \"travel_time\": 889.0\n },\n {\n \"stop_id\": \"F2\",\n \"reader_group_id\": \"M\",\n \"travel_time\": 1717.0\n },\n {\n \"stop_id\": \"F3\",\n \"reader_group_id\": \"A\",\n \"travel_time\": 287.0\n },\n {\n \"stop_id\": \"F3\",\n \"reader_group_id\": \"B\",\n \"travel_time\": 1732.0\n },\n {\n \"stop_id\": \"F3\",\n \"reader_group_id\": \"C\",\n \"travel_time\": 1817.0\n },\n {\n \"stop_id\": \"F3\",\n \"reader_group_id\": \"D\",\n \"travel_time\": 1057.0\n },\n {\n \"stop_id\": \"F3\",\n \"reader_group_id\": \"E\",\n \"travel_time\": 588.0\n },\n {\n \"stop_id\": \"F3\",\n \"reader_group_id\": \"F\",\n \"travel_time\": 1331.0\n },\n {\n \"stop_id\": \"F3\",\n \"reader_group_id\": \"G\",\n \"travel_time\": 1131.0\n },\n {\n \"stop_id\": \"F3\",\n \"reader_group_id\": \"H\",\n \"travel_time\": 1271.0\n },\n {\n \"stop_id\": \"F3\",\n \"reader_group_id\": \"I\",\n \"travel_time\": 1055.0\n },\n {\n \"stop_id\": \"F3\",\n \"reader_group_id\": \"J\",\n \"travel_time\": 775.0\n },\n {\n \"stop_id\": \"F3\",\n \"reader_group_id\": \"K\",\n \"travel_time\": 204.0\n },\n {\n \"stop_id\": \"F3\",\n \"reader_group_id\": \"L\",\n \"travel_time\": 586.0\n },\n {\n \"stop_id\": \"F3\",\n \"reader_group_id\": \"M\",\n \"travel_time\": 1125.0\n },\n {\n \"stop_id\": \"F4\",\n \"reader_group_id\": \"A\",\n \"travel_time\": 53.0\n },\n {\n \"stop_id\": \"F4\",\n \"reader_group_id\": \"B\",\n \"travel_time\": 1310.0\n },\n {\n \"stop_id\": \"F4\",\n \"reader_group_id\": \"C\",\n \"travel_time\": 1223.0\n },\n {\n \"stop_id\": \"F4\",\n \"reader_group_id\": \"D\",\n \"travel_time\": 708.0\n },\n {\n \"stop_id\": \"F4\",\n \"reader_group_id\": \"E\",\n \"travel_time\": 40.0\n },\n {\n \"stop_id\": \"F4\",\n \"reader_group_id\": \"F\",\n \"travel_time\": 1389.0\n },\n {\n \"stop_id\": \"F4\",\n \"reader_group_id\": \"G\",\n \"travel_time\": 1206.0\n },\n {\n \"stop_id\": \"F4\",\n \"reader_group_id\": \"H\",\n \"travel_time\": 1322.0\n },\n {\n \"stop_id\": \"F4\",\n \"reader_group_id\": \"I\",\n \"travel_time\": 607.0\n },\n {\n \"stop_id\": \"F4\",\n \"reader_group_id\": \"J\",\n \"travel_time\": 741.0\n },\n {\n \"stop_id\": \"F4\",\n \"reader_group_id\": \"K\",\n \"travel_time\": 54.0\n },\n {\n \"stop_id\": \"F4\",\n \"reader_group_id\": \"L\",\n \"travel_time\": 173.0\n },\n {\n \"stop_id\": \"F4\",\n \"reader_group_id\": \"M\",\n \"travel_time\": 1094.0\n },\n {\n \"stop_id\": \"F5\",\n \"reader_group_id\": \"A\",\n \"travel_time\": 36.0\n },\n {\n \"stop_id\": \"F5\",\n \"reader_group_id\": \"B\",\n \"travel_time\": 1492.0\n },\n {\n \"stop_id\": \"F5\",\n \"reader_group_id\": \"C\",\n \"travel_time\": 1334.0\n },\n {\n \"stop_id\": \"F5\",\n \"reader_group_id\": \"D\",\n \"travel_time\": 924.0\n },\n {\n \"stop_id\": \"F5\",\n \"reader_group_id\": \"E\",\n \"travel_time\": 101.0\n },\n {\n \"stop_id\": \"F5\",\n \"reader_group_id\": \"F\",\n \"travel_time\": 1609.0\n },\n {\n \"stop_id\": \"F5\",\n \"reader_group_id\": \"G\",\n \"travel_time\": 1423.0\n },\n {\n \"stop_id\": \"F5\",\n \"reader_group_id\": \"H\",\n \"travel_time\": 1542.0\n },\n {\n \"stop_id\": \"F5\",\n \"reader_group_id\": \"I\",\n \"travel_time\": 815.0\n },\n {\n \"stop_id\": \"F5\",\n \"reader_group_id\": \"J\",\n \"travel_time\": 959.0\n },\n {\n \"stop_id\": \"F5\",\n \"reader_group_id\": \"K\",\n \"travel_time\": 72.0\n },\n {\n \"stop_id\": \"F5\",\n \"reader_group_id\": \"L\",\n \"travel_time\": 385.0\n },\n {\n \"stop_id\": \"F5\",\n \"reader_group_id\": \"M\",\n \"travel_time\": 1316.0\n },\n {\n \"stop_id\": \"F6\",\n \"reader_group_id\": \"A\",\n \"travel_time\": 56.0\n },\n {\n \"stop_id\": \"F6\",\n \"reader_group_id\": \"B\",\n \"travel_time\": 763.0\n },\n {\n \"stop_id\": \"F6\",\n \"reader_group_id\": \"C\",\n \"travel_time\": 644.0\n },\n {\n \"stop_id\": \"F6\",\n \"reader_group_id\": \"D\",\n \"travel_time\": 304.0\n },\n {\n \"stop_id\": \"F6\",\n \"reader_group_id\": \"E\",\n \"travel_time\": 42.0\n },\n {\n \"stop_id\": \"F6\",\n \"reader_group_id\": \"F\",\n \"travel_time\": 1075.0\n },\n {\n \"stop_id\": \"F6\",\n \"reader_group_id\": \"G\",\n \"travel_time\": 913.0\n },\n {\n \"stop_id\": \"F6\",\n \"reader_group_id\": \"H\",\n \"travel_time\": 1009.0\n },\n {\n \"stop_id\": \"F6\",\n \"reader_group_id\": \"I\",\n \"travel_time\": 190.0\n },\n {\n \"stop_id\": \"F6\",\n \"reader_group_id\": \"J\",\n \"travel_time\": 477.0\n },\n {\n \"stop_id\": \"F6\",\n \"reader_group_id\": \"K\",\n \"travel_time\": 55.0\n },\n {\n \"stop_id\": \"F6\",\n \"reader_group_id\": \"L\",\n \"travel_time\": 67.0\n },\n {\n \"stop_id\": \"F6\",\n \"reader_group_id\": \"M\",\n \"travel_time\": 770.0\n }\n ]\n}\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": [ 213.0, 295.0, 379.0, 209.0, 405.0, 333.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 331.0, 1633.0, 1770.0, 974.0, 621.0, 1089.0, 891.0, 1032.0, 1000.0, 627.0, 246.0, 586.0, 930.0 ], [ 147.0, 2147.0, 2102.0, 1489.0, 684.0, 1959.0, 1760.0, 1896.0, 1427.0, 1345.0, 54.0, 889.0, 1717.0 ], [ 287.0, 1732.0, 1817.0, 1057.0, 588.0, 1331.0, 1131.0, 1271.0, 1055.0, 775.0, 204.0, 586.0, 1125.0 ], [ 53.0, 1310.0, 1223.0, 708.0, 40.0, 1389.0, 1206.0, 1322.0, 607.0, 741.0, 54.0, 173.0, 1094.0 ], [ 36.0, 1492.0, 1334.0, 924.0, 101.0, 1609.0, 1423.0, 1542.0, 815.0, 959.0, 72.0, 385.0, 1316.0 ], [ 56.0, 763.0, 644.0, 304.0, 42.0, 1075.0, 913.0, 1009.0, 190.0, 477.0, 55.0, 67.0, 770.0 ] ], "demands": [ 18.0, 23.0, 28.0, 12.0, 15.0, 22.0, 10.0, 13.0, 22.0, 25.0, 27.0, 19.0, 27.0 ], "objective": 6698.0 }, "solution": { "open_facilities": [ 5 ], "assignments": [ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 ] }, "obj": 6698.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 6, "num_customers": 13, "facilities": [ { "id": "F1", "opening_cost": 213.0, "capacity": 500.0 }, { "id": "F2", "opening_cost": 295.0, "capacity": 500.0 }, { "id": "F3", "opening_cost": 379.0, "capacity": 500.0 }, { "id": "F4", "opening_cost": 209.0, "capacity": 500.0 }, { "id": "F5", "opening_cost": 405.0, "capacity": 500.0 }, { "id": "F6", "opening_cost": 333.0, "capacity": 500.0 } ], "customers": [ { "id": "A", "demand": 18.0 }, { "id": "B", "demand": 23.0 }, { "id": "C", "demand": 28.0 }, { "id": "D", "demand": 12.0 }, { "id": "E", "demand": 15.0 }, { "id": "F", "demand": 22.0 }, { "id": "G", "demand": 10.0 }, { "id": "H", "demand": 13.0 }, { "id": "I", "demand": 22.0 }, { "id": "J", "demand": 25.0 }, { "id": "K", "demand": 27.0 }, { "id": "L", "demand": 19.0 }, { "id": "M", "demand": 27.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 331.0 }, { "facility": "F1", "customer": "B", "cost": 1633.0 }, { "facility": "F1", "customer": "C", "cost": 1770.0 }, { "facility": "F1", "customer": "D", "cost": 974.0 }, { "facility": "F1", "customer": "E", "cost": 621.0 }, { "facility": "F1", "customer": "F", "cost": 1089.0 }, { "facility": "F1", "customer": "G", "cost": 891.0 }, { "facility": "F1", "customer": "H", "cost": 1032.0 }, { "facility": "F1", "customer": "I", "cost": 1000.0 }, { "facility": "F1", "customer": "J", "cost": 627.0 }, { "facility": "F1", "customer": "K", "cost": 246.0 }, { "facility": "F1", "customer": "L", "cost": 586.0 }, { "facility": "F1", "customer": "M", "cost": 930.0 }, { "facility": "F2", "customer": "A", "cost": 147.0 }, { "facility": "F2", "customer": "B", "cost": 2147.0 }, { "facility": "F2", "customer": "C", "cost": 2102.0 }, { "facility": "F2", "customer": "D", "cost": 1489.0 }, { "facility": "F2", "customer": "E", "cost": 684.0 }, { "facility": "F2", "customer": "F", "cost": 1959.0 }, { "facility": "F2", "customer": "G", "cost": 1760.0 }, { "facility": "F2", "customer": "H", "cost": 1896.0 }, { "facility": "F2", "customer": "I", "cost": 1427.0 }, { "facility": "F2", "customer": "J", "cost": 1345.0 }, { "facility": "F2", "customer": "K", "cost": 54.0 }, { "facility": "F2", "customer": "L", "cost": 889.0 }, { "facility": "F2", "customer": "M", "cost": 1717.0 }, { "facility": "F3", "customer": "A", "cost": 287.0 }, { "facility": "F3", "customer": "B", "cost": 1732.0 }, { "facility": "F3", "customer": "C", "cost": 1817.0 }, { "facility": "F3", "customer": "D", "cost": 1057.0 }, { "facility": "F3", "customer": "E", "cost": 588.0 }, { "facility": "F3", "customer": "F", "cost": 1331.0 }, { "facility": "F3", "customer": "G", "cost": 1131.0 }, { "facility": "F3", "customer": "H", "cost": 1271.0 }, { "facility": "F3", "customer": "I", "cost": 1055.0 }, { "facility": "F3", "customer": "J", "cost": 775.0 }, { "facility": "F3", "customer": "K", "cost": 204.0 }, { "facility": "F3", "customer": "L", "cost": 586.0 }, { "facility": "F3", "customer": "M", "cost": 1125.0 }, { "facility": "F4", "customer": "A", "cost": 53.0 }, { "facility": "F4", "customer": "B", "cost": 1310.0 }, { "facility": "F4", "customer": "C", "cost": 1223.0 }, { "facility": "F4", "customer": "D", "cost": 708.0 }, { "facility": "F4", "customer": "E", "cost": 40.0 }, { "facility": "F4", "customer": "F", "cost": 1389.0 }, { "facility": "F4", "customer": "G", "cost": 1206.0 }, { "facility": "F4", "customer": "H", "cost": 1322.0 }, { "facility": "F4", "customer": "I", "cost": 607.0 }, { "facility": "F4", "customer": "J", "cost": 741.0 }, { "facility": "F4", "customer": "K", "cost": 54.0 }, { "facility": "F4", "customer": "L", "cost": 173.0 }, { "facility": "F4", "customer": "M", "cost": 1094.0 }, { "facility": "F5", "customer": "A", "cost": 36.0 }, { "facility": "F5", "customer": "B", "cost": 1492.0 }, { "facility": "F5", "customer": "C", "cost": 1334.0 }, { "facility": "F5", "customer": "D", "cost": 924.0 }, { "facility": "F5", "customer": "E", "cost": 101.0 }, { "facility": "F5", "customer": "F", "cost": 1609.0 }, { "facility": "F5", "customer": "G", "cost": 1423.0 }, { "facility": "F5", "customer": "H", "cost": 1542.0 }, { "facility": "F5", "customer": "I", "cost": 815.0 }, { "facility": "F5", "customer": "J", "cost": 959.0 }, { "facility": "F5", "customer": "K", "cost": 72.0 }, { "facility": "F5", "customer": "L", "cost": 385.0 }, { "facility": "F5", "customer": "M", "cost": 1316.0 }, { "facility": "F6", "customer": "A", "cost": 56.0 }, { "facility": "F6", "customer": "B", "cost": 763.0 }, { "facility": "F6", "customer": "C", "cost": 644.0 }, { "facility": "F6", "customer": "D", "cost": 304.0 }, { "facility": "F6", "customer": "E", "cost": 42.0 }, { "facility": "F6", "customer": "F", "cost": 1075.0 }, { "facility": "F6", "customer": "G", "cost": 913.0 }, { "facility": "F6", "customer": "H", "cost": 1009.0 }, { "facility": "F6", "customer": "I", "cost": 190.0 }, { "facility": "F6", "customer": "J", "cost": 477.0 }, { "facility": "F6", "customer": "K", "cost": 55.0 }, { "facility": "F6", "customer": "L", "cost": 67.0 }, { "facility": "F6", "customer": "M", "cost": 770.0 } ], "objective": 6698.0 }, "solution_variant": { "selected": [ "F6" ], "assignments": [ "F6", "F6", "F6", "F6", "F6", "F6", "F6", "F6", "F6", "F6", "F6", "F6", "F6" ] }, "context_index": 30, "input_format": "json", "input_index_base": "names" }, { "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\n# num_ghost_kitchens=6\n# num_orders=14\n# KITCHENS\nkitchen_id,activation_fee,kitchen_capacity\nF1,400.0,1382.0\nF2,400.0,1416.0\nF3,400.0,751.0\nF4,400.0,1067.0\nF5,400.0,1103.0\nF6,400.0,620.0\n# ORDERS\norder_id,order_size\n0,31.0\n1,50.0\n2,48.0\n3,27.0\n4,15.0\n5,46.0\n6,35.0\n7,32.0\n8,23.0\n9,45.0\n10,31.0\n11,26.0\n12,14.0\n13,49.0\n# FULFILLMENTS\nkitchen_id,order_id,fulfillment_cost\nF1,0,609.0\nF1,1,439.0\nF1,2,735.0\nF1,3,567.0\nF1,4,750.0\nF1,5,457.0\nF1,6,201.0\nF1,7,32.0\nF1,8,631.0\nF1,9,200.0\nF1,10,266.0\nF1,11,525.0\nF1,12,185.0\nF1,13,227.0\nF2,0,540.0\nF2,1,289.0\nF2,2,121.0\nF2,3,375.0\nF2,4,126.0\nF2,5,268.0\nF2,6,436.0\nF2,7,611.0\nF2,8,598.0\nF2,9,440.0\nF2,10,533.0\nF2,11,510.0\nF2,12,476.0\nF2,13,410.0\nF3,0,535.0\nF3,1,369.0\nF3,2,647.0\nF3,3,512.0\nF3,4,656.0\nF3,5,384.0\nF3,6,118.0\nF3,7,82.0\nF3,8,563.0\nF3,9,105.0\nF3,10,204.0\nF3,11,451.0\nF3,12,93.0\nF3,13,133.0\nF4,0,93.0\nF4,1,653.0\nF4,2,700.0\nF4,3,819.0\nF4,4,620.0\nF4,5,651.0\nF4,6,499.0\nF4,7,556.0\nF4,8,84.0\nF4,9,439.0\nF4,10,283.0\nF4,11,74.0\nF4,12,405.0\nF4,13,444.0\nF5,0,709.0\nF5,1,104.0\nF5,2,445.0\nF5,3,177.0\nF5,4,517.0\nF5,5,126.0\nF5,6,237.0\nF5,7,358.0\nF5,8,756.0\nF5,9,294.0\nF5,10,480.0\nF5,11,638.0\nF5,12,346.0\nF5,13,274.0\nF6,0,860.0\nF6,1,209.0\nF6,2,445.0\nF6,3,68.0\nF6,4,550.0\nF6,5,216.0\nF6,6,419.0\nF6,7,532.0\nF6,8,911.0\nF6,9,475.0\nF6,10,659.0\nF6,11,796.0\nF6,12,528.0\nF6,13,453.0\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": [ 400.0, 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 1382.0, 1416.0, 751.0, 1067.0, 1103.0, 620.0 ], "connection_costs": [ [ 609.0, 439.0, 735.0, 567.0, 750.0, 457.0, 201.0, 32.0, 631.0, 200.0, 266.0, 525.0, 185.0, 227.0 ], [ 540.0, 289.0, 121.0, 375.0, 126.0, 268.0, 436.0, 611.0, 598.0, 440.0, 533.0, 510.0, 476.0, 410.0 ], [ 535.0, 369.0, 647.0, 512.0, 656.0, 384.0, 118.0, 82.0, 563.0, 105.0, 204.0, 451.0, 93.0, 133.0 ], [ 93.0, 653.0, 700.0, 819.0, 620.0, 651.0, 499.0, 556.0, 84.0, 439.0, 283.0, 74.0, 405.0, 444.0 ], [ 709.0, 104.0, 445.0, 177.0, 517.0, 126.0, 237.0, 358.0, 756.0, 294.0, 480.0, 638.0, 346.0, 274.0 ], [ 860.0, 209.0, 445.0, 68.0, 550.0, 216.0, 419.0, 532.0, 911.0, 475.0, 659.0, 796.0, 528.0, 453.0 ] ], "demands": [ 31.0, 50.0, 48.0, 27.0, 15.0, 46.0, 35.0, 32.0, 23.0, 45.0, 31.0, 26.0, 14.0, 49.0 ], "objective": 3240.0 }, "solution": { "open_facilities": [ 1, 2, 3, 4 ], "assignments": [ 3, 4, 1, 4, 1, 4, 2, 2, 3, 2, 2, 3, 2, 2 ] }, "obj": 3240.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 6, "num_customers": 14, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 1382.0 }, { "id": "F2", "opening_cost": 400.0, "capacity": 1416.0 }, { "id": "F3", "opening_cost": 400.0, "capacity": 751.0 }, { "id": "F4", "opening_cost": 400.0, "capacity": 1067.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 1103.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 620.0 } ], "customers": [ { "id": 0, "demand": 31.0 }, { "id": 1, "demand": 50.0 }, { "id": 2, "demand": 48.0 }, { "id": 3, "demand": 27.0 }, { "id": 4, "demand": 15.0 }, { "id": 5, "demand": 46.0 }, { "id": 6, "demand": 35.0 }, { "id": 7, "demand": 32.0 }, { "id": 8, "demand": 23.0 }, { "id": 9, "demand": 45.0 }, { "id": 10, "demand": 31.0 }, { "id": 11, "demand": 26.0 }, { "id": 12, "demand": 14.0 }, { "id": 13, "demand": 49.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 609.0 }, { "facility": "F1", "customer": 1, "cost": 439.0 }, { "facility": "F1", "customer": 2, "cost": 735.0 }, { "facility": "F1", "customer": 3, "cost": 567.0 }, { "facility": "F1", "customer": 4, "cost": 750.0 }, { "facility": "F1", "customer": 5, "cost": 457.0 }, { "facility": "F1", "customer": 6, "cost": 201.0 }, { "facility": "F1", "customer": 7, "cost": 32.0 }, { "facility": "F1", "customer": 8, "cost": 631.0 }, { "facility": "F1", "customer": 9, "cost": 200.0 }, { "facility": "F1", "customer": 10, "cost": 266.0 }, { "facility": "F1", "customer": 11, "cost": 525.0 }, { "facility": "F1", "customer": 12, "cost": 185.0 }, { "facility": "F1", "customer": 13, "cost": 227.0 }, { "facility": "F2", "customer": 0, "cost": 540.0 }, { "facility": "F2", "customer": 1, "cost": 289.0 }, { "facility": "F2", "customer": 2, "cost": 121.0 }, { "facility": "F2", "customer": 3, "cost": 375.0 }, { "facility": "F2", "customer": 4, "cost": 126.0 }, { "facility": "F2", "customer": 5, "cost": 268.0 }, { "facility": "F2", "customer": 6, "cost": 436.0 }, { "facility": "F2", "customer": 7, "cost": 611.0 }, { "facility": "F2", "customer": 8, "cost": 598.0 }, { "facility": "F2", "customer": 9, "cost": 440.0 }, { "facility": "F2", "customer": 10, "cost": 533.0 }, { "facility": "F2", "customer": 11, "cost": 510.0 }, { "facility": "F2", "customer": 12, "cost": 476.0 }, { "facility": "F2", "customer": 13, "cost": 410.0 }, { "facility": "F3", "customer": 0, "cost": 535.0 }, { "facility": "F3", "customer": 1, "cost": 369.0 }, { "facility": "F3", "customer": 2, "cost": 647.0 }, { "facility": "F3", "customer": 3, "cost": 512.0 }, { "facility": "F3", "customer": 4, "cost": 656.0 }, { "facility": "F3", "customer": 5, "cost": 384.0 }, { "facility": "F3", "customer": 6, "cost": 118.0 }, { "facility": "F3", "customer": 7, "cost": 82.0 }, { "facility": "F3", "customer": 8, "cost": 563.0 }, { "facility": "F3", "customer": 9, "cost": 105.0 }, { "facility": "F3", "customer": 10, "cost": 204.0 }, { "facility": "F3", "customer": 11, "cost": 451.0 }, { "facility": "F3", "customer": 12, "cost": 93.0 }, { "facility": "F3", "customer": 13, "cost": 133.0 }, { "facility": "F4", "customer": 0, "cost": 93.0 }, { "facility": "F4", "customer": 1, "cost": 653.0 }, { "facility": "F4", "customer": 2, "cost": 700.0 }, { "facility": "F4", "customer": 3, "cost": 819.0 }, { "facility": "F4", "customer": 4, "cost": 620.0 }, { "facility": "F4", "customer": 5, "cost": 651.0 }, { "facility": "F4", "customer": 6, "cost": 499.0 }, { "facility": "F4", "customer": 7, "cost": 556.0 }, { "facility": "F4", "customer": 8, "cost": 84.0 }, { "facility": "F4", "customer": 9, "cost": 439.0 }, { "facility": "F4", "customer": 10, "cost": 283.0 }, { "facility": "F4", "customer": 11, "cost": 74.0 }, { "facility": "F4", "customer": 12, "cost": 405.0 }, { "facility": "F4", "customer": 13, "cost": 444.0 }, { "facility": "F5", "customer": 0, "cost": 709.0 }, { "facility": "F5", "customer": 1, "cost": 104.0 }, { "facility": "F5", "customer": 2, "cost": 445.0 }, { "facility": "F5", "customer": 3, "cost": 177.0 }, { "facility": "F5", "customer": 4, "cost": 517.0 }, { "facility": "F5", "customer": 5, "cost": 126.0 }, { "facility": "F5", "customer": 6, "cost": 237.0 }, { "facility": "F5", "customer": 7, "cost": 358.0 }, { "facility": "F5", "customer": 8, "cost": 756.0 }, { "facility": "F5", "customer": 9, "cost": 294.0 }, { "facility": "F5", "customer": 10, "cost": 480.0 }, { "facility": "F5", "customer": 11, "cost": 638.0 }, { "facility": "F5", "customer": 12, "cost": 346.0 }, { "facility": "F5", "customer": 13, "cost": 274.0 }, { "facility": "F6", "customer": 0, "cost": 860.0 }, { "facility": "F6", "customer": 1, "cost": 209.0 }, { "facility": "F6", "customer": 2, "cost": 445.0 }, { "facility": "F6", "customer": 3, "cost": 68.0 }, { "facility": "F6", "customer": 4, "cost": 550.0 }, { "facility": "F6", "customer": 5, "cost": 216.0 }, { "facility": "F6", "customer": 6, "cost": 419.0 }, { "facility": "F6", "customer": 7, "cost": 532.0 }, { "facility": "F6", "customer": 8, "cost": 911.0 }, { "facility": "F6", "customer": 9, "cost": 475.0 }, { "facility": "F6", "customer": 10, "cost": 659.0 }, { "facility": "F6", "customer": 11, "cost": 796.0 }, { "facility": "F6", "customer": 12, "cost": 528.0 }, { "facility": "F6", "customer": 13, "cost": 453.0 } ], "objective": 3240.0 }, "solution_variant": { "selected": [ "F2", "F3", "F4", "F5" ], "assignments": [ "F4", "F5", "F2", "F5", "F2", "F5", "F3", "F3", "F4", "F3", "F3", "F4", "F3", "F3" ] }, "context_index": 31, "input_format": "csv", "input_index_base": 0 }, { "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\nThe data lists 6 candidate collection points and 13 households.\nCollection point F1 has opening cost 400.0 and intake capacity 907.0.\nCollection point F2 has opening cost 400.0 and intake capacity 1335.0.\nCollection point F3 has opening cost 400.0 and intake capacity 1400.0.\nCollection point F4 has opening cost 400.0 and intake capacity 898.0.\nCollection point F5 has opening cost 400.0 and intake capacity 1103.0.\nCollection point F6 has opening cost 400.0 and intake capacity 620.0.\nHousehold A produces 28.0 recyclables and must be assigned to a single open point.\nHousehold B produces 14.0 recyclables and must be assigned to a single open point.\nHousehold C produces 24.0 recyclables and must be assigned to a single open point.\nHousehold D produces 39.0 recyclables and must be assigned to a single open point.\nHousehold E produces 10.0 recyclables and must be assigned to a single open point.\nHousehold F produces 42.0 recyclables and must be assigned to a single open point.\nHousehold G produces 24.0 recyclables and must be assigned to a single open point.\nHousehold H produces 15.0 recyclables and must be assigned to a single open point.\nHousehold I produces 49.0 recyclables and must be assigned to a single open point.\nHousehold J produces 12.0 recyclables and must be assigned to a single open point.\nHousehold K produces 14.0 recyclables and must be assigned to a single open point.\nHousehold L produces 27.0 recyclables and must be assigned to a single open point.\nHousehold M produces 29.0 recyclables and must be assigned to a single open point.\nIf household A uses collection point F1, the hauling cost is 273.0.\nIf household B uses collection point F1, the hauling cost is 376.0.\nIf household C uses collection point F1, the hauling cost is 414.0.\nIf household D uses collection point F1, the hauling cost is 574.0.\nIf household E uses collection point F1, the hauling cost is 511.0.\nIf household F uses collection point F1, the hauling cost is 448.0.\nIf household G uses collection point F1, the hauling cost is 246.0.\nIf household H uses collection point F1, the hauling cost is 502.0.\nIf household I uses collection point F1, the hauling cost is 29.0.\nIf household J uses collection point F1, the hauling cost is 100.0.\nIf household K uses collection point F1, the hauling cost is 51.0.\nIf household L uses collection point F1, the hauling cost is 361.0.\nIf household M uses collection point F1, the hauling cost is 498.0.\nIf household A uses collection point F2, the hauling cost is 268.0.\nIf household B uses collection point F2, the hauling cost is 736.0.\nIf household C uses collection point F2, the hauling cost is 682.0.\nIf household D uses collection point F2, the hauling cost is 102.0.\nIf household E uses collection point F2, the hauling cost is 446.0.\nIf household F uses collection point F2, the hauling cost is 300.0.\nIf household G uses collection point F2, the hauling cost is 446.0.\nIf household H uses collection point F2, the hauling cost is 598.0.\nIf household I uses collection point F2, the hauling cost is 527.0.\nIf household J uses collection point F2, the hauling cost is 558.0.\nIf household K uses collection point F2, the hauling cost is 568.0.\nIf household L uses collection point F2, the hauling cost is 635.0.\nIf household M uses collection point F2, the hauling cost is 385.0.\nIf household A uses collection point F3, the hauling cost is 459.0.\nIf household B uses collection point F3, the hauling cost is 116.0.\nIf household C uses collection point F3, the hauling cost is 16.0.\nIf household D uses collection point F3, the hauling cost is 685.0.\nIf household E uses collection point F3, the hauling cost is 352.0.\nIf household F uses collection point F3, the hauling cost is 433.0.\nIf household G uses collection point F3, the hauling cost is 269.0.\nIf household H uses collection point F3, the hauling cost is 197.0.\nIf household I uses collection point F3, the hauling cost is 455.0.\nIf household J uses collection point F3, the hauling cost is 331.0.\nIf household K uses collection point F3, the hauling cost is 407.0.\nIf household L uses collection point F3, the hauling cost is 72.0.\nIf household M uses collection point F3, the hauling cost is 396.0.\nIf household A uses collection point F4, the hauling cost is 272.0.\nIf household B uses collection point F4, the hauling cost is 249.0.\nIf household C uses collection point F4, the hauling cost is 178.0.\nIf household D uses collection point F4, the hauling cost is 495.0.\nIf household E uses collection point F4, the hauling cost is 220.0.\nIf household F uses collection point F4, the hauling cost is 252.0.\nIf household G uses collection point F4, the hauling cost is 96.0.\nIf household H uses collection point F4, the hauling cost is 175.0.\nIf household I uses collection point F4, the hauling cost is 357.0.\nIf household J uses collection point F4, the hauling cost is 257.0.\nIf household K uses collection point F4, the hauling cost is 330.0.\nIf household L uses collection point F4, the hauling cost is 133.0.\nIf household M uses collection point F4, the hauling cost is 241.0.\nIf household A uses collection point F5, the hauling cost is 402.0.\nIf household B uses collection point F5, the hauling cost is 328.0.\nIf household C uses collection point F5, the hauling cost is 213.0.\nIf household D uses collection point F5, the hauling cost is 537.0.\nIf household E uses collection point F5, the hauling cost is 153.0.\nIf household F uses collection point F5, the hauling cost is 280.0.\nIf household G uses collection point F5, the hauling cost is 265.0.\nIf household H uses collection point F5, the hauling cost is 26.0.\nIf household I uses collection point F5, the hauling cost is 532.0.\nIf household J uses collection point F5, the hauling cost is 430.0.\nIf household K uses collection point F5, the hauling cost is 505.0.\nIf household L uses collection point F5, the hauling cost is 214.0.\nIf household M uses collection point F5, the hauling cost is 211.0.\nIf household A uses collection point F6, the hauling cost is 509.0.\nIf household B uses collection point F6, the hauling cost is 506.0.\nIf household C uses collection point F6, the hauling cost is 389.0.\nIf household D uses collection point F6, the hauling cost is 541.0.\nIf household E uses collection point F6, the hauling cost is 181.0.\nIf household F uses collection point F6, the hauling cost is 323.0.\nIf household G uses collection point F6, the hauling cost is 420.0.\nIf household H uses collection point F6, the hauling cost is 199.0.\nIf household I uses collection point F6, the hauling cost is 693.0.\nIf household J uses collection point F6, the hauling cost is 602.0.\nIf household K uses collection point F6, the hauling cost is 673.0.\nIf household L uses collection point F6, the hauling cost is 396.0.\nIf household M uses collection point F6, the hauling cost is 232.0.\nThese entries are provided so someone can choose which points to open and assign every household while minimizing total cost.\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 ], "capacities": [ 907.0, 1335.0, 1400.0, 898.0, 1103.0, 620.0 ], "connection_costs": [ [ 273.0, 376.0, 414.0, 574.0, 511.0, 448.0, 246.0, 502.0, 29.0, 100.0, 51.0, 361.0, 498.0 ], [ 268.0, 736.0, 682.0, 102.0, 446.0, 300.0, 446.0, 598.0, 527.0, 558.0, 568.0, 635.0, 385.0 ], [ 459.0, 116.0, 16.0, 685.0, 352.0, 433.0, 269.0, 197.0, 455.0, 331.0, 407.0, 72.0, 396.0 ], [ 272.0, 249.0, 178.0, 495.0, 220.0, 252.0, 96.0, 175.0, 357.0, 257.0, 330.0, 133.0, 241.0 ], [ 402.0, 328.0, 213.0, 537.0, 153.0, 280.0, 265.0, 26.0, 532.0, 430.0, 505.0, 214.0, 211.0 ], [ 509.0, 506.0, 389.0, 541.0, 181.0, 323.0, 420.0, 199.0, 693.0, 602.0, 673.0, 396.0, 232.0 ] ], "demands": [ 28.0, 14.0, 24.0, 39.0, 10.0, 42.0, 24.0, 15.0, 49.0, 12.0, 14.0, 27.0, 29.0 ], "objective": 3270.0 }, "solution": { "open_facilities": [ 0, 1, 2, 4 ], "assignments": [ 1, 2, 2, 1, 4, 4, 0, 4, 0, 0, 0, 2, 4 ] }, "obj": 3270.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 6, "num_customers": 13, "facilities": [ { "id": "F1", "opening_cost": 400.0, "capacity": 907.0 }, { "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": 898.0 }, { "id": "F5", "opening_cost": 400.0, "capacity": 1103.0 }, { "id": "F6", "opening_cost": 400.0, "capacity": 620.0 } ], "customers": [ { "id": "A", "demand": 28.0 }, { "id": "B", "demand": 14.0 }, { "id": "C", "demand": 24.0 }, { "id": "D", "demand": 39.0 }, { "id": "E", "demand": 10.0 }, { "id": "F", "demand": 42.0 }, { "id": "G", "demand": 24.0 }, { "id": "H", "demand": 15.0 }, { "id": "I", "demand": 49.0 }, { "id": "J", "demand": 12.0 }, { "id": "K", "demand": 14.0 }, { "id": "L", "demand": 27.0 }, { "id": "M", "demand": 29.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 273.0 }, { "facility": "F1", "customer": "B", "cost": 376.0 }, { "facility": "F1", "customer": "C", "cost": 414.0 }, { "facility": "F1", "customer": "D", "cost": 574.0 }, { "facility": "F1", "customer": "E", "cost": 511.0 }, { "facility": "F1", "customer": "F", "cost": 448.0 }, { "facility": "F1", "customer": "G", "cost": 246.0 }, { "facility": "F1", "customer": "H", "cost": 502.0 }, { "facility": "F1", "customer": "I", "cost": 29.0 }, { "facility": "F1", "customer": "J", "cost": 100.0 }, { "facility": "F1", "customer": "K", "cost": 51.0 }, { "facility": "F1", "customer": "L", "cost": 361.0 }, { "facility": "F1", "customer": "M", "cost": 498.0 }, { "facility": "F2", "customer": "A", "cost": 268.0 }, { "facility": "F2", "customer": "B", "cost": 736.0 }, { "facility": "F2", "customer": "C", "cost": 682.0 }, { "facility": "F2", "customer": "D", "cost": 102.0 }, { "facility": "F2", "customer": "E", "cost": 446.0 }, { "facility": "F2", "customer": "F", "cost": 300.0 }, { "facility": "F2", "customer": "G", "cost": 446.0 }, { "facility": "F2", "customer": "H", "cost": 598.0 }, { "facility": "F2", "customer": "I", "cost": 527.0 }, { "facility": "F2", "customer": "J", "cost": 558.0 }, { "facility": "F2", "customer": "K", "cost": 568.0 }, { "facility": "F2", "customer": "L", "cost": 635.0 }, { "facility": "F2", "customer": "M", "cost": 385.0 }, { "facility": "F3", "customer": "A", "cost": 459.0 }, { "facility": "F3", "customer": "B", "cost": 116.0 }, { "facility": "F3", "customer": "C", "cost": 16.0 }, { "facility": "F3", "customer": "D", "cost": 685.0 }, { "facility": "F3", "customer": "E", "cost": 352.0 }, { "facility": "F3", "customer": "F", "cost": 433.0 }, { "facility": "F3", "customer": "G", "cost": 269.0 }, { "facility": "F3", "customer": "H", "cost": 197.0 }, { "facility": "F3", "customer": "I", "cost": 455.0 }, { "facility": "F3", "customer": "J", "cost": 331.0 }, { "facility": "F3", "customer": "K", "cost": 407.0 }, { "facility": "F3", "customer": "L", "cost": 72.0 }, { "facility": "F3", "customer": "M", "cost": 396.0 }, { "facility": "F4", "customer": "A", "cost": 272.0 }, { "facility": "F4", "customer": "B", "cost": 249.0 }, { "facility": "F4", "customer": "C", "cost": 178.0 }, { "facility": "F4", "customer": "D", "cost": 495.0 }, { "facility": "F4", "customer": "E", "cost": 220.0 }, { "facility": "F4", "customer": "F", "cost": 252.0 }, { "facility": "F4", "customer": "G", "cost": 96.0 }, { "facility": "F4", "customer": "H", "cost": 175.0 }, { "facility": "F4", "customer": "I", "cost": 357.0 }, { "facility": "F4", "customer": "J", "cost": 257.0 }, { "facility": "F4", "customer": "K", "cost": 330.0 }, { "facility": "F4", "customer": "L", "cost": 133.0 }, { "facility": "F4", "customer": "M", "cost": 241.0 }, { "facility": "F5", "customer": "A", "cost": 402.0 }, { "facility": "F5", "customer": "B", "cost": 328.0 }, { "facility": "F5", "customer": "C", "cost": 213.0 }, { "facility": "F5", "customer": "D", "cost": 537.0 }, { "facility": "F5", "customer": "E", "cost": 153.0 }, { "facility": "F5", "customer": "F", "cost": 280.0 }, { "facility": "F5", "customer": "G", "cost": 265.0 }, { "facility": "F5", "customer": "H", "cost": 26.0 }, { "facility": "F5", "customer": "I", "cost": 532.0 }, { "facility": "F5", "customer": "J", "cost": 430.0 }, { "facility": "F5", "customer": "K", "cost": 505.0 }, { "facility": "F5", "customer": "L", "cost": 214.0 }, { "facility": "F5", "customer": "M", "cost": 211.0 }, { "facility": "F6", "customer": "A", "cost": 509.0 }, { "facility": "F6", "customer": "B", "cost": 506.0 }, { "facility": "F6", "customer": "C", "cost": 389.0 }, { "facility": "F6", "customer": "D", "cost": 541.0 }, { "facility": "F6", "customer": "E", "cost": 181.0 }, { "facility": "F6", "customer": "F", "cost": 323.0 }, { "facility": "F6", "customer": "G", "cost": 420.0 }, { "facility": "F6", "customer": "H", "cost": 199.0 }, { "facility": "F6", "customer": "I", "cost": 693.0 }, { "facility": "F6", "customer": "J", "cost": 602.0 }, { "facility": "F6", "customer": "K", "cost": 673.0 }, { "facility": "F6", "customer": "L", "cost": 396.0 }, { "facility": "F6", "customer": "M", "cost": 232.0 } ], "objective": 3270.0 }, "solution_variant": { "selected": [ "F1", "F2", "F3", "F5" ], "assignments": [ "F2", "F3", "F3", "F2", "F5", "F5", "F1", "F5", "F1", "F1", "F1", "F3", "F5" ] }, "context_index": 32, "input_format": "nl", "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=4\n# num_vehicles=11\n# STATIONS\nstation_id,commissioning_cost,charging_capacity\nF1,300.0,522.0\nF2,300.0,418.0\nF3,300.0,490.0\nF4,300.0,503.0\n# VEHICLES\nvehicle_id,charging_demand\nA,24.0\nB,12.0\nC,13.0\nD,19.0\nE,30.0\nF,23.0\nG,16.0\nH,19.0\nI,14.0\nJ,17.0\nK,22.0\n# DETOURS\nstation_id,vehicle_id,detour_cost\nF1,A,60.0\nF1,B,258.0\nF1,C,637.0\nF1,D,997.0\nF1,E,68.0\nF1,F,288.0\nF1,G,857.0\nF1,H,38.0\nF1,I,173.0\nF1,J,947.0\nF1,K,205.0\nF2,A,173.0\nF2,B,62.0\nF2,C,328.0\nF2,D,690.0\nF2,E,203.0\nF2,F,53.0\nF2,G,552.0\nF2,H,100.0\nF2,I,49.0\nF2,J,657.0\nF2,K,571.0\nF3,A,555.0\nF3,B,356.0\nF3,C,761.0\nF3,D,807.0\nF3,E,670.0\nF3,F,887.0\nF3,G,996.0\nF3,H,455.0\nF3,I,182.0\nF3,J,562.0\nF3,K,1257.0\nF4,A,80.0\nF4,B,260.0\nF4,C,704.0\nF4,D,1052.0\nF4,E,90.0\nF4,F,362.0\nF4,G,949.0\nF4,H,41.0\nF4,I,160.0\nF4,J,976.0\nF4,K,399.0\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": [ 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 522.0, 418.0, 490.0, 503.0 ], "connection_costs": [ [ 60.0, 258.0, 637.0, 997.0, 68.0, 288.0, 857.0, 38.0, 173.0, 947.0, 205.0 ], [ 173.0, 62.0, 328.0, 690.0, 203.0, 53.0, 552.0, 100.0, 49.0, 657.0, 571.0 ], [ 555.0, 356.0, 761.0, 807.0, 670.0, 887.0, 996.0, 455.0, 182.0, 562.0, 1257.0 ], [ 80.0, 260.0, 704.0, 1052.0, 90.0, 362.0, 949.0, 41.0, 160.0, 976.0, 399.0 ] ], "demands": [ 24.0, 12.0, 13.0, 19.0, 30.0, 23.0, 16.0, 19.0, 14.0, 17.0, 22.0 ], "objective": 3362.0 }, "solution": { "open_facilities": [ 0, 1 ], "assignments": [ 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0 ] }, "obj": 3362.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 4, "num_customers": 11, "facilities": [ { "id": "F1", "opening_cost": 300.0, "capacity": 522.0 }, { "id": "F2", "opening_cost": 300.0, "capacity": 418.0 }, { "id": "F3", "opening_cost": 300.0, "capacity": 490.0 }, { "id": "F4", "opening_cost": 300.0, "capacity": 503.0 } ], "customers": [ { "id": "A", "demand": 24.0 }, { "id": "B", "demand": 12.0 }, { "id": "C", "demand": 13.0 }, { "id": "D", "demand": 19.0 }, { "id": "E", "demand": 30.0 }, { "id": "F", "demand": 23.0 }, { "id": "G", "demand": 16.0 }, { "id": "H", "demand": 19.0 }, { "id": "I", "demand": 14.0 }, { "id": "J", "demand": 17.0 }, { "id": "K", "demand": 22.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 60.0 }, { "facility": "F1", "customer": "B", "cost": 258.0 }, { "facility": "F1", "customer": "C", "cost": 637.0 }, { "facility": "F1", "customer": "D", "cost": 997.0 }, { "facility": "F1", "customer": "E", "cost": 68.0 }, { "facility": "F1", "customer": "F", "cost": 288.0 }, { "facility": "F1", "customer": "G", "cost": 857.0 }, { "facility": "F1", "customer": "H", "cost": 38.0 }, { "facility": "F1", "customer": "I", "cost": 173.0 }, { "facility": "F1", "customer": "J", "cost": 947.0 }, { "facility": "F1", "customer": "K", "cost": 205.0 }, { "facility": "F2", "customer": "A", "cost": 173.0 }, { "facility": "F2", "customer": "B", "cost": 62.0 }, { "facility": "F2", "customer": "C", "cost": 328.0 }, { "facility": "F2", "customer": "D", "cost": 690.0 }, { "facility": "F2", "customer": "E", "cost": 203.0 }, { "facility": "F2", "customer": "F", "cost": 53.0 }, { "facility": "F2", "customer": "G", "cost": 552.0 }, { "facility": "F2", "customer": "H", "cost": 100.0 }, { "facility": "F2", "customer": "I", "cost": 49.0 }, { "facility": "F2", "customer": "J", "cost": 657.0 }, { "facility": "F2", "customer": "K", "cost": 571.0 }, { "facility": "F3", "customer": "A", "cost": 555.0 }, { "facility": "F3", "customer": "B", "cost": 356.0 }, { "facility": "F3", "customer": "C", "cost": 761.0 }, { "facility": "F3", "customer": "D", "cost": 807.0 }, { "facility": "F3", "customer": "E", "cost": 670.0 }, { "facility": "F3", "customer": "F", "cost": 887.0 }, { "facility": "F3", "customer": "G", "cost": 996.0 }, { "facility": "F3", "customer": "H", "cost": 455.0 }, { "facility": "F3", "customer": "I", "cost": 182.0 }, { "facility": "F3", "customer": "J", "cost": 562.0 }, { "facility": "F3", "customer": "K", "cost": 1257.0 }, { "facility": "F4", "customer": "A", "cost": 80.0 }, { "facility": "F4", "customer": "B", "cost": 260.0 }, { "facility": "F4", "customer": "C", "cost": 704.0 }, { "facility": "F4", "customer": "D", "cost": 1052.0 }, { "facility": "F4", "customer": "E", "cost": 90.0 }, { "facility": "F4", "customer": "F", "cost": 362.0 }, { "facility": "F4", "customer": "G", "cost": 949.0 }, { "facility": "F4", "customer": "H", "cost": 41.0 }, { "facility": "F4", "customer": "I", "cost": 160.0 }, { "facility": "F4", "customer": "J", "cost": 976.0 }, { "facility": "F4", "customer": "K", "cost": 399.0 } ], "objective": 3362.0 }, "solution_variant": { "selected": [ "F1", "F2" ], "assignments": [ "F1", "F2", "F2", "F2", "F1", "F2", "F2", "F1", "F2", "F2", "F1" ] }, "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 5 candidate shared printers under consideration and 12 individual staff print jobs to assign.\nPrinter F1: installation cost 534.0, duty capacity 500.0 pages.\nPrinter F2: installation cost 289.0, duty capacity 500.0 pages.\nPrinter F3: installation cost 201.0, duty capacity 500.0 pages.\nPrinter F4: installation cost 379.0, duty capacity 500.0 pages.\nPrinter F5: installation cost 209.0, duty capacity 500.0 pages.\nPrint job 0: size 15.0 pages.\nPrint job 1: size 17.0 pages.\nPrint job 2: size 17.0 pages.\nPrint job 3: size 23.0 pages.\nPrint job 4: size 20.0 pages.\nPrint job 5: size 17.0 pages.\nPrint job 6: size 13.0 pages.\nPrint job 7: size 23.0 pages.\nPrint job 8: size 13.0 pages.\nPrint job 9: size 16.0 pages.\nPrint job 10: size 17.0 pages.\nPrint job 11: size 11.0 pages.\nPrinter F1 to job 0: transfer/delay cost 43.0.\nPrinter F1 to job 1: transfer/delay cost 632.0.\nPrinter F1 to job 2: transfer/delay cost 63.0.\nPrinter F1 to job 3: transfer/delay cost 73.0.\nPrinter F1 to job 4: transfer/delay cost 103.0.\nPrinter F1 to job 5: transfer/delay cost 80.0.\nPrinter F1 to job 6: transfer/delay cost 778.0.\nPrinter F1 to job 7: transfer/delay cost 188.0.\nPrinter F1 to job 8: transfer/delay cost 220.0.\nPrinter F1 to job 9: transfer/delay cost 281.0.\nPrinter F1 to job 10: transfer/delay cost 485.0.\nPrinter F1 to job 11: transfer/delay cost 169.0.\nPrinter F2 to job 0: transfer/delay cost 201.0.\nPrinter F2 to job 1: transfer/delay cost 1668.0.\nPrinter F2 to job 2: transfer/delay cost 1482.0.\nPrinter F2 to job 3: transfer/delay cost 80.0.\nPrinter F2 to job 4: transfer/delay cost 441.0.\nPrinter F2 to job 5: transfer/delay cost 669.0.\nPrinter F2 to job 6: transfer/delay cost 1652.0.\nPrinter F2 to job 7: transfer/delay cost 1113.0.\nPrinter F2 to job 8: transfer/delay cost 846.0.\nPrinter F2 to job 9: transfer/delay cost 782.0.\nPrinter F2 to job 10: transfer/delay cost 1439.0.\nPrinter F2 to job 11: transfer/delay cost 1570.0.\nPrinter F3 to job 0: transfer/delay cost 79.0.\nPrinter F3 to job 1: transfer/delay cost 352.0.\nPrinter F3 to job 2: transfer/delay cost 158.0.\nPrinter F3 to job 3: transfer/delay cost 107.0.\nPrinter F3 to job 4: transfer/delay cost 61.0.\nPrinter F3 to job 5: transfer/delay cost 37.0.\nPrinter F3 to job 6: transfer/delay cost 527.0.\nPrinter F3 to job 7: transfer/delay cost 69.0.\nPrinter F3 to job 8: transfer/delay cost 112.0.\nPrinter F3 to job 9: transfer/delay cost 394.0.\nPrinter F3 to job 10: transfer/delay cost 256.0.\nPrinter F3 to job 11: transfer/delay cost 80.0.\nPrinter F4 to job 0: transfer/delay cost 588.0.\nPrinter F4 to job 1: transfer/delay cost 1472.0.\nPrinter F4 to job 2: transfer/delay cost 1866.0.\nPrinter F4 to job 3: transfer/delay cost 421.0.\nPrinter F4 to job 4: transfer/delay cost 188.0.\nPrinter F4 to job 5: transfer/delay cost 680.0.\nPrinter F4 to job 6: transfer/delay cost 1271.0.\nPrinter F4 to job 7: transfer/delay cost 1131.0.\nPrinter F4 to job 8: transfer/delay cost 559.0.\nPrinter F4 to job 9: transfer/delay cost 1546.0.\nPrinter F4 to job 10: transfer/delay cost 1234.0.\nPrinter F4 to job 11: transfer/delay cost 1881.0.\nPrinter F5 to job 0: transfer/delay cost 40.0.\nPrinter F5 to job 1: transfer/delay cost 1342.0.\nPrinter F5 to job 2: transfer/delay cost 1310.0.\nPrinter F5 to job 3: transfer/delay cost 71.0.\nPrinter F5 to job 4: transfer/delay cost 194.0.\nPrinter F5 to job 5: transfer/delay cost 337.0.\nPrinter F5 to job 6: transfer/delay cost 1322.0.\nPrinter F5 to job 7: transfer/delay cost 797.0.\nPrinter F5 to job 8: transfer/delay cost 525.0.\nPrinter F5 to job 9: transfer/delay cost 848.0.\nPrinter F5 to job 10: transfer/delay cost 1109.0.\nPrinter F5 to job 11: transfer/delay cost 1368.0.\nThese entries enumerate all 5 candidate printers and 12 print jobs with their parameters.\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": [ 534.0, 289.0, 201.0, 379.0, 209.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 43.0, 632.0, 63.0, 73.0, 103.0, 80.0, 778.0, 188.0, 220.0, 281.0, 485.0, 169.0 ], [ 201.0, 1668.0, 1482.0, 80.0, 441.0, 669.0, 1652.0, 1113.0, 846.0, 782.0, 1439.0, 1570.0 ], [ 79.0, 352.0, 158.0, 107.0, 61.0, 37.0, 527.0, 69.0, 112.0, 394.0, 256.0, 80.0 ], [ 588.0, 1472.0, 1866.0, 421.0, 188.0, 680.0, 1271.0, 1131.0, 559.0, 1546.0, 1234.0, 1881.0 ], [ 40.0, 1342.0, 1310.0, 71.0, 194.0, 337.0, 1322.0, 797.0, 525.0, 848.0, 1109.0, 1368.0 ] ], "demands": [ 15.0, 17.0, 17.0, 23.0, 20.0, 17.0, 13.0, 23.0, 13.0, 16.0, 17.0, 11.0 ], "objective": 2433.0 }, "solution": { "open_facilities": [ 2 ], "assignments": [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ] }, "obj": 2433.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 12, "facilities": [ { "id": "F1", "opening_cost": 534.0, "capacity": 500.0 }, { "id": "F2", "opening_cost": 289.0, "capacity": 500.0 }, { "id": "F3", "opening_cost": 201.0, "capacity": 500.0 }, { "id": "F4", "opening_cost": 379.0, "capacity": 500.0 }, { "id": "F5", "opening_cost": 209.0, "capacity": 500.0 } ], "customers": [ { "id": 0, "demand": 15.0 }, { "id": 1, "demand": 17.0 }, { "id": 2, "demand": 17.0 }, { "id": 3, "demand": 23.0 }, { "id": 4, "demand": 20.0 }, { "id": 5, "demand": 17.0 }, { "id": 6, "demand": 13.0 }, { "id": 7, "demand": 23.0 }, { "id": 8, "demand": 13.0 }, { "id": 9, "demand": 16.0 }, { "id": 10, "demand": 17.0 }, { "id": 11, "demand": 11.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 43.0 }, { "facility": "F1", "customer": 1, "cost": 632.0 }, { "facility": "F1", "customer": 2, "cost": 63.0 }, { "facility": "F1", "customer": 3, "cost": 73.0 }, { "facility": "F1", "customer": 4, "cost": 103.0 }, { "facility": "F1", "customer": 5, "cost": 80.0 }, { "facility": "F1", "customer": 6, "cost": 778.0 }, { "facility": "F1", "customer": 7, "cost": 188.0 }, { "facility": "F1", "customer": 8, "cost": 220.0 }, { "facility": "F1", "customer": 9, "cost": 281.0 }, { "facility": "F1", "customer": 10, "cost": 485.0 }, { "facility": "F1", "customer": 11, "cost": 169.0 }, { "facility": "F2", "customer": 0, "cost": 201.0 }, { "facility": "F2", "customer": 1, "cost": 1668.0 }, { "facility": "F2", "customer": 2, "cost": 1482.0 }, { "facility": "F2", "customer": 3, "cost": 80.0 }, { "facility": "F2", "customer": 4, "cost": 441.0 }, { "facility": "F2", "customer": 5, "cost": 669.0 }, { "facility": "F2", "customer": 6, "cost": 1652.0 }, { "facility": "F2", "customer": 7, "cost": 1113.0 }, { "facility": "F2", "customer": 8, "cost": 846.0 }, { "facility": "F2", "customer": 9, "cost": 782.0 }, { "facility": "F2", "customer": 10, "cost": 1439.0 }, { "facility": "F2", "customer": 11, "cost": 1570.0 }, { "facility": "F3", "customer": 0, "cost": 79.0 }, { "facility": "F3", "customer": 1, "cost": 352.0 }, { "facility": "F3", "customer": 2, "cost": 158.0 }, { "facility": "F3", "customer": 3, "cost": 107.0 }, { "facility": "F3", "customer": 4, "cost": 61.0 }, { "facility": "F3", "customer": 5, "cost": 37.0 }, { "facility": "F3", "customer": 6, "cost": 527.0 }, { "facility": "F3", "customer": 7, "cost": 69.0 }, { "facility": "F3", "customer": 8, "cost": 112.0 }, { "facility": "F3", "customer": 9, "cost": 394.0 }, { "facility": "F3", "customer": 10, "cost": 256.0 }, { "facility": "F3", "customer": 11, "cost": 80.0 }, { "facility": "F4", "customer": 0, "cost": 588.0 }, { "facility": "F4", "customer": 1, "cost": 1472.0 }, { "facility": "F4", "customer": 2, "cost": 1866.0 }, { "facility": "F4", "customer": 3, "cost": 421.0 }, { "facility": "F4", "customer": 4, "cost": 188.0 }, { "facility": "F4", "customer": 5, "cost": 680.0 }, { "facility": "F4", "customer": 6, "cost": 1271.0 }, { "facility": "F4", "customer": 7, "cost": 1131.0 }, { "facility": "F4", "customer": 8, "cost": 559.0 }, { "facility": "F4", "customer": 9, "cost": 1546.0 }, { "facility": "F4", "customer": 10, "cost": 1234.0 }, { "facility": "F4", "customer": 11, "cost": 1881.0 }, { "facility": "F5", "customer": 0, "cost": 40.0 }, { "facility": "F5", "customer": 1, "cost": 1342.0 }, { "facility": "F5", "customer": 2, "cost": 1310.0 }, { "facility": "F5", "customer": 3, "cost": 71.0 }, { "facility": "F5", "customer": 4, "cost": 194.0 }, { "facility": "F5", "customer": 5, "cost": 337.0 }, { "facility": "F5", "customer": 6, "cost": 1322.0 }, { "facility": "F5", "customer": 7, "cost": 797.0 }, { "facility": "F5", "customer": 8, "cost": 525.0 }, { "facility": "F5", "customer": 9, "cost": 848.0 }, { "facility": "F5", "customer": 10, "cost": 1109.0 }, { "facility": "F5", "customer": 11, "cost": 1368.0 } ], "objective": 2433.0 }, "solution_variant": { "selected": [ "F3" ], "assignments": [ "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3", "F3" ] }, "context_index": 34, "input_format": "nl", "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\nBelow are the 5 candidate drop-off centers and the 10 neighborhoods to consider.\nCenter F1 has maintenance cost 300.0 and processing capacity 300.0.\nCenter F2 has maintenance cost 300.0 and processing capacity 300.0.\nCenter F3 has maintenance cost 300.0 and processing capacity 300.0.\nCenter F4 has maintenance cost 300.0 and processing capacity 300.0.\nCenter F5 has maintenance cost 300.0 and processing capacity 300.0.\nNeighborhood A produces 28.0 waste that must be sent intact to one center.\nNeighborhood B produces 12.0 waste that must be sent intact to one center.\nNeighborhood C produces 21.0 waste that must be sent intact to one center.\nNeighborhood D produces 12.0 waste that must be sent intact to one center.\nNeighborhood E produces 30.0 waste that must be sent intact to one center.\nNeighborhood F produces 30.0 waste that must be sent intact to one center.\nNeighborhood G produces 26.0 waste that must be sent intact to one center.\nNeighborhood H produces 14.0 waste that must be sent intact to one center.\nNeighborhood I produces 19.0 waste that must be sent intact to one center.\nNeighborhood J produces 12.0 waste that must be sent intact to one center.\nAssigning neighborhood A to center F1 incurs hauling cost 166.0.\nAssigning neighborhood B to center F1 incurs hauling cost 197.0.\nAssigning neighborhood C to center F1 incurs hauling cost 517.0.\nAssigning neighborhood D to center F1 incurs hauling cost 69.0.\nAssigning neighborhood E to center F1 incurs hauling cost 168.0.\nAssigning neighborhood F to center F1 incurs hauling cost 248.0.\nAssigning neighborhood G to center F1 incurs hauling cost 365.0.\nAssigning neighborhood H to center F1 incurs hauling cost 28.0.\nAssigning neighborhood I to center F1 incurs hauling cost 207.0.\nAssigning neighborhood J to center F1 incurs hauling cost 69.0.\nAssigning neighborhood A to center F2 incurs hauling cost 517.0.\nAssigning neighborhood B to center F2 incurs hauling cost 382.0.\nAssigning neighborhood C to center F2 incurs hauling cost 858.0.\nAssigning neighborhood D to center F2 incurs hauling cost 328.0.\nAssigning neighborhood E to center F2 incurs hauling cost 254.0.\nAssigning neighborhood F to center F2 incurs hauling cost 430.0.\nAssigning neighborhood G to center F2 incurs hauling cost 204.0.\nAssigning neighborhood H to center F2 incurs hauling cost 61.0.\nAssigning neighborhood I to center F2 incurs hauling cost 412.0.\nAssigning neighborhood J to center F2 incurs hauling cost 92.0.\nAssigning neighborhood A to center F3 incurs hauling cost 951.0.\nAssigning neighborhood B to center F3 incurs hauling cost 566.0.\nAssigning neighborhood C to center F3 incurs hauling cost 1168.0.\nAssigning neighborhood D to center F3 incurs hauling cost 714.0.\nAssigning neighborhood E to center F3 incurs hauling cost 327.0.\nAssigning neighborhood F to center F3 incurs hauling cost 605.0.\nAssigning neighborhood G to center F3 incurs hauling cost 179.0.\nAssigning neighborhood H to center F3 incurs hauling cost 141.0.\nAssigning neighborhood I to center F3 incurs hauling cost 623.0.\nAssigning neighborhood J to center F3 incurs hauling cost 628.0.\nAssigning neighborhood A to center F4 incurs hauling cost 114.0.\nAssigning neighborhood B to center F4 incurs hauling cost 160.0.\nAssigning neighborhood C to center F4 incurs hauling cost 444.0.\nAssigning neighborhood D to center F4 incurs hauling cost 39.0.\nAssigning neighborhood E to center F4 incurs hauling cost 148.0.\nAssigning neighborhood F to center F4 incurs hauling cost 210.0.\nAssigning neighborhood G to center F4 incurs hauling cost 424.0.\nAssigning neighborhood H to center F4 incurs hauling cost 31.0.\nAssigning neighborhood I to center F4 incurs hauling cost 167.0.\nAssigning neighborhood J to center F4 incurs hauling cost 122.0.\nAssigning neighborhood A to center F5 incurs hauling cost 1168.0.\nAssigning neighborhood B to center F5 incurs hauling cost 636.0.\nAssigning neighborhood C to center F5 incurs hauling cost 1291.0.\nAssigning neighborhood D to center F5 incurs hauling cost 924.0.\nAssigning neighborhood E to center F5 incurs hauling cost 344.0.\nAssigning neighborhood F to center F5 incurs hauling cost 670.0.\nAssigning neighborhood G to center F5 incurs hauling cost 383.0.\nAssigning neighborhood H to center F5 incurs hauling cost 182.0.\nAssigning neighborhood I to center F5 incurs hauling cost 711.0.\nAssigning neighborhood J to center F5 incurs hauling cost 966.0.\nUse these entries to choose centers and assignments that minimize total maintenance plus hauling while respecting capacities and keeping each neighborhood's waste intact.\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": [ 300.0, 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 300.0, 300.0, 300.0, 300.0, 300.0 ], "connection_costs": [ [ 166.0, 197.0, 517.0, 69.0, 168.0, 248.0, 365.0, 28.0, 207.0, 69.0 ], [ 517.0, 382.0, 858.0, 328.0, 254.0, 430.0, 204.0, 61.0, 412.0, 92.0 ], [ 951.0, 566.0, 1168.0, 714.0, 327.0, 605.0, 179.0, 141.0, 623.0, 628.0 ], [ 114.0, 160.0, 444.0, 39.0, 148.0, 210.0, 424.0, 31.0, 167.0, 122.0 ], [ 1168.0, 636.0, 1291.0, 924.0, 344.0, 670.0, 383.0, 182.0, 711.0, 966.0 ] ], "demands": [ 28.0, 12.0, 21.0, 12.0, 30.0, 30.0, 26.0, 14.0, 19.0, 12.0 ], "objective": 2159.0 }, "solution": { "open_facilities": [ 3 ], "assignments": [ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ] }, "obj": 2159.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 10, "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 } ], "customers": [ { "id": "A", "demand": 28.0 }, { "id": "B", "demand": 12.0 }, { "id": "C", "demand": 21.0 }, { "id": "D", "demand": 12.0 }, { "id": "E", "demand": 30.0 }, { "id": "F", "demand": 30.0 }, { "id": "G", "demand": 26.0 }, { "id": "H", "demand": 14.0 }, { "id": "I", "demand": 19.0 }, { "id": "J", "demand": 12.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 166.0 }, { "facility": "F1", "customer": "B", "cost": 197.0 }, { "facility": "F1", "customer": "C", "cost": 517.0 }, { "facility": "F1", "customer": "D", "cost": 69.0 }, { "facility": "F1", "customer": "E", "cost": 168.0 }, { "facility": "F1", "customer": "F", "cost": 248.0 }, { "facility": "F1", "customer": "G", "cost": 365.0 }, { "facility": "F1", "customer": "H", "cost": 28.0 }, { "facility": "F1", "customer": "I", "cost": 207.0 }, { "facility": "F1", "customer": "J", "cost": 69.0 }, { "facility": "F2", "customer": "A", "cost": 517.0 }, { "facility": "F2", "customer": "B", "cost": 382.0 }, { "facility": "F2", "customer": "C", "cost": 858.0 }, { "facility": "F2", "customer": "D", "cost": 328.0 }, { "facility": "F2", "customer": "E", "cost": 254.0 }, { "facility": "F2", "customer": "F", "cost": 430.0 }, { "facility": "F2", "customer": "G", "cost": 204.0 }, { "facility": "F2", "customer": "H", "cost": 61.0 }, { "facility": "F2", "customer": "I", "cost": 412.0 }, { "facility": "F2", "customer": "J", "cost": 92.0 }, { "facility": "F3", "customer": "A", "cost": 951.0 }, { "facility": "F3", "customer": "B", "cost": 566.0 }, { "facility": "F3", "customer": "C", "cost": 1168.0 }, { "facility": "F3", "customer": "D", "cost": 714.0 }, { "facility": "F3", "customer": "E", "cost": 327.0 }, { "facility": "F3", "customer": "F", "cost": 605.0 }, { "facility": "F3", "customer": "G", "cost": 179.0 }, { "facility": "F3", "customer": "H", "cost": 141.0 }, { "facility": "F3", "customer": "I", "cost": 623.0 }, { "facility": "F3", "customer": "J", "cost": 628.0 }, { "facility": "F4", "customer": "A", "cost": 114.0 }, { "facility": "F4", "customer": "B", "cost": 160.0 }, { "facility": "F4", "customer": "C", "cost": 444.0 }, { "facility": "F4", "customer": "D", "cost": 39.0 }, { "facility": "F4", "customer": "E", "cost": 148.0 }, { "facility": "F4", "customer": "F", "cost": 210.0 }, { "facility": "F4", "customer": "G", "cost": 424.0 }, { "facility": "F4", "customer": "H", "cost": 31.0 }, { "facility": "F4", "customer": "I", "cost": 167.0 }, { "facility": "F4", "customer": "J", "cost": 122.0 }, { "facility": "F5", "customer": "A", "cost": 1168.0 }, { "facility": "F5", "customer": "B", "cost": 636.0 }, { "facility": "F5", "customer": "C", "cost": 1291.0 }, { "facility": "F5", "customer": "D", "cost": 924.0 }, { "facility": "F5", "customer": "E", "cost": 344.0 }, { "facility": "F5", "customer": "F", "cost": 670.0 }, { "facility": "F5", "customer": "G", "cost": 383.0 }, { "facility": "F5", "customer": "H", "cost": 182.0 }, { "facility": "F5", "customer": "I", "cost": 711.0 }, { "facility": "F5", "customer": "J", "cost": 966.0 } ], "objective": 2159.0 }, "solution_variant": { "selected": [ "F4" ], "assignments": [ "F4", "F4", "F4", "F4", "F4", "F4", "F4", "F4", "F4", "F4" ] }, "context_index": 35, "input_format": "nl", "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# num_stations=5\n# num_guest_groups=11\n# STATIONS\nstation_id,setup_cost,station_capacity\nF1,400.0,500.0\nF2,400.0,500.0\nF3,400.0,500.0\nF4,400.0,500.0\nF5,400.0,500.0\n# GROUPS\ngroup_id,group_size\n1,21.0\n2,25.0\n3,28.0\n4,24.0\n5,26.0\n6,10.0\n7,27.0\n8,17.0\n9,14.0\n10,27.0\n11,23.0\n# SERVICES\nstation_id,group_id,service_cost\nF1,1,982.0\nF1,2,1375.0\nF1,3,974.0\nF1,4,368.0\nF1,5,222.0\nF1,6,1138.0\nF1,7,1543.0\nF1,8,989.0\nF1,9,192.0\nF1,10,1086.0\nF1,11,1509.0\nF2,1,858.0\nF2,2,668.0\nF2,3,63.0\nF2,4,63.0\nF2,5,83.0\nF2,6,938.0\nF2,7,781.0\nF2,8,59.0\nF2,9,61.0\nF2,10,788.0\nF2,11,54.0\nF3,1,162.0\nF3,2,558.0\nF3,3,674.0\nF3,4,366.0\nF3,5,202.0\nF3,6,206.0\nF3,7,691.0\nF3,8,647.0\nF3,9,173.0\nF3,10,54.0\nF3,11,1118.0\nF4,1,1642.0\nF4,2,2126.0\nF4,3,1619.0\nF4,4,721.0\nF4,5,795.0\nF4,6,1813.0\nF4,7,2293.0\nF4,8,1654.0\nF4,9,769.0\nF4,10,1804.0\nF4,11,2151.0\nF5,1,820.0\nF5,2,728.0\nF5,3,105.0\nF5,4,104.0\nF5,5,57.0\nF5,6,913.0\nF5,7,873.0\nF5,8,59.0\nF5,9,34.0\nF5,10,770.0\nF5,11,524.0\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": [ 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 982.0, 1375.0, 974.0, 368.0, 222.0, 1138.0, 1543.0, 989.0, 192.0, 1086.0, 1509.0 ], [ 858.0, 668.0, 63.0, 63.0, 83.0, 938.0, 781.0, 59.0, 61.0, 788.0, 54.0 ], [ 162.0, 558.0, 674.0, 366.0, 202.0, 206.0, 691.0, 647.0, 173.0, 54.0, 1118.0 ], [ 1642.0, 2126.0, 1619.0, 721.0, 795.0, 1813.0, 2293.0, 1654.0, 769.0, 1804.0, 2151.0 ], [ 820.0, 728.0, 105.0, 104.0, 57.0, 913.0, 873.0, 59.0, 34.0, 770.0, 524.0 ] ], "demands": [ 21.0, 25.0, 28.0, 24.0, 26.0, 10.0, 27.0, 17.0, 14.0, 27.0, 23.0 ], "objective": 2854.0 }, "solution": { "open_facilities": [ 1, 2 ], "assignments": [ 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1 ] }, "obj": 2854.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 11, "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 } ], "customers": [ { "id": 1, "demand": 21.0 }, { "id": 2, "demand": 25.0 }, { "id": 3, "demand": 28.0 }, { "id": 4, "demand": 24.0 }, { "id": 5, "demand": 26.0 }, { "id": 6, "demand": 10.0 }, { "id": 7, "demand": 27.0 }, { "id": 8, "demand": 17.0 }, { "id": 9, "demand": 14.0 }, { "id": 10, "demand": 27.0 }, { "id": 11, "demand": 23.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 982.0 }, { "facility": "F1", "customer": 2, "cost": 1375.0 }, { "facility": "F1", "customer": 3, "cost": 974.0 }, { "facility": "F1", "customer": 4, "cost": 368.0 }, { "facility": "F1", "customer": 5, "cost": 222.0 }, { "facility": "F1", "customer": 6, "cost": 1138.0 }, { "facility": "F1", "customer": 7, "cost": 1543.0 }, { "facility": "F1", "customer": 8, "cost": 989.0 }, { "facility": "F1", "customer": 9, "cost": 192.0 }, { "facility": "F1", "customer": 10, "cost": 1086.0 }, { "facility": "F1", "customer": 11, "cost": 1509.0 }, { "facility": "F2", "customer": 1, "cost": 858.0 }, { "facility": "F2", "customer": 2, "cost": 668.0 }, { "facility": "F2", "customer": 3, "cost": 63.0 }, { "facility": "F2", "customer": 4, "cost": 63.0 }, { "facility": "F2", "customer": 5, "cost": 83.0 }, { "facility": "F2", "customer": 6, "cost": 938.0 }, { "facility": "F2", "customer": 7, "cost": 781.0 }, { "facility": "F2", "customer": 8, "cost": 59.0 }, { "facility": "F2", "customer": 9, "cost": 61.0 }, { "facility": "F2", "customer": 10, "cost": 788.0 }, { "facility": "F2", "customer": 11, "cost": 54.0 }, { "facility": "F3", "customer": 1, "cost": 162.0 }, { "facility": "F3", "customer": 2, "cost": 558.0 }, { "facility": "F3", "customer": 3, "cost": 674.0 }, { "facility": "F3", "customer": 4, "cost": 366.0 }, { "facility": "F3", "customer": 5, "cost": 202.0 }, { "facility": "F3", "customer": 6, "cost": 206.0 }, { "facility": "F3", "customer": 7, "cost": 691.0 }, { "facility": "F3", "customer": 8, "cost": 647.0 }, { "facility": "F3", "customer": 9, "cost": 173.0 }, { "facility": "F3", "customer": 10, "cost": 54.0 }, { "facility": "F3", "customer": 11, "cost": 1118.0 }, { "facility": "F4", "customer": 1, "cost": 1642.0 }, { "facility": "F4", "customer": 2, "cost": 2126.0 }, { "facility": "F4", "customer": 3, "cost": 1619.0 }, { "facility": "F4", "customer": 4, "cost": 721.0 }, { "facility": "F4", "customer": 5, "cost": 795.0 }, { "facility": "F4", "customer": 6, "cost": 1813.0 }, { "facility": "F4", "customer": 7, "cost": 2293.0 }, { "facility": "F4", "customer": 8, "cost": 1654.0 }, { "facility": "F4", "customer": 9, "cost": 769.0 }, { "facility": "F4", "customer": 10, "cost": 1804.0 }, { "facility": "F4", "customer": 11, "cost": 2151.0 }, { "facility": "F5", "customer": 1, "cost": 820.0 }, { "facility": "F5", "customer": 2, "cost": 728.0 }, { "facility": "F5", "customer": 3, "cost": 105.0 }, { "facility": "F5", "customer": 4, "cost": 104.0 }, { "facility": "F5", "customer": 5, "cost": 57.0 }, { "facility": "F5", "customer": 6, "cost": 913.0 }, { "facility": "F5", "customer": 7, "cost": 873.0 }, { "facility": "F5", "customer": 8, "cost": 59.0 }, { "facility": "F5", "customer": 9, "cost": 34.0 }, { "facility": "F5", "customer": 10, "cost": 770.0 }, { "facility": "F5", "customer": 11, "cost": 524.0 } ], "objective": 2854.0 }, "solution_variant": { "selected": [ "F2", "F3" ], "assignments": [ "F3", "F3", "F2", "F2", "F2", "F3", "F3", "F2", "F2", "F3", "F2" ] }, "context_index": 36, "input_format": "csv", "input_index_base": 1 }, { "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\nThere are 5 candidate pantry locations and 12 families to assign.\nPantry F1 has an operating charge of 119.0 and a storage limit of 309.0.\nPantry F2 has an operating charge of 372.0 and a storage limit of 436.0.\nPantry F3 has an operating charge of 308.0 and a storage limit of 404.0.\nPantry F4 has an operating charge of 114.0 and a storage limit of 307.0.\nPantry F5 has an operating charge of 336.0 and a storage limit of 418.0.\nFamily 1 requires 20.0 units of pantry capacity.\nFamily 2 requires 20.0 units of pantry capacity.\nFamily 3 requires 10.0 units of pantry capacity.\nFamily 4 requires 20.0 units of pantry capacity.\nFamily 5 requires 20.0 units of pantry capacity.\nFamily 6 requires 40.0 units of pantry capacity.\nFamily 7 requires 10.0 units of pantry capacity.\nFamily 8 requires 9.0 units of pantry capacity.\nFamily 9 requires 5.0 units of pantry capacity.\nFamily 10 requires 31.0 units of pantry capacity.\nFamily 11 requires 19.0 units of pantry capacity.\nFamily 12 requires 35.0 units of pantry capacity.\nAssigning family 1 to pantry F1 incurs a service cost of 192.0.\nAssigning family 2 to pantry F1 incurs a service cost of 20.0.\nAssigning family 3 to pantry F1 incurs a service cost of 23.0.\nAssigning family 4 to pantry F1 incurs a service cost of 177.0.\nAssigning family 5 to pantry F1 incurs a service cost of 349.0.\nAssigning family 6 to pantry F1 incurs a service cost of 290.0.\nAssigning family 7 to pantry F1 incurs a service cost of 252.0.\nAssigning family 8 to pantry F1 incurs a service cost of 224.0.\nAssigning family 9 to pantry F1 incurs a service cost of 84.0.\nAssigning family 10 to pantry F1 incurs a service cost of 236.0.\nAssigning family 11 to pantry F1 incurs a service cost of 96.0.\nAssigning family 12 to pantry F1 incurs a service cost of 89.0.\nAssigning family 1 to pantry F2 incurs a service cost of 286.0.\nAssigning family 2 to pantry F2 incurs a service cost of 175.0.\nAssigning family 3 to pantry F2 incurs a service cost of 161.0.\nAssigning family 4 to pantry F2 incurs a service cost of 45.0.\nAssigning family 5 to pantry F2 incurs a service cost of 234.0.\nAssigning family 6 to pantry F2 incurs a service cost of 297.0.\nAssigning family 7 to pantry F2 incurs a service cost of 275.0.\nAssigning family 8 to pantry F2 incurs a service cost of 144.0.\nAssigning family 9 to pantry F2 incurs a service cost of 236.0.\nAssigning family 10 to pantry F2 incurs a service cost of 81.0.\nAssigning family 11 to pantry F2 incurs a service cost of 184.0.\nAssigning family 12 to pantry F2 incurs a service cost of 144.0.\nAssigning family 1 to pantry F3 incurs a service cost of 185.0.\nAssigning family 2 to pantry F3 incurs a service cost of 24.0.\nAssigning family 3 to pantry F3 incurs a service cost of 42.0.\nAssigning family 4 to pantry F3 incurs a service cost of 207.0.\nAssigning family 5 to pantry F3 incurs a service cost of 374.0.\nAssigning family 6 to pantry F3 incurs a service cost of 299.0.\nAssigning family 7 to pantry F3 incurs a service cost of 259.0.\nAssigning family 8 to pantry F3 incurs a service cost of 248.0.\nAssigning family 9 to pantry F3 incurs a service cost of 60.0.\nAssigning family 10 to pantry F3 incurs a service cost of 267.0.\nAssigning family 11 to pantry F3 incurs a service cost of 102.0.\nAssigning family 12 to pantry F3 incurs a service cost of 108.0.\nAssigning family 1 to pantry F4 incurs a service cost of 224.0.\nAssigning family 2 to pantry F4 incurs a service cost of 173.0.\nAssigning family 3 to pantry F4 incurs a service cost of 180.0.\nAssigning family 4 to pantry F4 incurs a service cost of 134.0.\nAssigning family 5 to pantry F4 incurs a service cost of 180.0.\nAssigning family 6 to pantry F4 incurs a service cost of 209.0.\nAssigning family 7 to pantry F4 incurs a service cost of 189.0.\nAssigning family 8 to pantry F4 incurs a service cost of 63.0.\nAssigning family 9 to pantry F4 incurs a service cost of 216.0.\nAssigning family 10 to pantry F4 incurs a service cost of 100.0.\nAssigning family 11 to pantry F4 incurs a service cost of 139.0.\nAssigning family 12 to pantry F4 incurs a service cost of 196.0.\nAssigning family 1 to pantry F5 incurs a service cost of 202.0.\nAssigning family 2 to pantry F5 incurs a service cost of 180.0.\nAssigning family 3 to pantry F5 incurs a service cost of 195.0.\nAssigning family 4 to pantry F5 incurs a service cost of 168.0.\nAssigning family 5 to pantry F5 incurs a service cost of 171.0.\nAssigning family 6 to pantry F5 incurs a service cost of 175.0.\nAssigning family 7 to pantry F5 incurs a service cost of 156.0.\nAssigning family 8 to pantry F5 incurs a service cost of 44.0.\nAssigning family 9 to pantry F5 incurs a service cost of 215.0.\nAssigning family 10 to pantry F5 incurs a service cost of 127.0.\nAssigning family 11 to pantry F5 incurs a service cost of 131.0.\nAssigning family 12 to pantry F5 incurs a service cost of 220.0.\nThe lists below specify each pantry's operating charge and storage limit, each family's demand, and each pantry–family service cost for evaluation.\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": [ 119.0, 372.0, 308.0, 114.0, 336.0 ], "capacities": [ 309.0, 436.0, 404.0, 307.0, 418.0 ], "connection_costs": [ [ 192.0, 20.0, 23.0, 177.0, 349.0, 290.0, 252.0, 224.0, 84.0, 236.0, 96.0, 89.0 ], [ 286.0, 175.0, 161.0, 45.0, 234.0, 297.0, 275.0, 144.0, 236.0, 81.0, 184.0, 144.0 ], [ 185.0, 24.0, 42.0, 207.0, 374.0, 299.0, 259.0, 248.0, 60.0, 267.0, 102.0, 108.0 ], [ 224.0, 173.0, 180.0, 134.0, 180.0, 209.0, 189.0, 63.0, 216.0, 100.0, 139.0, 196.0 ], [ 202.0, 180.0, 195.0, 168.0, 171.0, 175.0, 156.0, 44.0, 215.0, 127.0, 131.0, 220.0 ] ], "demands": [ 20.0, 20.0, 10.0, 20.0, 20.0, 40.0, 10.0, 9.0, 5.0, 31.0, 19.0, 35.0 ], "objective": 1612.0 }, "solution": { "open_facilities": [ 0, 3 ], "assignments": [ 0, 0, 0, 3, 3, 3, 3, 3, 0, 3, 0, 0 ] }, "obj": 1612.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 12, "facilities": [ { "id": "F1", "opening_cost": 119.0, "capacity": 309.0 }, { "id": "F2", "opening_cost": 372.0, "capacity": 436.0 }, { "id": "F3", "opening_cost": 308.0, "capacity": 404.0 }, { "id": "F4", "opening_cost": 114.0, "capacity": 307.0 }, { "id": "F5", "opening_cost": 336.0, "capacity": 418.0 } ], "customers": [ { "id": 1, "demand": 20.0 }, { "id": 2, "demand": 20.0 }, { "id": 3, "demand": 10.0 }, { "id": 4, "demand": 20.0 }, { "id": 5, "demand": 20.0 }, { "id": 6, "demand": 40.0 }, { "id": 7, "demand": 10.0 }, { "id": 8, "demand": 9.0 }, { "id": 9, "demand": 5.0 }, { "id": 10, "demand": 31.0 }, { "id": 11, "demand": 19.0 }, { "id": 12, "demand": 35.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 192.0 }, { "facility": "F1", "customer": 2, "cost": 20.0 }, { "facility": "F1", "customer": 3, "cost": 23.0 }, { "facility": "F1", "customer": 4, "cost": 177.0 }, { "facility": "F1", "customer": 5, "cost": 349.0 }, { "facility": "F1", "customer": 6, "cost": 290.0 }, { "facility": "F1", "customer": 7, "cost": 252.0 }, { "facility": "F1", "customer": 8, "cost": 224.0 }, { "facility": "F1", "customer": 9, "cost": 84.0 }, { "facility": "F1", "customer": 10, "cost": 236.0 }, { "facility": "F1", "customer": 11, "cost": 96.0 }, { "facility": "F1", "customer": 12, "cost": 89.0 }, { "facility": "F2", "customer": 1, "cost": 286.0 }, { "facility": "F2", "customer": 2, "cost": 175.0 }, { "facility": "F2", "customer": 3, "cost": 161.0 }, { "facility": "F2", "customer": 4, "cost": 45.0 }, { "facility": "F2", "customer": 5, "cost": 234.0 }, { "facility": "F2", "customer": 6, "cost": 297.0 }, { "facility": "F2", "customer": 7, "cost": 275.0 }, { "facility": "F2", "customer": 8, "cost": 144.0 }, { "facility": "F2", "customer": 9, "cost": 236.0 }, { "facility": "F2", "customer": 10, "cost": 81.0 }, { "facility": "F2", "customer": 11, "cost": 184.0 }, { "facility": "F2", "customer": 12, "cost": 144.0 }, { "facility": "F3", "customer": 1, "cost": 185.0 }, { "facility": "F3", "customer": 2, "cost": 24.0 }, { "facility": "F3", "customer": 3, "cost": 42.0 }, { "facility": "F3", "customer": 4, "cost": 207.0 }, { "facility": "F3", "customer": 5, "cost": 374.0 }, { "facility": "F3", "customer": 6, "cost": 299.0 }, { "facility": "F3", "customer": 7, "cost": 259.0 }, { "facility": "F3", "customer": 8, "cost": 248.0 }, { "facility": "F3", "customer": 9, "cost": 60.0 }, { "facility": "F3", "customer": 10, "cost": 267.0 }, { "facility": "F3", "customer": 11, "cost": 102.0 }, { "facility": "F3", "customer": 12, "cost": 108.0 }, { "facility": "F4", "customer": 1, "cost": 224.0 }, { "facility": "F4", "customer": 2, "cost": 173.0 }, { "facility": "F4", "customer": 3, "cost": 180.0 }, { "facility": "F4", "customer": 4, "cost": 134.0 }, { "facility": "F4", "customer": 5, "cost": 180.0 }, { "facility": "F4", "customer": 6, "cost": 209.0 }, { "facility": "F4", "customer": 7, "cost": 189.0 }, { "facility": "F4", "customer": 8, "cost": 63.0 }, { "facility": "F4", "customer": 9, "cost": 216.0 }, { "facility": "F4", "customer": 10, "cost": 100.0 }, { "facility": "F4", "customer": 11, "cost": 139.0 }, { "facility": "F4", "customer": 12, "cost": 196.0 }, { "facility": "F5", "customer": 1, "cost": 202.0 }, { "facility": "F5", "customer": 2, "cost": 180.0 }, { "facility": "F5", "customer": 3, "cost": 195.0 }, { "facility": "F5", "customer": 4, "cost": 168.0 }, { "facility": "F5", "customer": 5, "cost": 171.0 }, { "facility": "F5", "customer": 6, "cost": 175.0 }, { "facility": "F5", "customer": 7, "cost": 156.0 }, { "facility": "F5", "customer": 8, "cost": 44.0 }, { "facility": "F5", "customer": 9, "cost": 215.0 }, { "facility": "F5", "customer": 10, "cost": 127.0 }, { "facility": "F5", "customer": 11, "cost": 131.0 }, { "facility": "F5", "customer": 12, "cost": 220.0 } ], "objective": 1612.0 }, "solution_variant": { "selected": [ "F1", "F4" ], "assignments": [ "F1", "F1", "F1", "F4", "F4", "F4", "F4", "F4", "F1", "F4", "F1", "F1" ] }, "context_index": 37, "input_format": "nl", "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=4\n# num_applications=11\n# DATA_CENTERS\ndata_center_id,running_fee,server_capacity\nF1,400.0,700.0\nF2,400.0,700.0\nF3,400.0,700.0\nF4,400.0,700.0\n# APPLICATIONS\napplication_id,app_demand\n1,28.0\n2,28.0\n3,24.0\n4,17.0\n5,26.0\n6,12.0\n7,13.0\n8,19.0\n9,13.0\n10,13.0\n11,18.0\n# LATENCYS\ndata_center_id,application_id,latency_cost\nF1,1,145.0\nF1,2,314.0\nF1,3,205.0\nF1,4,813.0\nF1,5,76.0\nF1,6,99.0\nF1,7,63.0\nF1,8,755.0\nF1,9,66.0\nF1,10,79.0\nF1,11,769.0\nF2,1,257.0\nF2,2,155.0\nF2,3,139.0\nF2,4,590.0\nF2,5,53.0\nF2,6,51.0\nF2,7,33.0\nF2,8,524.0\nF2,9,46.0\nF2,10,162.0\nF2,11,602.0\nF3,1,764.0\nF3,2,498.0\nF3,3,108.0\nF3,4,952.0\nF3,5,74.0\nF3,6,27.0\nF3,7,29.0\nF3,8,1542.0\nF3,9,32.0\nF3,10,525.0\nF3,11,1640.0\nF4,1,586.0\nF4,2,70.0\nF4,3,85.0\nF4,4,601.0\nF4,5,71.0\nF4,6,24.0\nF4,7,30.0\nF4,8,1115.0\nF4,9,30.0\nF4,10,402.0\nF4,11,1232.0\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": [ 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 145.0, 314.0, 205.0, 813.0, 76.0, 99.0, 63.0, 755.0, 66.0, 79.0, 769.0 ], [ 257.0, 155.0, 139.0, 590.0, 53.0, 51.0, 33.0, 524.0, 46.0, 162.0, 602.0 ], [ 764.0, 498.0, 108.0, 952.0, 74.0, 27.0, 29.0, 1542.0, 32.0, 525.0, 1640.0 ], [ 586.0, 70.0, 85.0, 601.0, 71.0, 24.0, 30.0, 1115.0, 30.0, 402.0, 1232.0 ] ], "demands": [ 28.0, 28.0, 24.0, 17.0, 26.0, 12.0, 13.0, 19.0, 13.0, 13.0, 18.0 ], "objective": 3012.0 }, "solution": { "open_facilities": [ 1 ], "assignments": [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] }, "obj": 3012.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 4, "num_customers": 11, "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 } ], "customers": [ { "id": 1, "demand": 28.0 }, { "id": 2, "demand": 28.0 }, { "id": 3, "demand": 24.0 }, { "id": 4, "demand": 17.0 }, { "id": 5, "demand": 26.0 }, { "id": 6, "demand": 12.0 }, { "id": 7, "demand": 13.0 }, { "id": 8, "demand": 19.0 }, { "id": 9, "demand": 13.0 }, { "id": 10, "demand": 13.0 }, { "id": 11, "demand": 18.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 145.0 }, { "facility": "F1", "customer": 2, "cost": 314.0 }, { "facility": "F1", "customer": 3, "cost": 205.0 }, { "facility": "F1", "customer": 4, "cost": 813.0 }, { "facility": "F1", "customer": 5, "cost": 76.0 }, { "facility": "F1", "customer": 6, "cost": 99.0 }, { "facility": "F1", "customer": 7, "cost": 63.0 }, { "facility": "F1", "customer": 8, "cost": 755.0 }, { "facility": "F1", "customer": 9, "cost": 66.0 }, { "facility": "F1", "customer": 10, "cost": 79.0 }, { "facility": "F1", "customer": 11, "cost": 769.0 }, { "facility": "F2", "customer": 1, "cost": 257.0 }, { "facility": "F2", "customer": 2, "cost": 155.0 }, { "facility": "F2", "customer": 3, "cost": 139.0 }, { "facility": "F2", "customer": 4, "cost": 590.0 }, { "facility": "F2", "customer": 5, "cost": 53.0 }, { "facility": "F2", "customer": 6, "cost": 51.0 }, { "facility": "F2", "customer": 7, "cost": 33.0 }, { "facility": "F2", "customer": 8, "cost": 524.0 }, { "facility": "F2", "customer": 9, "cost": 46.0 }, { "facility": "F2", "customer": 10, "cost": 162.0 }, { "facility": "F2", "customer": 11, "cost": 602.0 }, { "facility": "F3", "customer": 1, "cost": 764.0 }, { "facility": "F3", "customer": 2, "cost": 498.0 }, { "facility": "F3", "customer": 3, "cost": 108.0 }, { "facility": "F3", "customer": 4, "cost": 952.0 }, { "facility": "F3", "customer": 5, "cost": 74.0 }, { "facility": "F3", "customer": 6, "cost": 27.0 }, { "facility": "F3", "customer": 7, "cost": 29.0 }, { "facility": "F3", "customer": 8, "cost": 1542.0 }, { "facility": "F3", "customer": 9, "cost": 32.0 }, { "facility": "F3", "customer": 10, "cost": 525.0 }, { "facility": "F3", "customer": 11, "cost": 1640.0 }, { "facility": "F4", "customer": 1, "cost": 586.0 }, { "facility": "F4", "customer": 2, "cost": 70.0 }, { "facility": "F4", "customer": 3, "cost": 85.0 }, { "facility": "F4", "customer": 4, "cost": 601.0 }, { "facility": "F4", "customer": 5, "cost": 71.0 }, { "facility": "F4", "customer": 6, "cost": 24.0 }, { "facility": "F4", "customer": 7, "cost": 30.0 }, { "facility": "F4", "customer": 8, "cost": 1115.0 }, { "facility": "F4", "customer": 9, "cost": 30.0 }, { "facility": "F4", "customer": 10, "cost": 402.0 }, { "facility": "F4", "customer": 11, "cost": 1232.0 } ], "objective": 3012.0 }, "solution_variant": { "selected": [ "F2" ], "assignments": [ "F2", "F2", "F2", "F2", "F2", "F2", "F2", "F2", "F2", "F2", "F2" ] }, "context_index": 38, "input_format": "csv", "input_index_base": 1 }, { "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# num_micro_centers=5\n# num_orders=11\n# CONNECTION_CENTERS\nconnection_center_id,activation_fee,center_throughput\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\n# CONNECTION_ORDERS\nconnection_order_id,order_parcel_count\nA,28.0\nB,18.0\nC,20.0\nD,18.0\nE,14.0\nF,17.0\nG,26.0\nH,23.0\nI,26.0\nJ,21.0\nK,29.0\n# ROUTINGS\nconnection_center_id,connection_order_id,routing_cost\nF1,A,140.0\nF1,B,213.0\nF1,C,136.0\nF1,D,208.0\nF1,E,368.0\nF1,F,1114.0\nF1,G,78.0\nF1,H,549.0\nF1,I,527.0\nF1,J,783.0\nF1,K,200.0\nF2,A,364.0\nF2,B,37.0\nF2,C,488.0\nF2,D,366.0\nF2,E,291.0\nF2,F,1088.0\nF2,G,735.0\nF2,H,1288.0\nF2,I,993.0\nF2,J,265.0\nF2,K,1164.0\nF3,A,838.0\nF3,B,147.0\nF3,C,1048.0\nF3,D,987.0\nF3,E,1093.0\nF3,F,2185.0\nF3,G,1034.0\nF3,H,2054.0\nF3,I,1825.0\nF3,J,1428.0\nF3,K,1552.0\nF4,A,330.0\nF4,B,269.0\nF4,C,447.0\nF4,D,499.0\nF4,E,699.0\nF4,F,1711.0\nF4,G,201.0\nF4,H,1344.0\nF4,I,1195.0\nF4,J,1149.0\nF4,K,711.0\nF5,A,451.0\nF5,B,36.0\nF5,C,612.0\nF5,D,492.0\nF5,E,464.0\nF5,F,1439.0\nF5,G,811.0\nF5,H,1517.0\nF5,I,1235.0\nF5,J,619.0\nF5,K,1275.0\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 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 140.0, 213.0, 136.0, 208.0, 368.0, 1114.0, 78.0, 549.0, 527.0, 783.0, 200.0 ], [ 364.0, 37.0, 488.0, 366.0, 291.0, 1088.0, 735.0, 1288.0, 993.0, 265.0, 1164.0 ], [ 838.0, 147.0, 1048.0, 987.0, 1093.0, 2185.0, 1034.0, 2054.0, 1825.0, 1428.0, 1552.0 ], [ 330.0, 269.0, 447.0, 499.0, 699.0, 1711.0, 201.0, 1344.0, 1195.0, 1149.0, 711.0 ], [ 451.0, 36.0, 612.0, 492.0, 464.0, 1439.0, 811.0, 1517.0, 1235.0, 619.0, 1275.0 ] ], "demands": [ 28.0, 18.0, 20.0, 18.0, 14.0, 17.0, 26.0, 23.0, 26.0, 21.0, 29.0 ], "objective": 4319.0 }, "solution": { "open_facilities": [ 0, 1 ], "assignments": [ 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0 ] }, "obj": 4319.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 11, "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 } ], "customers": [ { "id": "A", "demand": 28.0 }, { "id": "B", "demand": 18.0 }, { "id": "C", "demand": 20.0 }, { "id": "D", "demand": 18.0 }, { "id": "E", "demand": 14.0 }, { "id": "F", "demand": 17.0 }, { "id": "G", "demand": 26.0 }, { "id": "H", "demand": 23.0 }, { "id": "I", "demand": 26.0 }, { "id": "J", "demand": 21.0 }, { "id": "K", "demand": 29.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 140.0 }, { "facility": "F1", "customer": "B", "cost": 213.0 }, { "facility": "F1", "customer": "C", "cost": 136.0 }, { "facility": "F1", "customer": "D", "cost": 208.0 }, { "facility": "F1", "customer": "E", "cost": 368.0 }, { "facility": "F1", "customer": "F", "cost": 1114.0 }, { "facility": "F1", "customer": "G", "cost": 78.0 }, { "facility": "F1", "customer": "H", "cost": 549.0 }, { "facility": "F1", "customer": "I", "cost": 527.0 }, { "facility": "F1", "customer": "J", "cost": 783.0 }, { "facility": "F1", "customer": "K", "cost": 200.0 }, { "facility": "F2", "customer": "A", "cost": 364.0 }, { "facility": "F2", "customer": "B", "cost": 37.0 }, { "facility": "F2", "customer": "C", "cost": 488.0 }, { "facility": "F2", "customer": "D", "cost": 366.0 }, { "facility": "F2", "customer": "E", "cost": 291.0 }, { "facility": "F2", "customer": "F", "cost": 1088.0 }, { "facility": "F2", "customer": "G", "cost": 735.0 }, { "facility": "F2", "customer": "H", "cost": 1288.0 }, { "facility": "F2", "customer": "I", "cost": 993.0 }, { "facility": "F2", "customer": "J", "cost": 265.0 }, { "facility": "F2", "customer": "K", "cost": 1164.0 }, { "facility": "F3", "customer": "A", "cost": 838.0 }, { "facility": "F3", "customer": "B", "cost": 147.0 }, { "facility": "F3", "customer": "C", "cost": 1048.0 }, { "facility": "F3", "customer": "D", "cost": 987.0 }, { "facility": "F3", "customer": "E", "cost": 1093.0 }, { "facility": "F3", "customer": "F", "cost": 2185.0 }, { "facility": "F3", "customer": "G", "cost": 1034.0 }, { "facility": "F3", "customer": "H", "cost": 2054.0 }, { "facility": "F3", "customer": "I", "cost": 1825.0 }, { "facility": "F3", "customer": "J", "cost": 1428.0 }, { "facility": "F3", "customer": "K", "cost": 1552.0 }, { "facility": "F4", "customer": "A", "cost": 330.0 }, { "facility": "F4", "customer": "B", "cost": 269.0 }, { "facility": "F4", "customer": "C", "cost": 447.0 }, { "facility": "F4", "customer": "D", "cost": 499.0 }, { "facility": "F4", "customer": "E", "cost": 699.0 }, { "facility": "F4", "customer": "F", "cost": 1711.0 }, { "facility": "F4", "customer": "G", "cost": 201.0 }, { "facility": "F4", "customer": "H", "cost": 1344.0 }, { "facility": "F4", "customer": "I", "cost": 1195.0 }, { "facility": "F4", "customer": "J", "cost": 1149.0 }, { "facility": "F4", "customer": "K", "cost": 711.0 }, { "facility": "F5", "customer": "A", "cost": 451.0 }, { "facility": "F5", "customer": "B", "cost": 36.0 }, { "facility": "F5", "customer": "C", "cost": 612.0 }, { "facility": "F5", "customer": "D", "cost": 492.0 }, { "facility": "F5", "customer": "E", "cost": 464.0 }, { "facility": "F5", "customer": "F", "cost": 1439.0 }, { "facility": "F5", "customer": "G", "cost": 811.0 }, { "facility": "F5", "customer": "H", "cost": 1517.0 }, { "facility": "F5", "customer": "I", "cost": 1235.0 }, { "facility": "F5", "customer": "J", "cost": 619.0 }, { "facility": "F5", "customer": "K", "cost": 1275.0 } ], "objective": 4319.0 }, "solution_variant": { "selected": [ "F1", "F2" ], "assignments": [ "F1", "F2", "F1", "F1", "F2", "F2", "F1", "F1", "F1", "F2", "F1" ] }, "context_index": 39, "input_format": "csv", "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# total_mobile_clinic_sites=5\n# total_patients=12\n# SITES\nsite_id,deployment_cost,site_capacity\nF1,400.0,500.0\nF2,400.0,500.0\nF3,400.0,500.0\nF4,400.0,500.0\nF5,400.0,500.0\n# PATIENTS\npatient_id,patient_demand\n1,18.0\n2,12.0\n3,20.0\n4,26.0\n5,17.0\n6,18.0\n7,16.0\n8,23.0\n9,11.0\n10,15.0\n11,14.0\n12,21.0\n# TRAVEL_OR_TREATMENTS\nsite_id,patient_id,travel_or_treatment_cost\nF1,1,161.0\nF1,2,328.0\nF1,3,634.0\nF1,4,531.0\nF1,5,186.0\nF1,6,772.0\nF1,7,32.0\nF1,8,342.0\nF1,9,35.0\nF1,10,78.0\nF1,11,61.0\nF1,12,43.0\nF2,1,208.0\nF2,2,333.0\nF2,3,92.0\nF2,4,78.0\nF2,5,211.0\nF2,6,1070.0\nF2,7,491.0\nF2,8,288.0\nF2,9,629.0\nF2,10,1116.0\nF2,11,173.0\nF2,12,783.0\nF3,1,382.0\nF3,2,627.0\nF3,3,422.0\nF3,4,52.0\nF3,5,401.0\nF3,6,1448.0\nF3,7,671.0\nF3,8,562.0\nF3,9,871.0\nF3,10,1418.0\nF3,11,280.0\nF3,12,1020.0\nF4,1,626.0\nF4,2,1057.0\nF4,3,1025.0\nF4,4,388.0\nF4,5,680.0\nF4,6,1972.0\nF4,7,837.0\nF4,8,982.0\nF4,9,1132.0\nF4,10,1752.0\nF4,11,368.0\nF4,12,1258.0\nF5,1,165.0\nF5,2,440.0\nF5,3,735.0\nF5,4,547.0\nF5,5,201.0\nF5,6,1157.0\nF5,7,43.0\nF5,8,429.0\nF5,9,22.0\nF5,10,662.0\nF5,11,49.0\nF5,12,175.0\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 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 161.0, 328.0, 634.0, 531.0, 186.0, 772.0, 32.0, 342.0, 35.0, 78.0, 61.0, 43.0 ], [ 208.0, 333.0, 92.0, 78.0, 211.0, 1070.0, 491.0, 288.0, 629.0, 1116.0, 173.0, 783.0 ], [ 382.0, 627.0, 422.0, 52.0, 401.0, 1448.0, 671.0, 562.0, 871.0, 1418.0, 280.0, 1020.0 ], [ 626.0, 1057.0, 1025.0, 388.0, 680.0, 1972.0, 837.0, 982.0, 1132.0, 1752.0, 368.0, 1258.0 ], [ 165.0, 440.0, 735.0, 547.0, 201.0, 1157.0, 43.0, 429.0, 22.0, 662.0, 49.0, 175.0 ] ], "demands": [ 18.0, 12.0, 20.0, 26.0, 17.0, 18.0, 16.0, 23.0, 11.0, 15.0, 14.0, 21.0 ], "objective": 2954.0 }, "solution": { "open_facilities": [ 0, 1 ], "assignments": [ 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0 ] }, "obj": 2954.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 12, "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 } ], "customers": [ { "id": 1, "demand": 18.0 }, { "id": 2, "demand": 12.0 }, { "id": 3, "demand": 20.0 }, { "id": 4, "demand": 26.0 }, { "id": 5, "demand": 17.0 }, { "id": 6, "demand": 18.0 }, { "id": 7, "demand": 16.0 }, { "id": 8, "demand": 23.0 }, { "id": 9, "demand": 11.0 }, { "id": 10, "demand": 15.0 }, { "id": 11, "demand": 14.0 }, { "id": 12, "demand": 21.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 161.0 }, { "facility": "F1", "customer": 2, "cost": 328.0 }, { "facility": "F1", "customer": 3, "cost": 634.0 }, { "facility": "F1", "customer": 4, "cost": 531.0 }, { "facility": "F1", "customer": 5, "cost": 186.0 }, { "facility": "F1", "customer": 6, "cost": 772.0 }, { "facility": "F1", "customer": 7, "cost": 32.0 }, { "facility": "F1", "customer": 8, "cost": 342.0 }, { "facility": "F1", "customer": 9, "cost": 35.0 }, { "facility": "F1", "customer": 10, "cost": 78.0 }, { "facility": "F1", "customer": 11, "cost": 61.0 }, { "facility": "F1", "customer": 12, "cost": 43.0 }, { "facility": "F2", "customer": 1, "cost": 208.0 }, { "facility": "F2", "customer": 2, "cost": 333.0 }, { "facility": "F2", "customer": 3, "cost": 92.0 }, { "facility": "F2", "customer": 4, "cost": 78.0 }, { "facility": "F2", "customer": 5, "cost": 211.0 }, { "facility": "F2", "customer": 6, "cost": 1070.0 }, { "facility": "F2", "customer": 7, "cost": 491.0 }, { "facility": "F2", "customer": 8, "cost": 288.0 }, { "facility": "F2", "customer": 9, "cost": 629.0 }, { "facility": "F2", "customer": 10, "cost": 1116.0 }, { "facility": "F2", "customer": 11, "cost": 173.0 }, { "facility": "F2", "customer": 12, "cost": 783.0 }, { "facility": "F3", "customer": 1, "cost": 382.0 }, { "facility": "F3", "customer": 2, "cost": 627.0 }, { "facility": "F3", "customer": 3, "cost": 422.0 }, { "facility": "F3", "customer": 4, "cost": 52.0 }, { "facility": "F3", "customer": 5, "cost": 401.0 }, { "facility": "F3", "customer": 6, "cost": 1448.0 }, { "facility": "F3", "customer": 7, "cost": 671.0 }, { "facility": "F3", "customer": 8, "cost": 562.0 }, { "facility": "F3", "customer": 9, "cost": 871.0 }, { "facility": "F3", "customer": 10, "cost": 1418.0 }, { "facility": "F3", "customer": 11, "cost": 280.0 }, { "facility": "F3", "customer": 12, "cost": 1020.0 }, { "facility": "F4", "customer": 1, "cost": 626.0 }, { "facility": "F4", "customer": 2, "cost": 1057.0 }, { "facility": "F4", "customer": 3, "cost": 1025.0 }, { "facility": "F4", "customer": 4, "cost": 388.0 }, { "facility": "F4", "customer": 5, "cost": 680.0 }, { "facility": "F4", "customer": 6, "cost": 1972.0 }, { "facility": "F4", "customer": 7, "cost": 837.0 }, { "facility": "F4", "customer": 8, "cost": 982.0 }, { "facility": "F4", "customer": 9, "cost": 1132.0 }, { "facility": "F4", "customer": 10, "cost": 1752.0 }, { "facility": "F4", "customer": 11, "cost": 368.0 }, { "facility": "F4", "customer": 12, "cost": 1258.0 }, { "facility": "F5", "customer": 1, "cost": 165.0 }, { "facility": "F5", "customer": 2, "cost": 440.0 }, { "facility": "F5", "customer": 3, "cost": 735.0 }, { "facility": "F5", "customer": 4, "cost": 547.0 }, { "facility": "F5", "customer": 5, "cost": 201.0 }, { "facility": "F5", "customer": 6, "cost": 1157.0 }, { "facility": "F5", "customer": 7, "cost": 43.0 }, { "facility": "F5", "customer": 8, "cost": 429.0 }, { "facility": "F5", "customer": 9, "cost": 22.0 }, { "facility": "F5", "customer": 10, "cost": 662.0 }, { "facility": "F5", "customer": 11, "cost": 49.0 }, { "facility": "F5", "customer": 12, "cost": 175.0 } ], "objective": 2954.0 }, "solution_variant": { "selected": [ "F1", "F2" ], "assignments": [ "F1", "F1", "F2", "F2", "F1", "F1", "F1", "F2", "F1", "F1", "F1", "F1" ] }, "context_index": 40, "input_format": "csv", "input_index_base": 1 }, { "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 5 candidate docking stations and 11 riders to assign.\nDocking station F1 would cost 300.0 to activate and can serve up to 700.0 riders.\nDocking station F2 would cost 300.0 to activate and can serve up to 700.0 riders.\nDocking station F3 would cost 300.0 to activate and can serve up to 700.0 riders.\nDocking station F4 would cost 300.0 to activate and can serve up to 700.0 riders.\nDocking station F5 would cost 300.0 to activate and can serve up to 700.0 riders.\nRider 0 requires 14.0 capacity units.\nRider 1 requires 18.0 capacity units.\nRider 2 requires 24.0 capacity units.\nRider 3 requires 17.0 capacity units.\nRider 4 requires 23.0 capacity units.\nRider 5 requires 26.0 capacity units.\nRider 6 requires 12.0 capacity units.\nRider 7 requires 11.0 capacity units.\nRider 8 requires 24.0 capacity units.\nRider 9 requires 14.0 capacity units.\nRider 10 requires 29.0 capacity units.\nAssigning rider 0 to docking station F1 incurs access cost 479.0.\nAssigning rider 1 to docking station F1 incurs access cost 161.0.\nAssigning rider 2 to docking station F1 incurs access cost 368.0.\nAssigning rider 3 to docking station F1 incurs access cost 1697.0.\nAssigning rider 4 to docking station F1 incurs access cost 683.0.\nAssigning rider 5 to docking station F1 incurs access cost 456.0.\nAssigning rider 6 to docking station F1 incurs access cost 1184.0.\nAssigning rider 7 to docking station F1 incurs access cost 942.0.\nAssigning rider 8 to docking station F1 incurs access cost 1449.0.\nAssigning rider 9 to docking station F1 incurs access cost 496.0.\nAssigning rider 10 to docking station F1 incurs access cost 948.0.\nAssigning rider 0 to docking station F2 incurs access cost 171.0.\nAssigning rider 1 to docking station F2 incurs access cost 127.0.\nAssigning rider 2 to docking station F2 incurs access cost 258.0.\nAssigning rider 3 to docking station F2 incurs access cost 696.0.\nAssigning rider 4 to docking station F2 incurs access cost 236.0.\nAssigning rider 5 to docking station F2 incurs access cost 147.0.\nAssigning rider 6 to docking station F2 incurs access cost 429.0.\nAssigning rider 7 to docking station F2 incurs access cost 362.0.\nAssigning rider 8 to docking station F2 incurs access cost 835.0.\nAssigning rider 9 to docking station F2 incurs access cost 159.0.\nAssigning rider 10 to docking station F2 incurs access cost 311.0.\nAssigning rider 0 to docking station F3 incurs access cost 300.0.\nAssigning rider 1 to docking station F3 incurs access cost 70.0.\nAssigning rider 2 to docking station F3 incurs access cost 146.0.\nAssigning rider 3 to docking station F3 incurs access cost 158.0.\nAssigning rider 4 to docking station F3 incurs access cost 385.0.\nAssigning rider 5 to docking station F3 incurs access cost 266.0.\nAssigning rider 6 to docking station F3 incurs access cost 102.0.\nAssigning rider 7 to docking station F3 incurs access cost 105.0.\nAssigning rider 8 to docking station F3 incurs access cost 430.0.\nAssigning rider 9 to docking station F3 incurs access cost 44.0.\nAssigning rider 10 to docking station F3 incurs access cost 481.0.\nAssigning rider 0 to docking station F4 incurs access cost 723.0.\nAssigning rider 1 to docking station F4 incurs access cost 39.0.\nAssigning rider 2 to docking station F4 incurs access cost 48.0.\nAssigning rider 3 to docking station F4 incurs access cost 810.0.\nAssigning rider 4 to docking station F4 incurs access cost 888.0.\nAssigning rider 5 to docking station F4 incurs access cost 687.0.\nAssigning rider 6 to docking station F4 incurs access cost 360.0.\nAssigning rider 7 to docking station F4 incurs access cost 176.0.\nAssigning rider 8 to docking station F4 incurs access cost 143.0.\nAssigning rider 9 to docking station F4 incurs access cost 156.0.\nAssigning rider 10 to docking station F4 incurs access cost 1088.0.\nAssigning rider 0 to docking station F5 incurs access cost 1024.0.\nAssigning rider 1 to docking station F5 incurs access cost 50.0.\nAssigning rider 2 to docking station F5 incurs access cost 141.0.\nAssigning rider 3 to docking station F5 incurs access cost 1972.0.\nAssigning rider 4 to docking station F5 incurs access cost 1246.0.\nAssigning rider 5 to docking station F5 incurs access cost 1016.0.\nAssigning rider 6 to docking station F5 incurs access cost 1419.0.\nAssigning rider 7 to docking station F5 incurs access cost 1126.0.\nAssigning rider 8 to docking station F5 incurs access cost 1499.0.\nAssigning rider 9 to docking station F5 incurs access cost 735.0.\nAssigning rider 10 to docking station F5 incurs access cost 1522.0.\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": [ 300.0, 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 479.0, 161.0, 368.0, 1697.0, 683.0, 456.0, 1184.0, 942.0, 1449.0, 496.0, 948.0 ], [ 171.0, 127.0, 258.0, 696.0, 236.0, 147.0, 429.0, 362.0, 835.0, 159.0, 311.0 ], [ 300.0, 70.0, 146.0, 158.0, 385.0, 266.0, 102.0, 105.0, 430.0, 44.0, 481.0 ], [ 723.0, 39.0, 48.0, 810.0, 888.0, 687.0, 360.0, 176.0, 143.0, 156.0, 1088.0 ], [ 1024.0, 50.0, 141.0, 1972.0, 1246.0, 1016.0, 1419.0, 1126.0, 1499.0, 735.0, 1522.0 ] ], "demands": [ 14.0, 18.0, 24.0, 17.0, 23.0, 26.0, 12.0, 11.0, 24.0, 14.0, 29.0 ], "objective": 2404.0 }, "solution": { "open_facilities": [ 1, 2, 3 ], "assignments": [ 1, 3, 3, 2, 1, 1, 2, 2, 3, 2, 1 ] }, "obj": 2404.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 11, "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 } ], "customers": [ { "id": 0, "demand": 14.0 }, { "id": 1, "demand": 18.0 }, { "id": 2, "demand": 24.0 }, { "id": 3, "demand": 17.0 }, { "id": 4, "demand": 23.0 }, { "id": 5, "demand": 26.0 }, { "id": 6, "demand": 12.0 }, { "id": 7, "demand": 11.0 }, { "id": 8, "demand": 24.0 }, { "id": 9, "demand": 14.0 }, { "id": 10, "demand": 29.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 479.0 }, { "facility": "F1", "customer": 1, "cost": 161.0 }, { "facility": "F1", "customer": 2, "cost": 368.0 }, { "facility": "F1", "customer": 3, "cost": 1697.0 }, { "facility": "F1", "customer": 4, "cost": 683.0 }, { "facility": "F1", "customer": 5, "cost": 456.0 }, { "facility": "F1", "customer": 6, "cost": 1184.0 }, { "facility": "F1", "customer": 7, "cost": 942.0 }, { "facility": "F1", "customer": 8, "cost": 1449.0 }, { "facility": "F1", "customer": 9, "cost": 496.0 }, { "facility": "F1", "customer": 10, "cost": 948.0 }, { "facility": "F2", "customer": 0, "cost": 171.0 }, { "facility": "F2", "customer": 1, "cost": 127.0 }, { "facility": "F2", "customer": 2, "cost": 258.0 }, { "facility": "F2", "customer": 3, "cost": 696.0 }, { "facility": "F2", "customer": 4, "cost": 236.0 }, { "facility": "F2", "customer": 5, "cost": 147.0 }, { "facility": "F2", "customer": 6, "cost": 429.0 }, { "facility": "F2", "customer": 7, "cost": 362.0 }, { "facility": "F2", "customer": 8, "cost": 835.0 }, { "facility": "F2", "customer": 9, "cost": 159.0 }, { "facility": "F2", "customer": 10, "cost": 311.0 }, { "facility": "F3", "customer": 0, "cost": 300.0 }, { "facility": "F3", "customer": 1, "cost": 70.0 }, { "facility": "F3", "customer": 2, "cost": 146.0 }, { "facility": "F3", "customer": 3, "cost": 158.0 }, { "facility": "F3", "customer": 4, "cost": 385.0 }, { "facility": "F3", "customer": 5, "cost": 266.0 }, { "facility": "F3", "customer": 6, "cost": 102.0 }, { "facility": "F3", "customer": 7, "cost": 105.0 }, { "facility": "F3", "customer": 8, "cost": 430.0 }, { "facility": "F3", "customer": 9, "cost": 44.0 }, { "facility": "F3", "customer": 10, "cost": 481.0 }, { "facility": "F4", "customer": 0, "cost": 723.0 }, { "facility": "F4", "customer": 1, "cost": 39.0 }, { "facility": "F4", "customer": 2, "cost": 48.0 }, { "facility": "F4", "customer": 3, "cost": 810.0 }, { "facility": "F4", "customer": 4, "cost": 888.0 }, { "facility": "F4", "customer": 5, "cost": 687.0 }, { "facility": "F4", "customer": 6, "cost": 360.0 }, { "facility": "F4", "customer": 7, "cost": 176.0 }, { "facility": "F4", "customer": 8, "cost": 143.0 }, { "facility": "F4", "customer": 9, "cost": 156.0 }, { "facility": "F4", "customer": 10, "cost": 1088.0 }, { "facility": "F5", "customer": 0, "cost": 1024.0 }, { "facility": "F5", "customer": 1, "cost": 50.0 }, { "facility": "F5", "customer": 2, "cost": 141.0 }, { "facility": "F5", "customer": 3, "cost": 1972.0 }, { "facility": "F5", "customer": 4, "cost": 1246.0 }, { "facility": "F5", "customer": 5, "cost": 1016.0 }, { "facility": "F5", "customer": 6, "cost": 1419.0 }, { "facility": "F5", "customer": 7, "cost": 1126.0 }, { "facility": "F5", "customer": 8, "cost": 1499.0 }, { "facility": "F5", "customer": 9, "cost": 735.0 }, { "facility": "F5", "customer": 10, "cost": 1522.0 } ], "objective": 2404.0 }, "solution_variant": { "selected": [ "F2", "F3", "F4" ], "assignments": [ "F2", "F4", "F4", "F3", "F2", "F2", "F3", "F3", "F4", "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\n# num_vending_sites=4\n# num_customer_zones=9\n# VENDING_SITES\nvending_site_id,stocking_fee,stocking_capacity\nF1,300.0,300.0\nF2,300.0,300.0\nF3,300.0,300.0\nF4,300.0,300.0\n# CUSTOMER_ZONES\ncustomer_zone_id,zone_demand\nA,21.0\nB,23.0\nC,18.0\nD,13.0\nE,27.0\nF,26.0\nG,21.0\nH,11.0\nI,11.0\n# INCONVENIENCES\nvending_site_id,customer_zone_id,inconvenience_cost\nF1,A,1400.0\nF1,B,681.0\nF1,C,1418.0\nF1,D,37.0\nF1,E,1300.0\nF1,F,1329.0\nF1,G,1463.0\nF1,H,587.0\nF1,I,1570.0\nF2,A,554.0\nF2,B,298.0\nF2,C,418.0\nF2,D,65.0\nF2,E,416.0\nF2,F,360.0\nF2,G,839.0\nF2,H,113.0\nF2,I,854.0\nF3,A,46.0\nF3,B,689.0\nF3,C,414.0\nF3,D,153.0\nF3,E,734.0\nF3,F,607.0\nF3,G,1177.0\nF3,H,26.0\nF3,I,1147.0\nF4,A,1084.0\nF4,B,221.0\nF4,C,962.0\nF4,D,27.0\nF4,E,759.0\nF4,F,825.0\nF4,G,794.0\nF4,H,416.0\nF4,I,918.0\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 ], "capacities": [ 300.0, 300.0, 300.0, 300.0 ], "connection_costs": [ [ 1400.0, 681.0, 1418.0, 37.0, 1300.0, 1329.0, 1463.0, 587.0, 1570.0 ], [ 554.0, 298.0, 418.0, 65.0, 416.0, 360.0, 839.0, 113.0, 854.0 ], [ 46.0, 689.0, 414.0, 153.0, 734.0, 607.0, 1177.0, 26.0, 1147.0 ], [ 1084.0, 221.0, 962.0, 27.0, 759.0, 825.0, 794.0, 416.0, 918.0 ] ], "demands": [ 21.0, 23.0, 18.0, 13.0, 27.0, 26.0, 21.0, 11.0, 11.0 ], "objective": 3918.0 }, "solution": { "open_facilities": [ 1, 2 ], "assignments": [ 2, 1, 2, 1, 1, 1, 1, 2, 1 ] }, "obj": 3918.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 4, "num_customers": 9, "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 } ], "customers": [ { "id": "A", "demand": 21.0 }, { "id": "B", "demand": 23.0 }, { "id": "C", "demand": 18.0 }, { "id": "D", "demand": 13.0 }, { "id": "E", "demand": 27.0 }, { "id": "F", "demand": 26.0 }, { "id": "G", "demand": 21.0 }, { "id": "H", "demand": 11.0 }, { "id": "I", "demand": 11.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 1400.0 }, { "facility": "F1", "customer": "B", "cost": 681.0 }, { "facility": "F1", "customer": "C", "cost": 1418.0 }, { "facility": "F1", "customer": "D", "cost": 37.0 }, { "facility": "F1", "customer": "E", "cost": 1300.0 }, { "facility": "F1", "customer": "F", "cost": 1329.0 }, { "facility": "F1", "customer": "G", "cost": 1463.0 }, { "facility": "F1", "customer": "H", "cost": 587.0 }, { "facility": "F1", "customer": "I", "cost": 1570.0 }, { "facility": "F2", "customer": "A", "cost": 554.0 }, { "facility": "F2", "customer": "B", "cost": 298.0 }, { "facility": "F2", "customer": "C", "cost": 418.0 }, { "facility": "F2", "customer": "D", "cost": 65.0 }, { "facility": "F2", "customer": "E", "cost": 416.0 }, { "facility": "F2", "customer": "F", "cost": 360.0 }, { "facility": "F2", "customer": "G", "cost": 839.0 }, { "facility": "F2", "customer": "H", "cost": 113.0 }, { "facility": "F2", "customer": "I", "cost": 854.0 }, { "facility": "F3", "customer": "A", "cost": 46.0 }, { "facility": "F3", "customer": "B", "cost": 689.0 }, { "facility": "F3", "customer": "C", "cost": 414.0 }, { "facility": "F3", "customer": "D", "cost": 153.0 }, { "facility": "F3", "customer": "E", "cost": 734.0 }, { "facility": "F3", "customer": "F", "cost": 607.0 }, { "facility": "F3", "customer": "G", "cost": 1177.0 }, { "facility": "F3", "customer": "H", "cost": 26.0 }, { "facility": "F3", "customer": "I", "cost": 1147.0 }, { "facility": "F4", "customer": "A", "cost": 1084.0 }, { "facility": "F4", "customer": "B", "cost": 221.0 }, { "facility": "F4", "customer": "C", "cost": 962.0 }, { "facility": "F4", "customer": "D", "cost": 27.0 }, { "facility": "F4", "customer": "E", "cost": 759.0 }, { "facility": "F4", "customer": "F", "cost": 825.0 }, { "facility": "F4", "customer": "G", "cost": 794.0 }, { "facility": "F4", "customer": "H", "cost": 416.0 }, { "facility": "F4", "customer": "I", "cost": 918.0 } ], "objective": 3918.0 }, "solution_variant": { "selected": [ "F2", "F3" ], "assignments": [ "F3", "F2", "F3", "F2", "F2", "F2", "F2", "F3", "F2" ] }, "context_index": 42, "input_format": "csv", "input_index_base": "names" }, { "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{\n \"num_hubs\": 5,\n \"num_addresses\": 10,\n \"hub_id_refs\": [\n {\n \"hub_id_ref\": \"F1\",\n \"hub_running_cost\": 258.0,\n \"hub_capacity\": 366.0\n },\n {\n \"hub_id_ref\": \"F2\",\n \"hub_running_cost\": 128.0,\n \"hub_capacity\": 314.0\n },\n {\n \"hub_id_ref\": \"F3\",\n \"hub_running_cost\": 329.0,\n \"hub_capacity\": 456.0\n },\n {\n \"hub_id_ref\": \"F4\",\n \"hub_running_cost\": 179.0,\n \"hub_capacity\": 549.0\n },\n {\n \"hub_id_ref\": \"F5\",\n \"hub_running_cost\": 114.0,\n \"hub_capacity\": 310.0\n }\n ],\n \"address_id_refs\": [\n {\n \"address_id_ref\": 0,\n \"address_demand\": 13.0\n },\n {\n \"address_id_ref\": 1,\n \"address_demand\": 31.0\n },\n {\n \"address_id_ref\": 2,\n \"address_demand\": 45.0\n },\n {\n \"address_id_ref\": 3,\n \"address_demand\": 40.0\n },\n {\n \"address_id_ref\": 4,\n \"address_demand\": 28.0\n },\n {\n \"address_id_ref\": 5,\n \"address_demand\": 13.0\n },\n {\n \"address_id_ref\": 6,\n \"address_demand\": 27.0\n },\n {\n \"address_id_ref\": 7,\n \"address_demand\": 22.0\n },\n {\n \"address_id_ref\": 8,\n \"address_demand\": 14.0\n },\n {\n \"address_id_ref\": 9,\n \"address_demand\": 13.0\n }\n ],\n \"routings\": [\n {\n \"hub_id_ref\": \"F1\",\n \"address_id_ref\": 0,\n \"routing_cost\": 568.0\n },\n {\n \"hub_id_ref\": \"F1\",\n \"address_id_ref\": 1,\n \"routing_cost\": 392.0\n },\n {\n \"hub_id_ref\": \"F1\",\n \"address_id_ref\": 2,\n \"routing_cost\": 29.0\n },\n {\n \"hub_id_ref\": \"F1\",\n \"address_id_ref\": 3,\n \"routing_cost\": 656.0\n },\n {\n \"hub_id_ref\": \"F1\",\n \"address_id_ref\": 4,\n \"routing_cost\": 318.0\n },\n {\n \"hub_id_ref\": \"F1\",\n \"address_id_ref\": 5,\n \"routing_cost\": 414.0\n },\n {\n \"hub_id_ref\": \"F1\",\n \"address_id_ref\": 6,\n \"routing_cost\": 458.0\n },\n {\n \"hub_id_ref\": \"F1\",\n \"address_id_ref\": 7,\n \"routing_cost\": 758.0\n },\n {\n \"hub_id_ref\": \"F1\",\n \"address_id_ref\": 8,\n \"routing_cost\": 28.0\n },\n {\n \"hub_id_ref\": \"F1\",\n \"address_id_ref\": 9,\n \"routing_cost\": 139.0\n },\n {\n \"hub_id_ref\": \"F2\",\n \"address_id_ref\": 0,\n \"routing_cost\": 636.0\n },\n {\n \"hub_id_ref\": \"F2\",\n \"address_id_ref\": 1,\n \"routing_cost\": 28.0\n },\n {\n \"hub_id_ref\": \"F2\",\n \"address_id_ref\": 2,\n \"routing_cost\": 401.0\n },\n {\n \"hub_id_ref\": \"F2\",\n \"address_id_ref\": 3,\n \"routing_cost\": 551.0\n },\n {\n \"hub_id_ref\": \"F2\",\n \"address_id_ref\": 4,\n \"routing_cost\": 80.0\n },\n {\n \"hub_id_ref\": \"F2\",\n \"address_id_ref\": 5,\n \"routing_cost\": 107.0\n },\n {\n \"hub_id_ref\": \"F2\",\n \"address_id_ref\": 6,\n \"routing_cost\": 387.0\n },\n {\n \"hub_id_ref\": \"F2\",\n \"address_id_ref\": 7,\n \"routing_cost\": 516.0\n },\n {\n \"hub_id_ref\": \"F2\",\n \"address_id_ref\": 8,\n \"routing_cost\": 374.0\n },\n {\n \"hub_id_ref\": \"F2\",\n \"address_id_ref\": 9,\n \"routing_cost\": 459.0\n },\n {\n \"hub_id_ref\": \"F3\",\n \"address_id_ref\": 0,\n \"routing_cost\": 436.0\n },\n {\n \"hub_id_ref\": \"F3\",\n \"address_id_ref\": 1,\n \"routing_cost\": 387.0\n },\n {\n \"hub_id_ref\": \"F3\",\n \"address_id_ref\": 2,\n \"routing_cost\": 632.0\n },\n {\n \"hub_id_ref\": \"F3\",\n \"address_id_ref\": 3,\n \"routing_cost\": 200.0\n },\n {\n \"hub_id_ref\": \"F3\",\n \"address_id_ref\": 4,\n \"routing_cost\": 476.0\n },\n {\n \"hub_id_ref\": \"F3\",\n \"address_id_ref\": 5,\n \"routing_cost\": 309.0\n },\n {\n \"hub_id_ref\": \"F3\",\n \"address_id_ref\": 6,\n \"routing_cost\": 222.0\n },\n {\n \"hub_id_ref\": \"F3\",\n \"address_id_ref\": 7,\n \"routing_cost\": 124.0\n },\n {\n \"hub_id_ref\": \"F3\",\n \"address_id_ref\": 8,\n \"routing_cost\": 642.0\n },\n {\n \"hub_id_ref\": \"F3\",\n \"address_id_ref\": 9,\n \"routing_cost\": 612.0\n },\n {\n \"hub_id_ref\": \"F4\",\n \"address_id_ref\": 0,\n \"routing_cost\": 186.0\n },\n {\n \"hub_id_ref\": \"F4\",\n \"address_id_ref\": 1,\n \"routing_cost\": 742.0\n },\n {\n \"hub_id_ref\": \"F4\",\n \"address_id_ref\": 2,\n \"routing_cost\": 567.0\n },\n {\n \"hub_id_ref\": \"F4\",\n \"address_id_ref\": 3,\n \"routing_cost\": 458.0\n },\n {\n \"hub_id_ref\": \"F4\",\n \"address_id_ref\": 4,\n \"routing_cost\": 751.0\n },\n {\n \"hub_id_ref\": \"F4\",\n \"address_id_ref\": 5,\n \"routing_cost\": 693.0\n },\n {\n \"hub_id_ref\": \"F4\",\n \"address_id_ref\": 6,\n \"routing_cost\": 428.0\n },\n {\n \"hub_id_ref\": \"F4\",\n \"address_id_ref\": 7,\n \"routing_cost\": 702.0\n },\n {\n \"hub_id_ref\": \"F4\",\n \"address_id_ref\": 8,\n \"routing_cost\": 620.0\n },\n {\n \"hub_id_ref\": \"F4\",\n \"address_id_ref\": 9,\n \"routing_cost\": 460.0\n },\n {\n \"hub_id_ref\": \"F5\",\n \"address_id_ref\": 0,\n \"routing_cost\": 505.0\n },\n {\n \"hub_id_ref\": \"F5\",\n \"address_id_ref\": 1,\n \"routing_cost\": 535.0\n },\n {\n \"hub_id_ref\": \"F5\",\n \"address_id_ref\": 2,\n \"routing_cost\": 148.0\n },\n {\n \"hub_id_ref\": \"F5\",\n \"address_id_ref\": 3,\n \"routing_cost\": 664.0\n },\n {\n \"hub_id_ref\": \"F5\",\n \"address_id_ref\": 4,\n \"routing_cost\": 477.0\n },\n {\n \"hub_id_ref\": \"F5\",\n \"address_id_ref\": 5,\n \"routing_cost\": 539.0\n },\n {\n \"hub_id_ref\": \"F5\",\n \"address_id_ref\": 6,\n \"routing_cost\": 485.0\n },\n {\n \"hub_id_ref\": \"F5\",\n \"address_id_ref\": 7,\n \"routing_cost\": 816.0\n },\n {\n \"hub_id_ref\": \"F5\",\n \"address_id_ref\": 8,\n \"routing_cost\": 200.0\n },\n {\n \"hub_id_ref\": \"F5\",\n \"address_id_ref\": 9,\n \"routing_cost\": 83.0\n }\n ]\n}\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": [ 258.0, 128.0, 329.0, 179.0, 114.0 ], "capacities": [ 366.0, 314.0, 456.0, 549.0, 310.0 ], "connection_costs": [ [ 568.0, 392.0, 29.0, 656.0, 318.0, 414.0, 458.0, 758.0, 28.0, 139.0 ], [ 636.0, 28.0, 401.0, 551.0, 80.0, 107.0, 387.0, 516.0, 374.0, 459.0 ], [ 436.0, 387.0, 632.0, 200.0, 476.0, 309.0, 222.0, 124.0, 642.0, 612.0 ], [ 186.0, 742.0, 567.0, 458.0, 751.0, 693.0, 428.0, 702.0, 620.0, 460.0 ], [ 505.0, 535.0, 148.0, 664.0, 477.0, 539.0, 485.0, 816.0, 200.0, 83.0 ] ], "demands": [ 13.0, 31.0, 45.0, 40.0, 28.0, 13.0, 27.0, 22.0, 14.0, 13.0 ], "objective": 2037.0 }, "solution": { "open_facilities": [ 0, 1, 2, 3 ], "assignments": [ 3, 1, 0, 2, 1, 1, 2, 2, 0, 0 ] }, "obj": 2037.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 10, "facilities": [ { "id": "F1", "opening_cost": 258.0, "capacity": 366.0 }, { "id": "F2", "opening_cost": 128.0, "capacity": 314.0 }, { "id": "F3", "opening_cost": 329.0, "capacity": 456.0 }, { "id": "F4", "opening_cost": 179.0, "capacity": 549.0 }, { "id": "F5", "opening_cost": 114.0, "capacity": 310.0 } ], "customers": [ { "id": 0, "demand": 13.0 }, { "id": 1, "demand": 31.0 }, { "id": 2, "demand": 45.0 }, { "id": 3, "demand": 40.0 }, { "id": 4, "demand": 28.0 }, { "id": 5, "demand": 13.0 }, { "id": 6, "demand": 27.0 }, { "id": 7, "demand": 22.0 }, { "id": 8, "demand": 14.0 }, { "id": 9, "demand": 13.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 568.0 }, { "facility": "F1", "customer": 1, "cost": 392.0 }, { "facility": "F1", "customer": 2, "cost": 29.0 }, { "facility": "F1", "customer": 3, "cost": 656.0 }, { "facility": "F1", "customer": 4, "cost": 318.0 }, { "facility": "F1", "customer": 5, "cost": 414.0 }, { "facility": "F1", "customer": 6, "cost": 458.0 }, { "facility": "F1", "customer": 7, "cost": 758.0 }, { "facility": "F1", "customer": 8, "cost": 28.0 }, { "facility": "F1", "customer": 9, "cost": 139.0 }, { "facility": "F2", "customer": 0, "cost": 636.0 }, { "facility": "F2", "customer": 1, "cost": 28.0 }, { "facility": "F2", "customer": 2, "cost": 401.0 }, { "facility": "F2", "customer": 3, "cost": 551.0 }, { "facility": "F2", "customer": 4, "cost": 80.0 }, { "facility": "F2", "customer": 5, "cost": 107.0 }, { "facility": "F2", "customer": 6, "cost": 387.0 }, { "facility": "F2", "customer": 7, "cost": 516.0 }, { "facility": "F2", "customer": 8, "cost": 374.0 }, { "facility": "F2", "customer": 9, "cost": 459.0 }, { "facility": "F3", "customer": 0, "cost": 436.0 }, { "facility": "F3", "customer": 1, "cost": 387.0 }, { "facility": "F3", "customer": 2, "cost": 632.0 }, { "facility": "F3", "customer": 3, "cost": 200.0 }, { "facility": "F3", "customer": 4, "cost": 476.0 }, { "facility": "F3", "customer": 5, "cost": 309.0 }, { "facility": "F3", "customer": 6, "cost": 222.0 }, { "facility": "F3", "customer": 7, "cost": 124.0 }, { "facility": "F3", "customer": 8, "cost": 642.0 }, { "facility": "F3", "customer": 9, "cost": 612.0 }, { "facility": "F4", "customer": 0, "cost": 186.0 }, { "facility": "F4", "customer": 1, "cost": 742.0 }, { "facility": "F4", "customer": 2, "cost": 567.0 }, { "facility": "F4", "customer": 3, "cost": 458.0 }, { "facility": "F4", "customer": 4, "cost": 751.0 }, { "facility": "F4", "customer": 5, "cost": 693.0 }, { "facility": "F4", "customer": 6, "cost": 428.0 }, { "facility": "F4", "customer": 7, "cost": 702.0 }, { "facility": "F4", "customer": 8, "cost": 620.0 }, { "facility": "F4", "customer": 9, "cost": 460.0 }, { "facility": "F5", "customer": 0, "cost": 505.0 }, { "facility": "F5", "customer": 1, "cost": 535.0 }, { "facility": "F5", "customer": 2, "cost": 148.0 }, { "facility": "F5", "customer": 3, "cost": 664.0 }, { "facility": "F5", "customer": 4, "cost": 477.0 }, { "facility": "F5", "customer": 5, "cost": 539.0 }, { "facility": "F5", "customer": 6, "cost": 485.0 }, { "facility": "F5", "customer": 7, "cost": 816.0 }, { "facility": "F5", "customer": 8, "cost": 200.0 }, { "facility": "F5", "customer": 9, "cost": 83.0 } ], "objective": 2037.0 }, "solution_variant": { "selected": [ "F1", "F2", "F3", "F4" ], "assignments": [ "F4", "F2", "F1", "F3", "F2", "F2", "F3", "F3", "F1", "F1" ] }, "context_index": 43, "input_format": "json", "input_index_base": 0 }, { "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\nThere are 6 candidate shared garden plots and 13 gardeners.\nPlot F1: unlock fee 600.0, capacity 500.0.\nPlot F2: unlock fee 600.0, capacity 500.0.\nPlot F3: unlock fee 600.0, capacity 500.0.\nPlot F4: unlock fee 600.0, capacity 500.0.\nPlot F5: unlock fee 600.0, capacity 500.0.\nPlot F6: unlock fee 600.0, capacity 500.0.\nGardener 1: demand 38.0.\nGardener 2: demand 44.0.\nGardener 3: demand 42.0.\nGardener 4: demand 37.0.\nGardener 5: demand 28.0.\nGardener 6: demand 45.0.\nGardener 7: demand 27.0.\nGardener 8: demand 20.0.\nGardener 9: demand 35.0.\nGardener 10: demand 42.0.\nGardener 11: demand 48.0.\nGardener 12: demand 36.0.\nGardener 13: demand 25.0.\nEffort cost for gardener 1 on plot F1: 428.0.\nEffort cost for gardener 2 on plot F1: 161.0.\nEffort cost for gardener 3 on plot F1: 373.0.\nEffort cost for gardener 4 on plot F1: 465.0.\nEffort cost for gardener 5 on plot F1: 337.0.\nEffort cost for gardener 6 on plot F1: 70.0.\nEffort cost for gardener 7 on plot F1: 466.0.\nEffort cost for gardener 8 on plot F1: 244.0.\nEffort cost for gardener 9 on plot F1: 187.0.\nEffort cost for gardener 10 on plot F1: 294.0.\nEffort cost for gardener 11 on plot F1: 146.0.\nEffort cost for gardener 12 on plot F1: 406.0.\nEffort cost for gardener 13 on plot F1: 476.0.\nEffort cost for gardener 1 on plot F2: 560.0.\nEffort cost for gardener 2 on plot F2: 584.0.\nEffort cost for gardener 3 on plot F2: 245.0.\nEffort cost for gardener 4 on plot F2: 142.0.\nEffort cost for gardener 5 on plot F2: 353.0.\nEffort cost for gardener 6 on plot F2: 555.0.\nEffort cost for gardener 7 on plot F2: 292.0.\nEffort cost for gardener 8 on plot F2: 751.0.\nEffort cost for gardener 9 on plot F2: 393.0.\nEffort cost for gardener 10 on plot F2: 537.0.\nEffort cost for gardener 11 on plot F2: 549.0.\nEffort cost for gardener 12 on plot F2: 590.0.\nEffort cost for gardener 13 on plot F2: 326.0.\nEffort cost for gardener 1 on plot F3: 666.0.\nEffort cost for gardener 2 on plot F3: 528.0.\nEffort cost for gardener 3 on plot F3: 362.0.\nEffort cost for gardener 4 on plot F3: 351.0.\nEffort cost for gardener 5 on plot F3: 93.0.\nEffort cost for gardener 6 on plot F3: 369.0.\nEffort cost for gardener 7 on plot F3: 492.0.\nEffort cost for gardener 8 on plot F3: 665.0.\nEffort cost for gardener 9 on plot F3: 314.0.\nEffort cost for gardener 10 on plot F3: 574.0.\nEffort cost for gardener 11 on plot F3: 492.0.\nEffort cost for gardener 12 on plot F3: 249.0.\nEffort cost for gardener 13 on plot F3: 51.0.\nEffort cost for gardener 1 on plot F4: 651.0.\nEffort cost for gardener 2 on plot F4: 459.0.\nEffort cost for gardener 3 on plot F4: 400.0.\nEffort cost for gardener 4 on plot F4: 425.0.\nEffort cost for gardener 5 on plot F4: 109.0.\nEffort cost for gardener 6 on plot F4: 261.0.\nEffort cost for gardener 7 on plot F4: 535.0.\nEffort cost for gardener 8 on plot F4: 572.0.\nEffort cost for gardener 9 on plot F4: 277.0.\nEffort cost for gardener 10 on plot F4: 538.0.\nEffort cost for gardener 11 on plot F4: 427.0.\nEffort cost for gardener 12 on plot F4: 141.0.\nEffort cost for gardener 13 on plot F4: 194.0.\nEffort cost for gardener 1 on plot F5: 296.0.\nEffort cost for gardener 2 on plot F5: 25.0.\nEffort cost for gardener 3 on plot F5: 335.0.\nEffort cost for gardener 4 on plot F5: 438.0.\nEffort cost for gardener 5 on plot F5: 412.0.\nEffort cost for gardener 6 on plot F5: 201.0.\nEffort cost for gardener 7 on plot F5: 391.0.\nEffort cost for gardener 8 on plot F5: 181.0.\nEffort cost for gardener 9 on plot F5: 201.0.\nEffort cost for gardener 10 on plot F5: 162.0.\nEffort cost for gardener 11 on plot F5: 23.0.\nEffort cost for gardener 12 on plot F5: 532.0.\nEffort cost for gardener 13 on plot F5: 547.0.\nEffort cost for gardener 1 on plot F6: 174.0.\nEffort cost for gardener 2 on plot F6: 129.0.\nEffort cost for gardener 3 on plot F6: 256.0.\nEffort cost for gardener 4 on plot F6: 360.0.\nEffort cost for gardener 5 on plot F6: 437.0.\nEffort cost for gardener 6 on plot F6: 305.0.\nEffort cost for gardener 7 on plot F6: 274.0.\nEffort cost for gardener 8 on plot F6: 278.0.\nEffort cost for gardener 9 on plot F6: 214.0.\nEffort cost for gardener 10 on plot F6: 51.0.\nEffort cost for gardener 11 on plot F6: 118.0.\nEffort cost for gardener 12 on plot F6: 607.0.\nEffort cost for gardener 13 on plot F6: 557.0.\nThe council will add unlocked plot fees and gardeners’ effort costs to find the lowest total bill.\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 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 428.0, 161.0, 373.0, 465.0, 337.0, 70.0, 466.0, 244.0, 187.0, 294.0, 146.0, 406.0, 476.0 ], [ 560.0, 584.0, 245.0, 142.0, 353.0, 555.0, 292.0, 751.0, 393.0, 537.0, 549.0, 590.0, 326.0 ], [ 666.0, 528.0, 362.0, 351.0, 93.0, 369.0, 492.0, 665.0, 314.0, 574.0, 492.0, 249.0, 51.0 ], [ 651.0, 459.0, 400.0, 425.0, 109.0, 261.0, 535.0, 572.0, 277.0, 538.0, 427.0, 141.0, 194.0 ], [ 296.0, 25.0, 335.0, 438.0, 412.0, 201.0, 391.0, 181.0, 201.0, 162.0, 23.0, 532.0, 547.0 ], [ 174.0, 129.0, 256.0, 360.0, 437.0, 305.0, 274.0, 278.0, 214.0, 51.0, 118.0, 607.0, 557.0 ] ], "demands": [ 38.0, 44.0, 42.0, 37.0, 28.0, 45.0, 27.0, 20.0, 35.0, 42.0, 48.0, 36.0, 25.0 ], "objective": 3743.0 }, "solution": { "open_facilities": [ 2, 5 ], "assignments": [ 5, 5, 5, 2, 2, 5, 5, 5, 5, 5, 5, 2, 2 ] }, "obj": 3743.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 6, "num_customers": 13, "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 } ], "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": 45.0 }, { "id": 7, "demand": 27.0 }, { "id": 8, "demand": 20.0 }, { "id": 9, "demand": 35.0 }, { "id": 10, "demand": 42.0 }, { "id": 11, "demand": 48.0 }, { "id": 12, "demand": 36.0 }, { "id": 13, "demand": 25.0 } ], "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": 70.0 }, { "facility": "F1", "customer": 7, "cost": 466.0 }, { "facility": "F1", "customer": 8, "cost": 244.0 }, { "facility": "F1", "customer": 9, "cost": 187.0 }, { "facility": "F1", "customer": 10, "cost": 294.0 }, { "facility": "F1", "customer": 11, "cost": 146.0 }, { "facility": "F1", "customer": 12, "cost": 406.0 }, { "facility": "F1", "customer": 13, "cost": 476.0 }, { "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": 555.0 }, { "facility": "F2", "customer": 7, "cost": 292.0 }, { "facility": "F2", "customer": 8, "cost": 751.0 }, { "facility": "F2", "customer": 9, "cost": 393.0 }, { "facility": "F2", "customer": 10, "cost": 537.0 }, { "facility": "F2", "customer": 11, "cost": 549.0 }, { "facility": "F2", "customer": 12, "cost": 590.0 }, { "facility": "F2", "customer": 13, "cost": 326.0 }, { "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": 369.0 }, { "facility": "F3", "customer": 7, "cost": 492.0 }, { "facility": "F3", "customer": 8, "cost": 665.0 }, { "facility": "F3", "customer": 9, "cost": 314.0 }, { "facility": "F3", "customer": 10, "cost": 574.0 }, { "facility": "F3", "customer": 11, "cost": 492.0 }, { "facility": "F3", "customer": 12, "cost": 249.0 }, { "facility": "F3", "customer": 13, "cost": 51.0 }, { "facility": "F4", "customer": 1, "cost": 651.0 }, { "facility": "F4", "customer": 2, "cost": 459.0 }, { "facility": "F4", "customer": 3, "cost": 400.0 }, { "facility": "F4", "customer": 4, "cost": 425.0 }, { "facility": "F4", "customer": 5, "cost": 109.0 }, { "facility": "F4", "customer": 6, "cost": 261.0 }, { "facility": "F4", "customer": 7, "cost": 535.0 }, { "facility": "F4", "customer": 8, "cost": 572.0 }, { "facility": "F4", "customer": 9, "cost": 277.0 }, { "facility": "F4", "customer": 10, "cost": 538.0 }, { "facility": "F4", "customer": 11, "cost": 427.0 }, { "facility": "F4", "customer": 12, "cost": 141.0 }, { "facility": "F4", "customer": 13, "cost": 194.0 }, { "facility": "F5", "customer": 1, "cost": 296.0 }, { "facility": "F5", "customer": 2, "cost": 25.0 }, { "facility": "F5", "customer": 3, "cost": 335.0 }, { "facility": "F5", "customer": 4, "cost": 438.0 }, { "facility": "F5", "customer": 5, "cost": 412.0 }, { "facility": "F5", "customer": 6, "cost": 201.0 }, { "facility": "F5", "customer": 7, "cost": 391.0 }, { "facility": "F5", "customer": 8, "cost": 181.0 }, { "facility": "F5", "customer": 9, "cost": 201.0 }, { "facility": "F5", "customer": 10, "cost": 162.0 }, { "facility": "F5", "customer": 11, "cost": 23.0 }, { "facility": "F5", "customer": 12, "cost": 532.0 }, { "facility": "F5", "customer": 13, "cost": 547.0 }, { "facility": "F6", "customer": 1, "cost": 174.0 }, { "facility": "F6", "customer": 2, "cost": 129.0 }, { "facility": "F6", "customer": 3, "cost": 256.0 }, { "facility": "F6", "customer": 4, "cost": 360.0 }, { "facility": "F6", "customer": 5, "cost": 437.0 }, { "facility": "F6", "customer": 6, "cost": 305.0 }, { "facility": "F6", "customer": 7, "cost": 274.0 }, { "facility": "F6", "customer": 8, "cost": 278.0 }, { "facility": "F6", "customer": 9, "cost": 214.0 }, { "facility": "F6", "customer": 10, "cost": 51.0 }, { "facility": "F6", "customer": 11, "cost": 118.0 }, { "facility": "F6", "customer": 12, "cost": 607.0 }, { "facility": "F6", "customer": 13, "cost": 557.0 } ], "objective": 3743.0 }, "solution_variant": { "selected": [ "F3", "F6" ], "assignments": [ "F6", "F6", "F6", "F3", "F3", "F6", "F6", "F6", "F6", "F6", "F6", "F3", "F3" ] }, "context_index": 44, "input_format": "nl", "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\n{\n \"num_vans\": 6,\n \"num_requests\": 13,\n \"vans\": [\n {\n \"van_id\": \"F1\",\n \"deployment_cost\": 300.0,\n \"van_capacity\": 425.0\n },\n {\n \"van_id\": \"F2\",\n \"deployment_cost\": 300.0,\n \"van_capacity\": 430.0\n },\n {\n \"van_id\": \"F3\",\n \"deployment_cost\": 300.0,\n \"van_capacity\": 491.0\n },\n {\n \"van_id\": \"F4\",\n \"deployment_cost\": 300.0,\n \"van_capacity\": 378.0\n },\n {\n \"van_id\": \"F5\",\n \"deployment_cost\": 300.0,\n \"van_capacity\": 338.0\n },\n {\n \"van_id\": \"F6\",\n \"deployment_cost\": 300.0,\n \"van_capacity\": 403.0\n }\n ],\n \"requests\": [\n {\n \"request_id\": \"A\",\n \"service_demand\": 13.0\n },\n {\n \"request_id\": \"B\",\n \"service_demand\": 12.0\n },\n {\n \"request_id\": \"C\",\n \"service_demand\": 26.0\n },\n {\n \"request_id\": \"D\",\n \"service_demand\": 13.0\n },\n {\n \"request_id\": \"E\",\n \"service_demand\": 17.0\n },\n {\n \"request_id\": \"F\",\n \"service_demand\": 19.0\n },\n {\n \"request_id\": \"G\",\n \"service_demand\": 23.0\n },\n {\n \"request_id\": \"H\",\n \"service_demand\": 18.0\n },\n {\n \"request_id\": \"I\",\n \"service_demand\": 20.0\n },\n {\n \"request_id\": \"J\",\n \"service_demand\": 11.0\n },\n {\n \"request_id\": \"K\",\n \"service_demand\": 19.0\n },\n {\n \"request_id\": \"L\",\n \"service_demand\": 21.0\n },\n {\n \"request_id\": \"M\",\n \"service_demand\": 12.0\n }\n ],\n \"travels\": [\n {\n \"van_id\": \"F1\",\n \"request_id\": \"A\",\n \"travel_cost\": 2821.0\n },\n {\n \"van_id\": \"F1\",\n \"request_id\": \"B\",\n \"travel_cost\": 915.0\n },\n {\n \"van_id\": \"F1\",\n \"request_id\": \"C\",\n \"travel_cost\": 795.0\n },\n {\n \"van_id\": \"F1\",\n \"request_id\": \"D\",\n \"travel_cost\": 1716.0\n },\n {\n \"van_id\": \"F1\",\n \"request_id\": \"E\",\n \"travel_cost\": 2144.0\n },\n {\n \"van_id\": \"F1\",\n \"request_id\": \"F\",\n \"travel_cost\": 1904.0\n },\n {\n \"van_id\": \"F1\",\n \"request_id\": \"G\",\n \"travel_cost\": 2141.0\n },\n {\n \"van_id\": \"F1\",\n \"request_id\": \"H\",\n \"travel_cost\": 45.0\n },\n {\n \"van_id\": \"F1\",\n \"request_id\": \"I\",\n \"travel_cost\": 1161.0\n },\n {\n \"van_id\": \"F1\",\n \"request_id\": \"J\",\n \"travel_cost\": 1595.0\n },\n {\n \"van_id\": \"F1\",\n \"request_id\": \"K\",\n \"travel_cost\": 683.0\n },\n {\n \"van_id\": \"F1\",\n \"request_id\": \"L\",\n \"travel_cost\": 1685.0\n },\n {\n \"van_id\": \"F1\",\n \"request_id\": \"M\",\n \"travel_cost\": 1957.0\n },\n {\n \"van_id\": \"F2\",\n \"request_id\": \"A\",\n \"travel_cost\": 2629.0\n },\n {\n \"van_id\": \"F2\",\n \"request_id\": \"B\",\n \"travel_cost\": 865.0\n },\n {\n \"van_id\": \"F2\",\n \"request_id\": \"C\",\n \"travel_cost\": 579.0\n },\n {\n \"van_id\": \"F2\",\n \"request_id\": \"D\",\n \"travel_cost\": 1488.0\n },\n {\n \"van_id\": \"F2\",\n \"request_id\": \"E\",\n \"travel_cost\": 2035.0\n },\n {\n \"van_id\": \"F2\",\n \"request_id\": \"F\",\n \"travel_cost\": 1639.0\n },\n {\n \"van_id\": \"F2\",\n \"request_id\": \"G\",\n \"travel_cost\": 1940.0\n },\n {\n \"van_id\": \"F2\",\n \"request_id\": \"H\",\n \"travel_cost\": 49.0\n },\n {\n \"van_id\": \"F2\",\n \"request_id\": \"I\",\n \"travel_cost\": 919.0\n },\n {\n \"van_id\": \"F2\",\n \"request_id\": \"J\",\n \"travel_cost\": 1353.0\n },\n {\n \"van_id\": \"F2\",\n \"request_id\": \"K\",\n \"travel_cost\": 632.0\n },\n {\n \"van_id\": \"F2\",\n \"request_id\": \"L\",\n \"travel_cost\": 1428.0\n },\n {\n \"van_id\": \"F2\",\n \"request_id\": \"M\",\n \"travel_cost\": 1723.0\n },\n {\n \"van_id\": \"F3\",\n \"request_id\": \"A\",\n \"travel_cost\": 848.0\n },\n {\n \"van_id\": \"F3\",\n \"request_id\": \"B\",\n \"travel_cost\": 66.0\n },\n {\n \"van_id\": \"F3\",\n \"request_id\": \"C\",\n \"travel_cost\": 111.0\n },\n {\n \"van_id\": \"F3\",\n \"request_id\": \"D\",\n \"travel_cost\": 341.0\n },\n {\n \"van_id\": \"F3\",\n \"request_id\": \"E\",\n \"travel_cost\": 186.0\n },\n {\n \"van_id\": \"F3\",\n \"request_id\": \"F\",\n \"travel_cost\": 693.0\n },\n {\n \"van_id\": \"F3\",\n \"request_id\": \"G\",\n \"travel_cost\": 399.0\n },\n {\n \"van_id\": \"F3\",\n \"request_id\": \"H\",\n \"travel_cost\": 37.0\n },\n {\n \"van_id\": \"F3\",\n \"request_id\": \"I\",\n \"travel_cost\": 220.0\n },\n {\n \"van_id\": \"F3\",\n \"request_id\": \"J\",\n \"travel_cost\": 362.0\n },\n {\n \"van_id\": \"F3\",\n \"request_id\": \"K\",\n \"travel_cost\": 55.0\n },\n {\n \"van_id\": \"F3\",\n \"request_id\": \"L\",\n \"travel_cost\": 507.0\n },\n {\n \"van_id\": \"F3\",\n \"request_id\": \"M\",\n \"travel_cost\": 487.0\n },\n {\n \"van_id\": \"F4\",\n \"request_id\": \"A\",\n \"travel_cost\": 173.0\n },\n {\n \"van_id\": \"F4\",\n \"request_id\": \"B\",\n \"travel_cost\": 160.0\n },\n {\n \"van_id\": \"F4\",\n \"request_id\": \"C\",\n \"travel_cost\": 56.0\n },\n {\n \"van_id\": \"F4\",\n \"request_id\": \"D\",\n \"travel_cost\": 77.0\n },\n {\n \"van_id\": \"F4\",\n \"request_id\": \"E\",\n \"travel_cost\": 352.0\n },\n {\n \"van_id\": \"F4\",\n \"request_id\": \"F\",\n \"travel_cost\": 321.0\n },\n {\n \"van_id\": \"F4\",\n \"request_id\": \"G\",\n \"travel_cost\": 53.0\n },\n {\n \"van_id\": \"F4\",\n \"request_id\": \"H\",\n \"travel_cost\": 37.0\n },\n {\n \"van_id\": \"F4\",\n \"request_id\": \"I\",\n \"travel_cost\": 79.0\n },\n {\n \"van_id\": \"F4\",\n \"request_id\": \"J\",\n \"travel_cost\": 105.0\n },\n {\n \"van_id\": \"F4\",\n \"request_id\": \"K\",\n \"travel_cost\": 116.0\n },\n {\n \"van_id\": \"F4\",\n \"request_id\": \"L\",\n \"travel_cost\": 206.0\n },\n {\n \"van_id\": \"F4\",\n \"request_id\": \"M\",\n \"travel_cost\": 122.0\n },\n {\n \"van_id\": \"F5\",\n \"request_id\": \"A\",\n \"travel_cost\": 1342.0\n },\n {\n \"van_id\": \"F5\",\n \"request_id\": \"B\",\n \"travel_cost\": 523.0\n },\n {\n \"van_id\": \"F5\",\n \"request_id\": \"C\",\n \"travel_cost\": 145.0\n },\n {\n \"van_id\": \"F5\",\n \"request_id\": \"D\",\n \"travel_cost\": 306.0\n },\n {\n \"van_id\": \"F5\",\n \"request_id\": \"E\",\n \"travel_cost\": 1217.0\n },\n {\n \"van_id\": \"F5\",\n \"request_id\": \"F\",\n \"travel_cost\": 103.0\n },\n {\n \"van_id\": \"F5\",\n \"request_id\": \"G\",\n \"travel_cost\": 739.0\n },\n {\n \"van_id\": \"F5\",\n \"request_id\": \"H\",\n \"travel_cost\": 62.0\n },\n {\n \"van_id\": \"F5\",\n \"request_id\": \"I\",\n \"travel_cost\": 118.0\n },\n {\n \"van_id\": \"F5\",\n \"request_id\": \"J\",\n \"travel_cost\": 176.0\n },\n {\n \"van_id\": \"F5\",\n \"request_id\": \"K\",\n \"travel_cost\": 380.0\n },\n {\n \"van_id\": \"F5\",\n \"request_id\": \"L\",\n \"travel_cost\": 117.0\n },\n {\n \"van_id\": \"F5\",\n \"request_id\": \"M\",\n \"travel_cost\": 398.0\n },\n {\n \"van_id\": \"F6\",\n \"request_id\": \"A\",\n \"travel_cost\": 1364.0\n },\n {\n \"van_id\": \"F6\",\n \"request_id\": \"B\",\n \"travel_cost\": 389.0\n },\n {\n \"van_id\": \"F6\",\n \"request_id\": \"C\",\n \"travel_cost\": 71.0\n },\n {\n \"van_id\": \"F6\",\n \"request_id\": \"D\",\n \"travel_cost\": 192.0\n },\n {\n \"van_id\": \"F6\",\n \"request_id\": \"E\",\n \"travel_cost\": 1085.0\n },\n {\n \"van_id\": \"F6\",\n \"request_id\": \"F\",\n \"travel_cost\": 398.0\n },\n {\n \"van_id\": \"F6\",\n \"request_id\": \"G\",\n \"travel_cost\": 687.0\n },\n {\n \"van_id\": \"F6\",\n \"request_id\": \"H\",\n \"travel_cost\": 46.0\n },\n {\n \"van_id\": \"F6\",\n \"request_id\": \"I\",\n \"travel_cost\": 41.0\n },\n {\n \"van_id\": \"F6\",\n \"request_id\": \"J\",\n \"travel_cost\": 22.0\n },\n {\n \"van_id\": \"F6\",\n \"request_id\": \"K\",\n \"travel_cost\": 267.0\n },\n {\n \"van_id\": \"F6\",\n \"request_id\": \"L\",\n \"travel_cost\": 175.0\n },\n {\n \"van_id\": \"F6\",\n \"request_id\": \"M\",\n \"travel_cost\": 398.0\n }\n ]\n}\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": [ 300.0, 300.0, 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 425.0, 430.0, 491.0, 378.0, 338.0, 403.0 ], "connection_costs": [ [ 2821.0, 915.0, 795.0, 1716.0, 2144.0, 1904.0, 2141.0, 45.0, 1161.0, 1595.0, 683.0, 1685.0, 1957.0 ], [ 2629.0, 865.0, 579.0, 1488.0, 2035.0, 1639.0, 1940.0, 49.0, 919.0, 1353.0, 632.0, 1428.0, 1723.0 ], [ 848.0, 66.0, 111.0, 341.0, 186.0, 693.0, 399.0, 37.0, 220.0, 362.0, 55.0, 507.0, 487.0 ], [ 173.0, 160.0, 56.0, 77.0, 352.0, 321.0, 53.0, 37.0, 79.0, 105.0, 116.0, 206.0, 122.0 ], [ 1342.0, 523.0, 145.0, 306.0, 1217.0, 103.0, 739.0, 62.0, 118.0, 176.0, 380.0, 117.0, 398.0 ], [ 1364.0, 389.0, 71.0, 192.0, 1085.0, 398.0, 687.0, 46.0, 41.0, 22.0, 267.0, 175.0, 398.0 ] ], "demands": [ 13.0, 12.0, 26.0, 13.0, 17.0, 19.0, 23.0, 18.0, 20.0, 11.0, 19.0, 21.0, 12.0 ], "objective": 2129.0 }, "solution": { "open_facilities": [ 2, 3, 4 ], "assignments": [ 3, 2, 3, 3, 2, 4, 3, 2, 3, 3, 2, 4, 3 ] }, "obj": 2129.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 6, "num_customers": 13, "facilities": [ { "id": "F1", "opening_cost": 300.0, "capacity": 425.0 }, { "id": "F2", "opening_cost": 300.0, "capacity": 430.0 }, { "id": "F3", "opening_cost": 300.0, "capacity": 491.0 }, { "id": "F4", "opening_cost": 300.0, "capacity": 378.0 }, { "id": "F5", "opening_cost": 300.0, "capacity": 338.0 }, { "id": "F6", "opening_cost": 300.0, "capacity": 403.0 } ], "customers": [ { "id": "A", "demand": 13.0 }, { "id": "B", "demand": 12.0 }, { "id": "C", "demand": 26.0 }, { "id": "D", "demand": 13.0 }, { "id": "E", "demand": 17.0 }, { "id": "F", "demand": 19.0 }, { "id": "G", "demand": 23.0 }, { "id": "H", "demand": 18.0 }, { "id": "I", "demand": 20.0 }, { "id": "J", "demand": 11.0 }, { "id": "K", "demand": 19.0 }, { "id": "L", "demand": 21.0 }, { "id": "M", "demand": 12.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 2821.0 }, { "facility": "F1", "customer": "B", "cost": 915.0 }, { "facility": "F1", "customer": "C", "cost": 795.0 }, { "facility": "F1", "customer": "D", "cost": 1716.0 }, { "facility": "F1", "customer": "E", "cost": 2144.0 }, { "facility": "F1", "customer": "F", "cost": 1904.0 }, { "facility": "F1", "customer": "G", "cost": 2141.0 }, { "facility": "F1", "customer": "H", "cost": 45.0 }, { "facility": "F1", "customer": "I", "cost": 1161.0 }, { "facility": "F1", "customer": "J", "cost": 1595.0 }, { "facility": "F1", "customer": "K", "cost": 683.0 }, { "facility": "F1", "customer": "L", "cost": 1685.0 }, { "facility": "F1", "customer": "M", "cost": 1957.0 }, { "facility": "F2", "customer": "A", "cost": 2629.0 }, { "facility": "F2", "customer": "B", "cost": 865.0 }, { "facility": "F2", "customer": "C", "cost": 579.0 }, { "facility": "F2", "customer": "D", "cost": 1488.0 }, { "facility": "F2", "customer": "E", "cost": 2035.0 }, { "facility": "F2", "customer": "F", "cost": 1639.0 }, { "facility": "F2", "customer": "G", "cost": 1940.0 }, { "facility": "F2", "customer": "H", "cost": 49.0 }, { "facility": "F2", "customer": "I", "cost": 919.0 }, { "facility": "F2", "customer": "J", "cost": 1353.0 }, { "facility": "F2", "customer": "K", "cost": 632.0 }, { "facility": "F2", "customer": "L", "cost": 1428.0 }, { "facility": "F2", "customer": "M", "cost": 1723.0 }, { "facility": "F3", "customer": "A", "cost": 848.0 }, { "facility": "F3", "customer": "B", "cost": 66.0 }, { "facility": "F3", "customer": "C", "cost": 111.0 }, { "facility": "F3", "customer": "D", "cost": 341.0 }, { "facility": "F3", "customer": "E", "cost": 186.0 }, { "facility": "F3", "customer": "F", "cost": 693.0 }, { "facility": "F3", "customer": "G", "cost": 399.0 }, { "facility": "F3", "customer": "H", "cost": 37.0 }, { "facility": "F3", "customer": "I", "cost": 220.0 }, { "facility": "F3", "customer": "J", "cost": 362.0 }, { "facility": "F3", "customer": "K", "cost": 55.0 }, { "facility": "F3", "customer": "L", "cost": 507.0 }, { "facility": "F3", "customer": "M", "cost": 487.0 }, { "facility": "F4", "customer": "A", "cost": 173.0 }, { "facility": "F4", "customer": "B", "cost": 160.0 }, { "facility": "F4", "customer": "C", "cost": 56.0 }, { "facility": "F4", "customer": "D", "cost": 77.0 }, { "facility": "F4", "customer": "E", "cost": 352.0 }, { "facility": "F4", "customer": "F", "cost": 321.0 }, { "facility": "F4", "customer": "G", "cost": 53.0 }, { "facility": "F4", "customer": "H", "cost": 37.0 }, { "facility": "F4", "customer": "I", "cost": 79.0 }, { "facility": "F4", "customer": "J", "cost": 105.0 }, { "facility": "F4", "customer": "K", "cost": 116.0 }, { "facility": "F4", "customer": "L", "cost": 206.0 }, { "facility": "F4", "customer": "M", "cost": 122.0 }, { "facility": "F5", "customer": "A", "cost": 1342.0 }, { "facility": "F5", "customer": "B", "cost": 523.0 }, { "facility": "F5", "customer": "C", "cost": 145.0 }, { "facility": "F5", "customer": "D", "cost": 306.0 }, { "facility": "F5", "customer": "E", "cost": 1217.0 }, { "facility": "F5", "customer": "F", "cost": 103.0 }, { "facility": "F5", "customer": "G", "cost": 739.0 }, { "facility": "F5", "customer": "H", "cost": 62.0 }, { "facility": "F5", "customer": "I", "cost": 118.0 }, { "facility": "F5", "customer": "J", "cost": 176.0 }, { "facility": "F5", "customer": "K", "cost": 380.0 }, { "facility": "F5", "customer": "L", "cost": 117.0 }, { "facility": "F5", "customer": "M", "cost": 398.0 }, { "facility": "F6", "customer": "A", "cost": 1364.0 }, { "facility": "F6", "customer": "B", "cost": 389.0 }, { "facility": "F6", "customer": "C", "cost": 71.0 }, { "facility": "F6", "customer": "D", "cost": 192.0 }, { "facility": "F6", "customer": "E", "cost": 1085.0 }, { "facility": "F6", "customer": "F", "cost": 398.0 }, { "facility": "F6", "customer": "G", "cost": 687.0 }, { "facility": "F6", "customer": "H", "cost": 46.0 }, { "facility": "F6", "customer": "I", "cost": 41.0 }, { "facility": "F6", "customer": "J", "cost": 22.0 }, { "facility": "F6", "customer": "K", "cost": 267.0 }, { "facility": "F6", "customer": "L", "cost": 175.0 }, { "facility": "F6", "customer": "M", "cost": 398.0 } ], "objective": 2129.0 }, "solution_variant": { "selected": [ "F3", "F4", "F5" ], "assignments": [ "F4", "F3", "F4", "F4", "F3", "F5", "F4", "F3", "F4", "F4", "F3", "F5", "F4" ] }, "context_index": 45, "input_format": "json", "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\nThere are 5 offices and 11 subscribers in this instance.\n\n**Offices**\n| office_id | activation_cost | office_capacity |\n|---|---|---|\n| F1 | 300.0 | 700.0 |\n| F2 | 300.0 | 700.0 |\n| F3 | 300.0 | 700.0 |\n| F4 | 300.0 | 700.0 |\n| F5 | 300.0 | 700.0 |\n\n**Subscribers**\n| subscriber_id | subscriber_demand |\n|---|---|\n| 1 | 13.0 |\n| 2 | 23.0 |\n| 3 | 18.0 |\n| 4 | 14.0 |\n| 5 | 22.0 |\n| 6 | 27.0 |\n| 7 | 23.0 |\n| 8 | 18.0 |\n| 9 | 11.0 |\n| 10 | 19.0 |\n| 11 | 29.0 |\n\n**Connection Cost**\n| office_id | subscriber_id | connection_cost |\n|---|---|---|\n| F1 | 1 | 902.0 |\n| F1 | 2 | 415.0 |\n| F1 | 3 | 42.0 |\n| F1 | 4 | 100.0 |\n| F1 | 5 | 832.0 |\n| F1 | 6 | 179.0 |\n| F1 | 7 | 324.0 |\n| F1 | 8 | 36.0 |\n| F1 | 9 | 97.0 |\n| F1 | 10 | 57.0 |\n| F1 | 11 | 475.0 |\n| F2 | 1 | 2821.0 |\n| F2 | 2 | 2332.0 |\n| F2 | 3 | 1169.0 |\n| F2 | 4 | 1311.0 |\n| F2 | 5 | 2706.0 |\n| F2 | 6 | 2040.0 |\n| F2 | 7 | 2141.0 |\n| F2 | 8 | 45.0 |\n| F2 | 9 | 705.0 |\n| F2 | 10 | 1087.0 |\n| F2 | 11 | 1583.0 |\n| F3 | 1 | 1357.0 |\n| F3 | 2 | 930.0 |\n| F3 | 3 | 289.0 |\n| F3 | 4 | 458.0 |\n| F3 | 5 | 1343.0 |\n| F3 | 6 | 734.0 |\n| F3 | 7 | 879.0 |\n| F3 | 8 | 50.0 |\n| F3 | 9 | 26.0 |\n| F3 | 10 | 307.0 |\n| F3 | 11 | 77.0 |\n| F4 | 1 | 1775.0 |\n| F4 | 2 | 1310.0 |\n| F4 | 3 | 273.0 |\n| F4 | 4 | 249.0 |\n| F4 | 5 | 1633.0 |\n| F4 | 6 | 1023.0 |\n| F4 | 7 | 1084.0 |\n| F4 | 8 | 45.0 |\n| F4 | 9 | 339.0 |\n| F4 | 10 | 173.0 |\n| F4 | 11 | 1067.0 |\n| F5 | 1 | 1203.0 |\n| F5 | 2 | 763.0 |\n| F5 | 3 | 104.0 |\n| F5 | 4 | 37.0 |\n| F5 | 5 | 1051.0 |\n| F5 | 6 | 502.0 |\n| F5 | 7 | 522.0 |\n| F5 | 8 | 42.0 |\n| F5 | 9 | 247.0 |\n| F5 | 10 | 67.0 |\n| F5 | 11 | 831.0 |\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": [ 300.0, 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 700.0, 700.0, 700.0, 700.0, 700.0 ], "connection_costs": [ [ 902.0, 415.0, 42.0, 100.0, 832.0, 179.0, 324.0, 36.0, 97.0, 57.0, 475.0 ], [ 2821.0, 2332.0, 1169.0, 1311.0, 2706.0, 2040.0, 2141.0, 45.0, 705.0, 1087.0, 1583.0 ], [ 1357.0, 930.0, 289.0, 458.0, 1343.0, 734.0, 879.0, 50.0, 26.0, 307.0, 77.0 ], [ 1775.0, 1310.0, 273.0, 249.0, 1633.0, 1023.0, 1084.0, 45.0, 339.0, 173.0, 1067.0 ], [ 1203.0, 763.0, 104.0, 37.0, 1051.0, 502.0, 522.0, 42.0, 247.0, 67.0, 831.0 ] ], "demands": [ 13.0, 23.0, 18.0, 14.0, 22.0, 27.0, 23.0, 18.0, 11.0, 19.0, 29.0 ], "objective": 3590.0 }, "solution": { "open_facilities": [ 0, 2 ], "assignments": [ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2 ] }, "obj": 3590.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 11, "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 } ], "customers": [ { "id": 1, "demand": 13.0 }, { "id": 2, "demand": 23.0 }, { "id": 3, "demand": 18.0 }, { "id": 4, "demand": 14.0 }, { "id": 5, "demand": 22.0 }, { "id": 6, "demand": 27.0 }, { "id": 7, "demand": 23.0 }, { "id": 8, "demand": 18.0 }, { "id": 9, "demand": 11.0 }, { "id": 10, "demand": 19.0 }, { "id": 11, "demand": 29.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 902.0 }, { "facility": "F1", "customer": 2, "cost": 415.0 }, { "facility": "F1", "customer": 3, "cost": 42.0 }, { "facility": "F1", "customer": 4, "cost": 100.0 }, { "facility": "F1", "customer": 5, "cost": 832.0 }, { "facility": "F1", "customer": 6, "cost": 179.0 }, { "facility": "F1", "customer": 7, "cost": 324.0 }, { "facility": "F1", "customer": 8, "cost": 36.0 }, { "facility": "F1", "customer": 9, "cost": 97.0 }, { "facility": "F1", "customer": 10, "cost": 57.0 }, { "facility": "F1", "customer": 11, "cost": 475.0 }, { "facility": "F2", "customer": 1, "cost": 2821.0 }, { "facility": "F2", "customer": 2, "cost": 2332.0 }, { "facility": "F2", "customer": 3, "cost": 1169.0 }, { "facility": "F2", "customer": 4, "cost": 1311.0 }, { "facility": "F2", "customer": 5, "cost": 2706.0 }, { "facility": "F2", "customer": 6, "cost": 2040.0 }, { "facility": "F2", "customer": 7, "cost": 2141.0 }, { "facility": "F2", "customer": 8, "cost": 45.0 }, { "facility": "F2", "customer": 9, "cost": 705.0 }, { "facility": "F2", "customer": 10, "cost": 1087.0 }, { "facility": "F2", "customer": 11, "cost": 1583.0 }, { "facility": "F3", "customer": 1, "cost": 1357.0 }, { "facility": "F3", "customer": 2, "cost": 930.0 }, { "facility": "F3", "customer": 3, "cost": 289.0 }, { "facility": "F3", "customer": 4, "cost": 458.0 }, { "facility": "F3", "customer": 5, "cost": 1343.0 }, { "facility": "F3", "customer": 6, "cost": 734.0 }, { "facility": "F3", "customer": 7, "cost": 879.0 }, { "facility": "F3", "customer": 8, "cost": 50.0 }, { "facility": "F3", "customer": 9, "cost": 26.0 }, { "facility": "F3", "customer": 10, "cost": 307.0 }, { "facility": "F3", "customer": 11, "cost": 77.0 }, { "facility": "F4", "customer": 1, "cost": 1775.0 }, { "facility": "F4", "customer": 2, "cost": 1310.0 }, { "facility": "F4", "customer": 3, "cost": 273.0 }, { "facility": "F4", "customer": 4, "cost": 249.0 }, { "facility": "F4", "customer": 5, "cost": 1633.0 }, { "facility": "F4", "customer": 6, "cost": 1023.0 }, { "facility": "F4", "customer": 7, "cost": 1084.0 }, { "facility": "F4", "customer": 8, "cost": 45.0 }, { "facility": "F4", "customer": 9, "cost": 339.0 }, { "facility": "F4", "customer": 10, "cost": 173.0 }, { "facility": "F4", "customer": 11, "cost": 1067.0 }, { "facility": "F5", "customer": 1, "cost": 1203.0 }, { "facility": "F5", "customer": 2, "cost": 763.0 }, { "facility": "F5", "customer": 3, "cost": 104.0 }, { "facility": "F5", "customer": 4, "cost": 37.0 }, { "facility": "F5", "customer": 5, "cost": 1051.0 }, { "facility": "F5", "customer": 6, "cost": 502.0 }, { "facility": "F5", "customer": 7, "cost": 522.0 }, { "facility": "F5", "customer": 8, "cost": 42.0 }, { "facility": "F5", "customer": 9, "cost": 247.0 }, { "facility": "F5", "customer": 10, "cost": 67.0 }, { "facility": "F5", "customer": 11, "cost": 831.0 } ], "objective": 3590.0 }, "solution_variant": { "selected": [ "F1", "F3" ], "assignments": [ "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F3", "F1", "F3" ] }, "context_index": 46, "input_format": "markdown_table", "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\n{\n \"num_centers\": 6,\n \"num_beneficiaries\": 12,\n \"centers\": [\n {\n \"center_id\": \"F1\",\n \"center_opening_cost\": 440.0,\n \"center_capacity\": 500.0\n },\n {\n \"center_id\": \"F2\",\n \"center_opening_cost\": 462.0,\n \"center_capacity\": 500.0\n },\n {\n \"center_id\": \"F3\",\n \"center_opening_cost\": 468.0,\n \"center_capacity\": 500.0\n },\n {\n \"center_id\": \"F4\",\n \"center_opening_cost\": 518.0,\n \"center_capacity\": 500.0\n },\n {\n \"center_id\": \"F5\",\n \"center_opening_cost\": 333.0,\n \"center_capacity\": 500.0\n },\n {\n \"center_id\": \"F6\",\n \"center_opening_cost\": 450.0,\n \"center_capacity\": 500.0\n }\n ],\n \"beneficiarys\": [\n {\n \"beneficiary_id\": \"A\",\n \"beneficiary_need\": 27.0\n },\n {\n \"beneficiary_id\": \"B\",\n \"beneficiary_need\": 19.0\n },\n {\n \"beneficiary_id\": \"C\",\n \"beneficiary_need\": 20.0\n },\n {\n \"beneficiary_id\": \"D\",\n \"beneficiary_need\": 29.0\n },\n {\n \"beneficiary_id\": \"E\",\n \"beneficiary_need\": 22.0\n },\n {\n \"beneficiary_id\": \"F\",\n \"beneficiary_need\": 26.0\n },\n {\n \"beneficiary_id\": \"G\",\n \"beneficiary_need\": 27.0\n },\n {\n \"beneficiary_id\": \"H\",\n \"beneficiary_need\": 10.0\n },\n {\n \"beneficiary_id\": \"I\",\n \"beneficiary_need\": 11.0\n },\n {\n \"beneficiary_id\": \"J\",\n \"beneficiary_need\": 23.0\n },\n {\n \"beneficiary_id\": \"K\",\n \"beneficiary_need\": 17.0\n },\n {\n \"beneficiary_id\": \"L\",\n \"beneficiary_need\": 27.0\n }\n ],\n \"services\": [\n {\n \"center_id\": \"F1\",\n \"beneficiary_id\": \"A\",\n \"service_cost\": 259.0\n },\n {\n \"center_id\": \"F1\",\n \"beneficiary_id\": \"B\",\n \"service_cost\": 66.0\n },\n {\n \"center_id\": \"F1\",\n \"beneficiary_id\": \"C\",\n \"service_cost\": 370.0\n },\n {\n \"center_id\": \"F1\",\n \"beneficiary_id\": \"D\",\n \"service_cost\": 58.0\n },\n {\n \"center_id\": \"F1\",\n \"beneficiary_id\": \"E\",\n \"service_cost\": 671.0\n },\n {\n \"center_id\": \"F1\",\n \"beneficiary_id\": \"F\",\n \"service_cost\": 283.0\n },\n {\n \"center_id\": \"F1\",\n \"beneficiary_id\": \"G\",\n \"service_cost\": 273.0\n },\n {\n \"center_id\": \"F1\",\n \"beneficiary_id\": \"H\",\n \"service_cost\": 77.0\n },\n {\n \"center_id\": \"F1\",\n \"beneficiary_id\": \"I\",\n \"service_cost\": 66.0\n },\n {\n \"center_id\": \"F1\",\n \"beneficiary_id\": \"J\",\n \"service_cost\": 315.0\n },\n {\n \"center_id\": \"F1\",\n \"beneficiary_id\": \"K\",\n \"service_cost\": 332.0\n },\n {\n \"center_id\": \"F1\",\n \"beneficiary_id\": \"L\",\n \"service_cost\": 412.0\n },\n {\n \"center_id\": \"F2\",\n \"beneficiary_id\": \"A\",\n \"service_cost\": 792.0\n },\n {\n \"center_id\": \"F2\",\n \"beneficiary_id\": \"B\",\n \"service_cost\": 42.0\n },\n {\n \"center_id\": \"F2\",\n \"beneficiary_id\": \"C\",\n \"service_cost\": 1107.0\n },\n {\n \"center_id\": \"F2\",\n \"beneficiary_id\": \"D\",\n \"service_cost\": 101.0\n },\n {\n \"center_id\": \"F2\",\n \"beneficiary_id\": \"E\",\n \"service_cost\": 1336.0\n },\n {\n \"center_id\": \"F2\",\n \"beneficiary_id\": \"F\",\n \"service_cost\": 611.0\n },\n {\n \"center_id\": \"F2\",\n \"beneficiary_id\": \"G\",\n \"service_cost\": 895.0\n },\n {\n \"center_id\": \"F2\",\n \"beneficiary_id\": \"H\",\n \"service_cost\": 394.0\n },\n {\n \"center_id\": \"F2\",\n \"beneficiary_id\": \"I\",\n \"service_cost\": 942.0\n },\n {\n \"center_id\": \"F2\",\n \"beneficiary_id\": \"J\",\n \"service_cost\": 1443.0\n },\n {\n \"center_id\": \"F2\",\n \"beneficiary_id\": \"K\",\n \"service_cost\": 1164.0\n },\n {\n \"center_id\": \"F2\",\n \"beneficiary_id\": \"L\",\n \"service_cost\": 1086.0\n },\n {\n \"center_id\": \"F3\",\n \"beneficiary_id\": \"A\",\n \"service_cost\": 1237.0\n },\n {\n \"center_id\": \"F3\",\n \"beneficiary_id\": \"B\",\n \"service_cost\": 38.0\n },\n {\n \"center_id\": \"F3\",\n \"beneficiary_id\": \"C\",\n \"service_cost\": 1588.0\n },\n {\n \"center_id\": \"F3\",\n \"beneficiary_id\": \"D\",\n \"service_cost\": 446.0\n },\n {\n \"center_id\": \"F3\",\n \"beneficiary_id\": \"E\",\n \"service_cost\": 2013.0\n },\n {\n \"center_id\": \"F3\",\n \"beneficiary_id\": \"F\",\n \"service_cost\": 1309.0\n },\n {\n \"center_id\": \"F3\",\n \"beneficiary_id\": \"G\",\n \"service_cost\": 1374.0\n },\n {\n \"center_id\": \"F3\",\n \"beneficiary_id\": \"H\",\n \"service_cost\": 844.0\n },\n {\n \"center_id\": \"F3\",\n \"beneficiary_id\": \"I\",\n \"service_cost\": 1595.0\n },\n {\n \"center_id\": \"F3\",\n \"beneficiary_id\": \"J\",\n \"service_cost\": 2192.0\n },\n {\n \"center_id\": \"F3\",\n \"beneficiary_id\": \"K\",\n \"service_cost\": 1902.0\n },\n {\n \"center_id\": \"F3\",\n \"beneficiary_id\": \"L\",\n \"service_cost\": 1804.0\n },\n {\n \"center_id\": \"F4\",\n \"beneficiary_id\": \"A\",\n \"service_cost\": 214.0\n },\n {\n \"center_id\": \"F4\",\n \"beneficiary_id\": \"B\",\n \"service_cost\": 87.0\n },\n {\n \"center_id\": \"F4\",\n \"beneficiary_id\": \"C\",\n \"service_cost\": 338.0\n },\n {\n \"center_id\": \"F4\",\n \"beneficiary_id\": \"D\",\n \"service_cost\": 66.0\n },\n {\n \"center_id\": \"F4\",\n \"beneficiary_id\": \"E\",\n \"service_cost\": 1027.0\n },\n {\n \"center_id\": \"F4\",\n \"beneficiary_id\": \"F\",\n \"service_cost\": 475.0\n },\n {\n \"center_id\": \"F4\",\n \"beneficiary_id\": \"G\",\n \"service_cost\": 229.0\n },\n {\n \"center_id\": \"F4\",\n \"beneficiary_id\": \"H\",\n \"service_cost\": 46.0\n },\n {\n \"center_id\": \"F4\",\n \"beneficiary_id\": \"I\",\n \"service_cost\": 27.0\n },\n {\n \"center_id\": \"F4\",\n \"beneficiary_id\": \"J\",\n \"service_cost\": 755.0\n },\n {\n \"center_id\": \"F4\",\n \"beneficiary_id\": \"K\",\n \"service_cost\": 677.0\n },\n {\n \"center_id\": \"F4\",\n \"beneficiary_id\": \"L\",\n \"service_cost\": 725.0\n },\n {\n \"center_id\": \"F5\",\n \"beneficiary_id\": \"A\",\n \"service_cost\": 261.0\n },\n {\n \"center_id\": \"F5\",\n \"beneficiary_id\": \"B\",\n \"service_cost\": 83.0\n },\n {\n \"center_id\": \"F5\",\n \"beneficiary_id\": \"C\",\n \"service_cost\": 424.0\n },\n {\n \"center_id\": \"F5\",\n \"beneficiary_id\": \"D\",\n \"service_cost\": 64.0\n },\n {\n \"center_id\": \"F5\",\n \"beneficiary_id\": \"E\",\n \"service_cost\": 1075.0\n },\n {\n \"center_id\": \"F5\",\n \"beneficiary_id\": \"F\",\n \"service_cost\": 489.0\n },\n {\n \"center_id\": \"F5\",\n \"beneficiary_id\": \"G\",\n \"service_cost\": 287.0\n },\n {\n \"center_id\": \"F5\",\n \"beneficiary_id\": \"H\",\n \"service_cost\": 59.0\n },\n {\n \"center_id\": \"F5\",\n \"beneficiary_id\": \"I\",\n \"service_cost\": 58.0\n },\n {\n \"center_id\": \"F5\",\n \"beneficiary_id\": \"J\",\n \"service_cost\": 850.0\n },\n {\n \"center_id\": \"F5\",\n \"beneficiary_id\": \"K\",\n \"service_cost\": 736.0\n },\n {\n \"center_id\": \"F5\",\n \"beneficiary_id\": \"L\",\n \"service_cost\": 770.0\n },\n {\n \"center_id\": \"F6\",\n \"beneficiary_id\": \"A\",\n \"service_cost\": 709.0\n },\n {\n \"center_id\": \"F6\",\n \"beneficiary_id\": \"B\",\n \"service_cost\": 38.0\n },\n {\n \"center_id\": \"F6\",\n \"beneficiary_id\": \"C\",\n \"service_cost\": 978.0\n },\n {\n \"center_id\": \"F6\",\n \"beneficiary_id\": \"D\",\n \"service_cost\": 117.0\n },\n {\n \"center_id\": \"F6\",\n \"beneficiary_id\": \"E\",\n \"service_cost\": 701.0\n },\n {\n \"center_id\": \"F6\",\n \"beneficiary_id\": \"F\",\n \"service_cost\": 90.0\n },\n {\n \"center_id\": \"F6\",\n \"beneficiary_id\": \"G\",\n \"service_cost\": 784.0\n },\n {\n \"center_id\": \"F6\",\n \"beneficiary_id\": \"H\",\n \"service_cost\": 350.0\n },\n {\n \"center_id\": \"F6\",\n \"beneficiary_id\": \"I\",\n \"service_cost\": 676.0\n },\n {\n \"center_id\": \"F6\",\n \"beneficiary_id\": \"J\",\n \"service_cost\": 820.0\n },\n {\n \"center_id\": \"F6\",\n \"beneficiary_id\": \"K\",\n \"service_cost\": 509.0\n },\n {\n \"center_id\": \"F6\",\n \"beneficiary_id\": \"L\",\n \"service_cost\": 424.0\n }\n ]\n}\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": [ 440.0, 462.0, 468.0, 518.0, 333.0, 450.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 259.0, 66.0, 370.0, 58.0, 671.0, 283.0, 273.0, 77.0, 66.0, 315.0, 332.0, 412.0 ], [ 792.0, 42.0, 1107.0, 101.0, 1336.0, 611.0, 895.0, 394.0, 942.0, 1443.0, 1164.0, 1086.0 ], [ 1237.0, 38.0, 1588.0, 446.0, 2013.0, 1309.0, 1374.0, 844.0, 1595.0, 2192.0, 1902.0, 1804.0 ], [ 214.0, 87.0, 338.0, 66.0, 1027.0, 475.0, 229.0, 46.0, 27.0, 755.0, 677.0, 725.0 ], [ 261.0, 83.0, 424.0, 64.0, 1075.0, 489.0, 287.0, 59.0, 58.0, 850.0, 736.0, 770.0 ], [ 709.0, 38.0, 978.0, 117.0, 701.0, 90.0, 784.0, 350.0, 676.0, 820.0, 509.0, 424.0 ] ], "demands": [ 27.0, 19.0, 20.0, 29.0, 22.0, 26.0, 27.0, 10.0, 11.0, 23.0, 17.0, 27.0 ], "objective": 3622.0 }, "solution": { "open_facilities": [ 0 ], "assignments": [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] }, "obj": 3622.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 6, "num_customers": 12, "facilities": [ { "id": "F1", "opening_cost": 440.0, "capacity": 500.0 }, { "id": "F2", "opening_cost": 462.0, "capacity": 500.0 }, { "id": "F3", "opening_cost": 468.0, "capacity": 500.0 }, { "id": "F4", "opening_cost": 518.0, "capacity": 500.0 }, { "id": "F5", "opening_cost": 333.0, "capacity": 500.0 }, { "id": "F6", "opening_cost": 450.0, "capacity": 500.0 } ], "customers": [ { "id": "A", "demand": 27.0 }, { "id": "B", "demand": 19.0 }, { "id": "C", "demand": 20.0 }, { "id": "D", "demand": 29.0 }, { "id": "E", "demand": 22.0 }, { "id": "F", "demand": 26.0 }, { "id": "G", "demand": 27.0 }, { "id": "H", "demand": 10.0 }, { "id": "I", "demand": 11.0 }, { "id": "J", "demand": 23.0 }, { "id": "K", "demand": 17.0 }, { "id": "L", "demand": 27.0 } ], "connection_costs": [ { "facility": "F1", "customer": "A", "cost": 259.0 }, { "facility": "F1", "customer": "B", "cost": 66.0 }, { "facility": "F1", "customer": "C", "cost": 370.0 }, { "facility": "F1", "customer": "D", "cost": 58.0 }, { "facility": "F1", "customer": "E", "cost": 671.0 }, { "facility": "F1", "customer": "F", "cost": 283.0 }, { "facility": "F1", "customer": "G", "cost": 273.0 }, { "facility": "F1", "customer": "H", "cost": 77.0 }, { "facility": "F1", "customer": "I", "cost": 66.0 }, { "facility": "F1", "customer": "J", "cost": 315.0 }, { "facility": "F1", "customer": "K", "cost": 332.0 }, { "facility": "F1", "customer": "L", "cost": 412.0 }, { "facility": "F2", "customer": "A", "cost": 792.0 }, { "facility": "F2", "customer": "B", "cost": 42.0 }, { "facility": "F2", "customer": "C", "cost": 1107.0 }, { "facility": "F2", "customer": "D", "cost": 101.0 }, { "facility": "F2", "customer": "E", "cost": 1336.0 }, { "facility": "F2", "customer": "F", "cost": 611.0 }, { "facility": "F2", "customer": "G", "cost": 895.0 }, { "facility": "F2", "customer": "H", "cost": 394.0 }, { "facility": "F2", "customer": "I", "cost": 942.0 }, { "facility": "F2", "customer": "J", "cost": 1443.0 }, { "facility": "F2", "customer": "K", "cost": 1164.0 }, { "facility": "F2", "customer": "L", "cost": 1086.0 }, { "facility": "F3", "customer": "A", "cost": 1237.0 }, { "facility": "F3", "customer": "B", "cost": 38.0 }, { "facility": "F3", "customer": "C", "cost": 1588.0 }, { "facility": "F3", "customer": "D", "cost": 446.0 }, { "facility": "F3", "customer": "E", "cost": 2013.0 }, { "facility": "F3", "customer": "F", "cost": 1309.0 }, { "facility": "F3", "customer": "G", "cost": 1374.0 }, { "facility": "F3", "customer": "H", "cost": 844.0 }, { "facility": "F3", "customer": "I", "cost": 1595.0 }, { "facility": "F3", "customer": "J", "cost": 2192.0 }, { "facility": "F3", "customer": "K", "cost": 1902.0 }, { "facility": "F3", "customer": "L", "cost": 1804.0 }, { "facility": "F4", "customer": "A", "cost": 214.0 }, { "facility": "F4", "customer": "B", "cost": 87.0 }, { "facility": "F4", "customer": "C", "cost": 338.0 }, { "facility": "F4", "customer": "D", "cost": 66.0 }, { "facility": "F4", "customer": "E", "cost": 1027.0 }, { "facility": "F4", "customer": "F", "cost": 475.0 }, { "facility": "F4", "customer": "G", "cost": 229.0 }, { "facility": "F4", "customer": "H", "cost": 46.0 }, { "facility": "F4", "customer": "I", "cost": 27.0 }, { "facility": "F4", "customer": "J", "cost": 755.0 }, { "facility": "F4", "customer": "K", "cost": 677.0 }, { "facility": "F4", "customer": "L", "cost": 725.0 }, { "facility": "F5", "customer": "A", "cost": 261.0 }, { "facility": "F5", "customer": "B", "cost": 83.0 }, { "facility": "F5", "customer": "C", "cost": 424.0 }, { "facility": "F5", "customer": "D", "cost": 64.0 }, { "facility": "F5", "customer": "E", "cost": 1075.0 }, { "facility": "F5", "customer": "F", "cost": 489.0 }, { "facility": "F5", "customer": "G", "cost": 287.0 }, { "facility": "F5", "customer": "H", "cost": 59.0 }, { "facility": "F5", "customer": "I", "cost": 58.0 }, { "facility": "F5", "customer": "J", "cost": 850.0 }, { "facility": "F5", "customer": "K", "cost": 736.0 }, { "facility": "F5", "customer": "L", "cost": 770.0 }, { "facility": "F6", "customer": "A", "cost": 709.0 }, { "facility": "F6", "customer": "B", "cost": 38.0 }, { "facility": "F6", "customer": "C", "cost": 978.0 }, { "facility": "F6", "customer": "D", "cost": 117.0 }, { "facility": "F6", "customer": "E", "cost": 701.0 }, { "facility": "F6", "customer": "F", "cost": 90.0 }, { "facility": "F6", "customer": "G", "cost": 784.0 }, { "facility": "F6", "customer": "H", "cost": 350.0 }, { "facility": "F6", "customer": "I", "cost": 676.0 }, { "facility": "F6", "customer": "J", "cost": 820.0 }, { "facility": "F6", "customer": "K", "cost": 509.0 }, { "facility": "F6", "customer": "L", "cost": 424.0 } ], "objective": 3622.0 }, "solution_variant": { "selected": [ "F1" ], "assignments": [ "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1" ] }, "context_index": 47, "input_format": "json", "input_index_base": "names" }, { "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\nThere are 4 laundry rooms and 9 dorms in this instance.\n\n**Laundry Rooms**\n| laundry_room_id | operating_cost | laundry_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\n**Dorms**\n| dorm_id | dorm_demand |\n|---|---|\n| 1 | 24.0 |\n| 2 | 17.0 |\n| 3 | 17.0 |\n| 4 | 18.0 |\n| 5 | 27.0 |\n| 6 | 20.0 |\n| 7 | 24.0 |\n| 8 | 27.0 |\n| 9 | 22.0 |\n\n**Assignment Cost**\n| laundry_room_id | dorm_id | assignment_cost |\n|---|---|---|\n| F1 | 1 | 221.0 |\n| F1 | 2 | 590.0 |\n| F1 | 3 | 577.0 |\n| F1 | 4 | 166.0 |\n| F1 | 5 | 107.0 |\n| F1 | 6 | 403.0 |\n| F1 | 7 | 506.0 |\n| F1 | 8 | 401.0 |\n| F1 | 9 | 378.0 |\n| F2 | 1 | 643.0 |\n| F2 | 2 | 811.0 |\n| F2 | 3 | 1668.0 |\n| F2 | 4 | 1062.0 |\n| F2 | 5 | 1300.0 |\n| F2 | 6 | 113.0 |\n| F2 | 7 | 893.0 |\n| F2 | 8 | 754.0 |\n| F2 | 9 | 857.0 |\n| F3 | 1 | 173.0 |\n| F3 | 2 | 903.0 |\n| F3 | 3 | 673.0 |\n| F3 | 4 | 544.0 |\n| F3 | 5 | 416.0 |\n| F3 | 6 | 578.0 |\n| F3 | 7 | 840.0 |\n| F3 | 8 | 701.0 |\n| F3 | 9 | 704.0 |\n| F4 | 1 | 403.0 |\n| F4 | 2 | 952.0 |\n| F4 | 3 | 1342.0 |\n| F4 | 4 | 886.0 |\n| F4 | 5 | 1023.0 |\n| F4 | 6 | 471.0 |\n| F4 | 7 | 947.0 |\n| F4 | 8 | 783.0 |\n| F4 | 9 | 841.0 |\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": [ 300.0, 300.0, 300.0, 300.0 ], "capacities": [ 500.0, 500.0, 500.0, 500.0 ], "connection_costs": [ [ 221.0, 590.0, 577.0, 166.0, 107.0, 403.0, 506.0, 401.0, 378.0 ], [ 643.0, 811.0, 1668.0, 1062.0, 1300.0, 113.0, 893.0, 754.0, 857.0 ], [ 173.0, 903.0, 673.0, 544.0, 416.0, 578.0, 840.0, 701.0, 704.0 ], [ 403.0, 952.0, 1342.0, 886.0, 1023.0, 471.0, 947.0, 783.0, 841.0 ] ], "demands": [ 24.0, 17.0, 17.0, 18.0, 27.0, 20.0, 24.0, 27.0, 22.0 ], "objective": 3649.0 }, "solution": { "open_facilities": [ 0 ], "assignments": [ 0, 0, 0, 0, 0, 0, 0, 0, 0 ] }, "obj": 3649.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 4, "num_customers": 9, "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 } ], "customers": [ { "id": 1, "demand": 24.0 }, { "id": 2, "demand": 17.0 }, { "id": 3, "demand": 17.0 }, { "id": 4, "demand": 18.0 }, { "id": 5, "demand": 27.0 }, { "id": 6, "demand": 20.0 }, { "id": 7, "demand": 24.0 }, { "id": 8, "demand": 27.0 }, { "id": 9, "demand": 22.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 221.0 }, { "facility": "F1", "customer": 2, "cost": 590.0 }, { "facility": "F1", "customer": 3, "cost": 577.0 }, { "facility": "F1", "customer": 4, "cost": 166.0 }, { "facility": "F1", "customer": 5, "cost": 107.0 }, { "facility": "F1", "customer": 6, "cost": 403.0 }, { "facility": "F1", "customer": 7, "cost": 506.0 }, { "facility": "F1", "customer": 8, "cost": 401.0 }, { "facility": "F1", "customer": 9, "cost": 378.0 }, { "facility": "F2", "customer": 1, "cost": 643.0 }, { "facility": "F2", "customer": 2, "cost": 811.0 }, { "facility": "F2", "customer": 3, "cost": 1668.0 }, { "facility": "F2", "customer": 4, "cost": 1062.0 }, { "facility": "F2", "customer": 5, "cost": 1300.0 }, { "facility": "F2", "customer": 6, "cost": 113.0 }, { "facility": "F2", "customer": 7, "cost": 893.0 }, { "facility": "F2", "customer": 8, "cost": 754.0 }, { "facility": "F2", "customer": 9, "cost": 857.0 }, { "facility": "F3", "customer": 1, "cost": 173.0 }, { "facility": "F3", "customer": 2, "cost": 903.0 }, { "facility": "F3", "customer": 3, "cost": 673.0 }, { "facility": "F3", "customer": 4, "cost": 544.0 }, { "facility": "F3", "customer": 5, "cost": 416.0 }, { "facility": "F3", "customer": 6, "cost": 578.0 }, { "facility": "F3", "customer": 7, "cost": 840.0 }, { "facility": "F3", "customer": 8, "cost": 701.0 }, { "facility": "F3", "customer": 9, "cost": 704.0 }, { "facility": "F4", "customer": 1, "cost": 403.0 }, { "facility": "F4", "customer": 2, "cost": 952.0 }, { "facility": "F4", "customer": 3, "cost": 1342.0 }, { "facility": "F4", "customer": 4, "cost": 886.0 }, { "facility": "F4", "customer": 5, "cost": 1023.0 }, { "facility": "F4", "customer": 6, "cost": 471.0 }, { "facility": "F4", "customer": 7, "cost": 947.0 }, { "facility": "F4", "customer": 8, "cost": 783.0 }, { "facility": "F4", "customer": 9, "cost": 841.0 } ], "objective": 3649.0 }, "solution_variant": { "selected": [ "F1" ], "assignments": [ "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1", "F1" ] }, "context_index": 48, "input_format": "markdown_table", "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\nBelow, we list 5 candidate branches and 11 neighborhoods.\nWe can open branch F1 at a cost of 400.0 with capacity 300.0.\nWe can open branch F2 at a cost of 400.0 with capacity 300.0.\nWe can open branch F3 at a cost of 400.0 with capacity 300.0.\nWe can open branch F4 at a cost of 400.0 with capacity 300.0.\nWe can open branch F5 at a cost of 400.0 with capacity 300.0.\nWe must serve neighborhood 0 with 24.0 patrons from exactly one open branch.\nWe must serve neighborhood 1 with 13.0 patrons from exactly one open branch.\nWe must serve neighborhood 2 with 12.0 patrons from exactly one open branch.\nWe must serve neighborhood 3 with 22.0 patrons from exactly one open branch.\nWe must serve neighborhood 4 with 26.0 patrons from exactly one open branch.\nWe must serve neighborhood 5 with 27.0 patrons from exactly one open branch.\nWe must serve neighborhood 6 with 18.0 patrons from exactly one open branch.\nWe must serve neighborhood 7 with 20.0 patrons from exactly one open branch.\nWe must serve neighborhood 8 with 11.0 patrons from exactly one open branch.\nWe must serve neighborhood 9 with 12.0 patrons from exactly one open branch.\nWe must serve neighborhood 10 with 23.0 patrons from exactly one open branch.\nWe estimate a travel cost of 1185.0 if we send neighborhood 0 to branch F1.\nWe estimate a travel cost of 1000.0 if we send neighborhood 1 to branch F1.\nWe estimate a travel cost of 253.0 if we send neighborhood 2 to branch F1.\nWe estimate a travel cost of 1286.0 if we send neighborhood 3 to branch F1.\nWe estimate a travel cost of 53.0 if we send neighborhood 4 to branch F1.\nWe estimate a travel cost of 776.0 if we send neighborhood 5 to branch F1.\nWe estimate a travel cost of 43.0 if we send neighborhood 6 to branch F1.\nWe estimate a travel cost of 393.0 if we send neighborhood 7 to branch F1.\nWe estimate a travel cost of 86.0 if we send neighborhood 8 to branch F1.\nWe estimate a travel cost of 829.0 if we send neighborhood 9 to branch F1.\nWe estimate a travel cost of 1118.0 if we send neighborhood 10 to branch F1.\nWe estimate a travel cost of 816.0 if we send neighborhood 0 to branch F2.\nWe estimate a travel cost of 312.0 if we send neighborhood 1 to branch F2.\nWe estimate a travel cost of 53.0 if we send neighborhood 2 to branch F2.\nWe estimate a travel cost of 1438.0 if we send neighborhood 3 to branch F2.\nWe estimate a travel cost of 804.0 if we send neighborhood 4 to branch F2.\nWe estimate a travel cost of 91.0 if we send neighborhood 5 to branch F2.\nWe estimate a travel cost of 63.0 if we send neighborhood 6 to branch F2.\nWe estimate a travel cost of 150.0 if we send neighborhood 7 to branch F2.\nWe estimate a travel cost of 1002.0 if we send neighborhood 8 to branch F2.\nWe estimate a travel cost of 628.0 if we send neighborhood 9 to branch F2.\nWe estimate a travel cost of 686.0 if we send neighborhood 10 to branch F2.\nWe estimate a travel cost of 818.0 if we send neighborhood 0 to branch F3.\nWe estimate a travel cost of 712.0 if we send neighborhood 1 to branch F3.\nWe estimate a travel cost of 147.0 if we send neighborhood 2 to branch F3.\nWe estimate a travel cost of 829.0 if we send neighborhood 3 to branch F3.\nWe estimate a travel cost of 107.0 if we send neighborhood 4 to branch F3.\nWe estimate a travel cost of 570.0 if we send neighborhood 5 to branch F3.\nWe estimate a travel cost of 37.0 if we send neighborhood 6 to branch F3.\nWe estimate a travel cost of 220.0 if we send neighborhood 7 to branch F3.\nWe estimate a travel cost of 191.0 if we send neighborhood 8 to branch F3.\nWe estimate a travel cost of 487.0 if we send neighborhood 9 to branch F3.\nWe estimate a travel cost of 771.0 if we send neighborhood 10 to branch F3.\nWe estimate a travel cost of 1209.0 if we send neighborhood 0 to branch F4.\nWe estimate a travel cost of 727.0 if we send neighborhood 1 to branch F4.\nWe estimate a travel cost of 66.0 if we send neighborhood 2 to branch F4.\nWe estimate a travel cost of 1779.0 if we send neighborhood 3 to branch F4.\nWe estimate a travel cost of 915.0 if we send neighborhood 4 to branch F4.\nWe estimate a travel cost of 271.0 if we send neighborhood 5 to branch F4.\nWe estimate a travel cost of 63.0 if we send neighborhood 6 to branch F4.\nWe estimate a travel cost of 263.0 if we send neighborhood 7 to branch F4.\nWe estimate a travel cost of 1113.0 if we send neighborhood 8 to branch F4.\nWe estimate a travel cost of 966.0 if we send neighborhood 9 to branch F4.\nWe estimate a travel cost of 1081.0 if we send neighborhood 10 to branch F4.\nWe estimate a travel cost of 615.0 if we send neighborhood 0 to branch F5.\nWe estimate a travel cost of 399.0 if we send neighborhood 1 to branch F5.\nWe estimate a travel cost of 30.0 if we send neighborhood 2 to branch F5.\nWe estimate a travel cost of 1051.0 if we send neighborhood 3 to branch F5.\nWe estimate a travel cost of 489.0 if we send neighborhood 4 to branch F5.\nWe estimate a travel cost of 287.0 if we send neighborhood 5 to branch F5.\nWe estimate a travel cost of 42.0 if we send neighborhood 6 to branch F5.\nWe estimate a travel cost of 43.0 if we send neighborhood 7 to branch F5.\nWe estimate a travel cost of 673.0 if we send neighborhood 8 to branch F5.\nWe estimate a travel cost of 269.0 if we send neighborhood 9 to branch F5.\nWe estimate a travel cost of 524.0 if we send neighborhood 10 to branch F5.\nWe’ll use these figures to choose which branches to open and how to assign neighborhoods to minimize the total opening plus travel cost.\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": [ 400.0, 400.0, 400.0, 400.0, 400.0 ], "capacities": [ 300.0, 300.0, 300.0, 300.0, 300.0 ], "connection_costs": [ [ 1185.0, 1000.0, 253.0, 1286.0, 53.0, 776.0, 43.0, 393.0, 86.0, 829.0, 1118.0 ], [ 816.0, 312.0, 53.0, 1438.0, 804.0, 91.0, 63.0, 150.0, 1002.0, 628.0, 686.0 ], [ 818.0, 712.0, 147.0, 829.0, 107.0, 570.0, 37.0, 220.0, 191.0, 487.0, 771.0 ], [ 1209.0, 727.0, 66.0, 1779.0, 915.0, 271.0, 63.0, 263.0, 1113.0, 966.0, 1081.0 ], [ 615.0, 399.0, 30.0, 1051.0, 489.0, 287.0, 42.0, 43.0, 673.0, 269.0, 524.0 ] ], "demands": [ 24.0, 13.0, 12.0, 22.0, 26.0, 27.0, 18.0, 20.0, 11.0, 12.0, 23.0 ], "objective": 4131.0 }, "solution": { "open_facilities": [ 2, 4 ], "assignments": [ 4, 4, 4, 2, 2, 4, 2, 4, 2, 4, 4 ] }, "obj": 4131.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 5, "num_customers": 11, "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 } ], "customers": [ { "id": 0, "demand": 24.0 }, { "id": 1, "demand": 13.0 }, { "id": 2, "demand": 12.0 }, { "id": 3, "demand": 22.0 }, { "id": 4, "demand": 26.0 }, { "id": 5, "demand": 27.0 }, { "id": 6, "demand": 18.0 }, { "id": 7, "demand": 20.0 }, { "id": 8, "demand": 11.0 }, { "id": 9, "demand": 12.0 }, { "id": 10, "demand": 23.0 } ], "connection_costs": [ { "facility": "F1", "customer": 0, "cost": 1185.0 }, { "facility": "F1", "customer": 1, "cost": 1000.0 }, { "facility": "F1", "customer": 2, "cost": 253.0 }, { "facility": "F1", "customer": 3, "cost": 1286.0 }, { "facility": "F1", "customer": 4, "cost": 53.0 }, { "facility": "F1", "customer": 5, "cost": 776.0 }, { "facility": "F1", "customer": 6, "cost": 43.0 }, { "facility": "F1", "customer": 7, "cost": 393.0 }, { "facility": "F1", "customer": 8, "cost": 86.0 }, { "facility": "F1", "customer": 9, "cost": 829.0 }, { "facility": "F1", "customer": 10, "cost": 1118.0 }, { "facility": "F2", "customer": 0, "cost": 816.0 }, { "facility": "F2", "customer": 1, "cost": 312.0 }, { "facility": "F2", "customer": 2, "cost": 53.0 }, { "facility": "F2", "customer": 3, "cost": 1438.0 }, { "facility": "F2", "customer": 4, "cost": 804.0 }, { "facility": "F2", "customer": 5, "cost": 91.0 }, { "facility": "F2", "customer": 6, "cost": 63.0 }, { "facility": "F2", "customer": 7, "cost": 150.0 }, { "facility": "F2", "customer": 8, "cost": 1002.0 }, { "facility": "F2", "customer": 9, "cost": 628.0 }, { "facility": "F2", "customer": 10, "cost": 686.0 }, { "facility": "F3", "customer": 0, "cost": 818.0 }, { "facility": "F3", "customer": 1, "cost": 712.0 }, { "facility": "F3", "customer": 2, "cost": 147.0 }, { "facility": "F3", "customer": 3, "cost": 829.0 }, { "facility": "F3", "customer": 4, "cost": 107.0 }, { "facility": "F3", "customer": 5, "cost": 570.0 }, { "facility": "F3", "customer": 6, "cost": 37.0 }, { "facility": "F3", "customer": 7, "cost": 220.0 }, { "facility": "F3", "customer": 8, "cost": 191.0 }, { "facility": "F3", "customer": 9, "cost": 487.0 }, { "facility": "F3", "customer": 10, "cost": 771.0 }, { "facility": "F4", "customer": 0, "cost": 1209.0 }, { "facility": "F4", "customer": 1, "cost": 727.0 }, { "facility": "F4", "customer": 2, "cost": 66.0 }, { "facility": "F4", "customer": 3, "cost": 1779.0 }, { "facility": "F4", "customer": 4, "cost": 915.0 }, { "facility": "F4", "customer": 5, "cost": 271.0 }, { "facility": "F4", "customer": 6, "cost": 63.0 }, { "facility": "F4", "customer": 7, "cost": 263.0 }, { "facility": "F4", "customer": 8, "cost": 1113.0 }, { "facility": "F4", "customer": 9, "cost": 966.0 }, { "facility": "F4", "customer": 10, "cost": 1081.0 }, { "facility": "F5", "customer": 0, "cost": 615.0 }, { "facility": "F5", "customer": 1, "cost": 399.0 }, { "facility": "F5", "customer": 2, "cost": 30.0 }, { "facility": "F5", "customer": 3, "cost": 1051.0 }, { "facility": "F5", "customer": 4, "cost": 489.0 }, { "facility": "F5", "customer": 5, "cost": 287.0 }, { "facility": "F5", "customer": 6, "cost": 42.0 }, { "facility": "F5", "customer": 7, "cost": 43.0 }, { "facility": "F5", "customer": 8, "cost": 673.0 }, { "facility": "F5", "customer": 9, "cost": 269.0 }, { "facility": "F5", "customer": 10, "cost": 524.0 } ], "objective": 4131.0 }, "solution_variant": { "selected": [ "F3", "F5" ], "assignments": [ "F5", "F5", "F5", "F3", "F3", "F5", "F3", "F5", "F3", "F5", "F5" ] }, "context_index": 49, "input_format": "nl", "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 6 candidate stores and 14 households to consider.\nStore F1: opening expense 258.0, stocking capacity 366.0.\nStore F2: opening expense 128.0, stocking capacity 314.0.\nStore F3: opening expense 296.0, stocking capacity 504.0.\nStore F4: opening expense 329.0, stocking capacity 456.0.\nStore F5: opening expense 179.0, stocking capacity 549.0.\nStore F6: opening expense 321.0, stocking capacity 316.0.\nHousehold 1: demand 23.0.\nHousehold 2: demand 48.0.\nHousehold 3: demand 15.0.\nHousehold 4: demand 14.0.\nHousehold 5: demand 23.0.\nHousehold 6: demand 33.0.\nHousehold 7: demand 43.0.\nHousehold 8: demand 47.0.\nHousehold 9: demand 20.0.\nHousehold 10: demand 38.0.\nHousehold 11: demand 21.0.\nHousehold 12: demand 25.0.\nHousehold 13: demand 19.0.\nHousehold 14: demand 37.0.\nServing household 1 from store F1 costs 418.0.\nServing household 2 from store F1 costs 288.0.\nServing household 3 from store F1 costs 379.0.\nServing household 4 from store F1 costs 122.0.\nServing household 5 from store F1 costs 344.0.\nServing household 6 from store F1 costs 393.0.\nServing household 7 from store F1 costs 654.0.\nServing household 8 from store F1 costs 640.0.\nServing household 9 from store F1 costs 79.0.\nServing household 10 from store F1 costs 94.0.\nServing household 11 from store F1 costs 422.0.\nServing household 12 from store F1 costs 303.0.\nServing household 13 from store F1 costs 362.0.\nServing household 14 from store F1 costs 468.0.\nServing household 1 from store F2 costs 34.0.\nServing household 2 from store F2 costs 338.0.\nServing household 3 from store F2 costs 523.0.\nServing household 4 from store F2 costs 319.0.\nServing household 5 from store F2 costs 712.0.\nServing household 6 from store F2 costs 486.0.\nServing household 7 from store F2 costs 812.0.\nServing household 8 from store F2 costs 482.0.\nServing household 9 from store F2 costs 426.0.\nServing household 10 from store F2 costs 392.0.\nServing household 11 from store F2 costs 507.0.\nServing household 12 from store F2 costs 145.0.\nServing household 13 from store F2 costs 104.0.\nServing household 14 from store F2 costs 467.0.\nServing household 1 from store F3 costs 369.0.\nServing household 2 from store F3 costs 33.0.\nServing household 3 from store F3 costs 181.0.\nServing household 4 from store F3 costs 376.0.\nServing household 5 from store F3 costs 502.0.\nServing household 6 from store F3 costs 140.0.\nServing household 7 from store F3 costs 466.0.\nServing household 8 from store F3 costs 328.0.\nServing household 9 from store F3 costs 288.0.\nServing household 10 from store F3 costs 244.0.\nServing household 11 from store F3 costs 162.0.\nServing household 12 from store F3 costs 202.0.\nServing household 13 from store F3 costs 411.0.\nServing household 14 from store F3 costs 156.0.\nServing household 1 from store F4 costs 409.0.\nServing household 2 from store F4 costs 374.0.\nServing household 3 from store F4 costs 467.0.\nServing household 4 from store F4 costs 643.0.\nServing household 5 from store F4 costs 846.0.\nServing household 6 from store F4 costs 405.0.\nServing household 7 from store F4 costs 648.0.\nServing household 8 from store F4 costs 104.0.\nServing household 9 from store F4 costs 622.0.\nServing household 10 from store F4 costs 576.0.\nServing household 11 from store F4 costs 401.0.\nServing household 12 from store F4 costs 361.0.\nServing household 13 from store F4 costs 519.0.\nServing household 14 from store F4 costs 297.0.\nServing household 1 from store F5 costs 782.0.\nServing household 2 from store F5 costs 422.0.\nServing household 3 from store F5 costs 240.0.\nServing household 4 from store F5 costs 700.0.\nServing household 5 from store F5 costs 493.0.\nServing household 6 from store F5 costs 274.0.\nServing household 7 from store F5 costs 61.0.\nServing household 8 from store F5 costs 533.0.\nServing household 9 from store F5 costs 518.0.\nServing household 10 from store F5 costs 501.0.\nServing household 11 from store F5 costs 256.0.\nServing household 12 from store F5 costs 614.0.\nServing household 13 from store F5 costs 817.0.\nServing household 14 from store F5 costs 334.0.\nServing household 1 from store F6 costs 603.0.\nServing household 2 from store F6 costs 357.0.\nServing household 3 from store F6 costs 317.0.\nServing household 4 from store F6 costs 701.0.\nServing household 5 from store F6 costs 730.0.\nServing household 6 from store F6 costs 268.0.\nServing household 7 from store F6 costs 381.0.\nServing household 8 from store F6 costs 187.0.\nServing household 9 from store F6 costs 595.0.\nServing household 10 from store F6 costs 555.0.\nServing household 11 from store F6 costs 245.0.\nServing household 12 from store F6 costs 478.0.\nServing household 13 from store F6 costs 686.0.\nServing household 14 from store F6 costs 172.0.\nUse these details to pick stores and assignments that serve all 14 households within capacities while minimizing opening plus travel costs.\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": [ 258.0, 128.0, 296.0, 329.0, 179.0, 321.0 ], "capacities": [ 366.0, 314.0, 504.0, 456.0, 549.0, 316.0 ], "connection_costs": [ [ 418.0, 288.0, 379.0, 122.0, 344.0, 393.0, 654.0, 640.0, 79.0, 94.0, 422.0, 303.0, 362.0, 468.0 ], [ 34.0, 338.0, 523.0, 319.0, 712.0, 486.0, 812.0, 482.0, 426.0, 392.0, 507.0, 145.0, 104.0, 467.0 ], [ 369.0, 33.0, 181.0, 376.0, 502.0, 140.0, 466.0, 328.0, 288.0, 244.0, 162.0, 202.0, 411.0, 156.0 ], [ 409.0, 374.0, 467.0, 643.0, 846.0, 405.0, 648.0, 104.0, 622.0, 576.0, 401.0, 361.0, 519.0, 297.0 ], [ 782.0, 422.0, 240.0, 700.0, 493.0, 274.0, 61.0, 533.0, 518.0, 501.0, 256.0, 614.0, 817.0, 334.0 ], [ 603.0, 357.0, 317.0, 701.0, 730.0, 268.0, 381.0, 187.0, 595.0, 555.0, 245.0, 478.0, 686.0, 172.0 ] ], "demands": [ 23.0, 48.0, 15.0, 14.0, 23.0, 33.0, 43.0, 47.0, 20.0, 38.0, 21.0, 25.0, 19.0, 37.0 ], "objective": 2844.0 }, "solution": { "open_facilities": [ 0, 1, 2, 4 ], "assignments": [ 1, 2, 2, 0, 0, 2, 4, 2, 0, 0, 2, 1, 1, 2 ] }, "obj": 2844.0, "instance_variant": { "problem_type": "CFLP", "num_facilities": 6, "num_customers": 14, "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": 329.0, "capacity": 456.0 }, { "id": "F5", "opening_cost": 179.0, "capacity": 549.0 }, { "id": "F6", "opening_cost": 321.0, "capacity": 316.0 } ], "customers": [ { "id": 1, "demand": 23.0 }, { "id": 2, "demand": 48.0 }, { "id": 3, "demand": 15.0 }, { "id": 4, "demand": 14.0 }, { "id": 5, "demand": 23.0 }, { "id": 6, "demand": 33.0 }, { "id": 7, "demand": 43.0 }, { "id": 8, "demand": 47.0 }, { "id": 9, "demand": 20.0 }, { "id": 10, "demand": 38.0 }, { "id": 11, "demand": 21.0 }, { "id": 12, "demand": 25.0 }, { "id": 13, "demand": 19.0 }, { "id": 14, "demand": 37.0 } ], "connection_costs": [ { "facility": "F1", "customer": 1, "cost": 418.0 }, { "facility": "F1", "customer": 2, "cost": 288.0 }, { "facility": "F1", "customer": 3, "cost": 379.0 }, { "facility": "F1", "customer": 4, "cost": 122.0 }, { "facility": "F1", "customer": 5, "cost": 344.0 }, { "facility": "F1", "customer": 6, "cost": 393.0 }, { "facility": "F1", "customer": 7, "cost": 654.0 }, { "facility": "F1", "customer": 8, "cost": 640.0 }, { "facility": "F1", "customer": 9, "cost": 79.0 }, { "facility": "F1", "customer": 10, "cost": 94.0 }, { "facility": "F1", "customer": 11, "cost": 422.0 }, { "facility": "F1", "customer": 12, "cost": 303.0 }, { "facility": "F1", "customer": 13, "cost": 362.0 }, { "facility": "F1", "customer": 14, "cost": 468.0 }, { "facility": "F2", "customer": 1, "cost": 34.0 }, { "facility": "F2", "customer": 2, "cost": 338.0 }, { "facility": "F2", "customer": 3, "cost": 523.0 }, { "facility": "F2", "customer": 4, "cost": 319.0 }, { "facility": "F2", "customer": 5, "cost": 712.0 }, { "facility": "F2", "customer": 6, "cost": 486.0 }, { "facility": "F2", "customer": 7, "cost": 812.0 }, { "facility": "F2", "customer": 8, "cost": 482.0 }, { "facility": "F2", "customer": 9, "cost": 426.0 }, { "facility": "F2", "customer": 10, "cost": 392.0 }, { "facility": "F2", "customer": 11, "cost": 507.0 }, { "facility": "F2", "customer": 12, "cost": 145.0 }, { "facility": "F2", "customer": 13, "cost": 104.0 }, { "facility": "F2", "customer": 14, "cost": 467.0 }, { "facility": "F3", "customer": 1, "cost": 369.0 }, { "facility": "F3", "customer": 2, "cost": 33.0 }, { "facility": "F3", "customer": 3, "cost": 181.0 }, { "facility": "F3", "customer": 4, "cost": 376.0 }, { "facility": "F3", "customer": 5, "cost": 502.0 }, { "facility": "F3", "customer": 6, "cost": 140.0 }, { "facility": "F3", "customer": 7, "cost": 466.0 }, { "facility": "F3", "customer": 8, "cost": 328.0 }, { "facility": "F3", "customer": 9, "cost": 288.0 }, { "facility": "F3", "customer": 10, "cost": 244.0 }, { "facility": "F3", "customer": 11, "cost": 162.0 }, { "facility": "F3", "customer": 12, "cost": 202.0 }, { "facility": "F3", "customer": 13, "cost": 411.0 }, { "facility": "F3", "customer": 14, "cost": 156.0 }, { "facility": "F4", "customer": 1, "cost": 409.0 }, { "facility": "F4", "customer": 2, "cost": 374.0 }, { "facility": "F4", "customer": 3, "cost": 467.0 }, { "facility": "F4", "customer": 4, "cost": 643.0 }, { "facility": "F4", "customer": 5, "cost": 846.0 }, { "facility": "F4", "customer": 6, "cost": 405.0 }, { "facility": "F4", "customer": 7, "cost": 648.0 }, { "facility": "F4", "customer": 8, "cost": 104.0 }, { "facility": "F4", "customer": 9, "cost": 622.0 }, { "facility": "F4", "customer": 10, "cost": 576.0 }, { "facility": "F4", "customer": 11, "cost": 401.0 }, { "facility": "F4", "customer": 12, "cost": 361.0 }, { "facility": "F4", "customer": 13, "cost": 519.0 }, { "facility": "F4", "customer": 14, "cost": 297.0 }, { "facility": "F5", "customer": 1, "cost": 782.0 }, { "facility": "F5", "customer": 2, "cost": 422.0 }, { "facility": "F5", "customer": 3, "cost": 240.0 }, { "facility": "F5", "customer": 4, "cost": 700.0 }, { "facility": "F5", "customer": 5, "cost": 493.0 }, { "facility": "F5", "customer": 6, "cost": 274.0 }, { "facility": "F5", "customer": 7, "cost": 61.0 }, { "facility": "F5", "customer": 8, "cost": 533.0 }, { "facility": "F5", "customer": 9, "cost": 518.0 }, { "facility": "F5", "customer": 10, "cost": 501.0 }, { "facility": "F5", "customer": 11, "cost": 256.0 }, { "facility": "F5", "customer": 12, "cost": 614.0 }, { "facility": "F5", "customer": 13, "cost": 817.0 }, { "facility": "F5", "customer": 14, "cost": 334.0 }, { "facility": "F6", "customer": 1, "cost": 603.0 }, { "facility": "F6", "customer": 2, "cost": 357.0 }, { "facility": "F6", "customer": 3, "cost": 317.0 }, { "facility": "F6", "customer": 4, "cost": 701.0 }, { "facility": "F6", "customer": 5, "cost": 730.0 }, { "facility": "F6", "customer": 6, "cost": 268.0 }, { "facility": "F6", "customer": 7, "cost": 381.0 }, { "facility": "F6", "customer": 8, "cost": 187.0 }, { "facility": "F6", "customer": 9, "cost": 595.0 }, { "facility": "F6", "customer": 10, "cost": 555.0 }, { "facility": "F6", "customer": 11, "cost": 245.0 }, { "facility": "F6", "customer": 12, "cost": 478.0 }, { "facility": "F6", "customer": 13, "cost": 686.0 }, { "facility": "F6", "customer": 14, "cost": 172.0 } ], "objective": 2844.0 }, "solution_variant": { "selected": [ "F1", "F2", "F3", "F5" ], "assignments": [ "F2", "F3", "F3", "F1", "F1", "F3", "F5", "F3", "F1", "F1", "F3", "F2", "F2", "F3" ] }, "context_index": 50, "input_format": "nl", "input_index_base": 1 } ]