{"problem_id":"INV-001","family":"inventory","split":"development","interactive":true,"difficulty":"easy","language":"en","template_id":"D-A","seed":25001,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 192 currency units. Storage holds at most 19 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 192\nCAPACITY: 19\nCOVER_REQUIRED: 0\nSKU S1 demand=6,4,6 pack=1 cost=9 hold=1 short=8 stock=2\nSKU S2 demand=2,7,2 pack=2 cost=5 hold=1 short=7 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 192, \"warehouse_capacity\": 19, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 4, 6], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 8, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 7, 2], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 192 واحد پول و ظرفیت انبار 19 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 192\nCAPACITY: 19\nCOVER_REQUIRED: 0\nSKU S1 demand=6,4,6 pack=1 cost=9 hold=1 short=8 stock=2\nSKU S2 demand=2,7,2 pack=2 cost=5 hold=1 short=7 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 192, \"warehouse_capacity\": 19, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 4, 6], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 8, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 7, 2], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 192,\n \"warehouse_capacity\": 19,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 6,\n 4,\n 6\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 8,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 7,\n 2\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 5,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":192,"warehouse_capacity":19,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[6,4,6],"initial_stock":2,"unit_cost":9,"holding_cost":1,"shortage_cost":8,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,7,2],"initial_stock":2,"unit_cost":5,"holding_cost":1,"shortage_cost":7,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":159.0,"gold_bound":159.0,"gold_solution":{"family":"inventory","status":"optimal","objective":159.0,"bound":159.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":0},{"sku_id":"S1","period":3,"qty":0},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":6},{"sku_id":"S2","period":3,"qty":2}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"c064f38a5aa2b27c","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-002","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-B","seed":25002,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 111 currency units. Storage holds at most 19 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 111\nCAPACITY: 19\nCOVER_REQUIRED: 0\nSKU S1 demand=5,4,3 pack=3 cost=4 hold=3 short=9 stock=2\nSKU S2 demand=7,4,3 pack=2 cost=4 hold=3 short=8 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 111, \"warehouse_capacity\": 19, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 3], \"initial_stock\": 2, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 9, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [7, 4, 3], \"initial_stock\": 3, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 111 واحد پول و ظرفیت انبار 19 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 111\nCAPACITY: 19\nCOVER_REQUIRED: 0\nSKU S1 demand=5,4,3 pack=3 cost=4 hold=3 short=9 stock=2\nSKU S2 demand=7,4,3 pack=2 cost=4 hold=3 short=8 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 111, \"warehouse_capacity\": 19, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 3], \"initial_stock\": 2, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 9, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [7, 4, 3], \"initial_stock\": 3, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 111,\n \"warehouse_capacity\": 19,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 4,\n 3\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 4,\n \"holding_cost\": 3,\n \"shortage_cost\": 9,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 7,\n 4,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 4,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":111,"warehouse_capacity":19,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,4,3],"initial_stock":2,"unit_cost":4,"holding_cost":3,"shortage_cost":9,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[7,4,3],"initial_stock":3,"unit_cost":4,"holding_cost":3,"shortage_cost":8,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":93.0,"gold_bound":93.0,"gold_solution":{"family":"inventory","status":"optimal","objective":93.0,"bound":93.0,"orders":[{"sku_id":"S1","period":1,"qty":3},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":3},{"sku_id":"S2","period":1,"qty":4},{"sku_id":"S2","period":2,"qty":4},{"sku_id":"S2","period":3,"qty":2}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"5c4c80b9b28d8fdd","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-003","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"en","template_id":"D-C","seed":25003,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 311 currency units. Storage holds at most 31 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 311\nCAPACITY: 31\nCOVER_REQUIRED: 0\nSKU S1 demand=2,6,6 pack=1 cost=8 hold=3 short=14 stock=2\nSKU S2 demand=8,3,3 pack=1 cost=9 hold=3 short=12 stock=3\nSKU S3 demand=7,8,6 pack=2 cost=5 hold=3 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 311, \"warehouse_capacity\": 31, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 6, 6], \"initial_stock\": 2, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 3, 3], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 8, 6], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 311 واحد پول و ظرفیت انبار 31 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 311\nCAPACITY: 31\nCOVER_REQUIRED: 0\nSKU S1 demand=2,6,6 pack=1 cost=8 hold=3 short=14 stock=2\nSKU S2 demand=8,3,3 pack=1 cost=9 hold=3 short=12 stock=3\nSKU S3 demand=7,8,6 pack=2 cost=5 hold=3 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 311, \"warehouse_capacity\": 31, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 6, 6], \"initial_stock\": 2, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 3, 3], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 8, 6], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 311,\n \"warehouse_capacity\": 31,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 2,\n 6,\n 6\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 14,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 8,\n 3,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 3,\n \"shortage_cost\": 12,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 7,\n 8,\n 6\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 11,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":311,"warehouse_capacity":31,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[2,6,6],"initial_stock":2,"unit_cost":8,"holding_cost":3,"shortage_cost":14,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[8,3,3],"initial_stock":3,"unit_cost":9,"holding_cost":3,"shortage_cost":12,"pack_size":1,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[7,8,6],"initial_stock":2,"unit_cost":5,"holding_cost":3,"shortage_cost":11,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":296.0,"gold_bound":296.0,"gold_solution":{"family":"inventory","status":"optimal","objective":296.0,"bound":296.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":5},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":3},{"sku_id":"S3","period":1,"qty":4},{"sku_id":"S3","period":2,"qty":8},{"sku_id":"S3","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"b8ded0d56a7c873c","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-004","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-A","seed":25004,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 208 currency units. Storage holds at most 21 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 208\nCAPACITY: 21\nCOVER_REQUIRED: 0\nSKU S1 demand=3,3,6 pack=3 cost=5 hold=2 short=13 stock=0\nSKU S2 demand=2,5,7 pack=1 cost=9 hold=3 short=14 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 208, \"warehouse_capacity\": 21, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [3, 3, 6], \"initial_stock\": 0, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 5, 7], \"initial_stock\": 0, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 208 واحد پول و ظرفیت انبار 21 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 208\nCAPACITY: 21\nCOVER_REQUIRED: 0\nSKU S1 demand=3,3,6 pack=3 cost=5 hold=2 short=13 stock=0\nSKU S2 demand=2,5,7 pack=1 cost=9 hold=3 short=14 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 208, \"warehouse_capacity\": 21, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [3, 3, 6], \"initial_stock\": 0, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 5, 7], \"initial_stock\": 0, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 208,\n \"warehouse_capacity\": 21,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 3,\n 3,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 5,\n \"holding_cost\": 2,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 5,\n 7\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 9,\n \"holding_cost\": 3,\n \"shortage_cost\": 14,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":208,"warehouse_capacity":21,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[3,3,6],"initial_stock":0,"unit_cost":5,"holding_cost":2,"shortage_cost":13,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,5,7],"initial_stock":0,"unit_cost":9,"holding_cost":3,"shortage_cost":14,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":186.0,"gold_bound":186.0,"gold_solution":{"family":"inventory","status":"optimal","objective":186.0,"bound":186.0,"orders":[{"sku_id":"S1","period":1,"qty":3},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":2},{"sku_id":"S2","period":2,"qty":5},{"sku_id":"S2","period":3,"qty":7}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"224e408bade9beae","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-005","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":25005,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 224 currency units. Storage holds at most 28 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 224\nCAPACITY: 28\nCOVER_REQUIRED: 1\nSKU S1 demand=6,5,8 pack=3 cost=6 hold=3 short=13 stock=2\nSKU S2 demand=6,7,6 pack=3 cost=6 hold=2 short=6 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 224, \"warehouse_capacity\": 28, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 5, 8], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 7, 6], \"initial_stock\": 3, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 224 واحد پول و ظرفیت انبار 28 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 224\nCAPACITY: 28\nCOVER_REQUIRED: 1\nSKU S1 demand=6,5,8 pack=3 cost=6 hold=3 short=13 stock=2\nSKU S2 demand=6,7,6 pack=3 cost=6 hold=2 short=6 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 224, \"warehouse_capacity\": 28, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 5, 8], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 7, 6], \"initial_stock\": 3, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 224,\n \"warehouse_capacity\": 28,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 6,\n 5,\n 8\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 6,\n \"holding_cost\": 3,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 7,\n 6\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 6,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":224,"warehouse_capacity":28,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[6,5,8],"initial_stock":2,"unit_cost":6,"holding_cost":3,"shortage_cost":13,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,7,6],"initial_stock":3,"unit_cost":6,"holding_cost":2,"shortage_cost":6,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":232.99999999999997,"gold_bound":232.99999999999997,"gold_solution":{"family":"inventory","status":"optimal","objective":232.99999999999997,"bound":232.99999999999997,"orders":[{"sku_id":"S1","period":1,"qty":6},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":9},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":9},{"sku_id":"S2","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"df2f98c85b303667","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-006","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":25006,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 336 currency units. Storage holds at most 37 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 336\nCAPACITY: 37\nCOVER_REQUIRED: 0\nSKU S1 demand=6,8,2 pack=2 cost=9 hold=3 short=7 stock=1\nSKU S2 demand=6,4,8 pack=3 cost=6 hold=2 short=9 stock=1\nSKU S3 demand=5,3,4 pack=3 cost=6 hold=2 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 336, \"warehouse_capacity\": 37, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 8, 2], \"initial_stock\": 1, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 4, 8], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 9, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [5, 3, 4], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 336 واحد پول و ظرفیت انبار 37 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 336\nCAPACITY: 37\nCOVER_REQUIRED: 0\nSKU S1 demand=6,8,2 pack=2 cost=9 hold=3 short=7 stock=1\nSKU S2 demand=6,4,8 pack=3 cost=6 hold=2 short=9 stock=1\nSKU S3 demand=5,3,4 pack=3 cost=6 hold=2 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 336, \"warehouse_capacity\": 37, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 8, 2], \"initial_stock\": 1, \"unit_cost\": 9, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 4, 8], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 9, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [5, 3, 4], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 336,\n \"warehouse_capacity\": 37,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 6,\n 8,\n 2\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 9,\n \"holding_cost\": 3,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 4,\n 8\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 6,\n \"holding_cost\": 2,\n \"shortage_cost\": 9,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 5,\n 3,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 6,\n \"holding_cost\": 2,\n \"shortage_cost\": 11,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":336,"warehouse_capacity":37,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[6,8,2],"initial_stock":1,"unit_cost":9,"holding_cost":3,"shortage_cost":7,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,4,8],"initial_stock":1,"unit_cost":6,"holding_cost":2,"shortage_cost":9,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[5,3,4],"initial_stock":2,"unit_cost":6,"holding_cost":2,"shortage_cost":11,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":280.0,"gold_bound":280.0,"gold_solution":{"family":"inventory","status":"optimal","objective":280.0,"bound":280.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":0},{"sku_id":"S1","period":3,"qty":0},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S3","period":1,"qty":3},{"sku_id":"S3","period":2,"qty":3},{"sku_id":"S3","period":3,"qty":3}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"37b860c2e403d2c5","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-007","family":"inventory","split":"development","interactive":false,"difficulty":"hard","language":"en","template_id":"D-A","seed":25007,"prompt_en":"A B2B warehouse plans 4 weeks for 4 SKUs: S1 (bearing), S2 (seal), S3 (gasket), S4 (filter). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 596 currency units. Storage holds at most 56 units in total. Minimize purchase + holding + shortage.\nPERIODS: 4\nBUDGET: 596\nCAPACITY: 56\nCOVER_REQUIRED: 1\nSKU S1 demand=5,4,8,4 pack=1 cost=8 hold=2 short=6 stock=0\nSKU S2 demand=4,7,6,5 pack=1 cost=8 hold=3 short=7 stock=3\nSKU S3 demand=8,4,2,5 pack=3 cost=9 hold=1 short=11 stock=3\nSKU S4 demand=2,5,5,4 pack=1 cost=6 hold=2 short=12 stock=2\nSCHEMA_BEGIN\n{\"periods\": 4, \"budget\": 596, \"warehouse_capacity\": 56, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 8, 4], \"initial_stock\": 0, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 7, 6, 5], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [8, 4, 2, 5], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S4\", \"name\": \"filter\", \"demand\": [2, 5, 5, 4], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 4 هفته و 4 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر), S4 (فیلتر). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 596 واحد پول و ظرفیت انبار 56 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 4\nBUDGET: 596\nCAPACITY: 56\nCOVER_REQUIRED: 1\nSKU S1 demand=5,4,8,4 pack=1 cost=8 hold=2 short=6 stock=0\nSKU S2 demand=4,7,6,5 pack=1 cost=8 hold=3 short=7 stock=3\nSKU S3 demand=8,4,2,5 pack=3 cost=9 hold=1 short=11 stock=3\nSKU S4 demand=2,5,5,4 pack=1 cost=6 hold=2 short=12 stock=2\nSCHEMA_BEGIN\n{\"periods\": 4, \"budget\": 596, \"warehouse_capacity\": 56, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 8, 4], \"initial_stock\": 0, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 7, 6, 5], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [8, 4, 2, 5], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S4\", \"name\": \"filter\", \"demand\": [2, 5, 5, 4], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 4,\n \"budget\": 596,\n \"warehouse_capacity\": 56,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 4,\n 8,\n 4\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 8,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 7,\n 6,\n 5\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 7,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 8,\n 4,\n 2,\n 5\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 11,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S4\",\n \"name\": \"filter\",\n \"demand\": [\n 2,\n 5,\n 5,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 6,\n \"holding_cost\": 2,\n \"shortage_cost\": 12,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":4,"budget":596,"warehouse_capacity":56,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,4,8,4],"initial_stock":0,"unit_cost":8,"holding_cost":2,"shortage_cost":6,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,7,6,5],"initial_stock":3,"unit_cost":8,"holding_cost":3,"shortage_cost":7,"pack_size":1,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[8,4,2,5],"initial_stock":3,"unit_cost":9,"holding_cost":1,"shortage_cost":11,"pack_size":3,"lead_time":0},{"sku_id":"S4","name":"filter","demand":[2,5,5,4],"initial_stock":2,"unit_cost":6,"holding_cost":2,"shortage_cost":12,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":570.0,"gold_bound":570.0,"gold_solution":{"family":"inventory","status":"optimal","objective":570.0,"bound":570.0,"orders":[{"sku_id":"S1","period":1,"qty":5},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":8},{"sku_id":"S1","period":4,"qty":4},{"sku_id":"S2","period":1,"qty":1},{"sku_id":"S2","period":2,"qty":7},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S2","period":4,"qty":5},{"sku_id":"S3","period":1,"qty":6},{"sku_id":"S3","period":2,"qty":3},{"sku_id":"S3","period":3,"qty":3},{"sku_id":"S3","period":4,"qty":6},{"sku_id":"S4","period":1,"qty":0},{"sku_id":"S4","period":2,"qty":5},{"sku_id":"S4","period":3,"qty":5},{"sku_id":"S4","period":4,"qty":4}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"3e101f0e29677e33","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-008","family":"inventory","split":"development","interactive":true,"difficulty":"easy","language":"fa","template_id":"D-B","seed":25008,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 175 currency units. Storage holds at most 24 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 175\nCAPACITY: 24\nCOVER_REQUIRED: 0\nSKU S1 demand=6,8,4 pack=1 cost=8 hold=3 short=12 stock=1\nSKU S2 demand=2,4,3 pack=2 cost=4 hold=3 short=7 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 175, \"warehouse_capacity\": 24, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 8, 4], \"initial_stock\": 1, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 4, 3], \"initial_stock\": 3, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 175 واحد پول و ظرفیت انبار 24 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 175\nCAPACITY: 24\nCOVER_REQUIRED: 0\nSKU S1 demand=6,8,4 pack=1 cost=8 hold=3 short=12 stock=1\nSKU S2 demand=2,4,3 pack=2 cost=4 hold=3 short=7 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 175, \"warehouse_capacity\": 24, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [6, 8, 4], \"initial_stock\": 1, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 4, 3], \"initial_stock\": 3, \"unit_cost\": 4, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 175,\n \"warehouse_capacity\": 24,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 6,\n 8,\n 4\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 12,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 4,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 4,\n \"holding_cost\": 3,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":175,"warehouse_capacity":24,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[6,8,4],"initial_stock":1,"unit_cost":8,"holding_cost":3,"shortage_cost":12,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,4,3],"initial_stock":3,"unit_cost":4,"holding_cost":3,"shortage_cost":7,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":166.0,"gold_bound":166.0,"gold_solution":{"family":"inventory","status":"optimal","objective":166.0,"bound":166.0,"orders":[{"sku_id":"S1","period":1,"qty":5},{"sku_id":"S1","period":2,"qty":8},{"sku_id":"S1","period":3,"qty":4},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":4},{"sku_id":"S2","period":3,"qty":2}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"f2dfa9f008318786","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-009","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"en","template_id":"D-C","seed":25009,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 287 currency units. Storage holds at most 42 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 287\nCAPACITY: 42\nCOVER_REQUIRED: 0\nSKU S1 demand=8,4,4 pack=2 cost=3 hold=2 short=10 stock=0\nSKU S2 demand=5,8,6 pack=3 cost=6 hold=1 short=12 stock=0\nSKU S3 demand=7,8,7 pack=3 cost=4 hold=1 short=13 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 287, \"warehouse_capacity\": 42, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [8, 4, 4], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [5, 8, 6], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 12, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 8, 7], \"initial_stock\": 0, \"unit_cost\": 4, \"holding_cost\": 1, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 287 واحد پول و ظرفیت انبار 42 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 287\nCAPACITY: 42\nCOVER_REQUIRED: 0\nSKU S1 demand=8,4,4 pack=2 cost=3 hold=2 short=10 stock=0\nSKU S2 demand=5,8,6 pack=3 cost=6 hold=1 short=12 stock=0\nSKU S3 demand=7,8,7 pack=3 cost=4 hold=1 short=13 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 287, \"warehouse_capacity\": 42, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [8, 4, 4], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [5, 8, 6], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 12, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 8, 7], \"initial_stock\": 0, \"unit_cost\": 4, \"holding_cost\": 1, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 287,\n \"warehouse_capacity\": 42,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 8,\n 4,\n 4\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 3,\n \"holding_cost\": 2,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 5,\n 8,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 12,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 7,\n 8,\n 7\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":287,"warehouse_capacity":42,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[8,4,4],"initial_stock":0,"unit_cost":3,"holding_cost":2,"shortage_cost":10,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[5,8,6],"initial_stock":0,"unit_cost":6,"holding_cost":1,"shortage_cost":12,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[7,8,7],"initial_stock":0,"unit_cost":4,"holding_cost":1,"shortage_cost":13,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":267.0,"gold_bound":267.0,"gold_solution":{"family":"inventory","status":"optimal","objective":267.0,"bound":267.0,"orders":[{"sku_id":"S1","period":1,"qty":8},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":4},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":6},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S3","period":1,"qty":6},{"sku_id":"S3","period":2,"qty":9},{"sku_id":"S3","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"caebc391dc3f21a3","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-010","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-A","seed":25010,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 240 currency units. Storage holds at most 28 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 240\nCAPACITY: 28\nCOVER_REQUIRED: 1\nSKU S1 demand=8,4,6 pack=1 cost=8 hold=1 short=6 stock=1\nSKU S2 demand=2,6,8 pack=1 cost=7 hold=3 short=12 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 240, \"warehouse_capacity\": 28, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [8, 4, 6], \"initial_stock\": 1, \"unit_cost\": 8, \"holding_cost\": 1, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 6, 8], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 240 واحد پول و ظرفیت انبار 28 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 240\nCAPACITY: 28\nCOVER_REQUIRED: 1\nSKU S1 demand=8,4,6 pack=1 cost=8 hold=1 short=6 stock=1\nSKU S2 demand=2,6,8 pack=1 cost=7 hold=3 short=12 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 240, \"warehouse_capacity\": 28, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [8, 4, 6], \"initial_stock\": 1, \"unit_cost\": 8, \"holding_cost\": 1, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [2, 6, 8], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 3, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 240,\n \"warehouse_capacity\": 28,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 8,\n 4,\n 6\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 8,\n \"holding_cost\": 1,\n \"shortage_cost\": 6,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 6,\n 8\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 7,\n \"holding_cost\": 3,\n \"shortage_cost\": 12,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":240,"warehouse_capacity":28,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[8,4,6],"initial_stock":1,"unit_cost":8,"holding_cost":1,"shortage_cost":6,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,6,8],"initial_stock":3,"unit_cost":7,"holding_cost":3,"shortage_cost":12,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":230.0,"gold_bound":230.0,"gold_solution":{"family":"inventory","status":"optimal","objective":230.0,"bound":230.0,"orders":[{"sku_id":"S1","period":1,"qty":7},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":5},{"sku_id":"S2","period":3,"qty":8}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"f482821b43520a57","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-011","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":25011,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 167 currency units. Storage holds at most 16 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 167\nCAPACITY: 16\nCOVER_REQUIRED: 0\nSKU S1 demand=2,5,4 pack=2 cost=8 hold=2 short=11 stock=3\nSKU S2 demand=8,4,2 pack=3 cost=7 hold=1 short=14 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 167, \"warehouse_capacity\": 16, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 5, 4], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 11, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 4, 2], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 14, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 167 واحد پول و ظرفیت انبار 16 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 167\nCAPACITY: 16\nCOVER_REQUIRED: 0\nSKU S1 demand=2,5,4 pack=2 cost=8 hold=2 short=11 stock=3\nSKU S2 demand=8,4,2 pack=3 cost=7 hold=1 short=14 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 167, \"warehouse_capacity\": 16, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 5, 4], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 11, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 4, 2], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 14, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 167,\n \"warehouse_capacity\": 16,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 2,\n 5,\n 4\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 8,\n \"holding_cost\": 2,\n \"shortage_cost\": 11,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 8,\n 4,\n 2\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 7,\n \"holding_cost\": 1,\n \"shortage_cost\": 14,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":167,"warehouse_capacity":16,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[2,5,4],"initial_stock":3,"unit_cost":8,"holding_cost":2,"shortage_cost":11,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[8,4,2],"initial_stock":3,"unit_cost":7,"holding_cost":1,"shortage_cost":14,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":152.0,"gold_bound":152.0,"gold_solution":{"family":"inventory","status":"optimal","objective":152.0,"bound":152.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":4},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":3}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"8ad0f8164e7ede31","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-012","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":25012,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 277 currency units. Storage holds at most 31 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 277\nCAPACITY: 31\nCOVER_REQUIRED: 0\nSKU S1 demand=7,8,2 pack=3 cost=6 hold=3 short=11 stock=1\nSKU S2 demand=7,8,2 pack=3 cost=6 hold=2 short=10 stock=3\nSKU S3 demand=6,3,5 pack=1 cost=5 hold=3 short=8 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 277, \"warehouse_capacity\": 31, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 8, 2], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [7, 8, 2], \"initial_stock\": 3, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [6, 3, 5], \"initial_stock\": 3, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 277 واحد پول و ظرفیت انبار 31 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 277\nCAPACITY: 31\nCOVER_REQUIRED: 0\nSKU S1 demand=7,8,2 pack=3 cost=6 hold=3 short=11 stock=1\nSKU S2 demand=7,8,2 pack=3 cost=6 hold=2 short=10 stock=3\nSKU S3 demand=6,3,5 pack=1 cost=5 hold=3 short=8 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 277, \"warehouse_capacity\": 31, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 8, 2], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [7, 8, 2], \"initial_stock\": 3, \"unit_cost\": 6, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [6, 3, 5], \"initial_stock\": 3, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 277,\n \"warehouse_capacity\": 31,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 8,\n 2\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 6,\n \"holding_cost\": 3,\n \"shortage_cost\": 11,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 7,\n 8,\n 2\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 6,\n \"holding_cost\": 2,\n \"shortage_cost\": 10,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 6,\n 3,\n 5\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":277,"warehouse_capacity":31,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,8,2],"initial_stock":1,"unit_cost":6,"holding_cost":3,"shortage_cost":11,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[7,8,2],"initial_stock":3,"unit_cost":6,"holding_cost":2,"shortage_cost":10,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[6,3,5],"initial_stock":3,"unit_cost":5,"holding_cost":3,"shortage_cost":8,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":253.0,"gold_bound":253.0,"gold_solution":{"family":"inventory","status":"optimal","objective":253.0,"bound":253.0,"orders":[{"sku_id":"S1","period":1,"qty":6},{"sku_id":"S1","period":2,"qty":9},{"sku_id":"S1","period":3,"qty":0},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":9},{"sku_id":"S2","period":3,"qty":0},{"sku_id":"S3","period":1,"qty":3},{"sku_id":"S3","period":2,"qty":3},{"sku_id":"S3","period":3,"qty":5}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"3827beb73596c516","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-013","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":25013,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 256 currency units. Storage holds at most 21 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 256\nCAPACITY: 21\nCOVER_REQUIRED: 0\nSKU S1 demand=7,8,3 pack=3 cost=9 hold=2 short=7 stock=3\nSKU S2 demand=3,6,4 pack=2 cost=9 hold=2 short=6 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 256, \"warehouse_capacity\": 21, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 8, 3], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 7, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [3, 6, 4], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 256 واحد پول و ظرفیت انبار 21 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 256\nCAPACITY: 21\nCOVER_REQUIRED: 0\nSKU S1 demand=7,8,3 pack=3 cost=9 hold=2 short=7 stock=3\nSKU S2 demand=3,6,4 pack=2 cost=9 hold=2 short=6 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 256, \"warehouse_capacity\": 21, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 8, 3], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 7, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [3, 6, 4], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 6, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 256,\n \"warehouse_capacity\": 21,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 8,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 7,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 3,\n 6,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":256,"warehouse_capacity":21,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,8,3],"initial_stock":3,"unit_cost":9,"holding_cost":2,"shortage_cost":7,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[3,6,4],"initial_stock":2,"unit_cost":9,"holding_cost":2,"shortage_cost":6,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":171.0,"gold_bound":171.0,"gold_solution":{"family":"inventory","status":"optimal","objective":171.0,"bound":171.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":0},{"sku_id":"S1","period":3,"qty":0},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":0},{"sku_id":"S2","period":3,"qty":0}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"1a72f172d379cd66","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-014","family":"inventory","split":"development","interactive":true,"difficulty":"hard","language":"fa","template_id":"D-B","seed":25014,"prompt_en":"A B2B warehouse plans 4 weeks for 4 SKUs: S1 (bearing), S2 (seal), S3 (gasket), S4 (filter). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 451 currency units. Storage holds at most 57 units in total. Minimize purchase + holding + shortage.\nPERIODS: 4\nBUDGET: 451\nCAPACITY: 57\nCOVER_REQUIRED: 1\nSKU S1 demand=5,5,2,4 pack=2 cost=7 hold=3 short=7 stock=2\nSKU S2 demand=6,6,8,2 pack=2 cost=5 hold=2 short=9 stock=1\nSKU S3 demand=7,2,5,8 pack=2 cost=5 hold=2 short=13 stock=2\nSKU S4 demand=3,8,4,3 pack=1 cost=8 hold=3 short=10 stock=3\nSCHEMA_BEGIN\n{\"periods\": 4, \"budget\": 451, \"warehouse_capacity\": 57, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 5, 2, 4], \"initial_stock\": 2, \"unit_cost\": 7, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 6, 8, 2], \"initial_stock\": 1, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 9, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 2, 5, 8], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S4\", \"name\": \"filter\", \"demand\": [3, 8, 4, 3], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 10, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 4 هفته و 4 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر), S4 (فیلتر). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 451 واحد پول و ظرفیت انبار 57 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 4\nBUDGET: 451\nCAPACITY: 57\nCOVER_REQUIRED: 1\nSKU S1 demand=5,5,2,4 pack=2 cost=7 hold=3 short=7 stock=2\nSKU S2 demand=6,6,8,2 pack=2 cost=5 hold=2 short=9 stock=1\nSKU S3 demand=7,2,5,8 pack=2 cost=5 hold=2 short=13 stock=2\nSKU S4 demand=3,8,4,3 pack=1 cost=8 hold=3 short=10 stock=3\nSCHEMA_BEGIN\n{\"periods\": 4, \"budget\": 451, \"warehouse_capacity\": 57, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 5, 2, 4], \"initial_stock\": 2, \"unit_cost\": 7, \"holding_cost\": 3, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [6, 6, 8, 2], \"initial_stock\": 1, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 9, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 2, 5, 8], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S4\", \"name\": \"filter\", \"demand\": [3, 8, 4, 3], \"initial_stock\": 3, \"unit_cost\": 8, \"holding_cost\": 3, \"shortage_cost\": 10, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 4,\n \"budget\": 451,\n \"warehouse_capacity\": 57,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 5,\n 2,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 7,\n \"holding_cost\": 3,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 6,\n 8,\n 2\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 5,\n \"holding_cost\": 2,\n \"shortage_cost\": 9,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 7,\n 2,\n 5,\n 8\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 5,\n \"holding_cost\": 2,\n \"shortage_cost\": 13,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S4\",\n \"name\": \"filter\",\n \"demand\": [\n 3,\n 8,\n 4,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 10,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":4,"budget":451,"warehouse_capacity":57,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,5,2,4],"initial_stock":2,"unit_cost":7,"holding_cost":3,"shortage_cost":7,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,6,8,2],"initial_stock":1,"unit_cost":5,"holding_cost":2,"shortage_cost":9,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[7,2,5,8],"initial_stock":2,"unit_cost":5,"holding_cost":2,"shortage_cost":13,"pack_size":2,"lead_time":0},{"sku_id":"S4","name":"filter","demand":[3,8,4,3],"initial_stock":3,"unit_cost":8,"holding_cost":3,"shortage_cost":10,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":443.0,"gold_bound":443.0,"gold_solution":{"family":"inventory","status":"optimal","objective":443.0,"bound":443.0,"orders":[{"sku_id":"S1","period":1,"qty":4},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":2},{"sku_id":"S1","period":4,"qty":4},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":6},{"sku_id":"S2","period":3,"qty":8},{"sku_id":"S2","period":4,"qty":2},{"sku_id":"S3","period":1,"qty":6},{"sku_id":"S3","period":2,"qty":2},{"sku_id":"S3","period":3,"qty":4},{"sku_id":"S3","period":4,"qty":8},{"sku_id":"S4","period":1,"qty":0},{"sku_id":"S4","period":2,"qty":8},{"sku_id":"S4","period":3,"qty":4},{"sku_id":"S4","period":4,"qty":3}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"220c39206c2443c2","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-015","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"en","template_id":"D-C","seed":25015,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 277 currency units. Storage holds at most 27 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 277\nCAPACITY: 27\nCOVER_REQUIRED: 1\nSKU S1 demand=3,4,2 pack=1 cost=9 hold=2 short=10 stock=2\nSKU S2 demand=4,2,5 pack=2 cost=6 hold=1 short=10 stock=2\nSKU S3 demand=7,6,7 pack=1 cost=8 hold=2 short=12 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 277, \"warehouse_capacity\": 27, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [3, 4, 2], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 2, 5], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 10, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 6, 7], \"initial_stock\": 2, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 277 واحد پول و ظرفیت انبار 27 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 277\nCAPACITY: 27\nCOVER_REQUIRED: 1\nSKU S1 demand=3,4,2 pack=1 cost=9 hold=2 short=10 stock=2\nSKU S2 demand=4,2,5 pack=2 cost=6 hold=1 short=10 stock=2\nSKU S3 demand=7,6,7 pack=1 cost=8 hold=2 short=12 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 277, \"warehouse_capacity\": 27, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [3, 4, 2], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 10, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 2, 5], \"initial_stock\": 2, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 10, \"pack_size\": 2, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [7, 6, 7], \"initial_stock\": 2, \"unit_cost\": 8, \"holding_cost\": 2, \"shortage_cost\": 12, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 277,\n \"warehouse_capacity\": 27,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 3,\n 4,\n 2\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 10,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 2,\n 5\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 7,\n 6,\n 7\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 8,\n \"holding_cost\": 2,\n \"shortage_cost\": 12,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":277,"warehouse_capacity":27,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[3,4,2],"initial_stock":2,"unit_cost":9,"holding_cost":2,"shortage_cost":10,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,2,5],"initial_stock":2,"unit_cost":6,"holding_cost":1,"shortage_cost":10,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[7,6,7],"initial_stock":2,"unit_cost":8,"holding_cost":2,"shortage_cost":12,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":268.0,"gold_bound":268.0,"gold_solution":{"family":"inventory","status":"optimal","objective":268.0,"bound":268.0,"orders":[{"sku_id":"S1","period":1,"qty":1},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":2},{"sku_id":"S2","period":1,"qty":2},{"sku_id":"S2","period":2,"qty":2},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S3","period":1,"qty":5},{"sku_id":"S3","period":2,"qty":6},{"sku_id":"S3","period":3,"qty":7}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"06a75306f2f713c8","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-016","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-A","seed":25016,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 148 currency units. Storage holds at most 27 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 148\nCAPACITY: 27\nCOVER_REQUIRED: 0\nSKU S1 demand=2,8,8 pack=1 cost=3 hold=3 short=14 stock=0\nSKU S2 demand=4,5,5 pack=3 cost=7 hold=1 short=13 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 148, \"warehouse_capacity\": 27, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 8, 8], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 5, 5], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 148 واحد پول و ظرفیت انبار 27 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 148\nCAPACITY: 27\nCOVER_REQUIRED: 0\nSKU S1 demand=2,8,8 pack=1 cost=3 hold=3 short=14 stock=0\nSKU S2 demand=4,5,5 pack=3 cost=7 hold=1 short=13 stock=3\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 148, \"warehouse_capacity\": 27, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [2, 8, 8], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 3, \"shortage_cost\": 14, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 5, 5], \"initial_stock\": 3, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 13, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 148,\n \"warehouse_capacity\": 27,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 2,\n 8,\n 8\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 3,\n \"holding_cost\": 3,\n \"shortage_cost\": 14,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 5,\n 5\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 7,\n \"holding_cost\": 1,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":148,"warehouse_capacity":27,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[2,8,8],"initial_stock":0,"unit_cost":3,"holding_cost":3,"shortage_cost":14,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,5,5],"initial_stock":3,"unit_cost":7,"holding_cost":1,"shortage_cost":13,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":141.0,"gold_bound":141.0,"gold_solution":{"family":"inventory","status":"optimal","objective":141.0,"bound":141.0,"orders":[{"sku_id":"S1","period":1,"qty":2},{"sku_id":"S1","period":2,"qty":8},{"sku_id":"S1","period":3,"qty":8},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"7c84e87cc10f3c05","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-017","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":25017,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 182 currency units. Storage holds at most 23 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 182\nCAPACITY: 23\nCOVER_REQUIRED: 0\nSKU S1 demand=7,2,5 pack=3 cost=4 hold=1 short=10 stock=1\nSKU S2 demand=8,2,6 pack=2 cost=7 hold=1 short=9 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 182, \"warehouse_capacity\": 23, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 2, 5], \"initial_stock\": 1, \"unit_cost\": 4, \"holding_cost\": 1, \"shortage_cost\": 10, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 2, 6], \"initial_stock\": 0, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 9, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 182 واحد پول و ظرفیت انبار 23 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 182\nCAPACITY: 23\nCOVER_REQUIRED: 0\nSKU S1 demand=7,2,5 pack=3 cost=4 hold=1 short=10 stock=1\nSKU S2 demand=8,2,6 pack=2 cost=7 hold=1 short=9 stock=0\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 182, \"warehouse_capacity\": 23, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [7, 2, 5], \"initial_stock\": 1, \"unit_cost\": 4, \"holding_cost\": 1, \"shortage_cost\": 10, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [8, 2, 6], \"initial_stock\": 0, \"unit_cost\": 7, \"holding_cost\": 1, \"shortage_cost\": 9, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 182,\n \"warehouse_capacity\": 23,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 2,\n 5\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 8,\n 2,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 7,\n \"holding_cost\": 1,\n \"shortage_cost\": 9,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":182,"warehouse_capacity":23,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,2,5],"initial_stock":1,"unit_cost":4,"holding_cost":1,"shortage_cost":10,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[8,2,6],"initial_stock":0,"unit_cost":7,"holding_cost":1,"shortage_cost":9,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":171.0,"gold_bound":171.0,"gold_solution":{"family":"inventory","status":"optimal","objective":171.0,"bound":171.0,"orders":[{"sku_id":"S1","period":1,"qty":6},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":3},{"sku_id":"S2","period":1,"qty":8},{"sku_id":"S2","period":2,"qty":2},{"sku_id":"S2","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"7315654a4c498e83","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-018","family":"inventory","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":25018,"prompt_en":"A B2B warehouse plans 3 weeks for 3 SKUs: S1 (bearing), S2 (seal), S3 (gasket). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 209 currency units. Storage holds at most 28 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 209\nCAPACITY: 28\nCOVER_REQUIRED: 0\nSKU S1 demand=4,4,4 pack=1 cost=6 hold=1 short=7 stock=0\nSKU S2 demand=3,3,3 pack=3 cost=6 hold=1 short=7 stock=0\nSKU S3 demand=6,4,7 pack=1 cost=5 hold=3 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 209, \"warehouse_capacity\": 28, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [4, 4, 4], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [3, 3, 3], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [6, 4, 7], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 3 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 209 واحد پول و ظرفیت انبار 28 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 209\nCAPACITY: 28\nCOVER_REQUIRED: 0\nSKU S1 demand=4,4,4 pack=1 cost=6 hold=1 short=7 stock=0\nSKU S2 demand=3,3,3 pack=3 cost=6 hold=1 short=7 stock=0\nSKU S3 demand=6,4,7 pack=1 cost=5 hold=3 short=11 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 209, \"warehouse_capacity\": 28, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [4, 4, 4], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [3, 3, 3], \"initial_stock\": 0, \"unit_cost\": 6, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 3, \"lead_time\": 0}, {\"sku_id\": \"S3\", \"name\": \"gasket\", \"demand\": [6, 4, 7], \"initial_stock\": 2, \"unit_cost\": 5, \"holding_cost\": 3, \"shortage_cost\": 11, \"pack_size\": 1, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 209,\n \"warehouse_capacity\": 28,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 4,\n 4,\n 4\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 3,\n 3,\n 3\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 6,\n 4,\n 7\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 11,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":209,"warehouse_capacity":28,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[4,4,4],"initial_stock":0,"unit_cost":6,"holding_cost":1,"shortage_cost":7,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[3,3,3],"initial_stock":0,"unit_cost":6,"holding_cost":1,"shortage_cost":7,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[6,4,7],"initial_stock":2,"unit_cost":5,"holding_cost":3,"shortage_cost":11,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":201.0,"gold_bound":201.0,"gold_solution":{"family":"inventory","status":"optimal","objective":201.0,"bound":201.0,"orders":[{"sku_id":"S1","period":1,"qty":4},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":4},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":3},{"sku_id":"S3","period":1,"qty":4},{"sku_id":"S3","period":2,"qty":4},{"sku_id":"S3","period":3,"qty":7}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"2db06bd39b73849d","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-019","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":25019,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). Lost sales are allowed and charged. Orders are pack multiples. Lead time is 0. Budget is 169 currency units. Storage holds at most 25 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 169\nCAPACITY: 25\nCOVER_REQUIRED: 0\nSKU S1 demand=5,4,8 pack=1 cost=3 hold=1 short=6 stock=0\nSKU S2 demand=4,4,5 pack=2 cost=9 hold=1 short=7 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 169, \"warehouse_capacity\": 25, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 8], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 1, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 4, 5], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). کمبود مجاز است و جریمه دارد. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 169 واحد پول و ظرفیت انبار 25 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 169\nCAPACITY: 25\nCOVER_REQUIRED: 0\nSKU S1 demand=5,4,8 pack=1 cost=3 hold=1 short=6 stock=0\nSKU S2 demand=4,4,5 pack=2 cost=9 hold=1 short=7 stock=2\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 169, \"warehouse_capacity\": 25, \"cover_required\": false, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 4, 8], \"initial_stock\": 0, \"unit_cost\": 3, \"holding_cost\": 1, \"shortage_cost\": 6, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [4, 4, 5], \"initial_stock\": 2, \"unit_cost\": 9, \"holding_cost\": 1, \"shortage_cost\": 7, \"pack_size\": 2, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 169,\n \"warehouse_capacity\": 25,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 4,\n 8\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 3,\n \"holding_cost\": 1,\n \"shortage_cost\": 6,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 4,\n 5\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":169,"warehouse_capacity":25,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,4,8],"initial_stock":0,"unit_cost":3,"holding_cost":1,"shortage_cost":6,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,4,5],"initial_stock":2,"unit_cost":9,"holding_cost":1,"shortage_cost":7,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":128.0,"gold_bound":128.0,"gold_solution":{"family":"inventory","status":"optimal","objective":128.0,"bound":128.0,"orders":[{"sku_id":"S1","period":1,"qty":5},{"sku_id":"S1","period":2,"qty":4},{"sku_id":"S1","period":3,"qty":8},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":0},{"sku_id":"S2","period":3,"qty":0}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"5a0bc130cf4da2cb","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-020","family":"inventory","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-B","seed":25020,"prompt_en":"A B2B warehouse plans 3 weeks for 2 SKUs: S1 (bearing), S2 (seal). All demand must be covered; lost sales are forbidden. Orders are pack multiples. Lead time is 0. Budget is 191 currency units. Storage holds at most 20 units in total. Minimize purchase + holding + shortage.\nPERIODS: 3\nBUDGET: 191\nCAPACITY: 20\nCOVER_REQUIRED: 1\nSKU S1 demand=5,5,5 pack=1 cost=9 hold=2 short=13 stock=3\nSKU S2 demand=5,3,4 pack=3 cost=6 hold=3 short=8 stock=1\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 191, \"warehouse_capacity\": 20, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 5, 5], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [5, 3, 4], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_fa":"یک انبار B2B برای 3 هفته و 2 کالا برنامه می‌خرد: S1 (بلبرینگ), S2 (آب‌بند). پوشش کامل تقاضا الزامی است. سفارش مضرب بسته است. زمان تأمین صفر است. بودجه برابر 191 واحد پول و ظرفیت انبار 20 واحد است. هدف کمینه‌کردن خرید + نگهداری + کمبود است.\nPERIODS: 3\nBUDGET: 191\nCAPACITY: 20\nCOVER_REQUIRED: 1\nSKU S1 demand=5,5,5 pack=1 cost=9 hold=2 short=13 stock=3\nSKU S2 demand=5,3,4 pack=3 cost=6 hold=3 short=8 stock=1\nSCHEMA_BEGIN\n{\"periods\": 3, \"budget\": 191, \"warehouse_capacity\": 20, \"cover_required\": true, \"lost_sales\": true, \"skus\": [{\"sku_id\": \"S1\", \"name\": \"bearing\", \"demand\": [5, 5, 5], \"initial_stock\": 3, \"unit_cost\": 9, \"holding_cost\": 2, \"shortage_cost\": 13, \"pack_size\": 1, \"lead_time\": 0}, {\"sku_id\": \"S2\", \"name\": \"seal\", \"demand\": [5, 3, 4], \"initial_stock\": 1, \"unit_cost\": 6, \"holding_cost\": 3, \"shortage_cost\": 8, \"pack_size\": 3, \"lead_time\": 0}]}\nSCHEMA_END\n","prompt_json":"{\n \"periods\": 3,\n \"budget\": 191,\n \"warehouse_capacity\": 20,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 5,\n 5\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 13,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 5,\n 3,\n 4\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 6,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":191,"warehouse_capacity":20,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,5,5],"initial_stock":3,"unit_cost":9,"holding_cost":2,"shortage_cost":13,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[5,3,4],"initial_stock":1,"unit_cost":6,"holding_cost":3,"shortage_cost":8,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":195.0,"gold_bound":195.0,"gold_solution":{"family":"inventory","status":"optimal","objective":195.0,"bound":195.0,"orders":[{"sku_id":"S1","period":1,"qty":2},{"sku_id":"S1","period":2,"qty":5},{"sku_id":"S1","period":3,"qty":5},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":3}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"7504669a6087b21d","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-021","family":"inventory","split":"test","interactive":true,"difficulty":"hard","language":"en","template_id":"T-A","seed":25021,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket), S4 (filter) over a 4-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 667. On-hand stock across SKUs cannot exceed 56. S1 wants [6, 5, 5, 6] at pack 1; S2 wants [5, 3, 7, 4] at pack 3; S3 wants [8, 5, 4, 8] at pack 2; S4 wants [2, 8, 5, 5] at pack 1. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر), S4 (فیلتر) در افق 4 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 667 و سقف موجودی کل 56 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 4,\n \"budget\": 667,\n \"warehouse_capacity\": 56,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 6,\n 5,\n 5,\n 6\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 7,\n \"holding_cost\": 2,\n \"shortage_cost\": 14,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 5,\n 3,\n 7,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 8,\n \"holding_cost\": 2,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 8,\n 5,\n 4,\n 8\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 3,\n \"shortage_cost\": 9,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S4\",\n \"name\": \"filter\",\n \"demand\": [\n 2,\n 8,\n 5,\n 5\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 8,\n \"holding_cost\": 1,\n \"shortage_cost\": 9,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":4,"budget":667,"warehouse_capacity":56,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[6,5,5,6],"initial_stock":2,"unit_cost":7,"holding_cost":2,"shortage_cost":14,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[5,3,7,4],"initial_stock":2,"unit_cost":8,"holding_cost":2,"shortage_cost":13,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[8,5,4,8],"initial_stock":3,"unit_cost":9,"holding_cost":3,"shortage_cost":9,"pack_size":2,"lead_time":0},{"sku_id":"S4","name":"filter","demand":[2,8,5,5],"initial_stock":1,"unit_cost":8,"holding_cost":1,"shortage_cost":9,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":643.0,"gold_bound":643.0,"gold_solution":{"family":"inventory","status":"optimal","objective":643.0,"bound":643.0,"orders":[{"sku_id":"S1","period":1,"qty":4},{"sku_id":"S1","period":2,"qty":5},{"sku_id":"S1","period":3,"qty":5},{"sku_id":"S1","period":4,"qty":6},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":9},{"sku_id":"S2","period":4,"qty":3},{"sku_id":"S3","period":1,"qty":6},{"sku_id":"S3","period":2,"qty":4},{"sku_id":"S3","period":3,"qty":4},{"sku_id":"S3","period":4,"qty":8},{"sku_id":"S4","period":1,"qty":1},{"sku_id":"S4","period":2,"qty":8},{"sku_id":"S4","period":3,"qty":5},{"sku_id":"S4","period":4,"qty":5}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"43f6be8e459b5009","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-022","family":"inventory","split":"test","interactive":false,"difficulty":"easy","language":"fa","template_id":"T-B","seed":25022,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 117. On-hand stock across SKUs cannot exceed 19. S1 wants [2, 2, 3] at pack 1; S2 wants [6, 7, 7] at pack 2. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 117 و سقف موجودی کل 19 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 117,\n \"warehouse_capacity\": 19,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 2,\n 2,\n 3\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 3,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 7,\n 7\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":117,"warehouse_capacity":19,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[2,2,3],"initial_stock":2,"unit_cost":3,"holding_cost":2,"shortage_cost":6,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,7,7],"initial_stock":1,"unit_cost":4,"holding_cost":1,"shortage_cost":10,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":97.0,"gold_bound":97.0,"gold_solution":{"family":"inventory","status":"optimal","objective":97.0,"bound":97.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":2},{"sku_id":"S1","period":3,"qty":3},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":6},{"sku_id":"S2","period":3,"qty":8}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"e0b2178c1118eb1f","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-023","family":"inventory","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":25023,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 241. On-hand stock across SKUs cannot exceed 28. S1 wants [5, 5, 7] at pack 2; S2 wants [6, 3, 5] at pack 3. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 241 و سقف موجودی کل 28 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 241,\n \"warehouse_capacity\": 28,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 5,\n 7\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 13,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 3,\n 5\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":241,"warehouse_capacity":28,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,5,7],"initial_stock":1,"unit_cost":8,"holding_cost":3,"shortage_cost":13,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,3,5],"initial_stock":0,"unit_cost":6,"holding_cost":1,"shortage_cost":10,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":222.0,"gold_bound":222.0,"gold_solution":{"family":"inventory","status":"optimal","objective":222.0,"bound":222.0,"orders":[{"sku_id":"S1","period":1,"qty":4},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":6},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"85786f3b3f0dfbf9","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-024","family":"inventory","split":"test","interactive":false,"difficulty":"medium","language":"fa","template_id":"T-B","seed":25024,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 268. On-hand stock across SKUs cannot exceed 26. S1 wants [7, 2, 3] at pack 2; S2 wants [2, 3, 7] at pack 3; S3 wants [3, 8, 8] at pack 2. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 268 و سقف موجودی کل 26 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 268,\n \"warehouse_capacity\": 26,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 2,\n 3\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 7,\n \"holding_cost\": 2,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 3,\n 7\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 3,\n 8,\n 8\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 11,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":268,"warehouse_capacity":26,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,2,3],"initial_stock":3,"unit_cost":7,"holding_cost":2,"shortage_cost":7,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,3,7],"initial_stock":3,"unit_cost":5,"holding_cost":3,"shortage_cost":8,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[3,8,8],"initial_stock":3,"unit_cost":9,"holding_cost":1,"shortage_cost":11,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":258.0,"gold_bound":258.0,"gold_solution":{"family":"inventory","status":"optimal","objective":258.0,"bound":258.0,"orders":[{"sku_id":"S1","period":1,"qty":0},{"sku_id":"S1","period":2,"qty":0},{"sku_id":"S1","period":3,"qty":0},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S3","period":1,"qty":0},{"sku_id":"S3","period":2,"qty":8},{"sku_id":"S3","period":3,"qty":8}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"5c318f4fb63ecf81","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-025","family":"inventory","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":25025,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 284. On-hand stock across SKUs cannot exceed 27. S1 wants [7, 5, 6] at pack 3; S2 wants [3, 4, 6] at pack 3. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 284 و سقف موجودی کل 27 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 284,\n \"warehouse_capacity\": 27,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 5,\n 6\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 3,\n 4,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":284,"warehouse_capacity":27,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,5,6],"initial_stock":3,"unit_cost":9,"holding_cost":3,"shortage_cost":8,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[3,4,6],"initial_stock":0,"unit_cost":9,"holding_cost":2,"shortage_cost":6,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":284.0,"gold_bound":284.0,"gold_solution":{"family":"inventory","status":"optimal","objective":284.0,"bound":284.0,"orders":[{"sku_id":"S1","period":1,"qty":6},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":6},{"sku_id":"S2","period":3,"qty":6}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"34a94761719df506","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-026","family":"inventory","split":"test","interactive":false,"difficulty":"easy","language":"fa","template_id":"T-B","seed":25026,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 222. On-hand stock across SKUs cannot exceed 25. S1 wants [5, 5, 7] at pack 2; S2 wants [5, 7, 4] at pack 1. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 222 و سقف موجودی کل 25 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 222,\n \"warehouse_capacity\": 25,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 5,\n 5,\n 7\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 8,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 5,\n 7,\n 4\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 14,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":222,"warehouse_capacity":25,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[5,5,7],"initial_stock":0,"unit_cost":8,"holding_cost":1,"shortage_cost":10,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[5,7,4],"initial_stock":2,"unit_cost":4,"holding_cost":1,"shortage_cost":14,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":195.0,"gold_bound":195.0,"gold_solution":{"family":"inventory","status":"optimal","objective":195.0,"bound":195.0,"orders":[{"sku_id":"S1","period":1,"qty":4},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":6},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":7},{"sku_id":"S2","period":3,"qty":4}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"a2c2cf9f0e528f38","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-027","family":"inventory","split":"test","interactive":false,"difficulty":"medium","language":"en","template_id":"T-A","seed":25027,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 200. On-hand stock across SKUs cannot exceed 29. S1 wants [4, 5, 2] at pack 1; S2 wants [4, 8, 2] at pack 2; S3 wants [2, 6, 6] at pack 3. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 200 و سقف موجودی کل 29 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 200,\n \"warehouse_capacity\": 29,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 4,\n 5,\n 2\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 5,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 8,\n 2\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 3,\n \"holding_cost\": 2,\n \"shortage_cost\": 12,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 2,\n 6,\n 6\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 6,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":200,"warehouse_capacity":29,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[4,5,2],"initial_stock":3,"unit_cost":5,"holding_cost":1,"shortage_cost":7,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,8,2],"initial_stock":2,"unit_cost":3,"holding_cost":2,"shortage_cost":12,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[2,6,6],"initial_stock":3,"unit_cost":9,"holding_cost":1,"shortage_cost":6,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":143.0,"gold_bound":143.0,"gold_solution":{"family":"inventory","status":"optimal","objective":143.0,"bound":143.0,"orders":[{"sku_id":"S1","period":1,"qty":1},{"sku_id":"S1","period":2,"qty":5},{"sku_id":"S1","period":3,"qty":2},{"sku_id":"S2","period":1,"qty":2},{"sku_id":"S2","period":2,"qty":8},{"sku_id":"S2","period":3,"qty":2},{"sku_id":"S3","period":1,"qty":0},{"sku_id":"S3","period":2,"qty":0},{"sku_id":"S3","period":3,"qty":0}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"58e2d8d2872c433a","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-028","family":"inventory","split":"test","interactive":true,"difficulty":"hard","language":"fa","template_id":"T-B","seed":25028,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket), S4 (filter) over a 4-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 417. On-hand stock across SKUs cannot exceed 48. S1 wants [2, 6, 5, 4] at pack 2; S2 wants [6, 2, 5, 6] at pack 3; S3 wants [3, 2, 7, 5] at pack 1; S4 wants [7, 3, 4, 4] at pack 3. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر), S4 (فیلتر) در افق 4 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 417 و سقف موجودی کل 48 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 4,\n \"budget\": 417,\n \"warehouse_capacity\": 48,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 2,\n 6,\n 5,\n 4\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 2,\n 5,\n 6\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 13,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 3,\n 2,\n 7,\n 5\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 8,\n \"holding_cost\": 3,\n \"shortage_cost\": 9,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S4\",\n \"name\": \"filter\",\n \"demand\": [\n 7,\n 3,\n 4,\n 4\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 9,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":4,"budget":417,"warehouse_capacity":48,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[2,6,5,4],"initial_stock":1,"unit_cost":5,"holding_cost":3,"shortage_cost":10,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,2,5,6],"initial_stock":3,"unit_cost":5,"holding_cost":3,"shortage_cost":13,"pack_size":3,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[3,2,7,5],"initial_stock":0,"unit_cost":8,"holding_cost":3,"shortage_cost":9,"pack_size":1,"lead_time":0},{"sku_id":"S4","name":"filter","demand":[7,3,4,4],"initial_stock":3,"unit_cost":6,"holding_cost":1,"shortage_cost":9,"pack_size":3,"lead_time":0}]},"gold_status":"optimal","gold_objective":422.0,"gold_bound":422.0,"gold_solution":{"family":"inventory","status":"optimal","objective":422.0,"bound":422.0,"orders":[{"sku_id":"S1","period":1,"qty":2},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":4},{"sku_id":"S1","period":4,"qty":4},{"sku_id":"S2","period":1,"qty":3},{"sku_id":"S2","period":2,"qty":3},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S2","period":4,"qty":6},{"sku_id":"S3","period":1,"qty":3},{"sku_id":"S3","period":2,"qty":2},{"sku_id":"S3","period":3,"qty":7},{"sku_id":"S3","period":4,"qty":5},{"sku_id":"S4","period":1,"qty":6},{"sku_id":"S4","period":2,"qty":3},{"sku_id":"S4","period":3,"qty":3},{"sku_id":"S4","period":4,"qty":3}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"d4b291056d53e1b6","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-029","family":"inventory","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":25029,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 205. On-hand stock across SKUs cannot exceed 25. S1 wants [7, 6, 3] at pack 3; S2 wants [6, 4, 5] at pack 1. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 205 و سقف موجودی کل 25 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 205,\n \"warehouse_capacity\": 25,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 6,\n 3\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 8,\n \"holding_cost\": 1,\n \"shortage_cost\": 14,\n \"pack_size\": 3,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 4,\n 5\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":205,"warehouse_capacity":25,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,6,3],"initial_stock":0,"unit_cost":8,"holding_cost":1,"shortage_cost":14,"pack_size":3,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,4,5],"initial_stock":2,"unit_cost":4,"holding_cost":1,"shortage_cost":10,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":186.0,"gold_bound":186.0,"gold_solution":{"family":"inventory","status":"optimal","objective":186.0,"bound":186.0,"orders":[{"sku_id":"S1","period":1,"qty":6},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":3},{"sku_id":"S2","period":1,"qty":4},{"sku_id":"S2","period":2,"qty":4},{"sku_id":"S2","period":3,"qty":5}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"df4a252d2ab08ed3","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-030","family":"inventory","split":"test","interactive":false,"difficulty":"medium","language":"fa","template_id":"T-B","seed":25030,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 174. On-hand stock across SKUs cannot exceed 25. S1 wants [3, 3, 2] at pack 1; S2 wants [6, 2, 7] at pack 2; S3 wants [8, 3, 2] at pack 2. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 174 و سقف موجودی کل 25 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 174,\n \"warehouse_capacity\": 25,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 3,\n 3,\n 2\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 7,\n \"holding_cost\": 1,\n \"shortage_cost\": 9,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 6,\n 2,\n 7\n ],\n \"initial_stock\": 3,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 7,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 8,\n 3,\n 2\n ],\n \"initial_stock\": 1,\n \"unit_cost\": 3,\n \"holding_cost\": 2,\n \"shortage_cost\": 12,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":174,"warehouse_capacity":25,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[3,3,2],"initial_stock":0,"unit_cost":7,"holding_cost":1,"shortage_cost":9,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[6,2,7],"initial_stock":3,"unit_cost":5,"holding_cost":3,"shortage_cost":7,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[8,3,2],"initial_stock":1,"unit_cost":3,"holding_cost":2,"shortage_cost":12,"pack_size":2,"lead_time":0}]},"gold_status":"optimal","gold_objective":160.0,"gold_bound":160.0,"gold_solution":{"family":"inventory","status":"optimal","objective":160.0,"bound":160.0,"orders":[{"sku_id":"S1","period":1,"qty":3},{"sku_id":"S1","period":2,"qty":3},{"sku_id":"S1","period":3,"qty":2},{"sku_id":"S2","period":1,"qty":4},{"sku_id":"S2","period":2,"qty":2},{"sku_id":"S2","period":3,"qty":6},{"sku_id":"S3","period":1,"qty":8},{"sku_id":"S3","period":2,"qty":2},{"sku_id":"S3","period":3,"qty":2}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"7ab02a4b652b205f","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-031","family":"inventory","split":"test","interactive":true,"difficulty":"easy","language":"en","template_id":"T-A","seed":25031,"prompt_en":"Replenish S1 (bearing), S2 (seal) over a 3-week horizon. Lost sales are allowed and charged. The buyer cannot spend more than 178. On-hand stock across SKUs cannot exceed 25. S1 wants [7, 6, 5] at pack 1; S2 wants [2, 5, 5] at pack 1. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند) در افق 3 هفته خرید کنید. کمبود مجاز است و جریمه دارد. سقف هزینه 178 و سقف موجودی کل 25 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 178,\n \"warehouse_capacity\": 25,\n \"cover_required\": false,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 7,\n 6,\n 5\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 6,\n \"holding_cost\": 1,\n \"shortage_cost\": 7,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 2,\n 5,\n 5\n ],\n \"initial_stock\": 2,\n \"unit_cost\": 7,\n \"holding_cost\": 3,\n \"shortage_cost\": 9,\n \"pack_size\": 1,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":178,"warehouse_capacity":25,"cover_required":false,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[7,6,5],"initial_stock":2,"unit_cost":6,"holding_cost":1,"shortage_cost":7,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[2,5,5],"initial_stock":2,"unit_cost":7,"holding_cost":3,"shortage_cost":9,"pack_size":1,"lead_time":0}]},"gold_status":"optimal","gold_objective":166.0,"gold_bound":166.0,"gold_solution":{"family":"inventory","status":"optimal","objective":166.0,"bound":166.0,"orders":[{"sku_id":"S1","period":1,"qty":5},{"sku_id":"S1","period":2,"qty":6},{"sku_id":"S1","period":3,"qty":5},{"sku_id":"S2","period":1,"qty":0},{"sku_id":"S2","period":2,"qty":5},{"sku_id":"S2","period":3,"qty":5}],"assignments":[],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"17d8f21147efad41","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-032","family":"inventory","split":"test","interactive":false,"difficulty":"infeasible","language":"fa","template_id":"T-B","seed":25032,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 49. On-hand stock across SKUs cannot exceed 47. S1 wants [3, 8, 6] at pack 1; S2 wants [8, 3, 6] at pack 2; S3 wants [5, 3, 5] at pack 2. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 49 و سقف موجودی کل 47 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 49,\n \"warehouse_capacity\": 47,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 3,\n 8,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 3,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 8,\n 3,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 4,\n \"holding_cost\": 1,\n \"shortage_cost\": 14,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 5,\n 3,\n 5\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 9,\n \"holding_cost\": 2,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":49,"warehouse_capacity":47,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[3,8,6],"initial_stock":0,"unit_cost":3,"holding_cost":2,"shortage_cost":6,"pack_size":1,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[8,3,6],"initial_stock":0,"unit_cost":4,"holding_cost":1,"shortage_cost":14,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[5,3,5],"initial_stock":0,"unit_cost":9,"holding_cost":2,"shortage_cost":10,"pack_size":2,"lead_time":0}]},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"inventory","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"a81392c6044cd7df","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-033","family":"inventory","split":"test","interactive":false,"difficulty":"infeasible","language":"en","template_id":"T-A","seed":25033,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 42. On-hand stock across SKUs cannot exceed 41. S1 wants [3, 3, 3] at pack 2; S2 wants [4, 7, 7] at pack 2; S3 wants [3, 7, 4] at pack 3. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 42 و سقف موجودی کل 41 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 42,\n \"warehouse_capacity\": 41,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 3,\n 3,\n 3\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 5,\n \"holding_cost\": 3,\n \"shortage_cost\": 11,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 4,\n 7,\n 7\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 4,\n \"holding_cost\": 2,\n \"shortage_cost\": 6,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 3,\n 7,\n 4\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 6,\n \"holding_cost\": 3,\n \"shortage_cost\": 8,\n \"pack_size\": 3,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":42,"warehouse_capacity":41,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[3,3,3],"initial_stock":0,"unit_cost":5,"holding_cost":3,"shortage_cost":11,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[4,7,7],"initial_stock":0,"unit_cost":4,"holding_cost":2,"shortage_cost":6,"pack_size":2,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[3,7,4],"initial_stock":0,"unit_cost":6,"holding_cost":3,"shortage_cost":8,"pack_size":3,"lead_time":0}]},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"inventory","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"ea9231d0be843484","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"INV-034","family":"inventory","split":"test","interactive":true,"difficulty":"infeasible","language":"fa","template_id":"T-B","seed":25034,"prompt_en":"Replenish S1 (bearing), S2 (seal), S3 (gasket) over a 3-week horizon. All demand must be covered; lost sales are forbidden. The buyer cannot spend more than 56. On-hand stock across SKUs cannot exceed 52. S1 wants [4, 7, 6] at pack 2; S2 wants [8, 3, 8] at pack 1; S3 wants [6, 3, 7] at pack 2. Costs and opening stock are in the JSON companion.","prompt_fa":"برای S1 (بلبرینگ), S2 (آب‌بند), S3 (واشر) در افق 3 هفته خرید کنید. پوشش کامل تقاضا الزامی است. سقف هزینه 56 و سقف موجودی کل 52 است. جزئیات تقاضا و بسته در فایل JSON همراه است.","prompt_json":"{\n \"periods\": 3,\n \"budget\": 56,\n \"warehouse_capacity\": 52,\n \"cover_required\": true,\n \"lost_sales\": true,\n \"skus\": [\n {\n \"sku_id\": \"S1\",\n \"name\": \"bearing\",\n \"demand\": [\n 4,\n 7,\n 6\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 9,\n \"holding_cost\": 1,\n \"shortage_cost\": 10,\n \"pack_size\": 2,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S2\",\n \"name\": \"seal\",\n \"demand\": [\n 8,\n 3,\n 8\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 3,\n \"holding_cost\": 3,\n \"shortage_cost\": 9,\n \"pack_size\": 1,\n \"lead_time\": 0\n },\n {\n \"sku_id\": \"S3\",\n \"name\": \"gasket\",\n \"demand\": [\n 6,\n 3,\n 7\n ],\n \"initial_stock\": 0,\n \"unit_cost\": 4,\n \"holding_cost\": 2,\n \"shortage_cost\": 8,\n \"pack_size\": 2,\n \"lead_time\": 0\n }\n ]\n}","schema_payload":{"periods":3,"budget":56,"warehouse_capacity":52,"cover_required":true,"lost_sales":true,"skus":[{"sku_id":"S1","name":"bearing","demand":[4,7,6],"initial_stock":0,"unit_cost":9,"holding_cost":1,"shortage_cost":10,"pack_size":2,"lead_time":0},{"sku_id":"S2","name":"seal","demand":[8,3,8],"initial_stock":0,"unit_cost":3,"holding_cost":3,"shortage_cost":9,"pack_size":1,"lead_time":0},{"sku_id":"S3","name":"gasket","demand":[6,3,7],"initial_stock":0,"unit_cost":4,"holding_cost":2,"shortage_cost":8,"pack_size":2,"lead_time":0}]},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"inventory","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"da716bb0cb346fe1","notes":"lead time is 0; units are abstract currency and pieces"} {"problem_id":"ASN-001","family":"assignment","split":"development","interactive":true,"difficulty":"easy","language":"fa","template_id":"D-A","seed":50001,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills lift/weld, T2 size 1 skills inspect, T3 size 2 skills pack, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 6 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 22}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 40}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 38}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 13}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills lift/weld, T2 size 1 skills inspect, T3 size 2 skills pack, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 6 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 22}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 40}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 38}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 13}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 38\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["lift","weld"],"penalty":40},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect"],"penalty":22},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["pack"],"penalty":40},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["inspect","weld"],"penalty":38}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":12},{"task_id":"T1","agent_id":"A3","cost":13},{"task_id":"T2","agent_id":"A2","cost":4},{"task_id":"T2","agent_id":"A3","cost":5},{"task_id":"T3","agent_id":"A3","cost":12},{"task_id":"T4","agent_id":"A1","cost":11},{"task_id":"T4","agent_id":"A2","cost":7},{"task_id":"T4","agent_id":"A3","cost":13}]},"gold_status":"optimal","gold_objective":35.0,"gold_bound":35.0,"gold_solution":{"family":"assignment","status":"optimal","objective":35.0,"bound":35.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A2"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"1cddcd6462c5befc","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-002","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":50002,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills weld, T2 size 2 skills inspect/pack, T3 size 2 skills pack/weld, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 37}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 22}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 11}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills weld, T2 size 2 skills inspect/pack, T3 size 2 skills pack/weld, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 37}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 22}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 11}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 37\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["weld"],"penalty":37},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","pack"],"penalty":34},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["pack","weld"],"penalty":22},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["inspect","weld"],"penalty":37}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":11},{"task_id":"T1","agent_id":"A3","cost":13},{"task_id":"T2","agent_id":"A2","cost":4},{"task_id":"T2","agent_id":"A3","cost":11},{"task_id":"T3","agent_id":"A1","cost":6},{"task_id":"T3","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A1","cost":17},{"task_id":"T4","agent_id":"A2","cost":9},{"task_id":"T4","agent_id":"A3","cost":7}]},"gold_status":"optimal","gold_objective":26.0,"gold_bound":26.0,"gold_solution":{"family":"assignment","status":"optimal","objective":26.0,"bound":26.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"d2c2d3e77c899e5b","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-003","family":"assignment","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":50003,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills inspect/lift, T2 size 2 skills inspect/lift, T3 size 2 skills pack/weld, T4 size 2 skills pack/weld, T5 size 1 skills inspect/lift, T6 size 2 skills inspect/lift\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 31}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 25}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 28}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 39}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 38}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 5}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 14}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills inspect/lift, T2 size 2 skills inspect/lift, T3 size 2 skills pack/weld, T4 size 2 skills pack/weld, T5 size 1 skills inspect/lift, T6 size 2 skills inspect/lift\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 31}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 25}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 28}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 39}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 38}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 5}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 14}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 31\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 25\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 24\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["inspect","lift"],"penalty":31},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","lift"],"penalty":25},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["pack","weld"],"penalty":28},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["pack","weld"],"penalty":39},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["inspect","lift"],"penalty":38},{"task_id":"T6","name":"job-6","size":2,"required":true,"skills":["inspect","lift"],"penalty":24}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":6},{"task_id":"T1","agent_id":"A2","cost":18},{"task_id":"T1","agent_id":"A3","cost":17},{"task_id":"T2","agent_id":"A1","cost":8},{"task_id":"T2","agent_id":"A2","cost":5},{"task_id":"T2","agent_id":"A3","cost":13},{"task_id":"T3","agent_id":"A1","cost":9},{"task_id":"T3","agent_id":"A2","cost":8},{"task_id":"T3","agent_id":"A3","cost":6},{"task_id":"T4","agent_id":"A1","cost":15},{"task_id":"T4","agent_id":"A2","cost":8},{"task_id":"T4","agent_id":"A3","cost":12},{"task_id":"T5","agent_id":"A1","cost":6},{"task_id":"T5","agent_id":"A2","cost":9},{"task_id":"T5","agent_id":"A3","cost":18},{"task_id":"T6","agent_id":"A1","cost":5},{"task_id":"T6","agent_id":"A2","cost":16},{"task_id":"T6","agent_id":"A3","cost":14}]},"gold_status":"optimal","gold_objective":39.0,"gold_bound":39.0,"gold_solution":{"family":"assignment","status":"optimal","objective":39.0,"bound":39.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A2"},{"task_id":"T5","agent_id":"A1"},{"task_id":"T6","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"7cb9463c065ed495","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-004","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":50004,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills inspect/weld, T2 size 3 skills inspect, T3 size 3 skills lift/pack, T4 size 2 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 3 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 22}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 31}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills inspect/weld, T2 size 3 skills inspect, T3 size 3 skills lift/pack, T4 size 2 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 3 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 22}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 31}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 31\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 37\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","weld"],"penalty":40},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect"],"penalty":22},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["lift","pack"],"penalty":31},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["lift","weld"],"penalty":37}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":14},{"task_id":"T1","agent_id":"A2","cost":15},{"task_id":"T1","agent_id":"A3","cost":6},{"task_id":"T2","agent_id":"A2","cost":16},{"task_id":"T2","agent_id":"A3","cost":8},{"task_id":"T3","agent_id":"A3","cost":15},{"task_id":"T4","agent_id":"A1","cost":7},{"task_id":"T4","agent_id":"A3","cost":16}]},"gold_status":"optimal","gold_objective":44.0,"gold_bound":44.0,"gold_solution":{"family":"assignment","status":"optimal","objective":44.0,"bound":44.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"617e65bd9540551c","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-005","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-B","seed":50005,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills pack/weld, T2 size 2 skills inspect/weld, T3 size 3 skills pack, T4 size 3 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 5 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 24}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 34}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills pack/weld, T2 size 2 skills inspect/weld, T3 size 3 skills pack, T4 size 3 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 5 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 24}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 34}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 24\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 34\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["pack","weld"],"penalty":24},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","weld"],"penalty":33},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["pack"],"penalty":32},{"task_id":"T4","name":"job-4","size":3,"required":false,"skills":["inspect","weld"],"penalty":34}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":14},{"task_id":"T1","agent_id":"A3","cost":16},{"task_id":"T2","agent_id":"A1","cost":11},{"task_id":"T2","agent_id":"A2","cost":11},{"task_id":"T2","agent_id":"A3","cost":5},{"task_id":"T3","agent_id":"A3","cost":6},{"task_id":"T4","agent_id":"A1","cost":7},{"task_id":"T4","agent_id":"A2","cost":5},{"task_id":"T4","agent_id":"A3","cost":16}]},"gold_status":"optimal","gold_objective":30.0,"gold_bound":30.0,"gold_solution":{"family":"assignment","status":"optimal","objective":30.0,"bound":30.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A2"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"313df2be239a5ae9","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-006","family":"assignment","split":"development","interactive":true,"difficulty":"medium","language":"en","template_id":"D-C","seed":50006,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills inspect/lift, T2 size 3 skills inspect/lift, T3 size 3 skills lift, T4 size 1 skills inspect, T5 size 2 skills lift/pack, T6 size 2 skills lift\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 5 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 20}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 27}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 28}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 39}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 40}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 38}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills inspect/lift, T2 size 3 skills inspect/lift, T3 size 3 skills lift, T4 size 1 skills inspect, T5 size 2 skills lift/pack, T6 size 2 skills lift\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 5 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 20}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 27}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 28}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 39}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 40}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 38}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 27\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 38\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 11\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","lift"],"penalty":20},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","lift"],"penalty":27},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["lift"],"penalty":28},{"task_id":"T4","name":"job-4","size":1,"required":true,"skills":["inspect"],"penalty":39},{"task_id":"T5","name":"job-5","size":2,"required":true,"skills":["lift","pack"],"penalty":40},{"task_id":"T6","name":"job-6","size":2,"required":true,"skills":["lift"],"penalty":38}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":11},{"task_id":"T1","agent_id":"A2","cost":8},{"task_id":"T1","agent_id":"A3","cost":16},{"task_id":"T2","agent_id":"A1","cost":8},{"task_id":"T2","agent_id":"A2","cost":4},{"task_id":"T2","agent_id":"A3","cost":9},{"task_id":"T3","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A1","cost":11},{"task_id":"T4","agent_id":"A2","cost":18},{"task_id":"T4","agent_id":"A3","cost":14},{"task_id":"T5","agent_id":"A2","cost":15},{"task_id":"T5","agent_id":"A3","cost":7},{"task_id":"T6","agent_id":"A3","cost":11}]},"gold_status":"optimal","gold_objective":48.0,"gold_bound":48.0,"gold_solution":{"family":"assignment","status":"optimal","objective":48.0,"bound":48.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"633fec80b9b681c9","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-007","family":"assignment","split":"development","interactive":false,"difficulty":"hard","language":"fa","template_id":"D-A","seed":50007,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills inspect/lift, T2 size 3 skills inspect/lift, T3 size 3 skills inspect/lift, T4 size 2 skills lift/pack, T5 size 1 skills inspect/weld, T6 size 1 skills pack, T7 size 1 skills inspect/pack, T8 size 1 skills lift/weld\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 5 skills lift/pack, A4 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 29}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 30}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 22}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 21}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 32}, {\"task_id\": \"T7\", \"name\": \"job-7\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 23}, {\"task_id\": \"T8\", \"name\": \"job-8\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"lift\", \"pack\"]}, {\"agent_id\": \"A4\", \"name\": \"tech-4\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A4\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A4\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A4\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T5\", \"agent_id\": \"A4\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T6\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T7\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T7\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T7\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T7\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T8\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T8\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T8\", \"agent_id\": \"A4\", \"cost\": 8}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills inspect/lift, T2 size 3 skills inspect/lift, T3 size 3 skills inspect/lift, T4 size 2 skills lift/pack, T5 size 1 skills inspect/weld, T6 size 1 skills pack, T7 size 1 skills inspect/pack, T8 size 1 skills lift/weld\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 5 skills lift/pack, A4 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 29}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 30}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 22}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 21}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 32}, {\"task_id\": \"T7\", \"name\": \"job-7\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 23}, {\"task_id\": \"T8\", \"name\": \"job-8\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"lift\", \"pack\"]}, {\"agent_id\": \"A4\", \"name\": \"tech-4\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A4\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A4\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A4\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T5\", \"agent_id\": \"A4\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T6\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T7\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T7\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T7\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T7\", \"agent_id\": \"A4\", \"cost\": 5}, {\"task_id\": \"T8\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T8\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T8\", \"agent_id\": \"A4\", \"cost\": 8}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 21\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 21\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T7\",\n \"name\": \"job-7\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 23\n },\n {\n \"task_id\": \"T8\",\n \"name\": \"job-8\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 24\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"lift\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A4\",\n \"name\": \"tech-4\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A4\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A4\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A4\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A4\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A4\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A4\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A4\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A4\",\n \"cost\": 8\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["inspect","lift"],"penalty":21},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","lift"],"penalty":29},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["inspect","lift"],"penalty":30},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["lift","pack"],"penalty":22},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["inspect","weld"],"penalty":21},{"task_id":"T6","name":"job-6","size":1,"required":true,"skills":["pack"],"penalty":32},{"task_id":"T7","name":"job-7","size":1,"required":true,"skills":["inspect","pack"],"penalty":23},{"task_id":"T8","name":"job-8","size":1,"required":true,"skills":["lift","weld"],"penalty":24}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["lift","pack"]},{"agent_id":"A4","name":"tech-4","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":12},{"task_id":"T1","agent_id":"A2","cost":12},{"task_id":"T1","agent_id":"A3","cost":12},{"task_id":"T1","agent_id":"A4","cost":7},{"task_id":"T2","agent_id":"A1","cost":11},{"task_id":"T2","agent_id":"A2","cost":18},{"task_id":"T2","agent_id":"A3","cost":18},{"task_id":"T2","agent_id":"A4","cost":14},{"task_id":"T3","agent_id":"A1","cost":4},{"task_id":"T3","agent_id":"A2","cost":6},{"task_id":"T3","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A4","cost":5},{"task_id":"T4","agent_id":"A2","cost":13},{"task_id":"T4","agent_id":"A3","cost":6},{"task_id":"T4","agent_id":"A4","cost":17},{"task_id":"T5","agent_id":"A1","cost":10},{"task_id":"T5","agent_id":"A2","cost":9},{"task_id":"T5","agent_id":"A4","cost":18},{"task_id":"T6","agent_id":"A2","cost":12},{"task_id":"T6","agent_id":"A3","cost":7},{"task_id":"T6","agent_id":"A4","cost":5},{"task_id":"T7","agent_id":"A1","cost":14},{"task_id":"T7","agent_id":"A2","cost":15},{"task_id":"T7","agent_id":"A3","cost":13},{"task_id":"T7","agent_id":"A4","cost":5},{"task_id":"T8","agent_id":"A1","cost":17},{"task_id":"T8","agent_id":"A3","cost":18},{"task_id":"T8","agent_id":"A4","cost":8}]},"gold_status":"optimal","gold_objective":55.0,"gold_bound":55.0,"gold_solution":{"family":"assignment","status":"optimal","objective":55.0,"bound":55.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A4"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A1"},{"task_id":"T4","agent_id":"A3"},{"task_id":"T5","agent_id":"A2"},{"task_id":"T6","agent_id":"A4"},{"task_id":"T7","agent_id":"A4"},{"task_id":"T8","agent_id":"A4"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"4d73d8bdc819ff4a","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-008","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":50008,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills lift/weld, T2 size 1 skills inspect/weld, T3 size 1 skills inspect/pack, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 6 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 34}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 20}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 26}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills lift/weld, T2 size 1 skills inspect/weld, T3 size 1 skills inspect/pack, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 6 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 34}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 20}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 26}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 26\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["lift","weld"],"penalty":34},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","weld"],"penalty":33},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["inspect","pack"],"penalty":20},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["inspect","weld"],"penalty":26}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":12},{"task_id":"T1","agent_id":"A3","cost":16},{"task_id":"T2","agent_id":"A1","cost":4},{"task_id":"T2","agent_id":"A2","cost":5},{"task_id":"T2","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A2","cost":8},{"task_id":"T3","agent_id":"A3","cost":13},{"task_id":"T4","agent_id":"A1","cost":7},{"task_id":"T4","agent_id":"A2","cost":17},{"task_id":"T4","agent_id":"A3","cost":7}]},"gold_status":"optimal","gold_objective":31.0,"gold_bound":31.0,"gold_solution":{"family":"assignment","status":"optimal","objective":31.0,"bound":31.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A2"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"0e4781ed5b25d32c","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-009","family":"assignment","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":50009,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills inspect/lift, T2 size 2 skills lift/pack, T3 size 2 skills pack, T4 size 1 skills inspect/lift, T5 size 3 skills inspect/weld, T6 size 1 skills lift/weld\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 4 skills inspect/pack, A3 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 39}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 30}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 20}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 25}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 32}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 4, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 7}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 9}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills inspect/lift, T2 size 2 skills lift/pack, T3 size 2 skills pack, T4 size 1 skills inspect/lift, T5 size 3 skills inspect/weld, T6 size 1 skills lift/weld\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 4 skills inspect/pack, A3 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 39}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 30}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 20}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 25}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 32}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 4, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 7}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 11}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 9}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 25\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 32\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 9\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","lift"],"penalty":39},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["lift","pack"],"penalty":30},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["pack"],"penalty":20},{"task_id":"T4","name":"job-4","size":1,"required":true,"skills":["inspect","lift"],"penalty":25},{"task_id":"T5","name":"job-5","size":3,"required":true,"skills":["inspect","weld"],"penalty":32},{"task_id":"T6","name":"job-6","size":1,"required":true,"skills":["lift","weld"],"penalty":32}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":4,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":14},{"task_id":"T1","agent_id":"A2","cost":4},{"task_id":"T1","agent_id":"A3","cost":15},{"task_id":"T2","agent_id":"A2","cost":14},{"task_id":"T2","agent_id":"A3","cost":6},{"task_id":"T3","agent_id":"A2","cost":7},{"task_id":"T3","agent_id":"A3","cost":12},{"task_id":"T4","agent_id":"A1","cost":16},{"task_id":"T4","agent_id":"A2","cost":9},{"task_id":"T4","agent_id":"A3","cost":15},{"task_id":"T5","agent_id":"A1","cost":11},{"task_id":"T5","agent_id":"A2","cost":16},{"task_id":"T5","agent_id":"A3","cost":6},{"task_id":"T6","agent_id":"A1","cost":17},{"task_id":"T6","agent_id":"A3","cost":9}]},"gold_status":"optimal","gold_objective":51.0,"gold_bound":51.0,"gold_solution":{"family":"assignment","status":"optimal","objective":51.0,"bound":51.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A2"},{"task_id":"T4","agent_id":"A2"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"2ed0462d809cf9b4","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-010","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":50010,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills weld, T2 size 2 skills inspect/pack, T3 size 2 skills pack, T4 size 3 skills inspect/weld\nAGENTS: A1 cap 6 skills weld, A2 cap 4 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 38}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 39}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 20}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 4, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 17}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills weld, T2 size 2 skills inspect/pack, T3 size 2 skills pack, T4 size 3 skills inspect/weld\nAGENTS: A1 cap 6 skills weld, A2 cap 4 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 40}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 38}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 39}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 20}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 4, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 13}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 17}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 20\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["weld"],"penalty":40},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","pack"],"penalty":38},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["pack"],"penalty":39},{"task_id":"T4","name":"job-4","size":3,"required":false,"skills":["inspect","weld"],"penalty":20}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":4,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":15},{"task_id":"T1","agent_id":"A3","cost":5},{"task_id":"T2","agent_id":"A2","cost":4},{"task_id":"T2","agent_id":"A3","cost":13},{"task_id":"T3","agent_id":"A3","cost":7},{"task_id":"T4","agent_id":"A1","cost":8},{"task_id":"T4","agent_id":"A2","cost":8},{"task_id":"T4","agent_id":"A3","cost":17}]},"gold_status":"optimal","gold_objective":24.0,"gold_bound":24.0,"gold_solution":{"family":"assignment","status":"optimal","objective":24.0,"bound":24.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"f1b67e1305aef3ad","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-011","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-B","seed":50011,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills pack/weld, T2 size 3 skills inspect/weld, T3 size 3 skills lift/pack, T4 size 1 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 5 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 30}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 38}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 22}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 5}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills pack/weld, T2 size 3 skills inspect/weld, T3 size 3 skills lift/pack, T4 size 1 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 5 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 30}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 38}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 22}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 5}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 22\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["pack","weld"],"penalty":30},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","weld"],"penalty":34},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["lift","pack"],"penalty":38},{"task_id":"T4","name":"job-4","size":1,"required":false,"skills":["lift","weld"],"penalty":22}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":8},{"task_id":"T1","agent_id":"A3","cost":10},{"task_id":"T2","agent_id":"A1","cost":10},{"task_id":"T2","agent_id":"A2","cost":12},{"task_id":"T2","agent_id":"A3","cost":8},{"task_id":"T3","agent_id":"A3","cost":8},{"task_id":"T4","agent_id":"A1","cost":17},{"task_id":"T4","agent_id":"A3","cost":5}]},"gold_status":"optimal","gold_objective":29.0,"gold_bound":29.0,"gold_solution":{"family":"assignment","status":"optimal","objective":29.0,"bound":29.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"6e546d67a8410d0f","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-012","family":"assignment","split":"development","interactive":true,"difficulty":"medium","language":"en","template_id":"D-C","seed":50012,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills inspect/lift/pack, T2 size 2 skills inspect/lift, T3 size 1 skills inspect/lift, T4 size 3 skills inspect, T5 size 2 skills inspect, T6 size 3 skills lift/weld\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"pack\"], \"penalty\": 37}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 40}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 35}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 36}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills inspect/lift/pack, T2 size 2 skills inspect/lift, T3 size 1 skills inspect/lift, T4 size 3 skills inspect, T5 size 2 skills inspect, T6 size 3 skills lift/weld\nAGENTS: A1 cap 5 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"pack\"], \"penalty\": 37}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 34}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 40}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 35}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 3, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 36}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 35\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 36\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 11\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","lift","pack"],"penalty":37},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","lift"],"penalty":34},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["inspect","lift"],"penalty":32},{"task_id":"T4","name":"job-4","size":3,"required":true,"skills":["inspect"],"penalty":40},{"task_id":"T5","name":"job-5","size":2,"required":true,"skills":["inspect"],"penalty":35},{"task_id":"T6","name":"job-6","size":3,"required":true,"skills":["lift","weld"],"penalty":36}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":18},{"task_id":"T1","agent_id":"A2","cost":17},{"task_id":"T1","agent_id":"A3","cost":5},{"task_id":"T2","agent_id":"A1","cost":7},{"task_id":"T2","agent_id":"A2","cost":5},{"task_id":"T2","agent_id":"A3","cost":5},{"task_id":"T3","agent_id":"A1","cost":15},{"task_id":"T3","agent_id":"A2","cost":9},{"task_id":"T3","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A1","cost":4},{"task_id":"T4","agent_id":"A2","cost":8},{"task_id":"T4","agent_id":"A3","cost":7},{"task_id":"T5","agent_id":"A1","cost":17},{"task_id":"T5","agent_id":"A2","cost":15},{"task_id":"T5","agent_id":"A3","cost":10},{"task_id":"T6","agent_id":"A1","cost":15},{"task_id":"T6","agent_id":"A3","cost":11}]},"gold_status":"optimal","gold_objective":47.0,"gold_bound":47.0,"gold_solution":{"family":"assignment","status":"optimal","objective":47.0,"bound":47.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A2"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"2b47606bb2a45436","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-013","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-A","seed":50013,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills lift/weld, T2 size 1 skills inspect/lift, T3 size 1 skills pack, T4 size 1 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 6 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 39}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 24}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 18}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills lift/weld, T2 size 1 skills inspect/lift, T3 size 1 skills pack, T4 size 1 skills inspect/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 6 skills inspect, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 39}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\"], \"penalty\": 24}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 1, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 6, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 15}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 18}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 21\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 24\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 24\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["lift","weld"],"penalty":21},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","lift"],"penalty":39},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack"],"penalty":24},{"task_id":"T4","name":"job-4","size":1,"required":false,"skills":["inspect","weld"],"penalty":24}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":9},{"task_id":"T1","agent_id":"A3","cost":10},{"task_id":"T2","agent_id":"A2","cost":14},{"task_id":"T2","agent_id":"A3","cost":7},{"task_id":"T3","agent_id":"A3","cost":6},{"task_id":"T4","agent_id":"A1","cost":15},{"task_id":"T4","agent_id":"A2","cost":13},{"task_id":"T4","agent_id":"A3","cost":18}]},"gold_status":"optimal","gold_objective":35.0,"gold_bound":35.0,"gold_solution":{"family":"assignment","status":"optimal","objective":35.0,"bound":35.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A2"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"04a6ab674fa9c7ce","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-014","family":"assignment","split":"development","interactive":false,"difficulty":"hard","language":"en","template_id":"D-B","seed":50014,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills inspect/pack, T2 size 3 skills inspect/lift, T3 size 2 skills inspect/pack, T4 size 2 skills inspect/lift, T5 size 1 skills inspect/pack, T6 size 3 skills inspect/weld, T7 size 1 skills inspect/lift, T8 size 3 skills lift\nAGENTS: A1 cap 4 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills lift/pack, A4 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 40}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 31}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 35}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 20}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 28}, {\"task_id\": \"T7\", \"name\": \"job-7\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 22}, {\"task_id\": \"T8\", \"name\": \"job-8\", \"size\": 3, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 28}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"lift\", \"pack\"]}, {\"agent_id\": \"A4\", \"name\": \"tech-4\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A4\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A4\", \"cost\": 12}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T3\", \"agent_id\": \"A4\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A4\", \"cost\": 18}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T5\", \"agent_id\": \"A4\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T6\", \"agent_id\": \"A4\", \"cost\": 17}, {\"task_id\": \"T7\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T7\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T7\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T7\", \"agent_id\": \"A4\", \"cost\": 7}, {\"task_id\": \"T8\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T8\", \"agent_id\": \"A4\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills inspect/pack, T2 size 3 skills inspect/lift, T3 size 2 skills inspect/pack, T4 size 2 skills inspect/lift, T5 size 1 skills inspect/pack, T6 size 3 skills inspect/weld, T7 size 1 skills inspect/lift, T8 size 3 skills lift\nAGENTS: A1 cap 4 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills lift/pack, A4 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 21}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 40}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 31}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 35}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 20}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 28}, {\"task_id\": \"T7\", \"name\": \"job-7\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 22}, {\"task_id\": \"T8\", \"name\": \"job-8\", \"size\": 3, \"required\": true, \"skills\": [\"lift\"], \"penalty\": 28}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"lift\", \"pack\"]}, {\"agent_id\": \"A4\", \"name\": \"tech-4\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T1\", \"agent_id\": \"A4\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A4\", \"cost\": 12}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 16}, {\"task_id\": \"T3\", \"agent_id\": \"A4\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T4\", \"agent_id\": \"A4\", \"cost\": 18}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 18}, {\"task_id\": \"T5\", \"agent_id\": \"A4\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T6\", \"agent_id\": \"A4\", \"cost\": 17}, {\"task_id\": \"T7\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T7\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T7\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T7\", \"agent_id\": \"A4\", \"cost\": 7}, {\"task_id\": \"T8\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T8\", \"agent_id\": \"A4\", \"cost\": 11}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 21\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 31\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 35\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T7\",\n \"name\": \"job-7\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T8\",\n \"name\": \"job-8\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 28\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"lift\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A4\",\n \"name\": \"tech-4\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A4\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A4\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A4\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A4\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A4\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A4\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A4\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A4\",\n \"cost\": 11\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["inspect","pack"],"penalty":21},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","lift"],"penalty":40},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["inspect","pack"],"penalty":31},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["inspect","lift"],"penalty":35},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["inspect","pack"],"penalty":20},{"task_id":"T6","name":"job-6","size":3,"required":true,"skills":["inspect","weld"],"penalty":28},{"task_id":"T7","name":"job-7","size":1,"required":true,"skills":["inspect","lift"],"penalty":22},{"task_id":"T8","name":"job-8","size":3,"required":true,"skills":["lift"],"penalty":28}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":4,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["lift","pack"]},{"agent_id":"A4","name":"tech-4","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":9},{"task_id":"T1","agent_id":"A2","cost":15},{"task_id":"T1","agent_id":"A3","cost":15},{"task_id":"T1","agent_id":"A4","cost":13},{"task_id":"T2","agent_id":"A1","cost":14},{"task_id":"T2","agent_id":"A2","cost":4},{"task_id":"T2","agent_id":"A3","cost":16},{"task_id":"T2","agent_id":"A4","cost":12},{"task_id":"T3","agent_id":"A1","cost":10},{"task_id":"T3","agent_id":"A2","cost":5},{"task_id":"T3","agent_id":"A3","cost":16},{"task_id":"T3","agent_id":"A4","cost":4},{"task_id":"T4","agent_id":"A1","cost":18},{"task_id":"T4","agent_id":"A2","cost":14},{"task_id":"T4","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A4","cost":18},{"task_id":"T5","agent_id":"A1","cost":14},{"task_id":"T5","agent_id":"A2","cost":12},{"task_id":"T5","agent_id":"A3","cost":18},{"task_id":"T5","agent_id":"A4","cost":10},{"task_id":"T6","agent_id":"A1","cost":18},{"task_id":"T6","agent_id":"A2","cost":5},{"task_id":"T6","agent_id":"A4","cost":17},{"task_id":"T7","agent_id":"A1","cost":6},{"task_id":"T7","agent_id":"A2","cost":5},{"task_id":"T7","agent_id":"A3","cost":6},{"task_id":"T7","agent_id":"A4","cost":7},{"task_id":"T8","agent_id":"A3","cost":12},{"task_id":"T8","agent_id":"A4","cost":11}]},"gold_status":"optimal","gold_objective":64.0,"gold_bound":64.0,"gold_solution":{"family":"assignment","status":"optimal","objective":64.0,"bound":64.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A4"},{"task_id":"T4","agent_id":"A3"},{"task_id":"T5","agent_id":"A4"},{"task_id":"T6","agent_id":"A2"},{"task_id":"T7","agent_id":"A3"},{"task_id":"T8","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"8855bfdfd2935d7e","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-015","family":"assignment","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":50015,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 3 skills inspect, T2 size 2 skills inspect/weld, T3 size 3 skills pack/weld, T4 size 2 skills inspect, T5 size 2 skills inspect, T6 size 1 skills inspect/lift/weld\nAGENTS: A1 cap 4 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 31}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 23}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 27}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 10}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 3 skills inspect, T2 size 2 skills inspect/weld, T3 size 3 skills pack/weld, T4 size 2 skills inspect, T5 size 2 skills inspect, T6 size 1 skills inspect/lift/weld\nAGENTS: A1 cap 4 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 31}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 23}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 32}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 27}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 8, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 6}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 13}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 6}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 12}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 10}, {\"task_id\": \"T6\", \"agent_id\": \"A1\", \"cost\": 14}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 10}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 31\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 23\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 27\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect"],"penalty":32},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","weld"],"penalty":31},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["pack","weld"],"penalty":23},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["inspect"],"penalty":32},{"task_id":"T5","name":"job-5","size":2,"required":true,"skills":["inspect"],"penalty":32},{"task_id":"T6","name":"job-6","size":1,"required":true,"skills":["inspect","lift","weld"],"penalty":27}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":4,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":6},{"task_id":"T1","agent_id":"A2","cost":4},{"task_id":"T1","agent_id":"A3","cost":7},{"task_id":"T2","agent_id":"A1","cost":12},{"task_id":"T2","agent_id":"A2","cost":13},{"task_id":"T2","agent_id":"A3","cost":14},{"task_id":"T3","agent_id":"A1","cost":17},{"task_id":"T3","agent_id":"A2","cost":6},{"task_id":"T3","agent_id":"A3","cost":5},{"task_id":"T4","agent_id":"A1","cost":8},{"task_id":"T4","agent_id":"A2","cost":11},{"task_id":"T4","agent_id":"A3","cost":6},{"task_id":"T5","agent_id":"A1","cost":12},{"task_id":"T5","agent_id":"A2","cost":12},{"task_id":"T5","agent_id":"A3","cost":10},{"task_id":"T6","agent_id":"A1","cost":14},{"task_id":"T6","agent_id":"A2","cost":18},{"task_id":"T6","agent_id":"A3","cost":10}]},"gold_status":"optimal","gold_objective":47.0,"gold_bound":47.0,"gold_solution":{"family":"assignment","status":"optimal","objective":47.0,"bound":47.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A2"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"d507c6d1a92b00e1","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-016","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":50016,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills weld, T2 size 3 skills inspect/weld, T3 size 2 skills inspect/pack, T4 size 2 skills lift/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 5 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 27}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 25}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills weld, T2 size 3 skills inspect/weld, T3 size 2 skills inspect/pack, T4 size 2 skills lift/weld\nAGENTS: A1 cap 3 skills weld, A2 cap 5 skills inspect, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 27}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"pack\"], \"penalty\": 25}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 24}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 9}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 7}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 27\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 25\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 24\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["weld"],"penalty":27},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","weld"],"penalty":32},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["inspect","pack"],"penalty":25},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["lift","weld"],"penalty":24}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":8},{"task_id":"T1","agent_id":"A3","cost":12},{"task_id":"T2","agent_id":"A1","cost":10},{"task_id":"T2","agent_id":"A2","cost":18},{"task_id":"T2","agent_id":"A3","cost":4},{"task_id":"T3","agent_id":"A2","cost":9},{"task_id":"T3","agent_id":"A3","cost":5},{"task_id":"T4","agent_id":"A1","cost":12},{"task_id":"T4","agent_id":"A3","cost":7}]},"gold_status":"optimal","gold_objective":28.0,"gold_bound":28.0,"gold_solution":{"family":"assignment","status":"optimal","objective":28.0,"bound":28.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A2"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"f9b263c3d202188e","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-017","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-B","seed":50017,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills lift/weld, T2 size 2 skills inspect/lift, T3 size 1 skills pack/weld, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 4 skills weld, A2 cap 5 skills inspect, A3 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 22}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 37}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 14}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills lift/weld, T2 size 2 skills inspect/lift, T3 size 1 skills pack/weld, T4 size 2 skills inspect/weld\nAGENTS: A1 cap 4 skills weld, A2 cap 5 skills inspect, A3 cap 7 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"weld\"], \"penalty\": 22}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 37}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"inspect\", \"weld\"], \"penalty\": 33}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 4, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 7, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 9}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 10}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 7}, {\"task_id\": \"T4\", \"agent_id\": \"A2\", \"cost\": 11}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 14}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 33\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["lift","weld"],"penalty":22},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","lift"],"penalty":37},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack","weld"],"penalty":32},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["inspect","weld"],"penalty":33}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":4,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":9},{"task_id":"T1","agent_id":"A3","cost":7},{"task_id":"T2","agent_id":"A2","cost":11},{"task_id":"T2","agent_id":"A3","cost":4},{"task_id":"T3","agent_id":"A1","cost":10},{"task_id":"T3","agent_id":"A3","cost":17},{"task_id":"T4","agent_id":"A1","cost":7},{"task_id":"T4","agent_id":"A2","cost":11},{"task_id":"T4","agent_id":"A3","cost":14}]},"gold_status":"optimal","gold_objective":28.0,"gold_bound":28.0,"gold_solution":{"family":"assignment","status":"optimal","objective":28.0,"bound":28.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A1"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"f515c7358f0c6201","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-018","family":"assignment","split":"development","interactive":true,"difficulty":"medium","language":"en","template_id":"D-C","seed":50018,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills inspect, T2 size 2 skills inspect/lift/weld, T3 size 3 skills inspect/lift/weld, T4 size 3 skills weld, T5 size 1 skills inspect, T6 size 2 skills lift/pack\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 27}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 30}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 37}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 24}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 6}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills inspect, T2 size 2 skills inspect/lift/weld, T3 size 3 skills inspect/lift/weld, T4 size 3 skills weld, T5 size 1 skills inspect, T6 size 2 skills lift/pack\nAGENTS: A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 6 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 27}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 30}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\", \"weld\"], \"penalty\": 33}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 3, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 37}, {\"task_id\": \"T5\", \"name\": \"job-5\", \"size\": 1, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 24}, {\"task_id\": \"T6\", \"name\": \"job-6\", \"size\": 2, \"required\": true, \"skills\": [\"lift\", \"pack\"], \"penalty\": 37}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 6, \"skills\": [\"inspect\", \"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\", \"pack\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 6, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T1\", \"agent_id\": \"A2\", \"cost\": 8}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T2\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 15}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 18}, {\"task_id\": \"T3\", \"agent_id\": \"A2\", \"cost\": 18}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 17}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 12}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 4}, {\"task_id\": \"T5\", \"agent_id\": \"A1\", \"cost\": 17}, {\"task_id\": \"T5\", \"agent_id\": \"A2\", \"cost\": 16}, {\"task_id\": \"T5\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T6\", \"agent_id\": \"A2\", \"cost\": 17}, {\"task_id\": \"T6\", \"agent_id\": \"A3\", \"cost\": 6}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 27\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 24\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 37\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["inspect"],"penalty":27},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","lift","weld"],"penalty":30},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["inspect","lift","weld"],"penalty":33},{"task_id":"T4","name":"job-4","size":3,"required":true,"skills":["weld"],"penalty":37},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["inspect"],"penalty":24},{"task_id":"T6","name":"job-6","size":2,"required":true,"skills":["lift","pack"],"penalty":37}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":17},{"task_id":"T1","agent_id":"A2","cost":8},{"task_id":"T1","agent_id":"A3","cost":4},{"task_id":"T2","agent_id":"A1","cost":8},{"task_id":"T2","agent_id":"A2","cost":16},{"task_id":"T2","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A1","cost":18},{"task_id":"T3","agent_id":"A2","cost":18},{"task_id":"T3","agent_id":"A3","cost":17},{"task_id":"T4","agent_id":"A1","cost":12},{"task_id":"T4","agent_id":"A3","cost":4},{"task_id":"T5","agent_id":"A1","cost":17},{"task_id":"T5","agent_id":"A2","cost":16},{"task_id":"T5","agent_id":"A3","cost":14},{"task_id":"T6","agent_id":"A2","cost":17},{"task_id":"T6","agent_id":"A3","cost":6}]},"gold_status":"optimal","gold_objective":58.0,"gold_bound":58.0,"gold_solution":{"family":"assignment","status":"optimal","objective":58.0,"bound":58.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A2"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A1"},{"task_id":"T4","agent_id":"A3"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"aa2a372f888bbc65","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-019","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"fa","template_id":"D-A","seed":50019,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 1 skills weld, T2 size 3 skills inspect/lift, T3 size 1 skills pack/weld, T4 size 2 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 35}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 38}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 29}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 33}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 1 skills weld, T2 size 3 skills inspect/lift, T3 size 1 skills pack/weld, T4 size 2 skills lift/weld\nAGENTS: A1 cap 5 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 1, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 35}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 3, \"required\": true, \"skills\": [\"inspect\", \"lift\"], \"penalty\": 38}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 29}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"lift\", \"weld\"], \"penalty\": 33}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 5, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 5, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 5}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 12}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 16}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 6}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 35\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 33\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":1,"required":true,"skills":["weld"],"penalty":35},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","lift"],"penalty":38},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack","weld"],"penalty":29},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["lift","weld"],"penalty":33}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":4},{"task_id":"T1","agent_id":"A3","cost":5},{"task_id":"T2","agent_id":"A2","cost":5},{"task_id":"T2","agent_id":"A3","cost":12},{"task_id":"T3","agent_id":"A1","cost":16},{"task_id":"T3","agent_id":"A3","cost":5},{"task_id":"T4","agent_id":"A1","cost":16},{"task_id":"T4","agent_id":"A3","cost":6}]},"gold_status":"optimal","gold_objective":20.0,"gold_bound":20.0,"gold_solution":{"family":"assignment","status":"optimal","objective":20.0,"bound":20.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"94619056bf241dce","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-020","family":"assignment","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":50020,"prompt_en":"Assign each required maintenance task to at most one eligible technician. Do not exceed agent capacity. Optional leftover tasks pay a penalty.\nTASKS: T1 size 2 skills weld, T2 size 2 skills inspect, T3 size 1 skills pack/weld, T4 size 2 skills weld\nAGENTS: A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 39}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 26}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"weld\"], \"penalty\": 40}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_fa":"هر کار الزامی را حداکثر به یک تکنسین واجد مهارت بدهید و از ظرفیت نفر تجاوز نکنید. کار اختیاریِ انجام‌نشده جریمه دارد.\nTASKS: T1 size 2 skills weld, T2 size 2 skills inspect, T3 size 1 skills pack/weld, T4 size 2 skills weld\nAGENTS: A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 5 skills inspect/lift/pack/weld\nSCHEMA_BEGIN\n{\"tasks\": [{\"task_id\": \"T1\", \"name\": \"job-1\", \"size\": 2, \"required\": true, \"skills\": [\"weld\"], \"penalty\": 39}, {\"task_id\": \"T2\", \"name\": \"job-2\", \"size\": 2, \"required\": true, \"skills\": [\"inspect\"], \"penalty\": 26}, {\"task_id\": \"T3\", \"name\": \"job-3\", \"size\": 1, \"required\": true, \"skills\": [\"pack\", \"weld\"], \"penalty\": 32}, {\"task_id\": \"T4\", \"name\": \"job-4\", \"size\": 2, \"required\": false, \"skills\": [\"weld\"], \"penalty\": 40}], \"agents\": [{\"agent_id\": \"A1\", \"name\": \"tech-1\", \"capacity\": 3, \"skills\": [\"weld\"]}, {\"agent_id\": \"A2\", \"name\": \"tech-2\", \"capacity\": 3, \"skills\": [\"inspect\"]}, {\"agent_id\": \"A3\", \"name\": \"tech-3\", \"capacity\": 5, \"skills\": [\"inspect\", \"lift\", \"pack\", \"weld\"]}], \"costs\": [{\"task_id\": \"T1\", \"agent_id\": \"A1\", \"cost\": 4}, {\"task_id\": \"T1\", \"agent_id\": \"A3\", \"cost\": 7}, {\"task_id\": \"T2\", \"agent_id\": \"A2\", \"cost\": 14}, {\"task_id\": \"T2\", \"agent_id\": \"A3\", \"cost\": 14}, {\"task_id\": \"T3\", \"agent_id\": \"A1\", \"cost\": 8}, {\"task_id\": \"T3\", \"agent_id\": \"A3\", \"cost\": 8}, {\"task_id\": \"T4\", \"agent_id\": \"A1\", \"cost\": 5}, {\"task_id\": \"T4\", \"agent_id\": \"A3\", \"cost\": 16}]}\nSCHEMA_END\n","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 26\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 40\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["weld"],"penalty":39},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect"],"penalty":26},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack","weld"],"penalty":32},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["weld"],"penalty":40}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":4},{"task_id":"T1","agent_id":"A3","cost":7},{"task_id":"T2","agent_id":"A2","cost":14},{"task_id":"T2","agent_id":"A3","cost":14},{"task_id":"T3","agent_id":"A1","cost":8},{"task_id":"T3","agent_id":"A3","cost":8},{"task_id":"T4","agent_id":"A1","cost":5},{"task_id":"T4","agent_id":"A3","cost":16}]},"gold_status":"optimal","gold_objective":34.0,"gold_bound":34.0,"gold_solution":{"family":"assignment","status":"optimal","objective":34.0,"bound":34.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"a70e0db3d846416a","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-021","family":"assignment","split":"test","interactive":false,"difficulty":"hard","language":"fa","template_id":"T-A","seed":50021,"prompt_en":"A service desk has technicians A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 5 skills lift/pack, A4 cap 7 skills inspect/lift/pack/weld. Work orders: T1 size 3 skills inspect/lift/pack, T2 size 2 skills inspect/pack, T3 size 1 skills lift, T4 size 2 skills lift/pack, T5 size 1 skills lift/weld, T6 size 2 skills inspect/weld, T7 size 3 skills lift/weld, T8 size 2 skills pack/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 5 skills lift/pack, A4 cap 7 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 3 skills inspect/lift/pack, T2 size 2 skills inspect/pack, T3 size 1 skills lift, T4 size 2 skills lift/pack, T5 size 1 skills lift/weld, T6 size 2 skills inspect/weld, T7 size 3 skills lift/weld, T8 size 2 skills pack/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T7\",\n \"name\": \"job-7\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T8\",\n \"name\": \"job-8\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 22\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"lift\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A4\",\n \"name\": \"tech-4\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A4\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A4\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A4\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A4\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A4\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A4\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A4\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A4\",\n \"cost\": 9\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","lift","pack"],"penalty":32},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","pack"],"penalty":29},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["lift"],"penalty":33},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["lift","pack"],"penalty":28},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["lift","weld"],"penalty":40},{"task_id":"T6","name":"job-6","size":2,"required":true,"skills":["inspect","weld"],"penalty":32},{"task_id":"T7","name":"job-7","size":3,"required":true,"skills":["lift","weld"],"penalty":38},{"task_id":"T8","name":"job-8","size":2,"required":true,"skills":["pack","weld"],"penalty":22}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["lift","pack"]},{"agent_id":"A4","name":"tech-4","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":10},{"task_id":"T1","agent_id":"A2","cost":4},{"task_id":"T1","agent_id":"A3","cost":12},{"task_id":"T1","agent_id":"A4","cost":9},{"task_id":"T2","agent_id":"A1","cost":13},{"task_id":"T2","agent_id":"A2","cost":15},{"task_id":"T2","agent_id":"A3","cost":16},{"task_id":"T2","agent_id":"A4","cost":15},{"task_id":"T3","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A4","cost":15},{"task_id":"T4","agent_id":"A2","cost":14},{"task_id":"T4","agent_id":"A3","cost":16},{"task_id":"T4","agent_id":"A4","cost":7},{"task_id":"T5","agent_id":"A1","cost":18},{"task_id":"T5","agent_id":"A3","cost":16},{"task_id":"T5","agent_id":"A4","cost":9},{"task_id":"T6","agent_id":"A1","cost":15},{"task_id":"T6","agent_id":"A2","cost":7},{"task_id":"T6","agent_id":"A4","cost":17},{"task_id":"T7","agent_id":"A1","cost":4},{"task_id":"T7","agent_id":"A3","cost":6},{"task_id":"T7","agent_id":"A4","cost":17},{"task_id":"T8","agent_id":"A1","cost":16},{"task_id":"T8","agent_id":"A2","cost":6},{"task_id":"T8","agent_id":"A3","cost":4},{"task_id":"T8","agent_id":"A4","cost":9}]},"gold_status":"optimal","gold_objective":63.0,"gold_bound":63.0,"gold_solution":{"family":"assignment","status":"optimal","objective":63.0,"bound":63.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A2"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A4"},{"task_id":"T4","agent_id":"A4"},{"task_id":"T5","agent_id":"A4"},{"task_id":"T6","agent_id":"A2"},{"task_id":"T7","agent_id":"A1"},{"task_id":"T8","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"68e49e596eb52a85","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-022","family":"assignment","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-B","seed":50022,"prompt_en":"A service desk has technicians A1 cap 4 skills weld, A2 cap 4 skills inspect, A3 cap 6 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills lift/weld, T2 size 2 skills inspect/weld, T3 size 3 skills pack, T4 size 3 skills lift/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 4 skills weld, A2 cap 4 skills inspect, A3 cap 6 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills lift/weld, T2 size 2 skills inspect/weld, T3 size 3 skills pack, T4 size 3 skills lift/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 27\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 24\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["lift","weld"],"penalty":36},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","weld"],"penalty":22},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["pack"],"penalty":27},{"task_id":"T4","name":"job-4","size":3,"required":false,"skills":["lift","weld"],"penalty":24}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":4,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":4,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":9},{"task_id":"T1","agent_id":"A3","cost":11},{"task_id":"T2","agent_id":"A1","cost":16},{"task_id":"T2","agent_id":"A2","cost":15},{"task_id":"T2","agent_id":"A3","cost":5},{"task_id":"T3","agent_id":"A3","cost":17},{"task_id":"T4","agent_id":"A1","cost":10},{"task_id":"T4","agent_id":"A3","cost":18}]},"gold_status":"optimal","gold_objective":53.0,"gold_bound":53.0,"gold_solution":{"family":"assignment","status":"optimal","objective":53.0,"bound":53.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"91d5d0f2a7cdb2b3","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-023","family":"assignment","split":"test","interactive":false,"difficulty":"easy","language":"fa","template_id":"T-A","seed":50023,"prompt_en":"A service desk has technicians A1 cap 3 skills weld, A2 cap 4 skills inspect, A3 cap 7 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills lift/weld, T2 size 1 skills inspect/weld, T3 size 3 skills pack/weld, T4 size 1 skills inspect/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 3 skills weld, A2 cap 4 skills inspect, A3 cap 7 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills lift/weld, T2 size 1 skills inspect/weld, T3 size 3 skills pack/weld, T4 size 1 skills inspect/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": false,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 33\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["lift","weld"],"penalty":29},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","weld"],"penalty":22},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["pack","weld"],"penalty":36},{"task_id":"T4","name":"job-4","size":1,"required":false,"skills":["inspect","weld"],"penalty":33}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":4,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":4},{"task_id":"T1","agent_id":"A3","cost":18},{"task_id":"T2","agent_id":"A1","cost":18},{"task_id":"T2","agent_id":"A2","cost":8},{"task_id":"T2","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A1","cost":10},{"task_id":"T3","agent_id":"A3","cost":5},{"task_id":"T4","agent_id":"A1","cost":4},{"task_id":"T4","agent_id":"A2","cost":14},{"task_id":"T4","agent_id":"A3","cost":10}]},"gold_status":"optimal","gold_objective":21.0,"gold_bound":21.0,"gold_solution":{"family":"assignment","status":"optimal","objective":21.0,"bound":21.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"616463a38483d3aa","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-024","family":"assignment","split":"test","interactive":true,"difficulty":"medium","language":"en","template_id":"T-B","seed":50024,"prompt_en":"A service desk has technicians A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 9 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills weld, T2 size 3 skills pack, T3 size 3 skills lift/weld, T4 size 3 skills inspect/lift, T5 size 3 skills pack, T6 size 2 skills inspect/lift. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 6 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 9 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills weld, T2 size 3 skills pack, T3 size 3 skills lift/weld, T4 size 3 skills inspect/lift, T5 size 3 skills pack, T6 size 2 skills inspect/lift. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 26\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 38\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 22\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 9,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["weld"],"penalty":26},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["pack"],"penalty":36},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["lift","weld"],"penalty":38},{"task_id":"T4","name":"job-4","size":3,"required":true,"skills":["inspect","lift"],"penalty":40},{"task_id":"T5","name":"job-5","size":3,"required":true,"skills":["pack"],"penalty":40},{"task_id":"T6","name":"job-6","size":2,"required":true,"skills":["inspect","lift"],"penalty":22}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":9,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":8},{"task_id":"T1","agent_id":"A3","cost":4},{"task_id":"T2","agent_id":"A2","cost":13},{"task_id":"T2","agent_id":"A3","cost":4},{"task_id":"T3","agent_id":"A1","cost":11},{"task_id":"T3","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A1","cost":17},{"task_id":"T4","agent_id":"A2","cost":6},{"task_id":"T4","agent_id":"A3","cost":18},{"task_id":"T5","agent_id":"A2","cost":13},{"task_id":"T5","agent_id":"A3","cost":4},{"task_id":"T6","agent_id":"A1","cost":12},{"task_id":"T6","agent_id":"A2","cost":11},{"task_id":"T6","agent_id":"A3","cost":8}]},"gold_status":"optimal","gold_objective":38.0,"gold_bound":38.0,"gold_solution":{"family":"assignment","status":"optimal","objective":38.0,"bound":38.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A2"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"195cd833fdc05084","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-025","family":"assignment","split":"test","interactive":false,"difficulty":"easy","language":"fa","template_id":"T-A","seed":50025,"prompt_en":"A service desk has technicians A1 cap 5 skills weld, A2 cap 6 skills inspect, A3 cap 5 skills inspect/lift/pack/weld. Work orders: T1 size 3 skills inspect/weld, T2 size 1 skills inspect/pack, T3 size 1 skills inspect/pack, T4 size 2 skills weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 5 skills weld, A2 cap 6 skills inspect, A3 cap 5 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 3 skills inspect/weld, T2 size 1 skills inspect/pack, T3 size 1 skills inspect/pack, T4 size 2 skills weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 26\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": false,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 22\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","weld"],"penalty":39},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","pack"],"penalty":36},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["inspect","pack"],"penalty":26},{"task_id":"T4","name":"job-4","size":2,"required":false,"skills":["weld"],"penalty":22}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":10},{"task_id":"T1","agent_id":"A2","cost":11},{"task_id":"T1","agent_id":"A3","cost":16},{"task_id":"T2","agent_id":"A2","cost":12},{"task_id":"T2","agent_id":"A3","cost":5},{"task_id":"T3","agent_id":"A2","cost":18},{"task_id":"T3","agent_id":"A3","cost":12},{"task_id":"T4","agent_id":"A1","cost":16},{"task_id":"T4","agent_id":"A3","cost":7}]},"gold_status":"optimal","gold_objective":34.0,"gold_bound":34.0,"gold_solution":{"family":"assignment","status":"optimal","objective":34.0,"bound":34.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"2d5e70242c82e1c7","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-026","family":"assignment","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-B","seed":50026,"prompt_en":"A service desk has technicians A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 5 skills inspect/lift/pack/weld. Work orders: T1 size 3 skills pack/weld, T2 size 2 skills inspect/pack, T3 size 2 skills inspect/pack, T4 size 3 skills lift/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 3 skills weld, A2 cap 3 skills inspect, A3 cap 5 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 3 skills pack/weld, T2 size 2 skills inspect/pack, T3 size 2 skills inspect/pack, T4 size 3 skills lift/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 22\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["pack","weld"],"penalty":32},{"task_id":"T2","name":"job-2","size":2,"required":true,"skills":["inspect","pack"],"penalty":20},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["inspect","pack"],"penalty":20},{"task_id":"T4","name":"job-4","size":3,"required":false,"skills":["lift","weld"],"penalty":22}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":15},{"task_id":"T1","agent_id":"A3","cost":10},{"task_id":"T2","agent_id":"A2","cost":10},{"task_id":"T2","agent_id":"A3","cost":4},{"task_id":"T3","agent_id":"A2","cost":16},{"task_id":"T3","agent_id":"A3","cost":18},{"task_id":"T4","agent_id":"A1","cost":16},{"task_id":"T4","agent_id":"A3","cost":14}]},"gold_status":"optimal","gold_objective":46.0,"gold_bound":46.0,"gold_solution":{"family":"assignment","status":"optimal","objective":46.0,"bound":46.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A2"},{"task_id":"T4","agent_id":"A1"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"9cf7363994177683","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-027","family":"assignment","split":"test","interactive":false,"difficulty":"medium","language":"fa","template_id":"T-A","seed":50027,"prompt_en":"A service desk has technicians A1 cap 3 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 7 skills inspect/lift/pack/weld. Work orders: T1 size 3 skills inspect, T2 size 3 skills inspect, T3 size 1 skills inspect/lift/weld, T4 size 2 skills weld, T5 size 1 skills inspect/weld, T6 size 1 skills inspect/lift. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 3 skills inspect/weld, A2 cap 3 skills inspect/pack, A3 cap 7 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 3 skills inspect, T2 size 3 skills inspect, T3 size 1 skills inspect/lift/weld, T4 size 2 skills weld, T5 size 1 skills inspect/weld, T6 size 1 skills inspect/lift. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 35\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 7,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 12\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect"],"penalty":32},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect"],"penalty":32},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["inspect","lift","weld"],"penalty":34},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["weld"],"penalty":32},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["inspect","weld"],"penalty":20},{"task_id":"T6","name":"job-6","size":1,"required":true,"skills":["inspect","lift"],"penalty":35}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":3,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":7,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":12},{"task_id":"T1","agent_id":"A2","cost":16},{"task_id":"T1","agent_id":"A3","cost":13},{"task_id":"T2","agent_id":"A1","cost":9},{"task_id":"T2","agent_id":"A2","cost":8},{"task_id":"T2","agent_id":"A3","cost":6},{"task_id":"T3","agent_id":"A1","cost":8},{"task_id":"T3","agent_id":"A2","cost":18},{"task_id":"T3","agent_id":"A3","cost":14},{"task_id":"T4","agent_id":"A1","cost":14},{"task_id":"T4","agent_id":"A3","cost":14},{"task_id":"T5","agent_id":"A1","cost":14},{"task_id":"T5","agent_id":"A2","cost":18},{"task_id":"T5","agent_id":"A3","cost":18},{"task_id":"T6","agent_id":"A1","cost":11},{"task_id":"T6","agent_id":"A2","cost":5},{"task_id":"T6","agent_id":"A3","cost":6}]},"gold_status":"optimal","gold_objective":63.0,"gold_bound":63.0,"gold_solution":{"family":"assignment","status":"optimal","objective":63.0,"bound":63.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A1"},{"task_id":"T4","agent_id":"A3"},{"task_id":"T5","agent_id":"A1"},{"task_id":"T6","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"75c4dedc90aa87db","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-028","family":"assignment","split":"test","interactive":false,"difficulty":"hard","language":"en","template_id":"T-B","seed":50028,"prompt_en":"A service desk has technicians A1 cap 4 skills inspect/weld, A2 cap 4 skills inspect/pack, A3 cap 4 skills lift/pack, A4 cap 6 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills inspect/pack, T2 size 1 skills inspect/weld, T3 size 3 skills inspect/lift/weld, T4 size 1 skills inspect/lift/pack, T5 size 1 skills weld, T6 size 2 skills inspect/weld, T7 size 2 skills pack, T8 size 3 skills lift/pack. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 4 skills inspect/weld, A2 cap 4 skills inspect/pack, A3 cap 4 skills lift/pack, A4 cap 6 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills inspect/pack, T2 size 1 skills inspect/weld, T3 size 3 skills inspect/lift/weld, T4 size 1 skills inspect/lift/pack, T5 size 1 skills weld, T6 size 2 skills inspect/weld, T7 size 2 skills pack, T8 size 3 skills lift/pack. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 40\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 32\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T7\",\n \"name\": \"job-7\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 29\n },\n {\n \"task_id\": \"T8\",\n \"name\": \"job-8\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\",\n \"pack\"\n ],\n \"penalty\": 39\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 4,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 4,\n \"skills\": [\n \"lift\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A4\",\n \"name\": \"tech-4\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A4\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A4\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A4\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A4\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A4\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A4\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A3\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T7\",\n \"agent_id\": \"A4\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A2\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A3\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T8\",\n \"agent_id\": \"A4\",\n \"cost\": 14\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["inspect","pack"],"penalty":29},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","weld"],"penalty":40},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["inspect","lift","weld"],"penalty":32},{"task_id":"T4","name":"job-4","size":1,"required":true,"skills":["inspect","lift","pack"],"penalty":28},{"task_id":"T5","name":"job-5","size":1,"required":true,"skills":["weld"],"penalty":33},{"task_id":"T6","name":"job-6","size":2,"required":true,"skills":["inspect","weld"],"penalty":29},{"task_id":"T7","name":"job-7","size":2,"required":true,"skills":["pack"],"penalty":29},{"task_id":"T8","name":"job-8","size":3,"required":true,"skills":["lift","pack"],"penalty":39}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":4,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":4,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":4,"skills":["lift","pack"]},{"agent_id":"A4","name":"tech-4","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":4},{"task_id":"T1","agent_id":"A2","cost":8},{"task_id":"T1","agent_id":"A3","cost":15},{"task_id":"T1","agent_id":"A4","cost":15},{"task_id":"T2","agent_id":"A1","cost":9},{"task_id":"T2","agent_id":"A2","cost":11},{"task_id":"T2","agent_id":"A4","cost":17},{"task_id":"T3","agent_id":"A1","cost":11},{"task_id":"T3","agent_id":"A2","cost":10},{"task_id":"T3","agent_id":"A3","cost":6},{"task_id":"T3","agent_id":"A4","cost":18},{"task_id":"T4","agent_id":"A1","cost":13},{"task_id":"T4","agent_id":"A2","cost":6},{"task_id":"T4","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A4","cost":6},{"task_id":"T5","agent_id":"A1","cost":8},{"task_id":"T5","agent_id":"A4","cost":15},{"task_id":"T6","agent_id":"A1","cost":11},{"task_id":"T6","agent_id":"A2","cost":9},{"task_id":"T6","agent_id":"A4","cost":18},{"task_id":"T7","agent_id":"A2","cost":7},{"task_id":"T7","agent_id":"A3","cost":6},{"task_id":"T7","agent_id":"A4","cost":5},{"task_id":"T8","agent_id":"A2","cost":13},{"task_id":"T8","agent_id":"A3","cost":18},{"task_id":"T8","agent_id":"A4","cost":14}]},"gold_status":"optimal","gold_objective":59.0,"gold_bound":59.0,"gold_solution":{"family":"assignment","status":"optimal","objective":59.0,"bound":59.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A1"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"},{"task_id":"T5","agent_id":"A1"},{"task_id":"T6","agent_id":"A2"},{"task_id":"T7","agent_id":"A4"},{"task_id":"T8","agent_id":"A4"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"33e8008ea9f0e332","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-029","family":"assignment","split":"test","interactive":true,"difficulty":"easy","language":"fa","template_id":"T-A","seed":50029,"prompt_en":"A service desk has technicians A1 cap 5 skills weld, A2 cap 3 skills inspect, A3 cap 6 skills inspect/lift/pack/weld. Work orders: T1 size 3 skills inspect/weld, T2 size 1 skills inspect/lift, T3 size 1 skills pack, T4 size 1 skills pack/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 5 skills weld, A2 cap 3 skills inspect, A3 cap 6 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 3 skills inspect/weld, T2 size 1 skills inspect/lift, T3 size 1 skills pack, T4 size 1 skills pack/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 26\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 33\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 1,\n \"required\": false,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 25\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 5,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 3,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 12\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["inspect","weld"],"penalty":26},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","lift"],"penalty":36},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack"],"penalty":33},{"task_id":"T4","name":"job-4","size":1,"required":false,"skills":["pack","weld"],"penalty":25}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":5,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":3,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":6,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":15},{"task_id":"T1","agent_id":"A2","cost":14},{"task_id":"T1","agent_id":"A3","cost":8},{"task_id":"T2","agent_id":"A2","cost":7},{"task_id":"T2","agent_id":"A3","cost":4},{"task_id":"T3","agent_id":"A3","cost":10},{"task_id":"T4","agent_id":"A1","cost":13},{"task_id":"T4","agent_id":"A3","cost":12}]},"gold_status":"optimal","gold_objective":34.0,"gold_bound":34.0,"gold_solution":{"family":"assignment","status":"optimal","objective":34.0,"bound":34.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"a37065772aa4dfbf","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-030","family":"assignment","split":"test","interactive":false,"difficulty":"medium","language":"en","template_id":"T-B","seed":50030,"prompt_en":"A service desk has technicians A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills inspect/weld, T2 size 1 skills inspect/lift, T3 size 2 skills lift, T4 size 2 skills weld, T5 size 2 skills inspect, T6 size 1 skills inspect/lift. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 6 skills inspect/weld, A2 cap 6 skills inspect/pack, A3 cap 8 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills inspect/weld, T2 size 1 skills inspect/lift, T3 size 2 skills lift, T4 size 2 skills weld, T5 size 2 skills inspect, T6 size 1 skills inspect/lift. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ],\n \"penalty\": 35\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 22\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 28\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 6,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 8,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["inspect","weld"],"penalty":35},{"task_id":"T2","name":"job-2","size":1,"required":true,"skills":["inspect","lift"],"penalty":39},{"task_id":"T3","name":"job-3","size":2,"required":true,"skills":["lift"],"penalty":39},{"task_id":"T4","name":"job-4","size":2,"required":true,"skills":["weld"],"penalty":22},{"task_id":"T5","name":"job-5","size":2,"required":true,"skills":["inspect"],"penalty":30},{"task_id":"T6","name":"job-6","size":1,"required":true,"skills":["inspect","lift"],"penalty":28}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":6,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":6,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":8,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":18},{"task_id":"T1","agent_id":"A2","cost":16},{"task_id":"T1","agent_id":"A3","cost":4},{"task_id":"T2","agent_id":"A1","cost":9},{"task_id":"T2","agent_id":"A2","cost":18},{"task_id":"T2","agent_id":"A3","cost":9},{"task_id":"T3","agent_id":"A3","cost":4},{"task_id":"T4","agent_id":"A1","cost":4},{"task_id":"T4","agent_id":"A3","cost":15},{"task_id":"T5","agent_id":"A1","cost":8},{"task_id":"T5","agent_id":"A2","cost":6},{"task_id":"T5","agent_id":"A3","cost":4},{"task_id":"T6","agent_id":"A1","cost":15},{"task_id":"T6","agent_id":"A2","cost":5},{"task_id":"T6","agent_id":"A3","cost":10}]},"gold_status":"optimal","gold_objective":29.999999999999996,"gold_bound":29.999999999999996,"gold_solution":{"family":"assignment","status":"optimal","objective":29.999999999999996,"bound":29.999999999999996,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A3"},{"task_id":"T2","agent_id":"A3"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A1"},{"task_id":"T5","agent_id":"A3"},{"task_id":"T6","agent_id":"A2"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"ae3cf299b843c92f","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-031","family":"assignment","split":"test","interactive":false,"difficulty":"easy","language":"fa","template_id":"T-A","seed":50031,"prompt_en":"A service desk has technicians A1 cap 4 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld. Work orders: T1 size 2 skills pack/weld, T2 size 3 skills inspect/lift, T3 size 1 skills pack, T4 size 3 skills lift/weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 4 skills weld, A2 cap 5 skills inspect, A3 cap 5 skills inspect/lift/pack/weld را دارد. سفارش‌ها: T1 size 2 skills pack/weld, T2 size 3 skills inspect/lift, T3 size 1 skills pack, T4 size 3 skills lift/weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 2,\n \"required\": true,\n \"skills\": [\n \"pack\",\n \"weld\"\n ],\n \"penalty\": 23\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 1,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 24\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": false,\n \"skills\": [\n \"lift\",\n \"weld\"\n ],\n \"penalty\": 34\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 4,\n \"skills\": [\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 5,\n \"skills\": [\n \"inspect\",\n \"lift\",\n \"pack\",\n \"weld\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A1\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 13\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 10\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":2,"required":true,"skills":["pack","weld"],"penalty":23},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect","lift"],"penalty":39},{"task_id":"T3","name":"job-3","size":1,"required":true,"skills":["pack"],"penalty":24},{"task_id":"T4","name":"job-4","size":3,"required":false,"skills":["lift","weld"],"penalty":34}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":4,"skills":["weld"]},{"agent_id":"A2","name":"tech-2","capacity":5,"skills":["inspect"]},{"agent_id":"A3","name":"tech-3","capacity":5,"skills":["inspect","lift","pack","weld"]}],"costs":[{"task_id":"T1","agent_id":"A1","cost":7},{"task_id":"T1","agent_id":"A3","cost":13},{"task_id":"T2","agent_id":"A2","cost":7},{"task_id":"T2","agent_id":"A3","cost":7},{"task_id":"T3","agent_id":"A3","cost":13},{"task_id":"T4","agent_id":"A1","cost":10},{"task_id":"T4","agent_id":"A3","cost":10}]},"gold_status":"optimal","gold_objective":37.0,"gold_bound":37.0,"gold_solution":{"family":"assignment","status":"optimal","objective":37.0,"bound":37.0,"orders":[],"assignments":[{"task_id":"T1","agent_id":"A1"},{"task_id":"T2","agent_id":"A2"},{"task_id":"T3","agent_id":"A3"},{"task_id":"T4","agent_id":"A3"}],"unassigned":[],"starts":[],"message":"OPTIMAL"},"structural_key":"1b6764eba2517c16","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-032","family":"assignment","split":"test","interactive":false,"difficulty":"infeasible","language":"en","template_id":"T-B","seed":50032,"prompt_en":"A service desk has technicians A1 cap 1 skills inspect/weld, A2 cap 1 skills inspect/pack, A3 cap 1 skills lift/pack. Work orders: T1 size 3 skills pack, T2 size 3 skills inspect, T3 size 3 skills pack, T4 size 3 skills weld, T5 size 3 skills inspect, T6 size 3 skills weld. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 1 skills inspect/weld, A2 cap 1 skills inspect/pack, A3 cap 1 skills lift/pack را دارد. سفارش‌ها: T1 size 3 skills pack, T2 size 3 skills inspect, T3 size 3 skills pack, T4 size 3 skills weld, T5 size 3 skills inspect, T6 size 3 skills weld. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 37\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 39\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 27\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"weld\"\n ],\n \"penalty\": 28\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 1,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 1,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 1,\n \"skills\": [\n \"lift\",\n \"pack\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A1\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 4\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 16\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A1\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 6\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 10\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["pack"],"penalty":37},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["inspect"],"penalty":37},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["pack"],"penalty":39},{"task_id":"T4","name":"job-4","size":3,"required":true,"skills":["weld"],"penalty":27},{"task_id":"T5","name":"job-5","size":3,"required":true,"skills":["inspect"],"penalty":30},{"task_id":"T6","name":"job-6","size":3,"required":true,"skills":["weld"],"penalty":28}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":1,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":1,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":1,"skills":["lift","pack"]}],"costs":[{"task_id":"T1","agent_id":"A2","cost":8},{"task_id":"T1","agent_id":"A3","cost":7},{"task_id":"T2","agent_id":"A1","cost":6},{"task_id":"T2","agent_id":"A2","cost":4},{"task_id":"T3","agent_id":"A2","cost":7},{"task_id":"T3","agent_id":"A3","cost":17},{"task_id":"T4","agent_id":"A1","cost":16},{"task_id":"T5","agent_id":"A1","cost":15},{"task_id":"T5","agent_id":"A2","cost":6},{"task_id":"T6","agent_id":"A1","cost":10}]},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"assignment","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"2c4f1aa24275210a","notes":"skill intersection is the eligibility rule"} {"problem_id":"ASN-033","family":"assignment","split":"test","interactive":true,"difficulty":"infeasible","language":"fa","template_id":"T-A","seed":50033,"prompt_en":"A service desk has technicians A1 cap 1 skills inspect/weld, A2 cap 1 skills inspect/pack, A3 cap 1 skills lift/pack. Work orders: T1 size 3 skills lift, T2 size 3 skills pack, T3 size 3 skills inspect/lift, T4 size 3 skills inspect/pack, T5 size 3 skills pack, T6 size 3 skills inspect/lift. A task may use an agent only when they share a skill. Minimize assignment cost plus leftover penalties.","prompt_fa":"میز خدمت تکنسین‌های A1 cap 1 skills inspect/weld, A2 cap 1 skills inspect/pack, A3 cap 1 skills lift/pack را دارد. سفارش‌ها: T1 size 3 skills lift, T2 size 3 skills pack, T3 size 3 skills inspect/lift, T4 size 3 skills inspect/pack, T5 size 3 skills pack, T6 size 3 skills inspect/lift. تخصیص فقط با مهارت مشترک مجاز است. هزینه تخصیص به‌علاوه جریمه کار باقی‌مانده کمینه شود.","prompt_json":"{\n \"tasks\": [\n {\n \"task_id\": \"T1\",\n \"name\": \"job-1\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"lift\"\n ],\n \"penalty\": 36\n },\n {\n \"task_id\": \"T2\",\n \"name\": \"job-2\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 30\n },\n {\n \"task_id\": \"T3\",\n \"name\": \"job-3\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 28\n },\n {\n \"task_id\": \"T4\",\n \"name\": \"job-4\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ],\n \"penalty\": 34\n },\n {\n \"task_id\": \"T5\",\n \"name\": \"job-5\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"pack\"\n ],\n \"penalty\": 20\n },\n {\n \"task_id\": \"T6\",\n \"name\": \"job-6\",\n \"size\": 3,\n \"required\": true,\n \"skills\": [\n \"inspect\",\n \"lift\"\n ],\n \"penalty\": 20\n }\n ],\n \"agents\": [\n {\n \"agent_id\": \"A1\",\n \"name\": \"tech-1\",\n \"capacity\": 1,\n \"skills\": [\n \"inspect\",\n \"weld\"\n ]\n },\n {\n \"agent_id\": \"A2\",\n \"name\": \"tech-2\",\n \"capacity\": 1,\n \"skills\": [\n \"inspect\",\n \"pack\"\n ]\n },\n {\n \"agent_id\": \"A3\",\n \"name\": \"tech-3\",\n \"capacity\": 1,\n \"skills\": [\n \"lift\",\n \"pack\"\n ]\n }\n ],\n \"costs\": [\n {\n \"task_id\": \"T1\",\n \"agent_id\": \"A3\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T2\",\n \"agent_id\": \"A3\",\n \"cost\": 15\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A1\",\n \"cost\": 5\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A2\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T3\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A1\",\n \"cost\": 14\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A2\",\n \"cost\": 10\n },\n {\n \"task_id\": \"T4\",\n \"agent_id\": \"A3\",\n \"cost\": 8\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A2\",\n \"cost\": 7\n },\n {\n \"task_id\": \"T5\",\n \"agent_id\": \"A3\",\n \"cost\": 11\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A1\",\n \"cost\": 9\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A2\",\n \"cost\": 18\n },\n {\n \"task_id\": \"T6\",\n \"agent_id\": \"A3\",\n \"cost\": 17\n }\n ]\n}","schema_payload":{"tasks":[{"task_id":"T1","name":"job-1","size":3,"required":true,"skills":["lift"],"penalty":36},{"task_id":"T2","name":"job-2","size":3,"required":true,"skills":["pack"],"penalty":30},{"task_id":"T3","name":"job-3","size":3,"required":true,"skills":["inspect","lift"],"penalty":28},{"task_id":"T4","name":"job-4","size":3,"required":true,"skills":["inspect","pack"],"penalty":34},{"task_id":"T5","name":"job-5","size":3,"required":true,"skills":["pack"],"penalty":20},{"task_id":"T6","name":"job-6","size":3,"required":true,"skills":["inspect","lift"],"penalty":20}],"agents":[{"agent_id":"A1","name":"tech-1","capacity":1,"skills":["inspect","weld"]},{"agent_id":"A2","name":"tech-2","capacity":1,"skills":["inspect","pack"]},{"agent_id":"A3","name":"tech-3","capacity":1,"skills":["lift","pack"]}],"costs":[{"task_id":"T1","agent_id":"A3","cost":5},{"task_id":"T2","agent_id":"A2","cost":7},{"task_id":"T2","agent_id":"A3","cost":15},{"task_id":"T3","agent_id":"A1","cost":5},{"task_id":"T3","agent_id":"A2","cost":8},{"task_id":"T3","agent_id":"A3","cost":17},{"task_id":"T4","agent_id":"A1","cost":14},{"task_id":"T4","agent_id":"A2","cost":10},{"task_id":"T4","agent_id":"A3","cost":8},{"task_id":"T5","agent_id":"A2","cost":7},{"task_id":"T5","agent_id":"A3","cost":11},{"task_id":"T6","agent_id":"A1","cost":9},{"task_id":"T6","agent_id":"A2","cost":18},{"task_id":"T6","agent_id":"A3","cost":17}]},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"assignment","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"483125be5eebd870","notes":"skill intersection is the eligibility rule"} {"problem_id":"SCH-001","family":"scheduling","split":"development","interactive":true,"difficulty":"easy","language":"en","template_id":"D-A","seed":75001,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 5 rel 2 due 8, J2 dur 2 rel 0 due 10, J3 dur 3 rel 0 due 14, J4 dur 2 rel 2 due 14\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 2, \"due\": 8, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 0, \"due\": 10, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 14, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 2, \"due\": 14, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 20}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 5 rel 2 due 8, J2 dur 2 rel 0 due 10, J3 dur 3 rel 0 due 14, J4 dur 2 rel 2 due 14\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 2, \"due\": 8, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 0, \"due\": 10, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 14, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 2, \"due\": 14, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 20}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 2,\n \"due\": 8,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 14,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 20\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":2,"due":8,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":0,"due":10,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":14,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":2,"due":14,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":20},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":2,"end":7},{"job_id":"J2","machine_id":"M1","start":0,"end":2},{"job_id":"J3","machine_id":"M1","start":7,"end":10},{"job_id":"J4","machine_id":"M1","start":10,"end":12}],"message":"OPTIMAL"},"structural_key":"f3b26ff82b5918fb","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-002","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75002,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 0 due 4, J2 dur 5 rel 0 due 10, J3 dur 3 rel 0 due 14, J4 dur 5 rel 0 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 4, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 0, \"due\": 10, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 14, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 0, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 24}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 0 due 4, J2 dur 5 rel 0 due 10, J3 dur 3 rel 0 due 14, J4 dur 5 rel 0 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 4, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 0, \"due\": 10, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 14, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 0, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 24}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 4,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 19,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 24\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":4,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":5,"release":0,"due":10,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":14,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":5,"release":0,"due":19,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":24},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":3},{"job_id":"J2","machine_id":"M1","start":3,"end":8},{"job_id":"J3","machine_id":"M1","start":8,"end":11},{"job_id":"J4","machine_id":"M1","start":11,"end":16}],"message":"OPTIMAL"},"structural_key":"d340539d914c97df","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-003","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75003,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 1 due 6, J2 dur 3 rel 2 due 7, J3 dur 4 rel 0 due 13, J4 dur 3 rel 0 due 17, J5 dur 3 rel 0 due 20, J6 dur 2 rel 0 due 21\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 1, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 2, \"due\": 7, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 13, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 0, \"due\": 17, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 20, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 0, \"due\": 21, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 26}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 1 due 6, J2 dur 3 rel 2 due 7, J3 dur 4 rel 0 due 13, J4 dur 3 rel 0 due 17, J5 dur 3 rel 0 due 20, J6 dur 2 rel 0 due 21\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 1, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 2, \"due\": 7, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 13, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 0, \"due\": 17, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 20, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 0, \"due\": 21, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 26}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 7,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 13,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 20,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 21,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 26\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":1,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":3,"release":2,"due":7,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":13,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":0,"due":17,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":3,"release":0,"due":20,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":2,"release":0,"due":21,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":26},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":2,"end":5},{"job_id":"J2","machine_id":"M1","start":3,"end":6},{"job_id":"J3","machine_id":"M2","start":5,"end":9},{"job_id":"J4","machine_id":"M1","start":0,"end":3},{"job_id":"J5","machine_id":"M1","start":6,"end":9},{"job_id":"J6","machine_id":"M2","start":0,"end":2}],"message":"OPTIMAL"},"structural_key":"8d93269a62953269","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-004","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":75004,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 4 rel 0 due 7, J2 dur 3 rel 2 due 10, J3 dur 4 rel 0 due 15, J4 dur 4 rel 0 due 18\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 2, \"due\": 10, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 18, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 4 rel 0 due 7, J2 dur 3 rel 2 due 10, J3 dur 4 rel 0 due 15, J4 dur 4 rel 0 due 18\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 2, \"due\": 10, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 18, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 10,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 15,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 18,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 23\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":0,"due":7,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":3,"release":2,"due":10,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":15,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":0,"due":18,"weight":4,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":23},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":4},{"job_id":"J2","machine_id":"M1","start":4,"end":7},{"job_id":"J3","machine_id":"M1","start":11,"end":15},{"job_id":"J4","machine_id":"M1","start":7,"end":11}],"message":"OPTIMAL"},"structural_key":"ab08e0ff4cbe98a0","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-005","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75005,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 5 rel 0 due 6, J2 dur 3 rel 1 due 12, J3 dur 4 rel 2 due 16, J4 dur 2 rel 2 due 17\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 0, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 1, \"due\": 12, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 2, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 2, \"due\": 17, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 22}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 5 rel 0 due 6, J2 dur 3 rel 1 due 12, J3 dur 4 rel 2 due 16, J4 dur 2 rel 2 due 17\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 0, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 1, \"due\": 12, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 2, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 2, \"due\": 17, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 22}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 12,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 16,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 17,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 22\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":0,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":3,"release":1,"due":12,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":2,"due":16,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":2,"due":17,"weight":1,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":22},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":5},{"job_id":"J2","machine_id":"M1","start":7,"end":10},{"job_id":"J3","machine_id":"M1","start":10,"end":14},{"job_id":"J4","machine_id":"M1","start":5,"end":7}],"message":"OPTIMAL"},"structural_key":"3a19f6671a25fbea","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-006","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75006,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 0 due 6, J2 dur 5 rel 1 due 11, J3 dur 2 rel 0 due 13, J4 dur 3 rel 0 due 17, J5 dur 5 rel 0 due 21, J6 dur 2 rel 1 due 22\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 6, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 1, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 13, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 0, \"due\": 17, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 5, \"release\": 0, \"due\": 21, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 1, \"due\": 22, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 28}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 0 due 6, J2 dur 5 rel 1 due 11, J3 dur 2 rel 0 due 13, J4 dur 3 rel 0 due 17, J5 dur 5 rel 0 due 21, J6 dur 2 rel 1 due 22\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 6, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 1, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 13, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 0, \"due\": 17, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 5, \"release\": 0, \"due\": 21, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 1, \"due\": 22, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 28}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 5,\n \"release\": 1,\n \"due\": 11,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 13,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 21,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 22,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 28\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":6,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":5,"release":1,"due":11,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":13,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":0,"due":17,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":5,"release":0,"due":21,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":2,"release":1,"due":22,"weight":2,"hard_due":false,"machine_eligible":["M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":28},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":3},{"job_id":"J2","machine_id":"M2","start":5,"end":10},{"job_id":"J3","machine_id":"M1","start":5,"end":7},{"job_id":"J4","machine_id":"M1","start":7,"end":10},{"job_id":"J5","machine_id":"M1","start":0,"end":5},{"job_id":"J6","machine_id":"M2","start":3,"end":5}],"message":"OPTIMAL"},"structural_key":"28f92c4b29421b9e","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-007","family":"scheduling","split":"development","interactive":true,"difficulty":"hard","language":"en","template_id":"D-A","seed":75007,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3, J2->J5). Hard due dates are deadlines.\nJOBS: J1 dur 4 rel 0 due 7, J2 dur 5 rel 0 due 11, J3 dur 2 rel 1 due 15, J4 dur 2 rel 0 due 17, J5 dur 2 rel 0 due 17, J6 dur 4 rel 0 due 22, J7 dur 2 rel 1 due 22, J8 dur 3 rel 2 due 25\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 1, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 4, \"release\": 0, \"due\": 22, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J7\", \"name\": \"op-7\", \"duration\": 2, \"release\": 1, \"due\": 22, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J8\", \"name\": \"op-8\", \"duration\": 3, \"release\": 2, \"due\": 25, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}, {\"before\": \"J2\", \"after\": \"J5\"}], \"horizon\": 32}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3, J2->J5) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 4 rel 0 due 7, J2 dur 5 rel 0 due 11, J3 dur 2 rel 1 due 15, J4 dur 2 rel 0 due 17, J5 dur 2 rel 0 due 17, J6 dur 4 rel 0 due 22, J7 dur 2 rel 1 due 22, J8 dur 3 rel 2 due 25\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 1, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 4, \"release\": 0, \"due\": 22, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J7\", \"name\": \"op-7\", \"duration\": 2, \"release\": 1, \"due\": 22, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J8\", \"name\": \"op-8\", \"duration\": 3, \"release\": 2, \"due\": 25, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}, {\"before\": \"J2\", \"after\": \"J5\"}], \"horizon\": 32}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 15,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 22,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J7\",\n \"name\": \"op-7\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 22,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J8\",\n \"name\": \"op-8\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 25,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n },\n {\n \"before\": \"J2\",\n \"after\": \"J5\"\n }\n ],\n \"horizon\": 32\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":0,"due":7,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":5,"release":0,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":1,"due":15,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":17,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J5","name":"op-5","duration":2,"release":0,"due":17,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":4,"release":0,"due":22,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J7","name":"op-7","duration":2,"release":1,"due":22,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J8","name":"op-8","duration":3,"release":2,"due":25,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"},{"before":"J2","after":"J5"}],"horizon":32},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":4},{"job_id":"J2","machine_id":"M1","start":0,"end":5},{"job_id":"J3","machine_id":"M2","start":4,"end":6},{"job_id":"J4","machine_id":"M2","start":8,"end":10},{"job_id":"J5","machine_id":"M2","start":6,"end":8},{"job_id":"J6","machine_id":"M1","start":5,"end":9},{"job_id":"J7","machine_id":"M2","start":10,"end":12},{"job_id":"J8","machine_id":"M1","start":9,"end":12}],"message":"OPTIMAL"},"structural_key":"050bb292957ce323","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-008","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75008,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 4 rel 1 due 6, J2 dur 4 rel 0 due 12, J3 dur 4 rel 0 due 15, J4 dur 5 rel 1 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 1, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 12, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 15, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 1, \"due\": 19, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 25}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 4 rel 1 due 6, J2 dur 4 rel 0 due 12, J3 dur 4 rel 0 due 15, J4 dur 5 rel 1 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 1, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 12, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 15, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 1, \"due\": 19, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 25}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 15,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 5,\n \"release\": 1,\n \"due\": 19,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 25\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":1,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":12,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":15,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":5,"release":1,"due":19,"weight":3,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":25},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":1,"end":5},{"job_id":"J2","machine_id":"M1","start":5,"end":9},{"job_id":"J3","machine_id":"M1","start":9,"end":13},{"job_id":"J4","machine_id":"M1","start":13,"end":18}],"message":"OPTIMAL"},"structural_key":"98f68288cc66b7e8","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-009","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75009,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 2 rel 2 due 6, J3 dur 3 rel 0 due 11, J4 dur 2 rel 0 due 11, J5 dur 5 rel 1 due 18, J6 dur 2 rel 0 due 20\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 2, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 5, \"release\": 1, \"due\": 18, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 0, \"due\": 20, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 24}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 2 rel 2 due 6, J3 dur 3 rel 0 due 11, J4 dur 2 rel 0 due 11, J5 dur 5 rel 1 due 18, J6 dur 2 rel 0 due 20\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 2, \"due\": 6, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 5, \"release\": 1, \"due\": 18, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 0, \"due\": 20, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 24}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 5,\n \"release\": 1,\n \"due\": 18,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 20,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 24\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":0,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":2,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":11,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":5,"release":1,"due":18,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J6","name":"op-6","duration":2,"release":0,"due":20,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":24},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":2},{"job_id":"J2","machine_id":"M1","start":2,"end":4},{"job_id":"J3","machine_id":"M1","start":4,"end":7},{"job_id":"J4","machine_id":"M2","start":0,"end":2},{"job_id":"J5","machine_id":"M2","start":4,"end":9},{"job_id":"J6","machine_id":"M2","start":2,"end":4}],"message":"OPTIMAL"},"structural_key":"a82fa38af8e40896","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-010","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":75010,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 4 rel 0 due 5, J2 dur 2 rel 1 due 9, J3 dur 2 rel 0 due 12, J4 dur 4 rel 1 due 14\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 5, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 1, \"due\": 9, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 12, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 1, \"due\": 14, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 20}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 4 rel 0 due 5, J2 dur 2 rel 1 due 9, J3 dur 2 rel 0 due 12, J4 dur 4 rel 1 due 14\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 5, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 1, \"due\": 9, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 12, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 1, \"due\": 14, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 20}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 5,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 9,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 14,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 20\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":0,"due":5,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":1,"due":9,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":12,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":1,"due":14,"weight":3,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":20},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":4},{"job_id":"J2","machine_id":"M1","start":4,"end":6},{"job_id":"J3","machine_id":"M1","start":10,"end":12},{"job_id":"J4","machine_id":"M1","start":6,"end":10}],"message":"OPTIMAL"},"structural_key":"44defd099664afa8","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-011","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75011,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 4 rel 0 due 7, J3 dur 3 rel 0 due 11, J4 dur 4 rel 0 due 16\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 21}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 4 rel 0 due 7, J3 dur 3 rel 0 due 11, J4 dur 4 rel 0 due 16\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 7, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 21}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 16,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 21\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":0,"due":6,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":7,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":11,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":0,"due":16,"weight":4,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":21},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":2},{"job_id":"J2","machine_id":"M1","start":2,"end":6},{"job_id":"J3","machine_id":"M1","start":6,"end":9},{"job_id":"J4","machine_id":"M1","start":9,"end":13}],"message":"OPTIMAL"},"structural_key":"1f2e26b801fa687e","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-012","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75012,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 4 rel 0 due 6, J2 dur 2 rel 0 due 10, J3 dur 3 rel 1 due 12, J4 dur 3 rel 2 due 15, J5 dur 3 rel 0 due 16, J6 dur 2 rel 2 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 6, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 0, \"due\": 10, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 1, \"due\": 12, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 2, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 2, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 25}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 4 rel 0 due 6, J2 dur 2 rel 0 due 10, J3 dur 3 rel 1 due 12, J4 dur 3 rel 2 due 15, J5 dur 3 rel 0 due 16, J6 dur 2 rel 2 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 4, \"release\": 0, \"due\": 6, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 2, \"release\": 0, \"due\": 10, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 1, \"due\": 12, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 2, \"due\": 15, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 2, \"release\": 2, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 25}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 12,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 15,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 16,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 19,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 25\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":0,"due":6,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":2,"release":0,"due":10,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":3,"release":1,"due":12,"weight":1,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":2,"due":15,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":3,"release":0,"due":16,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":2,"release":2,"due":19,"weight":2,"hard_due":false,"machine_eligible":["M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":25},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":4},{"job_id":"J2","machine_id":"M1","start":0,"end":2},{"job_id":"J3","machine_id":"M2","start":6,"end":9},{"job_id":"J4","machine_id":"M1","start":2,"end":5},{"job_id":"J5","machine_id":"M1","start":5,"end":8},{"job_id":"J6","machine_id":"M2","start":4,"end":6}],"message":"OPTIMAL"},"structural_key":"e309923760f6714b","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-013","family":"scheduling","split":"development","interactive":true,"difficulty":"easy","language":"en","template_id":"D-A","seed":75013,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 5 rel 2 due 11, J3 dur 4 rel 1 due 14, J4 dur 2 rel 1 due 15\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 2, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 14, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 1, \"due\": 15, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 21}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 2 rel 0 due 6, J2 dur 5 rel 2 due 11, J3 dur 4 rel 1 due 14, J4 dur 2 rel 1 due 15\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 6, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 5, \"release\": 2, \"due\": 11, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 14, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 1, \"due\": 15, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 21}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 5,\n \"release\": 2,\n \"due\": 11,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 14,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 15,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 21\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":0,"due":6,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":5,"release":2,"due":11,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":1,"due":14,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":1,"due":15,"weight":3,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":21},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":2},{"job_id":"J2","machine_id":"M1","start":6,"end":11},{"job_id":"J3","machine_id":"M1","start":2,"end":6},{"job_id":"J4","machine_id":"M1","start":11,"end":13}],"message":"OPTIMAL"},"structural_key":"fa5346efc4f12de7","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-014","family":"scheduling","split":"development","interactive":false,"difficulty":"hard","language":"en","template_id":"D-B","seed":75014,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3, J2->J5). Hard due dates are deadlines.\nJOBS: J1 dur 2 rel 0 due 3, J2 dur 4 rel 1 due 8, J3 dur 4 rel 0 due 11, J4 dur 4 rel 2 due 16, J5 dur 3 rel 0 due 21, J6 dur 3 rel 1 due 23, J7 dur 3 rel 0 due 24, J8 dur 5 rel 0 due 31\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 3, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 1, \"due\": 8, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 2, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 21, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 3, \"release\": 1, \"due\": 23, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J7\", \"name\": \"op-7\", \"duration\": 3, \"release\": 0, \"due\": 24, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J8\", \"name\": \"op-8\", \"duration\": 5, \"release\": 0, \"due\": 31, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}, {\"before\": \"J2\", \"after\": \"J5\"}], \"horizon\": 36}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3, J2->J5) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 2 rel 0 due 3, J2 dur 4 rel 1 due 8, J3 dur 4 rel 0 due 11, J4 dur 4 rel 2 due 16, J5 dur 3 rel 0 due 21, J6 dur 3 rel 1 due 23, J7 dur 3 rel 0 due 24, J8 dur 5 rel 0 due 31\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 3, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 1, \"due\": 8, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 2, \"due\": 16, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 21, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 3, \"release\": 1, \"due\": 23, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J7\", \"name\": \"op-7\", \"duration\": 3, \"release\": 0, \"due\": 24, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J8\", \"name\": \"op-8\", \"duration\": 5, \"release\": 0, \"due\": 31, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}, {\"before\": \"J2\", \"after\": \"J5\"}], \"horizon\": 36}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 3,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 8,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 16,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 21,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 23,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J7\",\n \"name\": \"op-7\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 24,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J8\",\n \"name\": \"op-8\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 31,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n },\n {\n \"before\": \"J2\",\n \"after\": \"J5\"\n }\n ],\n \"horizon\": 36\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":0,"due":3,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":4,"release":1,"due":8,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":2,"due":16,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":3,"release":0,"due":21,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":3,"release":1,"due":23,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J7","name":"op-7","duration":3,"release":0,"due":24,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J8","name":"op-8","duration":5,"release":0,"due":31,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"},{"before":"J2","after":"J5"}],"horizon":36},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":2},{"job_id":"J2","machine_id":"M1","start":3,"end":7},{"job_id":"J3","machine_id":"M1","start":7,"end":11},{"job_id":"J4","machine_id":"M2","start":2,"end":6},{"job_id":"J5","machine_id":"M1","start":11,"end":14},{"job_id":"J6","machine_id":"M2","start":11,"end":14},{"job_id":"J7","machine_id":"M1","start":0,"end":3},{"job_id":"J8","machine_id":"M2","start":6,"end":11}],"message":"OPTIMAL"},"structural_key":"c4077ee842dab620","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-015","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75015,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 0 due 4, J2 dur 4 rel 1 due 11, J3 dur 3 rel 0 due 12, J4 dur 3 rel 1 due 15, J5 dur 3 rel 0 due 20, J6 dur 5 rel 2 due 23\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 4, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 1, \"due\": 11, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 12, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 1, \"due\": 15, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 20, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 5, \"release\": 2, \"due\": 23, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 29}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 0 due 4, J2 dur 4 rel 1 due 11, J3 dur 3 rel 0 due 12, J4 dur 3 rel 1 due 15, J5 dur 3 rel 0 due 20, J6 dur 5 rel 2 due 23\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 4, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 1, \"due\": 11, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 12, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 1, \"due\": 15, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 3, \"release\": 0, \"due\": 20, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 5, \"release\": 2, \"due\": 23, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M2\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 29}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 4,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 11,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 15,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 20,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 5,\n \"release\": 2,\n \"due\": 23,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 29\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":4,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":4,"release":1,"due":11,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":12,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":3,"release":1,"due":15,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":3,"release":0,"due":20,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":5,"release":2,"due":23,"weight":4,"hard_due":false,"machine_eligible":["M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":29},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":3},{"job_id":"J2","machine_id":"M1","start":3,"end":7},{"job_id":"J3","machine_id":"M1","start":7,"end":10},{"job_id":"J4","machine_id":"M2","start":3,"end":6},{"job_id":"J5","machine_id":"M2","start":0,"end":3},{"job_id":"J6","machine_id":"M2","start":6,"end":11}],"message":"OPTIMAL"},"structural_key":"f3cab51cd91813b0","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-016","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-A","seed":75016,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 2 due 5, J2 dur 3 rel 0 due 10, J3 dur 3 rel 2 due 12, J4 dur 5 rel 0 due 15\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 2, \"due\": 5, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 0, \"due\": 10, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 2, \"due\": 12, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 0, \"due\": 15, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 22}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 2 due 5, J2 dur 3 rel 0 due 10, J3 dur 3 rel 2 due 12, J4 dur 5 rel 0 due 15\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 2, \"due\": 5, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 0, \"due\": 10, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 2, \"due\": 12, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 5, \"release\": 0, \"due\": 15, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 22}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 5,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 12,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 15,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 22\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":2,"due":5,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":3,"release":0,"due":10,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":2,"due":12,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":5,"release":0,"due":15,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":22},"gold_status":"optimal","gold_objective":2.0,"gold_bound":2.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":2.0,"bound":2.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":3,"end":6},{"job_id":"J2","machine_id":"M1","start":0,"end":3},{"job_id":"J3","machine_id":"M1","start":6,"end":9},{"job_id":"J4","machine_id":"M1","start":9,"end":14}],"message":"OPTIMAL"},"structural_key":"77c5ca9a6efec0ce","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-017","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75017,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 0 due 6, J2 dur 3 rel 1 due 7, J3 dur 3 rel 0 due 11, J4 dur 2 rel 0 due 13\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 6, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 1, \"due\": 7, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 13, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 19}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 0 due 6, J2 dur 3 rel 1 due 7, J3 dur 3 rel 0 due 11, J4 dur 2 rel 0 due 13\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 0, \"due\": 6, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 3, \"release\": 1, \"due\": 7, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 3, \"release\": 0, \"due\": 11, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 13, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 19}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 6,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 7,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 13,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 19\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":6,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":3,"release":1,"due":7,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":13,"weight":4,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":19},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":0,"end":3},{"job_id":"J2","machine_id":"M1","start":3,"end":6},{"job_id":"J3","machine_id":"M1","start":6,"end":9},{"job_id":"J4","machine_id":"M1","start":9,"end":11}],"message":"OPTIMAL"},"structural_key":"321dcec5bcc2ab1a","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-018","family":"scheduling","split":"development","interactive":false,"difficulty":"medium","language":"fa","template_id":"D-C","seed":75018,"prompt_en":"Schedule jobs on machines M1, M2 without overlap. Respect release times and precedences (J1->J3). Hard due dates are deadlines.\nJOBS: J1 dur 2 rel 0 due 4, J2 dur 4 rel 0 due 10, J3 dur 2 rel 0 due 9, J4 dur 3 rel 2 due 14, J5 dur 4 rel 0 due 17, J6 dur 5 rel 0 due 22\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 4, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 10, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 9, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 2, \"due\": 14, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 4, \"release\": 0, \"due\": 17, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 5, \"release\": 0, \"due\": 22, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 28}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1, M2 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (J1->J3) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 2 rel 0 due 4, J2 dur 4 rel 0 due 10, J3 dur 2 rel 0 due 9, J4 dur 3 rel 2 due 14, J5 dur 4 rel 0 due 17, J6 dur 5 rel 0 due 22\nSCHEMA_BEGIN\n{\"machines\": [\"M1\", \"M2\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 2, \"release\": 0, \"due\": 4, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 10, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 2, \"release\": 0, \"due\": 9, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 3, \"release\": 2, \"due\": 14, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\", \"M2\"]}, {\"job_id\": \"J5\", \"name\": \"op-5\", \"duration\": 4, \"release\": 0, \"due\": 17, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J6\", \"name\": \"op-6\", \"duration\": 5, \"release\": 0, \"due\": 22, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [{\"before\": \"J1\", \"after\": \"J3\"}], \"horizon\": 28}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 4,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 14,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 22,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 28\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":0,"due":4,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":10,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":9,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":2,"due":14,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":4,"release":0,"due":17,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J6","name":"op-6","duration":5,"release":0,"due":22,"weight":1,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":28},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":2},{"job_id":"J2","machine_id":"M1","start":4,"end":8},{"job_id":"J3","machine_id":"M2","start":2,"end":4},{"job_id":"J4","machine_id":"M2","start":4,"end":7},{"job_id":"J5","machine_id":"M1","start":0,"end":4},{"job_id":"J6","machine_id":"M1","start":8,"end":13}],"message":"OPTIMAL"},"structural_key":"0a25d991b8ebc99b","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-019","family":"scheduling","split":"development","interactive":true,"difficulty":"easy","language":"en","template_id":"D-A","seed":75019,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 5 rel 0 due 7, J2 dur 4 rel 0 due 13, J3 dur 4 rel 1 due 17, J4 dur 2 rel 0 due 17\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 13, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 17, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 5 rel 0 due 7, J2 dur 4 rel 0 due 13, J3 dur 4 rel 1 due 17, J4 dur 2 rel 0 due 17\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 5, \"release\": 0, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 0, \"due\": 13, \"weight\": 1, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 17, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 2, \"release\": 0, \"due\": 17, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 13,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 17,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 23\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":0,"due":7,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":13,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":1,"due":17,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":17,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":23},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":2,"end":7},{"job_id":"J2","machine_id":"M1","start":7,"end":11},{"job_id":"J3","machine_id":"M1","start":11,"end":15},{"job_id":"J4","machine_id":"M1","start":0,"end":2}],"message":"OPTIMAL"},"structural_key":"21a2617ee4fc356c","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-020","family":"scheduling","split":"development","interactive":false,"difficulty":"easy","language":"en","template_id":"D-B","seed":75020,"prompt_en":"Schedule jobs on machines M1 without overlap. Respect release times and precedences (none). Hard due dates are deadlines.\nJOBS: J1 dur 3 rel 1 due 7, J2 dur 4 rel 2 due 8, J3 dur 4 rel 1 due 13, J4 dur 4 rel 0 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 1, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 2, \"due\": 8, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 13, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_fa":"کارها را روی ماشین‌های M1 بدون هم‌پوشانی زمان‌بندی کنید. زمان آزادسازی و تقدم (none) رعایت شود. موعد سخت ضرب‌الاجل است.\nJOBS: J1 dur 3 rel 1 due 7, J2 dur 4 rel 2 due 8, J3 dur 4 rel 1 due 13, J4 dur 4 rel 0 due 19\nSCHEMA_BEGIN\n{\"machines\": [\"M1\"], \"jobs\": [{\"job_id\": \"J1\", \"name\": \"op-1\", \"duration\": 3, \"release\": 1, \"due\": 7, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J2\", \"name\": \"op-2\", \"duration\": 4, \"release\": 2, \"due\": 8, \"weight\": 4, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J3\", \"name\": \"op-3\", \"duration\": 4, \"release\": 1, \"due\": 13, \"weight\": 3, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}, {\"job_id\": \"J4\", \"name\": \"op-4\", \"duration\": 4, \"release\": 0, \"due\": 19, \"weight\": 2, \"hard_due\": false, \"machine_eligible\": [\"M1\"]}], \"precedences\": [], \"horizon\": 23}\nSCHEMA_END\n","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 7,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 8,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 13,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 19,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 23\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":1,"due":7,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":4,"release":2,"due":8,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":1,"due":13,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":0,"due":19,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":23},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":1,"end":4},{"job_id":"J2","machine_id":"M1","start":4,"end":8},{"job_id":"J3","machine_id":"M1","start":8,"end":12},{"job_id":"J4","machine_id":"M1","start":12,"end":16}],"message":"OPTIMAL"},"structural_key":"76ab27078c9e56ec","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-021","family":"scheduling","split":"test","interactive":false,"difficulty":"hard","language":"fa","template_id":"T-A","seed":75021,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 3 rel 0 due 7, J2 dur 2 rel 0 due 9, J3 dur 2 rel 0 due 9, J4 dur 5 rel 0 due 16, J5 dur 4 rel 2 due 20, J6 dur 4 rel 0 due 23, J7 dur 3 rel 2 due 27, J8 dur 2 rel 0 due 26. Precedence: J1->J3, J2->J5. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 3 rel 0 due 7, J2 dur 2 rel 0 due 9, J3 dur 2 rel 0 due 9, J4 dur 5 rel 0 due 16, J5 dur 4 rel 2 due 20, J6 dur 4 rel 0 due 23, J7 dur 3 rel 2 due 27, J8 dur 2 rel 0 due 26. تقدم: J1->J3, J2->J5. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 16,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 20,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 23,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J7\",\n \"name\": \"op-7\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 27,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J8\",\n \"name\": \"op-8\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 26,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n },\n {\n \"before\": \"J2\",\n \"after\": \"J5\"\n }\n ],\n \"horizon\": 33\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":7,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":2,"release":0,"due":9,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":9,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":5,"release":0,"due":16,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J5","name":"op-5","duration":4,"release":2,"due":20,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J6","name":"op-6","duration":4,"release":0,"due":23,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J7","name":"op-7","duration":3,"release":2,"due":27,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J8","name":"op-8","duration":2,"release":0,"due":26,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"},{"before":"J2","after":"J5"}],"horizon":33},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":2,"end":5},{"job_id":"J2","machine_id":"M2","start":0,"end":2},{"job_id":"J3","machine_id":"M1","start":6,"end":8},{"job_id":"J4","machine_id":"M2","start":8,"end":13},{"job_id":"J5","machine_id":"M1","start":2,"end":6},{"job_id":"J6","machine_id":"M1","start":8,"end":12},{"job_id":"J7","machine_id":"M2","start":5,"end":8},{"job_id":"J8","machine_id":"M1","start":0,"end":2}],"message":"OPTIMAL"},"structural_key":"88a4981fddb98a2b","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-022","family":"scheduling","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-B","seed":75022,"prompt_en":"A shop has machines M1. Jobs: J1 dur 5 rel 0 due 9, J2 dur 3 rel 0 due 10, J3 dur 4 rel 2 due 13, J4 dur 2 rel 1 due 17. Precedence: none. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1 را دارد. کارها: J1 dur 5 rel 0 due 9, J2 dur 3 rel 0 due 10, J3 dur 4 rel 2 due 13, J4 dur 2 rel 1 due 17. تقدم: none. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 13,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 17,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 22\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":0,"due":9,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":3,"release":0,"due":10,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":2,"due":13,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":1,"due":17,"weight":1,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":22},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":3,"end":8},{"job_id":"J2","machine_id":"M1","start":0,"end":3},{"job_id":"J3","machine_id":"M1","start":8,"end":12},{"job_id":"J4","machine_id":"M1","start":12,"end":14}],"message":"OPTIMAL"},"structural_key":"fc27c47c78ea227c","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-023","family":"scheduling","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":75023,"prompt_en":"A shop has machines M1. Jobs: J1 dur 3 rel 0 due 7, J2 dur 2 rel 1 due 6, J3 dur 2 rel 0 due 10, J4 dur 2 rel 2 due 11. Precedence: none. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1 را دارد. کارها: J1 dur 3 rel 0 due 7, J2 dur 2 rel 1 due 6, J3 dur 2 rel 0 due 10, J4 dur 2 rel 2 due 11. تقدم: none. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 7,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 6,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 11,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 17\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":7,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":1,"due":6,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":10,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":2,"due":11,"weight":4,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":17},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":4,"end":7},{"job_id":"J2","machine_id":"M1","start":2,"end":4},{"job_id":"J3","machine_id":"M1","start":0,"end":2},{"job_id":"J4","machine_id":"M1","start":7,"end":9}],"message":"OPTIMAL"},"structural_key":"5dfdc5a6705389ef","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-024","family":"scheduling","split":"test","interactive":false,"difficulty":"medium","language":"fa","template_id":"T-B","seed":75024,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 5 rel 2 due 7, J2 dur 3 rel 2 due 11, J3 dur 2 rel 0 due 14, J4 dur 3 rel 0 due 17, J5 dur 2 rel 0 due 17, J6 dur 5 rel 0 due 24. Precedence: J1->J3. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 5 rel 2 due 7, J2 dur 3 rel 2 due 11, J3 dur 2 rel 0 due 14, J4 dur 3 rel 0 due 17, J5 dur 2 rel 0 due 17, J6 dur 5 rel 0 due 24. تقدم: J1->J3. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 2,\n \"due\": 7,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 11,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 24,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 28\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":2,"due":7,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":3,"release":2,"due":11,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":14,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":3,"release":0,"due":17,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":2,"release":0,"due":17,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":5,"release":0,"due":24,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":28},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":2,"end":7},{"job_id":"J2","machine_id":"M2","start":7,"end":10},{"job_id":"J3","machine_id":"M1","start":8,"end":10},{"job_id":"J4","machine_id":"M1","start":0,"end":3},{"job_id":"J5","machine_id":"M2","start":0,"end":2},{"job_id":"J6","machine_id":"M1","start":3,"end":8}],"message":"OPTIMAL"},"structural_key":"1a960892242a07ff","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-025","family":"scheduling","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":75025,"prompt_en":"A shop has machines M1. Jobs: J1 dur 4 rel 1 due 5, J2 dur 4 rel 0 due 12, J3 dur 2 rel 1 due 12, J4 dur 2 rel 0 due 14. Precedence: none. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1 را دارد. کارها: J1 dur 4 rel 1 due 5, J2 dur 4 rel 0 due 12, J3 dur 2 rel 1 due 12, J4 dur 2 rel 0 due 14. تقدم: none. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 5,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 12,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 20\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":1,"due":5,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":4,"release":0,"due":12,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":2,"release":1,"due":12,"weight":2,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":14,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":20},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":1,"end":5},{"job_id":"J2","machine_id":"M1","start":5,"end":9},{"job_id":"J3","machine_id":"M1","start":9,"end":11},{"job_id":"J4","machine_id":"M1","start":11,"end":13}],"message":"OPTIMAL"},"structural_key":"754a69c12ebd799b","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-026","family":"scheduling","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-B","seed":75026,"prompt_en":"A shop has machines M1. Jobs: J1 dur 5 rel 0 due 9, J2 dur 2 rel 1 due 10, J3 dur 4 rel 0 due 14, J4 dur 2 rel 0 due 15. Precedence: none. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1 را دارد. کارها: J1 dur 5 rel 0 due 9, J2 dur 2 rel 1 due 10, J3 dur 4 rel 0 due 14, J4 dur 2 rel 0 due 15. تقدم: none. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 10,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 14,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 15,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 21\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":0,"due":9,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":1,"due":10,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":0,"due":14,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":15,"weight":4,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":21},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":4,"end":9},{"job_id":"J2","machine_id":"M1","start":2,"end":4},{"job_id":"J3","machine_id":"M1","start":9,"end":13},{"job_id":"J4","machine_id":"M1","start":0,"end":2}],"message":"OPTIMAL"},"structural_key":"cec5818c37927030","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-027","family":"scheduling","split":"test","interactive":true,"difficulty":"medium","language":"fa","template_id":"T-A","seed":75027,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 3 rel 0 due 5, J2 dur 2 rel 1 due 8, J3 dur 3 rel 0 due 10, J4 dur 4 rel 1 due 14, J5 dur 4 rel 0 due 20, J6 dur 3 rel 0 due 22. Precedence: J1->J3. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 3 rel 0 due 5, J2 dur 2 rel 1 due 8, J3 dur 3 rel 0 due 10, J4 dur 4 rel 1 due 14, J5 dur 4 rel 0 due 20, J6 dur 3 rel 0 due 22. تقدم: J1->J3. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 5,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 8,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 10,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 14,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 20,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 3,\n \"release\": 0,\n \"due\": 22,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 27\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":3,"release":0,"due":5,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":2,"release":1,"due":8,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":3,"release":0,"due":10,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":4,"release":1,"due":14,"weight":2,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J5","name":"op-5","duration":4,"release":0,"due":20,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":3,"release":0,"due":22,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":27},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M2","start":0,"end":3},{"job_id":"J2","machine_id":"M1","start":1,"end":3},{"job_id":"J3","machine_id":"M1","start":3,"end":6},{"job_id":"J4","machine_id":"M2","start":6,"end":10},{"job_id":"J5","machine_id":"M1","start":6,"end":10},{"job_id":"J6","machine_id":"M2","start":3,"end":6}],"message":"OPTIMAL"},"structural_key":"94894e246dcfd2a7","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-028","family":"scheduling","split":"test","interactive":false,"difficulty":"hard","language":"en","template_id":"T-B","seed":75028,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 5 rel 0 due 9, J2 dur 2 rel 0 due 8, J3 dur 2 rel 0 due 12, J4 dur 4 rel 0 due 17, J5 dur 5 rel 0 due 20, J6 dur 3 rel 2 due 22, J7 dur 4 rel 0 due 26, J8 dur 4 rel 2 due 32. Precedence: J1->J3, J2->J5. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 5 rel 0 due 9, J2 dur 2 rel 0 due 8, J3 dur 2 rel 0 due 12, J4 dur 4 rel 0 due 17, J5 dur 5 rel 0 due 20, J6 dur 3 rel 2 due 22, J7 dur 4 rel 0 due 26, J8 dur 4 rel 2 due 32. تقدم: J1->J3, J2->J5. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 9,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 8,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 12,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 17,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 5,\n \"release\": 0,\n \"due\": 20,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 22,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J7\",\n \"name\": \"op-7\",\n \"duration\": 4,\n \"release\": 0,\n \"due\": 26,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J8\",\n \"name\": \"op-8\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 32,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n },\n {\n \"before\": \"J2\",\n \"after\": \"J5\"\n }\n ],\n \"horizon\": 37\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":5,"release":0,"due":9,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":0,"due":8,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J3","name":"op-3","duration":2,"release":0,"due":12,"weight":1,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":0,"due":17,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":5,"release":0,"due":20,"weight":2,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J6","name":"op-6","duration":3,"release":2,"due":22,"weight":4,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J7","name":"op-7","duration":4,"release":0,"due":26,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J8","name":"op-8","duration":4,"release":2,"due":32,"weight":1,"hard_due":false,"machine_eligible":["M2"]}],"precedences":[{"before":"J1","after":"J3"},{"before":"J2","after":"J5"}],"horizon":37},"gold_status":"optimal","gold_objective":0.0,"gold_bound":0.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":0.0,"bound":0.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":4,"end":9},{"job_id":"J2","machine_id":"M2","start":0,"end":2},{"job_id":"J3","machine_id":"M1","start":9,"end":11},{"job_id":"J4","machine_id":"M1","start":0,"end":4},{"job_id":"J5","machine_id":"M2","start":6,"end":11},{"job_id":"J6","machine_id":"M2","start":11,"end":14},{"job_id":"J7","machine_id":"M1","start":11,"end":15},{"job_id":"J8","machine_id":"M2","start":2,"end":6}],"message":"OPTIMAL"},"structural_key":"786d201a96694b14","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-029","family":"scheduling","split":"test","interactive":false,"difficulty":"easy","language":"en","template_id":"T-A","seed":75029,"prompt_en":"A shop has machines M1. Jobs: J1 dur 4 rel 2 due 6, J2 dur 2 rel 2 due 9, J3 dur 4 rel 2 due 14, J4 dur 4 rel 2 due 15. Precedence: none. Minimize weighted tardiness. Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1 را دارد. کارها: J1 dur 4 rel 2 due 6, J2 dur 2 rel 2 due 9, J3 dur 4 rel 2 due 14, J4 dur 4 rel 2 due 15. تقدم: none. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 6,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 2,\n \"release\": 2,\n \"due\": 9,\n \"weight\": 4,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 14,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 4,\n \"release\": 2,\n \"due\": 15,\n \"weight\": 2,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\"\n ]\n }\n ],\n \"precedences\": [],\n \"horizon\": 22\n}","schema_payload":{"machines":["M1"],"jobs":[{"job_id":"J1","name":"op-1","duration":4,"release":2,"due":6,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J2","name":"op-2","duration":2,"release":2,"due":9,"weight":4,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":4,"release":2,"due":14,"weight":3,"hard_due":false,"machine_eligible":["M1"]},{"job_id":"J4","name":"op-4","duration":4,"release":2,"due":15,"weight":2,"hard_due":false,"machine_eligible":["M1"]}],"precedences":[],"horizon":22},"gold_status":"optimal","gold_objective":2.0,"gold_bound":2.0,"gold_solution":{"family":"scheduling","status":"optimal","objective":2.0,"bound":2.0,"orders":[],"assignments":[],"unassigned":[],"starts":[{"job_id":"J1","machine_id":"M1","start":2,"end":6},{"job_id":"J2","machine_id":"M1","start":6,"end":8},{"job_id":"J3","machine_id":"M1","start":8,"end":12},{"job_id":"J4","machine_id":"M1","start":12,"end":16}],"message":"OPTIMAL"},"structural_key":"c1def371d6464506","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-030","family":"scheduling","split":"test","interactive":false,"difficulty":"medium","language":"fa","template_id":"T-B","seed":75030,"prompt_en":"A shop has machines M1, M2. Jobs: J1 dur 2 rel 2 due 4, J2 dur 4 rel 0 due 10, J3 dur 4 rel 0 due 11, J4 dur 3 rel 0 due 15, J5 dur 4 rel 1 due 21, J6 dur 4 rel 2 due 22. Precedence: J1->J3. Minimize weighted tardiness. 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Jobs: J1 dur 3 rel 0 due 2 hard, J2 dur 5 rel 1 due 5 hard, J3 dur 2 rel 0 due 14, J4 dur 4 rel 0 due 18, J5 dur 5 rel 0 due 21, J6 dur 3 rel 0 due 26. Precedence: J1->J3. Minimize weighted tardiness. 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Do not overlap a machine.","prompt_fa":"کارگاه ماشین‌های M1, M2 را دارد. کارها: J1 dur 2 rel 1 due 2 hard, J2 dur 4 rel 1 due 4 hard, J3 dur 3 rel 2 due 12, J4 dur 2 rel 0 due 13, J5 dur 2 rel 1 due 15, J6 dur 3 rel 1 due 18. تقدم: J1->J3. تأخیر وزنی کمینه شود و ماشین هم‌پوشانی نداشته باشد.","prompt_json":"{\n \"machines\": [\n \"M1\",\n \"M2\"\n ],\n \"jobs\": [\n {\n \"job_id\": \"J1\",\n \"name\": \"op-1\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 2,\n \"weight\": 2,\n \"hard_due\": true,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J2\",\n \"name\": \"op-2\",\n \"duration\": 4,\n \"release\": 1,\n \"due\": 4,\n \"weight\": 2,\n \"hard_due\": true,\n \"machine_eligible\": [\n \"M1\"\n ]\n },\n {\n \"job_id\": \"J3\",\n \"name\": \"op-3\",\n \"duration\": 3,\n \"release\": 2,\n \"due\": 12,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J4\",\n \"name\": \"op-4\",\n \"duration\": 2,\n \"release\": 0,\n \"due\": 13,\n \"weight\": 1,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J5\",\n \"name\": \"op-5\",\n \"duration\": 2,\n \"release\": 1,\n \"due\": 15,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M2\"\n ]\n },\n {\n \"job_id\": \"J6\",\n \"name\": \"op-6\",\n \"duration\": 3,\n \"release\": 1,\n \"due\": 18,\n \"weight\": 3,\n \"hard_due\": false,\n \"machine_eligible\": [\n \"M1\",\n \"M2\"\n ]\n }\n ],\n \"precedences\": [\n {\n \"before\": \"J1\",\n \"after\": \"J3\"\n }\n ],\n \"horizon\": 24\n}","schema_payload":{"machines":["M1","M2"],"jobs":[{"job_id":"J1","name":"op-1","duration":2,"release":1,"due":2,"weight":2,"hard_due":true,"machine_eligible":["M1","M2"]},{"job_id":"J2","name":"op-2","duration":4,"release":1,"due":4,"weight":2,"hard_due":true,"machine_eligible":["M1"]},{"job_id":"J3","name":"op-3","duration":3,"release":2,"due":12,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J4","name":"op-4","duration":2,"release":0,"due":13,"weight":1,"hard_due":false,"machine_eligible":["M1","M2"]},{"job_id":"J5","name":"op-5","duration":2,"release":1,"due":15,"weight":3,"hard_due":false,"machine_eligible":["M2"]},{"job_id":"J6","name":"op-6","duration":3,"release":1,"due":18,"weight":3,"hard_due":false,"machine_eligible":["M1","M2"]}],"precedences":[{"before":"J1","after":"J3"}],"horizon":24},"gold_status":"infeasible","gold_objective":null,"gold_bound":null,"gold_solution":{"family":"scheduling","status":"infeasible","objective":null,"bound":null,"orders":[],"assignments":[],"unassigned":[],"starts":[],"message":"INFEASIBLE"},"structural_key":"56a2b20635ec8a65","notes":"objective reported as weighted tardiness; makespan is a tie-break inside the solver only"} {"problem_id":"SCH-033","family":"scheduling","split":"test","interactive":true,"difficulty":"infeasible","language":"fa","template_id":"T-A","seed":75033,"prompt_en":"A shop has machines M1, M2. 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