cases/case_knapsack.json

{
  "case_id": "case_knapsack",
  "problem_type": "knapsack",
  "natural_language": "Select items to maximize profit. Item profits are 24, 13, 23, 15, 16 and weights are 12, 7, 11, 8, 9. Knapsack capacity is 26. Each item can be taken at most once.",
  "binding": {
    "problem_hint": "knapsack",
    "entities": {
      "items": [
        {
          "id": "I1",
          "label": null,
          "attributes": {}
        },
        {
          "id": "I2",
          "label": null,
          "attributes": {}
        },
        {
          "id": "I3",
          "label": null,
          "attributes": {}
        },
        {
          "id": "I4",
          "label": null,
          "attributes": {}
        },
        {
          "id": "I5",
          "label": null,
          "attributes": {}
        }
      ]
    },
    "parameters": {
      "profit": {
        "name": "profit",
        "value": [
          24.0,
          13.0,
          23.0,
          15.0,
          16.0
        ],
        "unit": null,
        "source_span": null
      },
      "weight": {
        "name": "weight",
        "value": [
          12.0,
          7.0,
          11.0,
          8.0,
          9.0
        ],
        "unit": null,
        "source_span": null
      }
    },
    "scalars": {
      "capacity": 26.0
    },
    "binding_confidence": 0.88
  },
  "formulation": {
    "problem_type": "knapsack",
    "sets": {
      "I": "items"
    },
    "parameters": [
      "profit",
      "weight"
    ],
    "variables": [
      {
        "name": "x",
        "indices": [
          "i"
        ],
        "domain": "binary",
        "non_negative": true,
        "description": "1 if item i is selected"
      }
    ],
    "objective": {
      "sense": "maximize",
      "expression": "sum(profit[i] * x[i] for i in I)",
      "description": "Maximize total profit"
    },
    "constraints": [
      {
        "name": "capacity",
        "expression": "sum(weight[i] * x[i] for i in I)",
        "sense": "<=",
        "rhs_expression": "capacity",
        "description": "Respect knapsack capacity"
      }
    ],
    "notes": []
  },
  "ground_truth_objective": 51.0
}