Stochastic Capacitated Facility Location Problem (SCFLP)

{
  "num_facilities": "<int> Number of candidate facility locations.",
  "num_customers": "<int> Number of customers whose demand must be satisfied.",
  "num_scenarios": "<int> Number of demand scenarios considered.",
  "capacity_factor": "<float> Ratio of total facility capacity to total expected demand, controlling how tight capacity is.",
  "variance_level": "<str> Level of demand variability across scenarios ('normal' or 'high').",
  "facilities": [
    {
      "id": "<int> Zero-based index identifying the facility.",
      "opening_cost": "<float> Fixed cost incurred if this facility is opened.",
      "capacity": "<float> Maximum total units this facility can ship across all customers in any scenario.",
      "location_x": "<float> X-coordinate of the facility location, used to compute transportation costs.",
      "location_y": "<float> Y-coordinate of the facility location, used to compute transportation costs."
    }
  ],
  "customers": [
    {
      "id": "<int> Zero-based index identifying the customer.",
      "deterministic_demand": "<float> Expected (mean) demand of this customer.",
      "demand_std_fraction": "<float> Ratio of demand standard deviation to mean demand for this customer.",
      "location_x": "<float> X-coordinate of the customer location, used to compute transportation costs.",
      "location_y": "<float> Y-coordinate of the customer location, used to compute transportation costs."
    }
  ],
  "transportation_costs": "<list[list[float]], shape [num_facilities][num_customers]> Per-unit cost of shipping from each facility to each customer, equal to the Euclidean distance between them.",
  "scenarios": [
    {
      "id": "<int> Zero-based index identifying the scenario.",
      "probability": "<float> Probability of this scenario occurring.",
      "demands": "<list[float], length num_customers> Realized demand of each customer under this scenario."
    }
  ]
}

{
  "objective_value": "<float> Total expected cost combining facility opening costs and the probability-weighted transportation costs across all demand scenarios.",
  "open_facilities": "<list[int]> Identifiers of the facilities selected to be opened.",
  "x": "<dict, key: '{facility}'> Whether each facility is opened (1 = opened, 0 = closed).",
  "y": "<dict, nested keys: '{scenario}' -> '{facility}' -> '{customer}'> Quantity shipped from each facility to each customer under each demand scenario."
}