sailco.json

{
  "Problem": {
  "Name": "sailco",
  "Reference": "https://www.ibm.com/support/knowledgecenter/SSSA5P_12.7.1/ilog.odms.ide.help/OPL_Studio/opllanguser/topics/opl_languser_app_areas_pwl_inventory.html",
  "Author": "Jeremy A. Bloom (jeremyblmca@gmail.com)",
  "Notices": "Copyright © 2019 Jeremy A. Bloom"
  },
  "Input_Data_Model": {
    "periods": {"+period":     "Integer"},
    "demands": {
      "*period":               "Integer",
      "demand":                "Double"
    },
    "parameters": {
      "regularCost":           "Double",
      "extraCost":             "Double",
      "capacity":              "Double",
      "initialInventory":      "Double",
      "inventoryCost":         "Double"
    }
  },
  "Output_Data_Model": {
    "production": {
      "*period":               "Double",
      "regular":               "Double",
      "extra":                 "Double",
      "inventory":             "Double",
      "marginalCapacityValue": "Double"
    }
  },
  "Data": {
    "periods": [
      {"period": 1},
      {"period": 2},
      {"period": 3},
      {"period": 4}
    ],
    "demands": [
      {"period": 1, "demand": 40.0},
      {"period": 2, "demand": 60.0},
      {"period": 3, "demand": 72.0},
      {"period": 4, "demand": 25.0}
    ],
    "parameters": [
      {"regularCost":      400.0},
      {"extraCost":        450.0},
      {"capacity":         40.0},
      {"initialInventory": 10.0},
      {"inventoryCost":    20.0}
    ]
  },
  "Variables": [
    {
      "Name": "regular",
      "Type": "Continuous",
      "Index": "periods",
      "Bounds": "Non-negative"
    },
    {
      "Name": "extra",
      "Type": "Continuous",
      "Index": "periods",
      "Bounds": "Non-negative"
    },
    {
      "Name": "inventory",
      "Type": "Continuous",
      "Index": "periods",
      "Bounds": "Non-negative"
    }
  ],
  "Constraints": [
    {
      "Name": "ctCapacity",
      "Type": "Linear",
      "Index": "periods",
      "Sense": "<=",
      "RHS": "parameters.capacity"
    },
    {
      "Name": "ctBoat",
      "Type": "Linear",
      "Index": "periods.period >1",
      "Sense": "==",
      "RHS": "demands.demand"
    },
    {
      "Name": "ctBoat",
      "Type": "Linear",
      "Index": "periods.period ==1",
      "Sense": "==",
      "RHS": "demands.demand + parameters.initialInventory"
    }
  ],
  "Decision_Expressions": [
    {
      "Name": "totalCost",
      "Type": "Linear",
      "Index": "Self",
      "Sense": "minimize"
    }
  ],
  "Coefficients": [
    {
      "Name": "ctCapacity_regular",
      "Constraints": "ctCapacity",
      "Variables": "regular",
      "Entries": 1.0
    },
    {
      "Name": "ctBoat_regular",
      "Constraints": "ctBoat",
      "Variables": "regular",
      "Entries": 1.0
    },
    {
      "Name": "ctBoat_extra",
      "Constraints": "ctBoat",
      "Variables": "extra",
      "Entries": 1.0
    },
    {
      "Name": "ctBoat_inventory",
      "Constraints": "ctBoat",
      "Variables": "inventory",
      "Entries": 1.0
    },
    {
      "Name": "ctBoat_lagged_inventory",
      "Constraints": {"Name": "ctBoat", "Index": "periods.period > 1"},
      "Variables": {"Name":"inventory", "Index": "periods.period-1"},
      "Entries": -1.0
    }
  ]
}