Simple Warehouse Problem (WHOUSE)

whouse.py

"""
Simple Warehouse Problem (WHOUSE)

A warehouse can store limited units of a commodity. Given an
initial stock, the manager has to decide when to buy or sell in
order to minimize total cost.


Dantzig, G B, Chapter 3.6. In Linear Programming and Extensions.
Princeton University Press, Princeton, New Jersey, 1963.

Keywords: linear programming, warehouse management, inventory
"""
from __future__ import annotations

import os

import numpy as np

from gamspy import Container
from gamspy import Equation
from gamspy import Model
from gamspy import Parameter
from gamspy import Sense
from gamspy import Set
from gamspy import Sum
from gamspy import Variable


def main():
    m = Container(
        system_directory=os.getenv("SYSTEM_DIRECTORY", None),
        delayed_execution=int(os.getenv("DELAYED_EXECUTION", False)),
    )

    # Sets
    t = Set(m, name="t", records=[f"q-{i}" for i in range(1, 5)])

    # Parameters
    price = Parameter(
        m, name="price", domain=[t], records=np.array([10, 12, 8, 9])
    )
    istock = Parameter(
        m, name="istock", domain=[t], records=np.array([50, 0, 0, 0])
    )  # OR records=pd.DataFrame([["q-1", 50]])

    # Scalars
    storecost = Parameter(m, name="storecost", records=1)
    storecap = Parameter(m, name="storecap", records=100)

    # Variables
    stock = Variable(m, name="stock", domain=[t], type="Positive")
    sell = Variable(m, name="sell", domain=[t], type="Positive")
    buy = Variable(m, name="buy", domain=[t], type="Positive")
    cost = Variable(m, name="cost")

    # Equations
    sb = Equation(m, name="sb", domain=[t])
    at = Equation(m, name="at")

    sb[t] = (
        stock[t] == stock[t.lag(1, "linear")] + buy[t] - sell[t] + istock[t]
    )
    at[...] = cost == Sum(
        t, price[t] * (buy[t] - sell[t]) + storecost * stock[t]
    )

    stock.up[t] = storecap

    swp = Model(
        m,
        name="swp",
        equations=m.getEquations(),
        problem="LP",
        sense=Sense.MIN,
        objective=cost,
    )
    swp.solve()

    import math

    assert math.isclose(swp.objective_value, -600, rel_tol=0.001)

    print("Objective function value: ", swp.objective_value)


if __name__ == "__main__":
    main()