Simple Warehouse Problem (WHOUSE)

whouse.py

"""
## GAMSSOURCE: https://www.gams.com/latest/gamslib_ml/libhtml/gamslib_whouse.html
## LICENSETYPE: Demo
## MODELTYPE: LP
## KEYWORDS: linear programming, warehouse management, inventory


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.
"""

from __future__ import annotations

import os

import numpy as np
from gamspy import (
    Container,
    Equation,
    Model,
    Parameter,
    Sense,
    Set,
    Sum,
    Variable,
)


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

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

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

    # Scalars
    storecost = Parameter(
        m,
        name="storecost",
        records=1,
        description="storage cost  ($ per quarter per unit)",
    )
    storecap = Parameter(
        m,
        name="storecap",
        records=100,
        description="stocking capacity of warehouse (units)",
    )

    # Variables
    stock = Variable(
        m,
        name="stock",
        domain=t,
        type="Positive",
        description="stock stored at time t (units)",
    )
    sell = Variable(
        m,
        name="sell",
        domain=t,
        type="Positive",
        description="stock sold at time t   (units)",
    )
    buy = Variable(
        m,
        name="buy",
        domain=t,
        type="Positive",
        description="stock bought at time t (units)",
    )

    # Equations
    sb = Equation(
        m, name="sb", domain=t, description="stock balance at time t (units)"
    )

    sb[t] = (
        stock[t] == stock[t.lag(1, "linear")] + buy[t] - sell[t] + istock[t]
    )

    # ObjectFunction; accounting: total cost      ($)
    at = 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=at,
    )
    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()