A Production Mix Problem (PRODMIX)

prodmix.py

"""
## GAMSSOURCE: https://www.gams.com/latest/gamslib_ml/libhtml/gamslib_prodmix.html
## LICENSETYPE: Demo
## MODELTYPE: LP
## KEYWORDS: linear programming, production planning, manufacturing, furniture production


A Production Mix Problem (PRODMIX)

A furniture company wants to maximize its profits from the
manufacture of different types of desks.


Dantzig, G B, Chapter 3.5. 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),
    )

    # Set
    desk = Set(m, name="desk", records=["d1", "d2", "d3", "d4"])
    shop = Set(m, name="shop", records=["carpentry", "finishing"])

    # Data
    labor = Parameter(
        m,
        name="labor",
        domain=[shop, desk],
        records=np.array([[4, 9, 7, 10], [1, 1, 3, 40]]),
        description="labor requirements (man-hours)",
    )
    caplim = Parameter(
        m,
        name="caplim",
        domain=shop,
        records=np.array([6000, 4000]),
        description="capacity (man hours)",
    )
    price = Parameter(
        m,
        name="price",
        domain=desk,
        records=np.array([12, 20, 18, 40]),
        description="per unit sold ($)",
    )

    # Variable
    mix = Variable(
        m,
        name="mix",
        domain=desk,
        type="Positive",
        description="mix of desks produced (number of desks)",
    )

    # Equations
    cap = Equation(
        m,
        name="cap",
        domain=shop,
        description="capacity constraint (man-hours)",
    )

    cap[shop] = Sum(desk, labor[shop, desk] * mix[desk]) <= caplim[shop]

    ap = Sum(desk, price[desk] * mix[desk])  # accounting: total profit    ($)

    pmp = Model(
        m,
        name="pmp",
        equations=m.getEquations(),
        problem="LP",
        sense=Sense.MAX,
        objective=ap,
    )

    pmp.solve()

    import math

    assert math.isclose(pmp.objective_value, 18666, rel_tol=0.0001)

    print("Total Profit: ", pmp.objective_value)


if __name__ == "__main__":
    main()