Capacitated Lot-Sizing Problem (CLSP)

clsp.py

"""
## LICENSETYPE: Demo
## MODELTYPE: MIP


Capacitated Lot-Sizing Problem (CLSP)
"""

from __future__ import annotations

import os
from itertools import product

import pandas as pd

from gamspy import Alias
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 model_data():
    # Sets
    products = ["Product_A", "Product_B", "Product_C"]
    time_periods = [1, 2, 3, 4]
    resources = ["Resource_A", "Resource_B"]

    kj = pd.DataFrame(
        product(products, resources)
    )  # product-resource combinations -->  ("Product_A", "Resource_A"), ("Product_B", "Resource_A"), ...

    # Parameters
    demand_data = pd.DataFrame({
        "Product_A": {1: 100, 2: 150, 3: 120, 4: 180},
        "Product_B": {1: 80, 2: 100, 3: 90, 4: 120},
        "Product_C": {1: 50, 2: 60, 3: 70, 4: 80},
    }).unstack()

    setup_cost_data = pd.DataFrame(
        [("Product_A", 100), ("Product_B", 200), ("Product_C", 300)]
    )
    holding_cost_data = pd.DataFrame(
        [("Product_A", 0.2), ("Product_B", 0.1), ("Product_C", 0.6)]
    )

    capacity_data = pd.DataFrame([
        ("Resource_A", 1, 340),
        ("Resource_B", 1, 340),
        ("Resource_A", 2, 330),
        ("Resource_B", 2, 330),
        ("Resource_A", 3, 300),
        ("Resource_B", 3, 300),
        ("Resource_A", 4, 380),
        ("Resource_B", 4, 380),
    ])

    return {
        "products": products,
        "time_periods": time_periods,
        "resources": resources,
        "kj": kj,
        "demand_data": demand_data,
        "setup_cost_data": setup_cost_data,
        "holding_cost_data": holding_cost_data,
        "capacity_data": capacity_data,
    }


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

    # SETS
    k = Set(
        m,
        name="k",
        description="products",
        records=data["products"],
    )
    j = Set(m, name="j", description="resources", records=data["resources"])
    t = Set(
        m, name="t", description="time periods", records=data["time_periods"]
    )

    KJ = Set(
        m,
        name="KJ",
        domain=[k, j],
        description="products k that can be handled by resource j",
        records=data["kj"],
    )

    # ALIAS
    tau = Alias(m, name="tau", alias_with=t)

    # PARAMETERS
    d = Parameter(
        m,
        name="d",
        domain=[k, t],
        description="demand of product k in period t",
        records=data["demand_data"],
    )
    s = Parameter(
        m,
        name="s",
        domain=k,
        description="fixed setup cost for product k",
        records=data["setup_cost_data"],
    )
    h = Parameter(
        m,
        name="h",
        domain=k,
        description="holding cost for product k",
        records=data["holding_cost_data"],
    )
    c = Parameter(
        m,
        name="c",
        domain=[j, t],
        description="production capacity of resource j in period t",
        records=data["capacity_data"],
    )

    # VARIABLES
    X = Variable(
        m,
        name="X",
        domain=[k, t],
        type="positive",
        description="lot size of product k in period t",
    )
    Y = Variable(
        m,
        name="Y",
        domain=[k, t],
        type="binary",
        description="indicates if product k is manufactured in period t",
    )
    Z = Variable(
        m,
        name="Z",
        domain=[k, t],
        type="positive",
        description="stock of product k in period t",
    )

    # EQUATIONS
    objective = Sum((k, t), s[k] * Y[k, t] + h[k] * Z[k, t])

    stock = Equation(
        m, name="stock", domain=[k, t], description="Stock balance equation"
    )
    stock[...] = Z[k, t] == Z[k, t.lag(1)] + X[k, t] - d[k, t]

    production = Equation(
        m, name="production", domain=[k, t], description="Ensure production"
    )
    production[...] = X[k, t] <= Y[k, t] * Sum(tau, d[k, tau])

    capacity = Equation(
        m, name="capacity", domain=[j, t], description="Capacity restriction"
    )
    capacity[...] = Sum(KJ[k, j], X[k, t]) <= c[j, t]

    Z.fx[k, t].where[t.last] = 0

    # Model definition
    clsp = Model(
        m,
        name="CLSP",
        problem="MIP",
        equations=m.getEquations(),
        sense=Sense.MIN,
        objective=objective,
    )

    clsp.solve()

    import math

    assert math.isclose(clsp.objective_value, 1694, rel_tol=0.001)

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

    print("X: \n", X.pivot(index="t", columns="k"))

    print("Z: \n", Z.pivot(index="t", columns="k"))


if __name__ == "__main__":
    main()