Thai Navy Problem (THAI)

thai.py thai.gdx

"""
Thai Navy Problem (THAI)

This model is used to allocate ships to transport personnel from
different port to a training center.


Choypeng, P, Puakpong, P, and Rosenthal, R E, Optimal Ship Routing
and Personnel Assignment for Naval Recruitment in Thailand.
Interfaces 16, 4 (1986), 356-366.

Keywords: mixed integer linear programming, routing, naval recruitment,
          scheduling
"""
from __future__ import annotations

import os
from pathlib import Path

from gamspy import Container
from gamspy import Domain
from gamspy import Model
from gamspy import Sense
from gamspy import Sum


def main():
    m = Container(
        system_directory=os.getenv("SYSTEM_DIRECTORY", None),
        delayed_execution=int(os.getenv("DELAYED_EXECUTION", False)),
        load_from=str(Path(__file__).parent.absolute()) + "/thai.gdx",
    )

    # Sets
    i, j, k, sc, vc = m.getSymbols(["i", "j", "k", "sc", "vc"])

    # Parameters
    (d, shipcap, n, a, w1, w2, w3) = m.getSymbols(
        ["d", "shipcap", "n", "a", "w1", "w2", "w3"]
    )

    # Variables
    z, y, obj = m.getSymbols(["z", "y", "obj"])

    # Equations
    (
        objdef,
        demand,
        voycap,
        shiplim,
    ) = m.getSymbols(
        [
            "objdef",
            "demand",
            "voycap",
            "shiplim",
        ]
    )

    objdef[...] = obj == w1 * Sum(
        Domain(j, k).where[vc[j, k]], z[j, k]
    ) + w2 * Sum(
        Domain(j, k).where[vc[j, k]], a[j, "dist"] * z[j, k]
    ) + w3 * Sum(
        Domain(j, k, i).where[a[j, i].where[vc[j, k]]],
        a[j, "dist"] * y[j, k, i],
    )

    demand[i] = (
        Sum(Domain(j, k).where[a[j, i].where[vc[j, k]]], y[j, k, i]) >= d[i]
    )
    voycap[j, k].where[vc[j, k]] = (
        Sum(i.where[a[j, i]], y[j, k, i]) <= shipcap[k] * z[j, k]
    )
    shiplim[k] = Sum(j.where[vc[j, k]], z[j, k]) <= n[k]

    thainavy = Model(
        m,
        name="thainavy",
        equations=m.getEquations(),
        problem="MIP",
        sense=Sense.MIN,
        objective=obj,
    )
    z.up[j, k].where[vc[j, k]] = n[k]
    thainavy.solve()


if __name__ == "__main__":
    main()