facility.py

#!/usr/bin/env python3.11

# Copyright 2025, Gurobi Optimization, LLC

# Facility location: a company currently ships its product from 5 plants
# to 4 warehouses. It is considering closing some plants to reduce
# costs. What plant(s) should the company close, in order to minimize
# transportation and fixed costs?
#
# Note that this example uses lists instead of dictionaries.  Since
# it does not work with sparse data, lists are a reasonable option.
#
# Based on an example from Frontline Systems:
#   http://www.solver.com/disfacility.htm
# Used with permission.

import gurobipy as gp
from gurobipy import GRB


# Warehouse demand in thousands of units
demand = [15, 18, 14, 20]

# Plant capacity in thousands of units
capacity = [20, 22, 17, 19, 18]

# Fixed costs for each plant
fixedCosts = [12000, 15000, 17000, 13000, 16000]

# Transportation costs per thousand units
transCosts = [
    [4000, 2000, 3000, 2500, 4500],
    [2500, 2600, 3400, 3000, 4000],
    [1200, 1800, 2600, 4100, 3000],
    [2200, 2600, 3100, 3700, 3200],
]

# Range of plants and warehouses
plants = range(len(capacity))
warehouses = range(len(demand))

# Model
m = gp.Model("facility")

# Plant open decision variables: open[p] == 1 if plant p is open.
open = m.addVars(plants, vtype=GRB.BINARY, obj=fixedCosts, name="open")

# Transportation decision variables: transport[w,p] captures the
# optimal quantity to transport to warehouse w from plant p
transport = m.addVars(warehouses, plants, obj=transCosts, name="trans")

# You could use Python looping constructs and m.addVar() to create
# these decision variables instead.  The following would be equivalent
# to the preceding two statements...
#
# open = []
# for p in plants:
#     open.append(m.addVar(vtype=GRB.BINARY,
#                          obj=fixedCosts[p],
#                          name="open[%d]" % p))
#
# transport = []
# for w in warehouses:
#     transport.append([])
#     for p in plants:
#         transport[w].append(m.addVar(obj=transCosts[w][p],
#                                      name="trans[%d,%d]" % (w, p)))

# The objective is to minimize the total fixed and variable costs
m.ModelSense = GRB.MINIMIZE

# Production constraints
# Note that the right-hand limit sets the production to zero if the plant
# is closed
m.addConstrs(
    (transport.sum("*", p) <= capacity[p] * open[p] for p in plants), "Capacity"
)

# Using Python looping constructs, the preceding would be...
#
# for p in plants:
#     m.addConstr(sum(transport[w][p] for w in warehouses)
#                 <= capacity[p] * open[p], "Capacity[%d]" % p)

# Demand constraints
m.addConstrs((transport.sum(w) == demand[w] for w in warehouses), "Demand")

# ... and the preceding would be ...
# for w in warehouses:
#     m.addConstr(sum(transport[w][p] for p in plants) == demand[w],
#                 "Demand[%d]" % w)

# Save model
m.write("facilityPY.lp")

# Guess at the starting point: close the plant with the highest fixed costs;
# open all others

# First open all plants
for p in plants:
    open[p].Start = 1.0

# Now close the plant with the highest fixed cost
print("Initial guess:")
maxFixed = max(fixedCosts)
for p in plants:
    if fixedCosts[p] == maxFixed:
        open[p].Start = 0.0
        print(f"Closing plant {p}")
        break
print("")

# Use barrier to solve root relaxation
m.Params.Method = 2

# Solve
m.optimize()

# Print solution
print(f"\nTOTAL COSTS: {m.ObjVal:g}")
print("SOLUTION:")
for p in plants:
    if open[p].X > 0.99:
        print(f"Plant {p} open")
        for w in warehouses:
            if transport[w, p].X > 0:
                print(f"  Transport {transport[w, p].X:g} units to warehouse {w}")
    else:
        print(f"Plant {p} closed!")