facility.py
#!/usr/bin/python
# Copyright 2011, Gurobi Optimization, Inc.
# 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.
from gurobipy import *
# 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 = Model("facility")
# Plant open decision variables: open[p] == 1 if plant p is open.
open = []
for p in plants:
open.append(m.addVar(vtype=GRB.BINARY, name="Open%d" % p))
# Set optimization objective - minimize sum of fixed costs
m.setObjective(quicksum([fixedCosts[p]*open[p] for p in plants]))
# Transportation decision variables: how much to transport from
# a plant p to a warehouse w
transport = []
for w in warehouses:
transport.append([])
for p in plants:
transport[w].append(m.addVar(obj=transCosts[w][p],
name="Trans%d.%d" % (p, w)))
# The objective is to minimize the total fixed and variable costs
m.modelSense = GRB.MINIMIZE
# Update model to integrate new variables
m.update()
# Production constraints
# Note that the right-hand limit sets the production to zero if the plant
# is closed
for p in plants:
m.addConstr(
quicksum(transport[w][p] for w in warehouses) <= capacity[p] * open[p],
"Capacity%d" % p)
# Demand constraints
for w in warehouses:
m.addConstr(quicksum(transport[w][p] for p in plants) == demand[w],
"Demand%d" % w)
# 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 'Closing plant', p
break
print
# Use barrier to solve root relaxation
m.params.method = 2
# Solve
m.optimize()
# Print solution
print '\nTOTAL COSTS:', m.objVal
print 'SOLUTION:'
for p in plants:
if open[p].x == 1.0:
print 'Plant', p, 'open:'
for w in warehouses:
if transport[w][p].x > 0:
print ' Transport', transport[w][p].x, 'units to warehouse', w
else:
print 'Plant', p, 'closed!'