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### facility.py

#!/usr/bin/env python3.7

# Copyright 2021, 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.
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:
#                          obj=fixedCosts[p],
#                          name="open[%d]" % p))
#
# transport = []
# for w in warehouses:
#     transport.append([])
#     for p in plants:
#                                      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
(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
(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('Closing plant %s' % p)
break
print('')

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

# Solve
m.optimize()

# Print solution
print('\nTOTAL COSTS: %g' % m.objVal)
print('SOLUTION:')
for p in plants:
if open[p].x > 0.99:
print('Plant %s open' % p)
for w in warehouses:
if transport[w, p].x > 0:
print('  Transport %g units to warehouse %s' %
(transport[w, p].x, w))
else:
print('Plant %s closed!' % p)