# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.com
#
# Licensed under the Apache License, Version 2.0 (the 'License');
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an 'AS IS' BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
P-median problem in Google CP Solver.
Model and data from the OPL Manual, which describes the problem:
'''
The P-Median problem is a well known problem in Operations Research.
The problem can be stated very simply, like this: given a set of customers
with known amounts of demand, a set of candidate locations for warehouses,
and the distance between each pair of customer-warehouse, choose P
warehouses to open that minimize the demand-weighted distance of serving
all customers from those P warehouses.
'''
Compare with the following models:
* MiniZinc: http://hakank.org/minizinc/p_median.mzn
* Comet: http://hakank.org/comet/p_median.co
This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
Also see my other Google CP Solver models:
http://www.hakank.org/google_or_tools/
"""
import sys
from ortools.constraint_solver import pywrapcp
def main():
# Create the solver.
solver = pywrapcp.Solver('P-median problem')
#
# data
#
p = 2
num_customers = 4
customers = range(num_customers)
Albert, Bob, Chris, Daniel = customers
num_warehouses = 3
warehouses = range(num_warehouses)
Santa_Clara, San_Jose, Berkeley = warehouses
demand = [100, 80, 80, 70]
distance = [
[2, 10, 50],
[2, 10, 52],
[50, 60, 3],
[40, 60, 1]
]
#
# declare variables
#
open = [solver.IntVar(warehouses, 'open[%i]% % i')
for w in warehouses]
ship = {}
for c in customers:
for w in warehouses:
ship[c, w] = solver.IntVar(0, 1, 'ship[%i,%i]' % (c, w))
ship_flat = [ship[c, w]
for c in customers
for w in warehouses]
z = solver.IntVar(0, 1000, 'z')
#
# constraints
#
z_sum = solver.Sum([demand[c] * distance[c][w] * ship[c, w]
for c in customers
for w in warehouses])
solver.Add(z == z_sum)
for c in customers:
s = solver.Sum([ship[c, w]
for w in warehouses])
solver.Add(s == 1)
solver.Add(solver.Sum(open) == p)
for c in customers:
for w in warehouses:
solver.Add(ship[c, w] <= open[w])
# objective
objective = solver.Minimize(z, 1)
#
# solution and search
#
db = solver.Phase(open + ship_flat,
solver.INT_VAR_DEFAULT,
solver.INT_VALUE_DEFAULT)
solver.NewSearch(db, [objective])
num_solutions = 0
while solver.NextSolution():
num_solutions += 1
print 'z:', z.Value()
print 'open:', [open[w].Value() for w in warehouses]
for c in customers:
for w in warehouses:
print ship[c, w].Value(),
print
print
print 'num_solutions:', num_solutions
print 'failures:', solver.Failures()
print 'branches:', solver.Branches()
print 'WallTime:', solver.WallTime(), 'ms'
if __name__ == '__main__':
main()