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# Copyright 2010 Hakan Kjellerstrand hakank@gmail.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@gmail.com)
  Also see my other Google CP Solver models:
  http://www.hakank.org/google_or_tools/
"""
from __future__ import print_function
import sys
from ortools.constraint_solver import pywrapcp



# Create the solver.
solver = pywrapcp.Solver('P-median problem')

#
# data
#
p = 2

num_customers = 4
customers = list(range(num_customers))
Albert, Bob, Chris, Daniel = customers
num_warehouses = 3
warehouses = list(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(), end=' ')
    print()
  print()

print('num_solutions:', num_solutions)
print('failures:', solver.Failures())
print('branches:', solver.Branches())
print('WallTime:', solver.WallTime(), 'ms')