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# Copyright 2011 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.
"""

  Assignment problem using MIP in Google or-tools.

  From GLPK:s example assign.mod:
  '''
  The assignment problem is one of the fundamental combinatorial
  optimization problems.

  In its most general form, the problem is as follows:

  There are a number of agents and a number of tasks. Any agent can be
  assigned to perform any task, incurring some cost that may vary
  depending on the agent-task assignment. It is required to perform all
  tasks by assigning exactly one agent to each task in such a way that
  the total cost of the assignment is minimized.

  (From Wikipedia, the free encyclopedia.)
  '''

  Compare with the Comet model:
     http://www.hakank.org/comet/assignment6.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.linear_solver import pywraplp



# Create the solver.
print('Solver: ', sol)

# using GLPK
if sol == 'GLPK':
  solver = pywraplp.Solver('CoinsGridGLPK',
                           pywraplp.Solver.GLPK_MIXED_INTEGER_PROGRAMMING)
else:
  # Using CBC
  solver = pywraplp.Solver('CoinsGridCBC',
                           pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)

#
# data
#

# number of agents
m = 8

# number of tasks
n = 8

# set of agents
I = list(range(m))

# set of tasks
J = list(range(n))

# cost of allocating task j to agent i
# """
# These data correspond to an example from [Christofides].
#
# Optimal solution is 76
# """
c = [[13, 21, 20, 12, 8, 26, 22, 11], [12, 36, 25, 41, 40, 11, 4, 8],
     [35, 32, 13, 36, 26, 21, 13, 37], [34, 54, 7, 8, 12, 22, 11, 40],
     [21, 6, 45, 18, 24, 34, 12, 48], [42, 19, 39, 15, 14, 16, 28, 46],
     [16, 34, 38, 3, 34, 40, 22, 24], [26, 20, 5, 17, 45, 31, 37, 43]]

#
# variables
#

# For the output: the assignment as task number.
assigned = [solver.IntVar(0, 10000, 'assigned[%i]' % j) for j in J]

costs = [solver.IntVar(0, 10000, 'costs[%i]' % i) for i in I]

x = {}
for i in range(n):
  for j in range(n):
    x[i, j] = solver.IntVar(0, 1, 'x[%i,%i]' % (i, j))

# total cost, to be minimized
z = solver.Sum([c[i][j] * x[i, j] for i in I for j in J])

#
# constraints
#
# each agent can perform at most one task
for i in I:
  solver.Add(solver.Sum([x[i, j] for j in J]) <= 1)

# each task must be assigned exactly to one agent
for j in J:
  solver.Add(solver.Sum([x[i, j] for i in I]) == 1)

# to which task and what cost is person i assigned (for output in MiniZinc)
for i in I:
  solver.Add(assigned[i] == solver.Sum([j * x[i, j] for j in J]))
  solver.Add(costs[i] == solver.Sum([c[i][j] * x[i, j] for j in J]))

# objective
objective = solver.Minimize(z)

#
# solution and search
#
solver.Solve()

print()
print('z: ', int(solver.Objective().Value()))

print('Assigned')
for j in J:
  print(int(assigned[j].SolutionValue()), end=' ')
print()

print('Matrix:')
for i in I:
  for j in J:
    print(int(x[i, j].SolutionValue()), end=' ')
  print()
print()

print()
print('walltime  :', solver.WallTime(), 'ms')
if sol == 'CBC':
  print('iterations:', solver.Iterations())