ortools-clone/examples/python/assignment_sat.py

# Copyright 2010-2017 Google
# 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.

from __future__ import print_function
from ortools.sat.python import cp_model


def main():
  # Instantiate a cp model.
  cost = [[90, 76, 75, 70, 50, 74, 12, 68], [35, 85, 55, 65, 48, 101, 70, 83],
          [125, 95, 90, 105, 59, 120, 36, 73],
          [45, 110, 95, 115, 104, 83, 37, 71],
          [60, 105, 80, 75, 59, 62, 93, 88], [45, 65, 110, 95, 47, 31, 81, 34],
          [38, 51, 107, 41, 69, 99, 115, 48], [47, 85, 57, 71, 92, 77, 109, 36],
          [39, 63, 97, 49, 118, 56, 92, 61], [47, 101, 71, 60, 88, 109, 52, 90]]

  sizes = [10, 7, 3, 12, 15, 4, 11, 5]
  total_size_max = 15
  num_workers = len(cost)
  num_tasks = len(cost[1])
  all_workers = range(num_workers)
  all_tasks = range(num_tasks)

  model = cp_model.CpModel()
  # Variables
  total_cost = model.NewIntVar(0, 1000, 'total_cost')
  x = []
  for i in all_workers:
    t = []
    for j in all_tasks:
      t.append(model.NewBoolVar('x[%i,%i]' % (i, j)))
    x.append(t)

  # Constraints

  # Each task is assigned to at least one worker.
  [model.Add(sum(x[i][j] for i in all_workers) >= 1) for j in all_tasks]

  # Total task size for each worker is at most total_size_max
  for i in all_workers:
    model.Add(sum(sizes[j] * x[i][j] for j in all_tasks) <= total_size_max)

  # Total cost
  model.Add(total_cost == sum(
      x[i][j] * cost[i][j] for j in all_tasks for i in all_workers))
  model.Minimize(total_cost)

  solver = cp_model.CpSolver()
  status = solver.Solve(model)

  if status == cp_model.OPTIMAL:
    print('Total cost = %i' % solver.ObjectiveValue())
    print()
    for i in all_workers:
      for j in all_tasks:
        if solver.Value(x[i][j]) == 1:
          print('Worker ', i, ' assigned to task ', j, '  Cost = ', cost[i][j])

    print()

  print('Statistics')
  print('  - conflicts : %i' % solver.NumConflicts())
  print('  - branches  : %i' % solver.NumBranches())
  print('  - wall time : %f ms' % solver.WallTime())


if __name__ == '__main__':
  main()