assignment_sat.py

# Copyright 2010-2018 Google LLC
# 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.
"""Solve a simple assignment problem."""
# [START program]
# [START import]
from ortools.sat.python import cp_model
# [END import]


def main():
    # Data
    # [START data_model]
    costs = [
        [90, 80, 75, 70],
        [35, 85, 55, 65],
        [125, 95, 90, 95],
        [45, 110, 95, 115],
        [50, 100, 90, 100],
    ]
    num_workers = len(costs)
    num_tasks = len(costs[0])
    # [END data_model]

    # Model
    # [START model]
    model = cp_model.CpModel()
    # [END model]

    # Variables
    # [START variables]
    x = []
    for i in range(num_workers):
        t = []
        for j in range(num_tasks):
            t.append(model.NewBoolVar('x[%i,%i]' % (i, j)))
        x.append(t)
    # [END variables]

    # Constraints
    # [START constraints]
    # Each worker is assigned to at most one task.
    for i in range(num_workers):
        model.Add(sum(x[i][j] for j in range(num_tasks)) <= 1)

    # Each task is assigned to exactly one worker.
    for j in range(num_tasks):
        model.Add(sum(x[i][j] for i in range(num_workers)) == 1)
    # [END constraints]

    # Objective
    # [START objective]
    objective_terms = []
    for i in range(num_workers):
        for j in range(num_tasks):
            objective_terms.append(costs[i][j] * x[i][j])
    model.Minimize(sum(objective_terms))
    # [END objective]

    # Solve
    # [START solve]
    solver = cp_model.CpSolver()
    status = solver.Solve(model)
    # [END solve]

    # Print solution.
    # [START print_solution]
    if status == cp_model.OPTIMAL or status == cp_model.FEASIBLE:
        print('Total cost = %i' % solver.ObjectiveValue())
        print()
        for i in range(num_workers):
            for j in range(num_tasks):
                if solver.BooleanValue(x[i][j]):
                    print('Worker ', i, ' assigned to task ', j, '  Cost = ',
                          costs[i][j])
    else:
        print('No solution found.')
    # [END print_solution]


if __name__ == '__main__':
    main()
# [END program]