93 lines
2.5 KiB
Python
93 lines
2.5 KiB
Python
# Copyright 2010-2018 Google LLC
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""Solve a simple assignment problem."""
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# [START program]
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# [START import]
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from ortools.sat.python import cp_model
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# [END import]
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def main():
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# Data
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# [START data_model]
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costs = [
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[90, 80, 75, 70],
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[35, 85, 55, 65],
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[125, 95, 90, 95],
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[45, 110, 95, 115],
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[50, 100, 90, 100],
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]
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num_workers = len(costs)
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num_tasks = len(costs[0])
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# [END data_model]
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# Model
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# [START model]
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model = cp_model.CpModel()
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# [END model]
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# Variables
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# [START variables]
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x = []
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for i in range(num_workers):
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t = []
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for j in range(num_tasks):
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t.append(model.NewBoolVar(f'x[{i},{j}]'))
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x.append(t)
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# [END variables]
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# Constraints
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# [START constraints]
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# Each worker is assigned to at most one task.
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for i in range(num_workers):
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model.Add(sum(x[i][j] for j in range(num_tasks)) <= 1)
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# Each task is assigned to exactly one worker.
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for j in range(num_tasks):
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model.Add(sum(x[i][j] for i in range(num_workers)) == 1)
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# [END constraints]
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# Objective
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# [START objective]
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objective_terms = []
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for i in range(num_workers):
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for j in range(num_tasks):
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objective_terms.append(costs[i][j] * x[i][j])
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model.Minimize(sum(objective_terms))
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# [END objective]
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# Solve
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# [START solve]
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solver = cp_model.CpSolver()
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status = solver.Solve(model)
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# [END solve]
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# Print solution.
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# [START print_solution]
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if status == cp_model.OPTIMAL or status == cp_model.FEASIBLE:
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print(f'Total cost = {solver.ObjectiveValue()}')
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print()
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for i in range(num_workers):
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for j in range(num_tasks):
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if solver.BooleanValue(x[i][j]):
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print(
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f'Worker {i} assigned to task {j} Cost = {costs[i][j]}')
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else:
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print('No solution found.')
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# [END print_solution]
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if __name__ == '__main__':
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main()
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# [END program]
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