89 lines
2.7 KiB
Python
89 lines
2.7 KiB
Python
#!/usr/bin/env python3
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# Copyright 2010-2022 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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"""MIP example that solves an assignment problem."""
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# [START program]
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# [START import]
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import numpy as np
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from ortools.linear_solver.python import model_builder
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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 = np.array([
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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, num_tasks = costs.shape
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# [END data_model]
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# Solver
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# Create the model.
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model = model_builder.ModelBuilder()
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# [END model]
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# Variables
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# [START variables]
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# x[i, j] is an array of 0-1 variables, which will be 1
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# if worker i is assigned to task j.
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x = model.new_bool_var_array(shape=[num_workers, num_tasks], name='x') # pytype: disable=wrong-arg-types # numpy-scalars
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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 1 task.
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for i in range(num_workers):
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model.add(np.sum(x[i, :]) <= 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(np.sum(x[:, j]) == 1)
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# [END constraints]
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# Objective
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# [START objective]
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model.minimize(np.dot(x.flatten(), costs.flatten()))
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# [END objective]
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# [START solve]
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# Create the solver with the CP-SAT backend, and solve the model.
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solver = model_builder.ModelSolver('sat')
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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 == model_builder.SolveStatus.OPTIMAL or
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status == model_builder.SolveStatus.FEASIBLE):
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print(f'Total cost = {solver.objective_value}\n')
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for i in range(num_workers):
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for j in range(num_tasks):
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# Test if x[i,j] is 1 (with tolerance for floating point arithmetic).
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if solver.value(x[i, j]) > 0.5:
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print(f'Worker {i} assigned to task {j}.' +
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f' 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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