135 lines
4.0 KiB
Python
135 lines
4.0 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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"""solve an assignment problem with combination constraints on workers."""
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from typing import Sequence
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from absl import app
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from ortools.sat.python import cp_model
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def solve_assignment():
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"""solve the assignment problem."""
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# Data.
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cost = [
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[90, 76, 75, 70, 50, 74],
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[35, 85, 55, 65, 48, 101],
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[125, 95, 90, 105, 59, 120],
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[45, 110, 95, 115, 104, 83],
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[60, 105, 80, 75, 59, 62],
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[45, 65, 110, 95, 47, 31],
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[38, 51, 107, 41, 69, 99],
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[47, 85, 57, 71, 92, 77],
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[39, 63, 97, 49, 118, 56],
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[47, 101, 71, 60, 88, 109],
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[17, 39, 103, 64, 61, 92],
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[101, 45, 83, 59, 92, 27],
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]
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group1 = [
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[0, 0, 1, 1], # Workers 2, 3
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[0, 1, 0, 1], # Workers 1, 3
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[0, 1, 1, 0], # Workers 1, 2
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[1, 1, 0, 0], # Workers 0, 1
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[1, 0, 1, 0],
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] # Workers 0, 2
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group2 = [
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[0, 0, 1, 1], # Workers 6, 7
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[0, 1, 0, 1], # Workers 5, 7
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[0, 1, 1, 0], # Workers 5, 6
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[1, 1, 0, 0], # Workers 4, 5
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[1, 0, 0, 1],
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] # Workers 4, 7
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group3 = [
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[0, 0, 1, 1], # Workers 10, 11
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[0, 1, 0, 1], # Workers 9, 11
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[0, 1, 1, 0], # Workers 9, 10
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[1, 0, 1, 0], # Workers 8, 10
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[1, 0, 0, 1],
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] # Workers 8, 11
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sizes = [10, 7, 3, 12, 15, 4, 11, 5]
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total_size_max = 15
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num_workers = len(cost)
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num_tasks = len(cost[1])
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all_workers = range(num_workers)
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all_tasks = range(num_tasks)
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# Model.
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model = cp_model.CpModel()
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# Variables
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selected = [
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[model.new_bool_var("x[%i,%i]" % (i, j)) for j in all_tasks]
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for i in all_workers
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]
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works = [model.new_bool_var("works[%i]" % i) for i in all_workers]
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# Constraints
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# Link selected and workers.
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for i in range(num_workers):
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model.add_max_equality(works[i], selected[i])
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# Each task is assigned to at least one worker.
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for j in all_tasks:
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model.add(sum(selected[i][j] for i in all_workers) >= 1)
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# Total task size for each worker is at most total_size_max
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for i in all_workers:
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model.add(sum(sizes[j] * selected[i][j] for j in all_tasks) <= total_size_max)
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# Group constraints.
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model.add_allowed_assignments([works[0], works[1], works[2], works[3]], group1)
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model.add_allowed_assignments([works[4], works[5], works[6], works[7]], group2)
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model.add_allowed_assignments([works[8], works[9], works[10], works[11]], group3)
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# Objective
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model.minimize(
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sum(selected[i][j] * cost[i][j] for j in all_tasks for i in all_workers)
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)
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# Solve and output solution.
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solver = cp_model.CpSolver()
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status = solver.solve(model)
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if status == cp_model.OPTIMAL:
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print("Total cost = %i" % solver.objective_value)
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print()
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for i in all_workers:
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for j in all_tasks:
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if solver.boolean_value(selected[i][j]):
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print(
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"Worker ", i, " assigned to task ", j, " Cost = ", cost[i][j]
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)
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print()
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print("Statistics")
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print(" - conflicts : %i" % solver.num_conflicts)
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print(" - branches : %i" % solver.num_branches)
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print(" - wall time : %f s" % solver.wall_time)
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def main(argv: Sequence[str]) -> None:
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if len(argv) > 1:
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raise app.UsageError("Too many command-line arguments.")
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solve_assignment()
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if __name__ == "__main__":
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app.run(main)
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