145 lines
4.4 KiB
Python
145 lines
4.4 KiB
Python
#!/usr/bin/env python3
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# Copyright 2010-2025 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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# [START program]
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"""Solves an assignment problem for given group of workers."""
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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() -> None:
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# Data
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# [START data]
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costs = [
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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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num_workers = len(costs)
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num_tasks = len(costs[0])
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# [END data]
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# Allowed groups of workers:
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# [START allowed_groups]
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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], # Workers 0, 2
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]
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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], # Workers 4, 7
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]
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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], # Workers 8, 11
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]
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# [END allowed_groups]
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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 worker in range(num_workers):
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for task in range(num_tasks):
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x[worker, task] = model.new_bool_var(f"x[{worker},{task}]")
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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 worker in range(num_workers):
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model.add_at_most_one(x[worker, task] for task in range(num_tasks))
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# Each task is assigned to exactly one worker.
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for task in range(num_tasks):
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model.add_exactly_one(x[worker, task] for worker in range(num_workers))
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# [END constraints]
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# [START assignments]
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# Create variables for each worker, indicating whether they work on some task.
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work = {}
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for worker in range(num_workers):
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work[worker] = model.new_bool_var(f"work[{worker}]")
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for worker in range(num_workers):
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for task in range(num_tasks):
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model.add(work[worker] == sum(x[worker, task] for task in range(num_tasks)))
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# Define the allowed groups of worders
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model.add_allowed_assignments([work[0], work[1], work[2], work[3]], group1)
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model.add_allowed_assignments([work[4], work[5], work[6], work[7]], group2)
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model.add_allowed_assignments([work[8], work[9], work[10], work[11]], group3)
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# [END assignments]
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# Objective
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# [START objective]
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objective_terms = []
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for worker in range(num_workers):
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for task in range(num_tasks):
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objective_terms.append(costs[worker][task] * x[worker, task])
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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.objective_value}\n")
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for worker in range(num_workers):
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for task in range(num_tasks):
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if solver.boolean_value(x[worker, task]):
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print(
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f"Worker {worker} assigned to task {task}."
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+ f" Cost = {costs[worker][task]}"
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)
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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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