184 lines
5.6 KiB
Python
184 lines
5.6 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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"""Solve assignment problem for given group of workers."""
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# [START import]
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from ortools.linear_solver import pywraplp
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# [END import]
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def main():
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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 = [ # Subgroups of workers 0 - 3
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[2, 3],
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[1, 3],
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[1, 2],
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[0, 1],
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[0, 2],
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]
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group2 = [ # Subgroups of workers 4 - 7
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[6, 7],
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[5, 7],
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[5, 6],
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[4, 5],
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[4, 7],
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]
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group3 = [ # Subgroups of workers 8 - 11
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[10, 11],
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[9, 11],
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[9, 10],
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[8, 10],
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[8, 11],
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]
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# [END allowed_groups]
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# Solver.
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# [START solver]
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# Create the mip solver with the SCIP backend.
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solver = pywraplp.Solver.CreateSolver("SCIP")
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if not solver:
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return
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# [END solver]
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# Variables
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# [START variables]
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# x[worker, task] is an array of 0-1 variables, which will be 1
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# if the worker is assigned to the task.
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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] = solver.BoolVar(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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# The total size of the tasks each worker takes on is at most total_size_max.
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for worker in range(num_workers):
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solver.Add(solver.Sum([x[worker, task] for task in range(num_tasks)]) <= 1)
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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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solver.Add(solver.Sum([x[worker, task] for worker in range(num_workers)]) == 1)
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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] = solver.BoolVar(f"work[{worker}]")
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for worker in range(num_workers):
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solver.Add(
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work[worker] == solver.Sum([x[worker, task] for task in range(num_tasks)])
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)
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# Group1
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constraint_g1 = solver.Constraint(1, 1)
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for index, _ in enumerate(group1):
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# a*b can be transformed into 0 <= a + b - 2*p <= 1 with p in [0,1]
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# p is True if a AND b, False otherwise
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constraint = solver.Constraint(0, 1)
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constraint.SetCoefficient(work[group1[index][0]], 1)
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constraint.SetCoefficient(work[group1[index][1]], 1)
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p = solver.BoolVar(f"g1_p{index}")
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constraint.SetCoefficient(p, -2)
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constraint_g1.SetCoefficient(p, 1)
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# Group2
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constraint_g2 = solver.Constraint(1, 1)
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for index, _ in enumerate(group2):
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# a*b can be transformed into 0 <= a + b - 2*p <= 1 with p in [0,1]
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# p is True if a AND b, False otherwise
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constraint = solver.Constraint(0, 1)
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constraint.SetCoefficient(work[group2[index][0]], 1)
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constraint.SetCoefficient(work[group2[index][1]], 1)
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p = solver.BoolVar(f"g2_p{index}")
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constraint.SetCoefficient(p, -2)
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constraint_g2.SetCoefficient(p, 1)
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# Group3
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constraint_g3 = solver.Constraint(1, 1)
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for index, _ in enumerate(group3):
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# a*b can be transformed into 0 <= a + b - 2*p <= 1 with p in [0,1]
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# p is True if a AND b, False otherwise
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constraint = solver.Constraint(0, 1)
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constraint.SetCoefficient(work[group3[index][0]], 1)
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constraint.SetCoefficient(work[group3[index][1]], 1)
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p = solver.BoolVar(f"g3_p{index}")
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constraint.SetCoefficient(p, -2)
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constraint_g3.SetCoefficient(p, 1)
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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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solver.Minimize(solver.Sum(objective_terms))
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# [END objective]
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# Solve
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# [START solve]
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print(f"Solving with {solver.SolverVersion()}")
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status = solver.Solve()
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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 == pywraplp.Solver.OPTIMAL or status == pywraplp.Solver.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 x[worker, task].solution_value() > 0.5:
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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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