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assignment_task_sizes_mip.py
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assignment_task_sizes_mip.py
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#!/usr/bin/env python3
# Copyright 2010-2021 Google LLC
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# [START program]
"""MIP example that solves an assignment problem."""
# [START import]
from ortools.linear_solver import pywraplp
# [END import]
def main():
# Data
# [START data]
costs = [
[90, 76, 75, 70, 50, 74, 12, 68],
[35, 85, 55, 65, 48, 101, 70, 83],
[125, 95, 90, 105, 59, 120, 36, 73],
[45, 110, 95, 115, 104, 83, 37, 71],
[60, 105, 80, 75, 59, 62, 93, 88],
[45, 65, 110, 95, 47, 31, 81, 34],
[38, 51, 107, 41, 69, 99, 115, 48],
[47, 85, 57, 71, 92, 77, 109, 36],
[39, 63, 97, 49, 118, 56, 92, 61],
[47, 101, 71, 60, 88, 109, 52, 90],
]
num_workers = len(costs)
num_tasks = len(costs[0])
task_sizes = [10, 7, 3, 12, 15, 4, 11, 5]
# Maximum total of task sizes for any worker
total_size_max = 15
# [END data]
# Solver
# [START solver]
# Create the mip solver with the SCIP backend.
solver = pywraplp.Solver.CreateSolver('SCIP')
# [END solver]
# Variables
# [START variables]
# x[i, j] is an array of 0-1 variables, which will be 1
# if worker i is assigned to task j.
x = {}
for worker in range(num_workers):
for task in range(num_tasks):
x[worker, task] = solver.BoolVar(f'x[{worker},{task}]')
# [END variables]
# Constraints
# [START constraints]
# The total size of the tasks each worker takes on is at most total_size_max.
for worker in range(num_workers):
solver.Add(
solver.Sum([
task_sizes[task] * x[worker, task] for task in range(num_tasks)
]) <= total_size_max)
# Each task is assigned to exactly one worker.
for task in range(num_tasks):
solver.Add(
solver.Sum([x[worker, task] for worker in range(num_workers)]) == 1)
# [END constraints]
# Objective
# [START objective]
objective_terms = []
for worker in range(num_workers):
for task in range(num_tasks):
objective_terms.append(costs[worker][task] * x[worker, task])
solver.Minimize(solver.Sum(objective_terms))
# [END objective]
# Solve
# [START solve]
status = solver.Solve()
# [END solve]
# Print solution.
# [START print_solution]
if status == pywraplp.Solver.OPTIMAL or status == pywraplp.Solver.FEASIBLE:
print(f'Total cost = {solver.Objective().Value()}\n')
for worker in range(num_workers):
for task in range(num_tasks):
if x[worker, task].solution_value() > 0.5:
print(f'Worker {worker} assigned to task {task}.' +
f' Cost: {costs[worker][task]}')
else:
print('No solution found.')
# [END print_solution]
if __name__ == '__main__':
main()
# [END program]