120 lines
3.9 KiB
Python
120 lines
3.9 KiB
Python
# Copyright 2010-2018 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.
|
|
"""Solve an assignment problem with combination constraints on workers."""
|
|
|
|
|
|
from ortools.sat.python import cp_model
|
|
|
|
|
|
def solve_assignment():
|
|
"""Solve the assignment problem."""
|
|
# Data.
|
|
cost = [[90, 76, 75, 70, 50, 74], [35, 85, 55, 65, 48,
|
|
101], [125, 95, 90, 105, 59, 120],
|
|
[45, 110, 95, 115, 104, 83], [60, 105, 80, 75, 59, 62], [
|
|
45, 65, 110, 95, 47, 31
|
|
], [38, 51, 107, 41, 69, 99], [47, 85, 57, 71,
|
|
92, 77], [39, 63, 97, 49, 118, 56],
|
|
[47, 101, 71, 60, 88, 109], [17, 39, 103, 64, 61,
|
|
92], [101, 45, 83, 59, 92, 27]]
|
|
|
|
group1 = [
|
|
[0, 0, 1, 1], # Workers 2, 3
|
|
[0, 1, 0, 1], # Workers 1, 3
|
|
[0, 1, 1, 0], # Workers 1, 2
|
|
[1, 1, 0, 0], # Workers 0, 1
|
|
[1, 0, 1, 0]
|
|
] # Workers 0, 2
|
|
|
|
group2 = [
|
|
[0, 0, 1, 1], # Workers 6, 7
|
|
[0, 1, 0, 1], # Workers 5, 7
|
|
[0, 1, 1, 0], # Workers 5, 6
|
|
[1, 1, 0, 0], # Workers 4, 5
|
|
[1, 0, 0, 1]
|
|
] # Workers 4, 7
|
|
|
|
group3 = [
|
|
[0, 0, 1, 1], # Workers 10, 11
|
|
[0, 1, 0, 1], # Workers 9, 11
|
|
[0, 1, 1, 0], # Workers 9, 10
|
|
[1, 0, 1, 0], # Workers 8, 10
|
|
[1, 0, 0, 1]
|
|
] # Workers 8, 11
|
|
|
|
sizes = [10, 7, 3, 12, 15, 4, 11, 5]
|
|
total_size_max = 15
|
|
num_workers = len(cost)
|
|
num_tasks = len(cost[1])
|
|
all_workers = range(num_workers)
|
|
all_tasks = range(num_tasks)
|
|
|
|
# Model.
|
|
|
|
model = cp_model.CpModel()
|
|
# Variables
|
|
selected = [[model.NewBoolVar('x[%i,%i]' % (i, j)) for j in all_tasks]
|
|
for i in all_workers]
|
|
works = [model.NewBoolVar('works[%i]' % i) for i in all_workers]
|
|
|
|
# Constraints
|
|
|
|
# Link selected and workers.
|
|
for i in range(num_workers):
|
|
model.AddMaxEquality(works[i], selected[i])
|
|
|
|
# Each task is assigned to at least one worker.
|
|
for j in all_tasks:
|
|
model.Add(sum(selected[i][j] for i in all_workers) >= 1)
|
|
|
|
# Total task size for each worker is at most total_size_max
|
|
for i in all_workers:
|
|
model.Add(
|
|
sum(sizes[j] * selected[i][j] for j in all_tasks) <= total_size_max)
|
|
|
|
# Group constraints.
|
|
model.AddAllowedAssignments([works[0], works[1], works[2], works[3]],
|
|
group1)
|
|
model.AddAllowedAssignments([works[4], works[5], works[6], works[7]],
|
|
group2)
|
|
model.AddAllowedAssignments([works[8], works[9], works[10], works[11]],
|
|
group3)
|
|
|
|
# Objective
|
|
model.Minimize(
|
|
sum(selected[i][j] * cost[i][j] for j in all_tasks
|
|
for i in all_workers))
|
|
|
|
# Solve and output solution.
|
|
solver = cp_model.CpSolver()
|
|
status = solver.Solve(model)
|
|
|
|
if status == cp_model.OPTIMAL:
|
|
print('Total cost = %i' % solver.ObjectiveValue())
|
|
print()
|
|
for i in all_workers:
|
|
for j in all_tasks:
|
|
if solver.BooleanValue(selected[i][j]):
|
|
print('Worker ', i, ' assigned to task ', j, ' Cost = ',
|
|
cost[i][j])
|
|
|
|
print()
|
|
|
|
print('Statistics')
|
|
print(' - conflicts : %i' % solver.NumConflicts())
|
|
print(' - branches : %i' % solver.NumBranches())
|
|
print(' - wall time : %f s' % solver.WallTime())
|
|
|
|
|
|
solve_assignment()
|