1#!/usr/bin/env python3
2# Copyright 2010-2021 Google LLC
3# Licensed under the Apache License, Version 2.0 (the "License");
4# you may not use this file except in compliance with the License.
5# You may obtain a copy of the License at
6#
7#     http://www.apache.org/licenses/LICENSE-2.0
8#
9# Unless required by applicable law or agreed to in writing, software
10# distributed under the License is distributed on an "AS IS" BASIS,
11# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12# See the License for the specific language governing permissions and
13# limitations under the License.
14# [START program]
15"""Solve assignment problem for given group of workers."""
16# [START import]
17from ortools.linear_solver import pywraplp
18# [END import]
19
20
21def main():
22    # Data
23    # [START data]
24    costs = [
25        [90, 76, 75, 70, 50, 74],
26        [35, 85, 55, 65, 48, 101],
27        [125, 95, 90, 105, 59, 120],
28        [45, 110, 95, 115, 104, 83],
29        [60, 105, 80, 75, 59, 62],
30        [45, 65, 110, 95, 47, 31],
31        [38, 51, 107, 41, 69, 99],
32        [47, 85, 57, 71, 92, 77],
33        [39, 63, 97, 49, 118, 56],
34        [47, 101, 71, 60, 88, 109],
35        [17, 39, 103, 64, 61, 92],
36        [101, 45, 83, 59, 92, 27],
37    ]
38    # [END data]
39
40    # Allowed groups of workers:
41    # [START allowed_groups]
42    group1 = [  # Subgroups of workers 0 - 3
43        [2, 3],
44        [1, 3],
45        [1, 2],
46        [0, 1],
47        [0, 2],
48    ]
49
50    group2 = [  # Subgroups of workers 4 - 7
51        [6, 7],
52        [5, 7],
53        [5, 6],
54        [4, 5],
55        [4, 7],
56    ]
57
58    group3 = [  # Subgroups of workers 8 - 11
59        [10, 11],
60        [9, 11],
61        [9, 10],
62        [8, 10],
63        [8, 11],
64    ]
65
66    allowed_groups = []
67    for workers_g1 in group1:
68        for workers_g2 in group2:
69            for workers_g3 in group3:
70                allowed_groups.append(workers_g1 + workers_g2 + workers_g3)
71    # [END allowed_groups]
72
73    # [START solves]
74    min_val = 1e6
75    total_time = 0
76    for group in allowed_groups:
77        res = assignment(costs, group)
78        status_tmp = res[0]
79        solver_tmp = res[1]
80        x_tmp = res[2]
81        if status_tmp == pywraplp.Solver.OPTIMAL or status_tmp == pywraplp.Solver.FEASIBLE:
82            if solver_tmp.Objective().Value() < min_val:
83                min_val = solver_tmp.Objective().Value()
84                min_group = group
85                min_solver = solver_tmp
86                min_x = x_tmp
87        total_time += solver_tmp.WallTime()
88    # [END solves]
89
90    # Print best solution.
91    # [START print_solution]
92    if min_val < 1e6:
93        print(f'Total cost = {min_solver.Objective().Value()}\n')
94        num_tasks = len(costs[0])
95        for worker in min_group:
96            for task in range(num_tasks):
97                if min_x[worker, task].solution_value() > 0.5:
98                    print(f'Worker {worker} assigned to task {task}.' +
99                          f' Cost = {costs[worker][task]}')
100    else:
101        print('No solution found.')
102    print(f'Time = {total_time} ms')
103    # [END print_solution]
104
105
106def assignment(costs, group):
107    """Solve the assignment problem for one allowed group combinaison."""
108    num_tasks = len(costs[1])
109    # Solver
110    # [START solver]
111    # Create the mip solver with the SCIP backend.
112    solver = pywraplp.Solver.CreateSolver('SCIP')
113    # [END solver]
114
115    # Variables
116    # [START variables]
117    # x[worker, task] is an array of 0-1 variables, which will be 1
118    # if the worker is assigned to the task.
119    x = {}
120    for worker in group:
121        for task in range(num_tasks):
122            x[worker, task] = solver.BoolVar(f'x[{worker},{task}]')
123    # [END variables]
124
125    # Constraints
126    # [START constraints]
127    # The total size of the tasks each worker takes on is at most total_size_max.
128    for worker in group:
129        solver.Add(
130            solver.Sum([x[worker, task] for task in range(num_tasks)]) <= 1)
131
132    # Each task is assigned to exactly one worker.
133    for task in range(num_tasks):
134        solver.Add(solver.Sum([x[worker, task] for worker in group]) == 1)
135    # [END constraints]
136
137    # Objective
138    # [START objective]
139    objective_terms = []
140    for worker in group:
141        for task in range(num_tasks):
142            objective_terms.append(costs[worker][task] * x[worker, task])
143    solver.Minimize(solver.Sum(objective_terms))
144    # [END objective]
145
146    # Solve
147    # [START solve]
148    status = solver.Solve()
149    # [END solve]
150
151    return [status, solver, x]
152
153
154if __name__ == '__main__':
155    main()
156# [END program]
157