211 lines
7.3 KiB
C#
211 lines
7.3 KiB
C#
// Copyright 2010-2024 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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// [START import]
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using System;
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using System.Collections.Generic;
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using System.Linq;
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using Google.OrTools.LinearSolver;
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// [END import]
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public class AssignmentGroupsMip
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{
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static void Main()
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{
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// Data.
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// [START data]
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int[,] costs = {
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{ 90, 76, 75, 70, 50, 74 }, { 35, 85, 55, 65, 48, 101 }, { 125, 95, 90, 105, 59, 120 },
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{ 45, 110, 95, 115, 104, 83 }, { 60, 105, 80, 75, 59, 62 }, { 45, 65, 110, 95, 47, 31 },
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{ 38, 51, 107, 41, 69, 99 }, { 47, 85, 57, 71, 92, 77 }, { 39, 63, 97, 49, 118, 56 },
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{ 47, 101, 71, 60, 88, 109 }, { 17, 39, 103, 64, 61, 92 }, { 101, 45, 83, 59, 92, 27 },
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};
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int numWorkers = costs.GetLength(0);
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int numTasks = costs.GetLength(1);
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int[] allWorkers = Enumerable.Range(0, numWorkers).ToArray();
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int[] allTasks = Enumerable.Range(0, numTasks).ToArray();
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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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int[,] group1 = {
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// group of worker 0-3
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{ 2, 3 }, { 1, 3 }, { 1, 2 }, { 0, 1 }, { 0, 2 },
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};
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int[,] group2 = {
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// group of worker 4-7
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{ 6, 7 }, { 5, 7 }, { 5, 6 }, { 4, 5 }, { 4, 7 },
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};
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int[,] group3 = {
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// group of worker 8-11
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{ 10, 11 }, { 9, 11 }, { 9, 10 }, { 8, 10 }, { 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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Solver solver = Solver.CreateSolver("SCIP");
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if (solver is null)
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{
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return;
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}
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// [END solver]
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// Variables.
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// [START variables]
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// x[i, j] is an array of 0-1 variables, which will be 1
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// if worker i is assigned to task j.
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Variable[,] x = new Variable[numWorkers, numTasks];
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foreach (int worker in allWorkers)
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{
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foreach (int task in allTasks)
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{
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x[worker, task] = solver.MakeBoolVar($"x[{worker},{task}]");
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}
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}
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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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foreach (int worker in allWorkers)
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{
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Constraint constraint = solver.MakeConstraint(0, 1, "");
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foreach (int task in allTasks)
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{
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constraint.SetCoefficient(x[worker, task], 1);
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}
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}
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// Each task is assigned to exactly one worker.
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foreach (int task in allTasks)
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{
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Constraint constraint = solver.MakeConstraint(1, 1, "");
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foreach (int worker in allWorkers)
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{
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constraint.SetCoefficient(x[worker, task], 1);
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}
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}
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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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Variable[] work = new Variable[numWorkers];
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foreach (int worker in allWorkers)
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{
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work[worker] = solver.MakeBoolVar($"work[{worker}]");
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}
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foreach (int worker in allWorkers)
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{
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Variable[] vars = new Variable[numTasks];
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foreach (int task in allTasks)
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{
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vars[task] = x[worker, task];
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}
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solver.Add(work[worker] == LinearExprArrayHelper.Sum(vars));
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}
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// Group1
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Constraint constraint_g1 = solver.MakeConstraint(1, 1, "");
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for (int i = 0; i < group1.GetLength(0); ++i)
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{
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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 constraint = solver.MakeConstraint(0, 1, "");
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constraint.SetCoefficient(work[group1[i, 0]], 1);
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constraint.SetCoefficient(work[group1[i, 1]], 1);
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Variable p = solver.MakeBoolVar($"g1_p{i}");
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constraint.SetCoefficient(p, -2);
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constraint_g1.SetCoefficient(p, 1);
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}
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// Group2
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Constraint constraint_g2 = solver.MakeConstraint(1, 1, "");
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for (int i = 0; i < group2.GetLength(0); ++i)
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{
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// a*b can be transformed into 0 <= a + b - 2*p <= 1 with p in [0,1]
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// p is True if a AND b, False otherwise
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Constraint constraint = solver.MakeConstraint(0, 1, "");
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constraint.SetCoefficient(work[group2[i, 0]], 1);
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constraint.SetCoefficient(work[group2[i, 1]], 1);
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Variable p = solver.MakeBoolVar($"g2_p{i}");
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constraint.SetCoefficient(p, -2);
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constraint_g2.SetCoefficient(p, 1);
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}
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// Group3
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Constraint constraint_g3 = solver.MakeConstraint(1, 1, "");
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for (int i = 0; i < group3.GetLength(0); ++i)
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{
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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 constraint = solver.MakeConstraint(0, 1, "");
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constraint.SetCoefficient(work[group3[i, 0]], 1);
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constraint.SetCoefficient(work[group3[i, 1]], 1);
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Variable p = solver.MakeBoolVar($"g3_p{i}");
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constraint.SetCoefficient(p, -2);
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constraint_g3.SetCoefficient(p, 1);
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}
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// [END assignments]
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// Objective
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// [START objective]
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Objective objective = solver.Objective();
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foreach (int worker in allWorkers)
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{
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foreach (int task in allTasks)
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{
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objective.SetCoefficient(x[worker, task], costs[worker, task]);
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}
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}
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objective.SetMinimization();
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// [END objective]
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// Solve
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// [START solve]
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Solver.ResultStatus resultStatus = 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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// Check that the problem has a feasible solution.
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if (resultStatus == Solver.ResultStatus.OPTIMAL || resultStatus == Solver.ResultStatus.FEASIBLE)
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{
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Console.WriteLine($"Total cost: {solver.Objective().Value()}\n");
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foreach (int worker in allWorkers)
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{
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foreach (int task in allTasks)
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{
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// Test if x[i, j] is 0 or 1 (with tolerance for floating point
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// arithmetic).
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if (x[worker, task].SolutionValue() > 0.5)
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{
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Console.WriteLine($"Worker {worker} assigned to task {task}. Cost: {costs[worker, task]}");
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}
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}
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}
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}
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else
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{
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Console.WriteLine("No solution found.");
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}
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// [END print_solution]
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}
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}
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// [END program]
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