136 lines
4.5 KiB
C#
136 lines
4.5 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 AssignmentTaskSizesMip
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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, 12, 68 }, { 35, 85, 55, 65, 48, 101, 70, 83 },
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{ 125, 95, 90, 105, 59, 120, 36, 73 }, { 45, 110, 95, 115, 104, 83, 37, 71 },
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{ 60, 105, 80, 75, 59, 62, 93, 88 }, { 45, 65, 110, 95, 47, 31, 81, 34 },
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{ 38, 51, 107, 41, 69, 99, 115, 48 }, { 47, 85, 57, 71, 92, 77, 109, 36 },
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{ 39, 63, 97, 49, 118, 56, 92, 61 }, { 47, 101, 71, 60, 88, 109, 52, 90 },
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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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int[] taskSizes = { 10, 7, 3, 12, 15, 4, 11, 5 };
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// Maximum total of task sizes for any worker
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int totalSizeMax = 15;
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// [END data]
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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 max task size.
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foreach (int worker in allWorkers)
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{
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Constraint constraint = solver.MakeConstraint(0, totalSizeMax, "");
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foreach (int task in allTasks)
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{
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constraint.SetCoefficient(x[worker, task], taskSizes[task]);
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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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// 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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