117 lines
3.3 KiB
C#
117 lines
3.3 KiB
C#
// Copyright 2010-2018 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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using System;
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using Google.OrTools.LinearSolver;
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public class AssignmentMip
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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_model]
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int[,] costs = {
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{90, 80, 75, 70},
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{35, 85, 55, 65},
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{125, 95, 90, 95},
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{45, 110, 95, 115},
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{50, 100, 90, 100},
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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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// [END data_model]
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// Model.
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// [START model]
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Solver solver = Solver.CreateSolver("AssignmentMip", "CBC_MIXED_INTEGER_PROGRAMMING");
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// [END model]
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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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for (int i = 0; i < numWorkers; ++i)
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{
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for (int j = 0; j < numTasks; ++j)
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{
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x[i, j] = solver.MakeIntVar(0, 1, $"worker_{i}_task_{j}");
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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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for (int i = 0; i < numWorkers; ++i)
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{
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Constraint constraint = solver.MakeConstraint(0, 1, "");
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for (int j = 0; j < numTasks; ++j)
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{
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constraint.SetCoefficient(x[i, j], 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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for (int j = 0; j < numTasks; ++j)
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{
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Constraint constraint = solver.MakeConstraint(1, 1, "");
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for (int i = 0; i < numWorkers; ++i)
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{
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constraint.SetCoefficient(x[i, j], 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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for (int i = 0; i < numWorkers; ++i)
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{
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for (int j = 0; j < numTasks; ++j)
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{
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objective.SetCoefficient(x[i, j], 1);
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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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for (int i = 0; i < numWorkers; ++i)
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{
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for (int j = 0; j < numTasks; ++j)
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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[i, j].SolutionValue() > 0.5)
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{
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Console.WriteLine($"Worker {i} assigned to task {j}. Cost: {costs[i, j]}");
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}
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}
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}
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} else {
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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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