127 lines
4.0 KiB
C#
127 lines
4.0 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 Google.OrTools.Sat;
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// [END import]
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public class AssignmentSat
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{
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public static void Main(String[] args)
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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 }, { 35, 85, 55, 65 }, { 125, 95, 90, 95 }, { 45, 110, 95, 115 }, { 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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CpModel model = new CpModel();
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// [END model]
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// Variables.
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// [START variables]
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BoolVar[,] x = new BoolVar[numWorkers, numTasks];
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// Variables in a 1-dim array.
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for (int worker = 0; worker < numWorkers; ++worker)
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{
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for (int task = 0; task < numTasks; ++task)
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{
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x[worker, task] = model.NewBoolVar($"worker_{worker}_task_{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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for (int worker = 0; worker < numWorkers; ++worker)
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{
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List<ILiteral> tasks = new List<ILiteral>();
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for (int task = 0; task < numTasks; ++task)
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{
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tasks.Add(x[worker, task]);
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}
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model.AddAtMostOne(tasks);
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}
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// Each task is assigned to exactly one worker.
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for (int task = 0; task < numTasks; ++task)
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{
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List<ILiteral> workers = new List<ILiteral>();
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for (int worker = 0; worker < numWorkers; ++worker)
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{
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workers.Add(x[worker, task]);
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}
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model.AddExactlyOne(workers);
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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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LinearExprBuilder obj = LinearExpr.NewBuilder();
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for (int worker = 0; worker < numWorkers; ++worker)
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{
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for (int task = 0; task < numTasks; ++task)
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{
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obj.AddTerm((IntVar)x[worker, task], costs[worker, task]);
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}
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}
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model.Minimize(obj);
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// [END objective]
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// Solve
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// [START solve]
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CpSolver solver = new CpSolver();
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CpSolverStatus status = solver.Solve(model);
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Console.WriteLine($"Solve status: {status}");
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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 (status == CpSolverStatus.Optimal || status == CpSolverStatus.Feasible)
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{
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Console.WriteLine($"Total cost: {solver.ObjectiveValue}\n");
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for (int i = 0; i < numWorkers; ++i)
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{
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for (int j = 0; j < numTasks; ++j)
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{
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if (solver.Value(x[i, j]) > 0.5)
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{
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Console.WriteLine($"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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}
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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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Console.WriteLine("Statistics");
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Console.WriteLine($" - conflicts : {solver.NumConflicts()}");
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Console.WriteLine($" - branches : {solver.NumBranches()}");
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Console.WriteLine($" - wall time : {solver.WallTime()}s");
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}
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}
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// [END program]
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