130 lines
4.2 KiB
Java
130 lines
4.2 KiB
Java
// Copyright 2010-2021 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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// CP-SAT example that solves an assignment problem.
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// [START program]
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package com.google.ortools.sat.samples;
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// [START import]
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import com.google.ortools.Loader;
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import com.google.ortools.sat.CpModel;
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import com.google.ortools.sat.CpSolver;
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import com.google.ortools.sat.CpSolverStatus;
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import com.google.ortools.sat.IntVar;
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import com.google.ortools.sat.LinearExpr;
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import java.util.stream.IntStream;
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// [END import]
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/** Assignment problem. */
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public class AssignmentTaskSizesSat {
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public static void main(String[] args) {
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Loader.loadNativeLibraries();
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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},
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{35, 85, 55, 65, 48, 101, 70, 83},
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{125, 95, 90, 105, 59, 120, 36, 73},
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{45, 110, 95, 115, 104, 83, 37, 71},
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{60, 105, 80, 75, 59, 62, 93, 88},
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{45, 65, 110, 95, 47, 31, 81, 34},
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{38, 51, 107, 41, 69, 99, 115, 48},
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{47, 85, 57, 71, 92, 77, 109, 36},
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{39, 63, 97, 49, 118, 56, 92, 61},
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{47, 101, 71, 60, 88, 109, 52, 90},
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};
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final int numWorkers = costs.length;
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final int numTasks = costs[0].length;
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final int[] allWorkers = IntStream.range(0, numWorkers).toArray();
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final int[] allTasks = IntStream.range(0, numTasks).toArray();
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final 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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final int totalSizeMax = 15;
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// [END data]
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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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IntVar[][] x = new IntVar[numWorkers][numTasks];
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// Variables in a 1-dim array.
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IntVar[] xFlat = new IntVar[numWorkers * numTasks];
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int[] costsFlat = new int[numWorkers * numTasks];
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for (int worker : allWorkers) {
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for (int task : allTasks) {
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x[worker][task] = model.newBoolVar("x[" + worker + "," + task + "]");
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int k = worker * numTasks + task;
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xFlat[k] = x[worker][task];
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costsFlat[k] = costs[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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for (int worker : allWorkers) {
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IntVar[] vars = new IntVar[numTasks];
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for (int task : allTasks) {
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vars[task] = x[worker][task];
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}
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model.addLessOrEqual(LinearExpr.scalProd(vars, taskSizes), totalSizeMax);
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}
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// Each task is assigned to exactly one worker.
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for (int task : allTasks) {
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// LinearExpr taskSum;
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IntVar[] vars = new IntVar[numWorkers];
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for (int worker : allWorkers) {
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vars[worker] = x[worker][task];
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}
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model.addEquality(LinearExpr.sum(vars), 1);
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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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model.minimize(LinearExpr.scalProd(xFlat, costsFlat));
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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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// [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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System.out.println("Total cost: " + solver.objectiveValue() + "\n");
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for (int worker : allWorkers) {
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for (int task : allTasks) {
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if (solver.value(x[worker][task]) == 1) {
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System.out.println("Worker " + worker + " assigned to task " + task
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+ ". Cost: " + costs[worker][task]);
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}
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}
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}
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} else {
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System.err.println("No solution found.");
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}
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// [END print_solution]
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}
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private AssignmentTaskSizesSat() {}
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}
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