ortools-clone/ortools/sat/samples/AssignmentGroupsSat.java

// Copyright 2010-2021 Google LLC
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

// CP-SAT example that solves an assignment problem.
// [START program]
package com.google.ortools.sat.samples;
// [START import]
import com.google.ortools.Loader;
import com.google.ortools.sat.CpModel;
import com.google.ortools.sat.CpSolver;
import com.google.ortools.sat.CpSolverStatus;
import com.google.ortools.sat.IntVar;
import com.google.ortools.sat.LinearExpr;
import java.util.stream.IntStream;
// [END import]

/** Assignment problem. */
public class AssignmentGroupsSat {
  public static void main(String[] args) {
    Loader.loadNativeLibraries();
    // Data
    // [START data]
    int[][] costs = {
      { 90, 76, 75, 70, 50, 74 },    { 35, 85, 55, 65, 48, 101 }, { 125, 95, 90, 105, 59, 120 },
      { 45, 110, 95, 115, 104, 83 }, { 60, 105, 80, 75, 59, 62 }, { 45, 65, 110, 95, 47, 31 },
      { 38, 51, 107, 41, 69, 99 },   { 47, 85, 57, 71, 92, 77 },  { 39, 63, 97, 49, 118, 56 },
      { 47, 101, 71, 60, 88, 109 },  { 17, 39, 103, 64, 61, 92 }, { 101, 45, 83, 59, 92, 27 },
    };
    final int numWorkers = costs.length;
    final int numTasks = costs[0].length;

    final int[] allWorkers = IntStream.range(0, numWorkers).toArray();
    final int[] allTasks = IntStream.range(0, numTasks).toArray();
    // [END data]

    // Allowed groups of workers:
    // [START allowed_groups]
    int[][] group1 = {
      { 0, 0, 1, 1 }, // Workers 2, 3
      { 0, 1, 0, 1 }, // Workers 1, 3
      { 0, 1, 1, 0 }, // Workers 1, 2
      { 1, 1, 0, 0 }, // Workers 0, 1
      { 1, 0, 1, 0 }, // Workers 0, 2
    };

    int[][] group2 = {
      { 0, 0, 1, 1 }, // Workers 6, 7
      { 0, 1, 0, 1 }, // Workers 5, 7
      { 0, 1, 1, 0 }, // Workers 5, 6
      { 1, 1, 0, 0 }, // Workers 4, 5
      { 1, 0, 0, 1 }, // Workers 4, 7
    };

    int[][] group3 = {
      { 0, 0, 1, 1 }, // Workers 10, 11
      { 0, 1, 0, 1 }, // Workers 9, 11
      { 0, 1, 1, 0 }, // Workers 9, 10
      { 1, 0, 1, 0 }, // Workers 8, 10
      { 1, 0, 0, 1 }, // Workers 8, 11
    };
    // [END allowed_groups]

    // Model
    // [START model]
    CpModel model = new CpModel();
    // [END model]

    // Variables
    // [START variables]
    IntVar[][] x = new IntVar[numWorkers][numTasks];
    // Variables in a 1-dim array.
    IntVar[] xFlat = new IntVar[numWorkers * numTasks];
    int[] costsFlat = new int[numWorkers * numTasks];
    for (int worker : allWorkers) {
      for (int task : allTasks) {
        x[worker][task] = model.newBoolVar("x["+worker+","+task+"]");
        int k = worker * numTasks + task;
        xFlat[k] = x[worker][task];
        costsFlat[k] = costs[worker][task];
      }
    }
    // [END variables]

    // Constraints
    // [START constraints]
    // Each worker is assigned to at most one task.
    for (int worker : allWorkers) {
      IntVar[] vars = new IntVar[numTasks];
      for (int task : allTasks) {
        vars[task] = x[worker][task];
      }
      model.addLessOrEqual(LinearExpr.sum(vars), 1);
    }
    // Each task is assigned to exactly one worker.
    for (int task : allTasks) {
      // LinearExpr taskSum;
      IntVar[] vars = new IntVar[numWorkers];
      for (int worker : allWorkers) {
        vars[worker] = x[worker][task];
      }
      model.addEquality(LinearExpr.sum(vars), 1);
    }
    // [END constraints]

    // [START assignments]
    // Create variables for each worker, indicating whether they work on some task.
    IntVar[] work = new IntVar[numWorkers];
    for (int worker : allWorkers) {
      work[worker] = model.newBoolVar("work["+worker+"]");
    }

    for (int worker : allWorkers) {
      IntVar[] vars = new IntVar[numTasks];
      for (int task : allTasks) {
        vars[task] = x[worker][task];
      }
      model.addEquality(work[worker], LinearExpr.sum(vars));
    }

    // Define the allowed groups of worders
    model.addAllowedAssignments(new IntVar[] { work[0], work[1], work[2], work[3] }, group1);
    model.addAllowedAssignments(new IntVar[] { work[4], work[5], work[6], work[7] }, group2);
    model.addAllowedAssignments(new IntVar[] { work[8], work[9], work[10], work[11] }, group3);
    // [END assignments]

    // Objective
    // [START objective]
    model.minimize(LinearExpr.scalProd(xFlat, costsFlat));
    // [END objective]

    // Solve
    // [START solve]
    CpSolver solver = new CpSolver();
    CpSolverStatus status = solver.solve(model);
    // [END solve]

    // Print solution.
    // [START print_solution]
    // Check that the problem has a feasible solution.
    if (status == CpSolverStatus.OPTIMAL || status == CpSolverStatus.FEASIBLE) {
      System.out.println("Total cost: " + solver.objectiveValue() + "\n");
      for (int worker : allWorkers) {
        for (int task : allTasks) {
          if (solver.value(x[worker][task]) == 1) {
            System.out.println(
                "Worker " + worker + " assigned to task " + task + ".  Cost: " + costs[worker][task]);
          }
        }
      }
    } else {
      System.err.println("No solution found.");
    }
    // [END print_solution]
  }

  private AssignmentGroupsSat() {}
}