AssignmentGroupsMip.java

// Copyright 2010-2024 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.

// [START program]
package com.google.ortools.linearsolver.samples;
// [START import]
import com.google.ortools.Loader;
import com.google.ortools.linearsolver.MPConstraint;
import com.google.ortools.linearsolver.MPObjective;
import com.google.ortools.linearsolver.MPSolver;
import com.google.ortools.linearsolver.MPVariable;
import java.util.stream.IntStream;
// [END import]

/** MIP example that solves an assignment problem. */
public class AssignmentGroupsMip {
  public static void main(String[] args) {
    Loader.loadNativeLibraries();
    // Data
    // [START data]
    double[][] 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},
    };
    int numWorkers = costs.length;
    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 = {
        // group of worker 0-3
        {2, 3},
        {1, 3},
        {1, 2},
        {0, 1},
        {0, 2},
    };

    int[][] group2 = {
        // group of worker 4-7
        {6, 7},
        {5, 7},
        {5, 6},
        {4, 5},
        {4, 7},
    };

    int[][] group3 = {
        // group of worker 8-11
        {10, 11},
        {9, 11},
        {9, 10},
        {8, 10},
        {8, 11},
    };
    // [END allowed_groups]

    // Solver
    // [START solver]
    // Create the linear solver with the SCIP backend.
    MPSolver solver = MPSolver.createSolver("SCIP");
    if (solver == null) {
      System.out.println("Could not create solver SCIP");
      return;
    }
    // [END solver]

    // Variables
    // [START variables]
    // x[i][j] is an array of 0-1 variables, which will be 1
    // if worker i is assigned to task j.
    MPVariable[][] x = new MPVariable[numWorkers][numTasks];
    for (int worker : allWorkers) {
      for (int task : allTasks) {
        x[worker][task] = solver.makeBoolVar("x[" + worker + "," + task + "]");
      }
    }
    // [END variables]

    // Constraints
    // [START constraints]
    // Each worker is assigned to at most one task.
    for (int worker : allWorkers) {
      MPConstraint constraint = solver.makeConstraint(0, 1, "");
      for (int task : allTasks) {
        constraint.setCoefficient(x[worker][task], 1);
      }
    }
    // Each task is assigned to exactly one worker.
    for (int task : allTasks) {
      MPConstraint constraint = solver.makeConstraint(1, 1, "");
      for (int worker : allWorkers) {
        constraint.setCoefficient(x[worker][task], 1);
      }
    }
    // [END constraints]

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

    for (int worker : allWorkers) {
      // MPVariable[] vars = new MPVariable[numTasks];
      MPConstraint constraint = solver.makeConstraint(0, 0, "");
      for (int task : allTasks) {
        // vars[task] = x[worker][task];
        constraint.setCoefficient(x[worker][task], 1);
      }
      // solver.addEquality(work[worker], LinearExpr.sum(vars));
      constraint.setCoefficient(work[worker], -1);
    }

    // Group1
    MPConstraint constraintG1 = solver.makeConstraint(1, 1, "");
    for (int i = 0; i < group1.length; ++i) {
      // a*b can be transformed into 0 <= a + b - 2*p <= 1 with p in [0,1]
      // p is True if a AND b, False otherwise
      MPConstraint constraint = solver.makeConstraint(0, 1, "");
      constraint.setCoefficient(work[group1[i][0]], 1);
      constraint.setCoefficient(work[group1[i][1]], 1);
      MPVariable p = solver.makeBoolVar("g1_p" + i);
      constraint.setCoefficient(p, -2);

      constraintG1.setCoefficient(p, 1);
    }
    // Group2
    MPConstraint constraintG2 = solver.makeConstraint(1, 1, "");
    for (int i = 0; i < group2.length; ++i) {
      // a*b can be transformed into 0 <= a + b - 2*p <= 1 with p in [0,1]
      // p is True if a AND b, False otherwise
      MPConstraint constraint = solver.makeConstraint(0, 1, "");
      constraint.setCoefficient(work[group2[i][0]], 1);
      constraint.setCoefficient(work[group2[i][1]], 1);
      MPVariable p = solver.makeBoolVar("g2_p" + i);
      constraint.setCoefficient(p, -2);

      constraintG2.setCoefficient(p, 1);
    }
    // Group3
    MPConstraint constraintG3 = solver.makeConstraint(1, 1, "");
    for (int i = 0; i < group3.length; ++i) {
      // a*b can be transformed into 0 <= a + b - 2*p <= 1 with p in [0,1]
      // p is True if a AND b, False otherwise
      MPConstraint constraint = solver.makeConstraint(0, 1, "");
      constraint.setCoefficient(work[group3[i][0]], 1);
      constraint.setCoefficient(work[group3[i][1]], 1);
      MPVariable p = solver.makeBoolVar("g3_p" + i);
      constraint.setCoefficient(p, -2);

      constraintG3.setCoefficient(p, 1);
    }
    // [END assignments]

    // Objective
    // [START objective]
    MPObjective objective = solver.objective();
    for (int worker : allWorkers) {
      for (int task : allTasks) {
        objective.setCoefficient(x[worker][task], costs[worker][task]);
      }
    }
    objective.setMinimization();
    // [END objective]

    // Solve
    // [START solve]
    MPSolver.ResultStatus resultStatus = solver.solve();
    // [END solve]

    // Print solution.
    // [START print_solution]
    // Check that the problem has a feasible solution.
    if (resultStatus == MPSolver.ResultStatus.OPTIMAL
        || resultStatus == MPSolver.ResultStatus.FEASIBLE) {
      System.out.println("Total cost: " + objective.value() + "\n");
      for (int worker : allWorkers) {
        for (int task : allTasks) {
          // Test if x[i][j] is 0 or 1 (with tolerance for floating point
          // arithmetic).
          if (x[worker][task].solutionValue() > 0.5) {
            System.out.println("Worker " + worker + " assigned to task " + task
                + ".  Cost: " + costs[worker][task]);
          }
        }
      }
    } else {
      System.err.println("No solution found.");
    }
    // [END print_solution]
  }

  private AssignmentGroupsMip() {}
}
// [END program]