assignment.cs

//
// Copyright 2012 Hakan Kjellerstrand
//
// 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.

using System;
using System.Collections;
using System.IO;
using System.Linq;
using System.Text.RegularExpressions;
using Google.OrTools.ConstraintSolver;

public class Assignment
{

  /**
   *
   * Assignment problem
   *
   * From Wayne Winston "Operations Research",
   * Assignment Problems, page 393f
   * (generalized version with added test column)
   *
   * See  See http://www.hakank.org/or-tools/assignment.py
   *
   */
  private static void Solve()
  {

    Solver solver = new Solver("Assignment");

    //
    // data
    //

    // Problem instance
    // hakank: I added the fifth column to make it more
    //         interesting
    int rows = 4;
    int cols = 5;
    int[,] cost = {
      {14,  5, 8,  7,  15},
      { 2, 12, 6,  5,   3},
      { 7,  8, 3,  9,   7},
      { 2,  4, 6, 10,   1}
    };


    //
    // Decision variables
    //
    IntVar[,] x = solver.MakeBoolVarMatrix(rows, cols, "x");
    IntVar[] x_flat = x.Flatten();

    //
    // Constraints
    //

    // Exacly one assignment per row (task),
    // i.e. all rows must be assigned with one worker
    for(int i = 0; i < rows; i++) {
      solver.Add((from j in Enumerable.Range(0, cols)
                  select x[i,j]).ToArray().Sum() == 1);
    }

    // At most one assignments per column (worker)
    for(int j = 0; j < cols; j++) {
      solver.Add((from i in Enumerable.Range(0, rows)
                  select x[i,j]).ToArray().Sum() <= 1);
    }

    // Total cost
    IntVar total_cost = (from i in Enumerable.Range(0, rows)
                         from j in Enumerable.Range(0, cols)
                         select (cost[i,j] * x[i,j])).ToArray().Sum().Var();

    //
    // objective
    //
    OptimizeVar objective = total_cost.Minimize(1);


    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(x_flat,
                                          Solver.INT_VAR_DEFAULT,
                                          Solver.INT_VALUE_DEFAULT);

    solver.NewSearch(db, objective);

    while (solver.NextSolution()) {
      Console.WriteLine("total_cost: {0}", total_cost.Value());
      for(int i = 0; i < rows; i++) {
        for(int j = 0; j < cols; j++) {
          Console.Write(x[i,j].Value() + " ");
        }
        Console.WriteLine();
      }
      Console.WriteLine();
      Console.WriteLine("Assignments:");
      for(int i = 0; i < rows; i++) {
        Console.Write("Task " + i);
        for(int j = 0; j < cols; j++) {
          if (x[i,j].Value() == 1) {
            Console.WriteLine(" is done by " + j);
          }
        }
      }
      Console.WriteLine();

    }

    Console.WriteLine("\nSolutions: {0}", solver.Solutions());
    Console.WriteLine("WallTime: {0}ms", solver.WallTime());
    Console.WriteLine("Failures: {0}", solver.Failures());
    Console.WriteLine("Branches: {0} ", solver.Branches());

    solver.EndSearch();

  }

  public static void Main(String[] args)
  {
    Solve();
  }
}