post_office_problem2.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.Linq;
using System.Text.RegularExpressions;
using Google.OrTools.ConstraintSolver;


public class PostOfficeProblem2
{

  /**
   *
   * Post office problem.
   *
   * Problem statement:
   * http://www-128.ibm.com/developerworks/linux/library/l-glpk2/
   *
   * From Winston 'Operations Research: Applications and Algorithms':
   * """
   * A post office requires a different number of full-time employees working
   * on different days of the week [summarized below]. Union rules state that
   * each full-time employee must work for 5 consecutive days and then receive
   * two days off. For example, an employee who works on Monday to Friday
   * must be off on Saturday and Sunday. The post office wants to meet its
   * daily requirements using only full-time employees. Minimize the number
   * of employees that must be hired.
   *
   * To summarize the important information about the problem:
   *
   * Every full-time worker works for 5 consecutive days and takes 2 days off
   * - Day 1 (Monday): 17 workers needed
   * - Day 2 : 13 workers needed
   * - Day 3 : 15 workers needed
   * - Day 4 : 19 workers needed
   * - Day 5 : 14 workers needed
   * - Day 6 : 16 workers needed
   * - Day 7 (Sunday) : 11 workers needed
   *
   * The post office needs to minimize the number of employees it needs
   * to hire to meet its demand.
   * """
   *
   * Also see http://www.hakank.org/or-tools/post_office_problem2.py
   *
   */
  private static void Solve()
  {

    Solver solver = new Solver("PostOfficeProblem2");

    //
    // Data
    //

    // days 0..6, monday 0
    int n = 7;
    int[] need = {17, 13, 15, 19, 14, 16, 11};

    // Total cost for the 5 day schedule.
    // Base cost per day is 100.
    // Working saturday is 100 extra
    // Working sunday is 200 extra.
    int[] cost = {500, 600, 800, 800, 800, 800, 700};


    //
    // Decision variables
    //

    // No. of workers starting at day i
    IntVar[] x = solver.MakeIntVarArray(n, 0, 100, "x");

    IntVar total_cost = x.ScalProd(cost).Var();
    IntVar num_workers = x.Sum().Var();

    //
    // Constraints
    //
    for(int i = 0; i < n; i++) {
      IntVar s = (from j in Enumerable.Range(0, n)
                  where j != (i+5) % n && j != (i+6) % n
                  select x[j]).ToArray().Sum().Var();
      solver.Add(s >= need[i]);
    }

    // Add a limit for the cost
    solver.Add(total_cost <= 20000);

    //

    // objective
    //
    //
    OptimizeVar obj = total_cost.Minimize(100);



    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(x,
                                          Solver.CHOOSE_MIN_SIZE_LOWEST_MIN,
                                          Solver.ASSIGN_MIN_VALUE);


    solver.NewSearch(db, obj);

    while (solver.NextSolution()) {
      Console.WriteLine("num_workers: {0}", num_workers.Value());
      Console.WriteLine("total_cost: {0}", total_cost.Value());
      Console.Write("x: ");
      for(int i = 0; i < n; i++) {
        Console.Write(x[i].Value() + " ");
      }
      Console.WriteLine("\n");
    }

    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();
  }
}