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//
// 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();
}
}