/**
*
* 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();
}
