} // END WorkerLP
// This method creates the master ILP (arc variables x and degree constraints).
//
// Modeling variables:
// forall (i,j) in A:
// x(i,j) = 1, if arc (i,j) is selected
// = 0, otherwise
//
// Objective:
// minimize sum((i,j) in A) c(i,j) * x(i,j)
//
// Degree constraints:
// forall i in V: sum((i,j) in delta+(i)) x(i,j) = 1
// forall i in V: sum((j,i) in delta-(i)) x(j,i) = 1
//
// Binary constraints on arc variables:
// forall (i,j) in A: x(i,j) in {0, 1}
//
internal static void CreateMasterILP(IModeler model,
Data data,
IIntVar[][] x)
{
int i, j;
int numNodes = data.numNodes;
// Create variables x(i,j) for (i,j) in A
// For simplicity, also dummy variables x(i,i) are created.
// Those variables are fixed to 0 and do not partecipate to
// the constraints.
for (i = 0; i < numNodes; ++i)
{
x[i] = new IIntVar[numNodes];
for (j = 0; j < numNodes; ++j)
{
x[i][j] = model.BoolVar("x." + i + "." + j);
model.Add(x[i][j]);
}
x[i][i].UB = 0;
}
// Create objective function: minimize sum((i,j) in A ) c(i,j) * x(i,j)
ILinearNumExpr objExpr = model.LinearNumExpr();
for (i = 0; i < numNodes; ++i)
{
objExpr.Add(model.ScalProd(x[i], data.arcCost[i]));
}
model.AddMinimize(objExpr);
// Add the out degree constraints.
// forall i in V: sum((i,j) in delta+(i)) x(i,j) = 1
for (i = 0; i < numNodes; ++i)
{
ILinearNumExpr expr = model.LinearNumExpr();
for (j = 0; j < i; ++j)
{
expr.AddTerm(x[i][j], 1.0);
}
for (j = i + 1; j < numNodes; ++j)
{
expr.AddTerm(x[i][j], 1.0);
}
model.AddEq(expr, 1.0);
}
// Add the in degree constraints.
// forall i in V: sum((j,i) in delta-(i)) x(j,i) = 1
for (i = 0; i < numNodes; ++i)
{
ILinearNumExpr expr = model.LinearNumExpr();
for (j = 0; j < i; ++j)
{
expr.AddTerm(x[j][i], 1.0);
}
for (j = i + 1; j < numNodes; ++j)
{
expr.AddTerm(x[j][i], 1.0);
}
model.AddEq(expr, 1.0);
}
} // END CreateMasterILP
public static void Main(string[] args)
{
try {
string filename = "../../../../examples/data/facility.dat";
if (args.Length > 0)
{
filename = args[0];
}
ReadData(filename);
Cplex cplex = new Cplex();
INumVar[] open = cplex.BoolVarArray(_nbLocations);
INumVar[][] supply = new INumVar[_nbClients][];
for (int i = 0; i < _nbClients; i++)
{
supply[i] = cplex.BoolVarArray(_nbLocations);
}
for (int i = 0; i < _nbClients; i++)
{
cplex.AddEq(cplex.Sum(supply[i]), 1);
}
for (int j = 0; j < _nbLocations; j++)
{
ILinearNumExpr v = cplex.LinearNumExpr();
for (int i = 0; i < _nbClients; i++)
{
v.AddTerm(1.0, supply[i][j]);
}
cplex.AddLe(v, cplex.Prod(_capacity[j], open[j]));
}
ILinearNumExpr obj = cplex.ScalProd(_fixedCost, open);
for (int i = 0; i < _nbClients; i++)
{
obj.Add(cplex.ScalProd(_cost[i], supply[i]));
}
cplex.AddMinimize(obj);
if (cplex.Solve())
{
System.Console.WriteLine("Solution status = " + cplex.GetStatus());
double tolerance = cplex.GetParam(Cplex.Param.MIP.Tolerances.Integrality);
System.Console.WriteLine("Optimal value: " + cplex.ObjValue);
for (int j = 0; j < _nbLocations; j++)
{
if (cplex.GetValue(open[j]) >= 1 - tolerance)
{
System.Console.Write("Facility " + j + " is open, it serves clients ");
for (int i = 0; i < _nbClients; i++)
{
if (cplex.GetValue(supply[i][j]) >= 1 - tolerance)
{
System.Console.Write(" " + i);
}
}
System.Console.WriteLine();
}
}
}
cplex.End();
}
catch (ILOG.Concert.Exception exc) {
System.Console.WriteLine("Concert exception '" + exc + "' caught");
}
catch (System.IO.IOException exc) {
System.Console.WriteLine("Error reading file " + args[0] + ": " + exc);
}
catch (InputDataReader.InputDataReaderException exc) {
System.Console.WriteLine(exc);
}
}