private static void SolveMinCostFlow()
{
Console.WriteLine("Min Cost Flow Problem");
int numSources = 4;
int numTargets = 4;
int[,] costs = { { 90, 75, 75, 80 },
{ 35, 85, 55, 65 },
{ 125, 95, 90, 105 },
{ 45, 110, 95, 115 } };
int expectedCost = 275;
MinCostFlow minCostFlow = new MinCostFlow();
for (int source = 0; source < numSources; ++source)
{
for (int target = 0; target < numTargets; ++target)
{
minCostFlow.AddArcWithCapacityAndUnitCost(
source, /*target=*/ numSources + target, /*capacity=*/ 1,
/*flow unit cost=*/ costs[source, target]);
}
}
for (int source = 0; source < numSources; ++source)
{
minCostFlow.SetNodeSupply(source, 1);
}
for (int target = 0; target < numTargets; ++target)
{
minCostFlow.SetNodeSupply(numSources + target, -1);
}
Console.WriteLine("Solving min cost flow with " + numSources +
" sources, and " + numTargets + " targets.");
MinCostFlow.Status solveStatus = minCostFlow.Solve();
if (solveStatus == MinCostFlow.Status.OPTIMAL)
{
Console.WriteLine("total computed flow cost = " +
minCostFlow.OptimalCost() +
", expected = " + expectedCost);
}
else
{
Console.WriteLine("Solving the min cost flow problem failed." +
" Solver status: " + solveStatus);
}
}
static void Main()
{
// [START data]
// Define four parallel arrays: sources, destinations, capacities, and unit costs
// between each pair. For instance, the arc from node 0 to node 1 has a
// capacity of 15.
// Problem taken From Taha's 'Introduction to Operations Research',
// example 6.4-2.
int[] startNodes = { 0, 0, 1, 1, 1, 2, 2, 3, 4 };
int[] endNodes = { 1, 2, 2, 3, 4, 3, 4, 4, 2 };
int[] capacities = { 15, 8, 20, 4, 10, 15, 4, 20, 5 };
int[] unitCosts = { 4, 4, 2, 2, 6, 1, 3, 2, 3 };
// Define an array of supplies at each node.
int[] supplies = { 20, 0, 0, -5, -15 };
// [END data]
// [START constraints]
// Instantiate a SimpleMinCostFlow solver.
MinCostFlow minCostFlow = new MinCostFlow();
// Add each arc.
for (int i = 0; i < startNodes.Length; ++i)
{
int arc =
minCostFlow.AddArcWithCapacityAndUnitCost(startNodes[i], endNodes[i], capacities[i], unitCosts[i]);
if (arc != i)
{
throw new Exception("Internal error");
}
}
// Add node supplies.
for (int i = 0; i < supplies.Length; ++i)
{
minCostFlow.SetNodeSupply(i, supplies[i]);
}
// [END constraints]
// [START solve]
// Find the min cost flow.
MinCostFlow.Status solveStatus = minCostFlow.Solve();
// [END solve]
// [START print_solution]
if (solveStatus == MinCostFlow.Status.OPTIMAL)
{
Console.WriteLine("Minimum cost: " + minCostFlow.OptimalCost());
Console.WriteLine("");
Console.WriteLine(" Edge Flow / Capacity Cost");
for (int i = 0; i < minCostFlow.NumArcs(); ++i)
{
long cost = minCostFlow.Flow(i) * minCostFlow.UnitCost(i);
Console.WriteLine(minCostFlow.Tail(i) + " -> " + minCostFlow.Head(i) + " " +
string.Format("{0,3}", minCostFlow.Flow(i)) + " / " +
string.Format("{0,3}", minCostFlow.Capacity(i)) + " " +
string.Format("{0,3}", cost));
}
}
else
{
Console.WriteLine("Solving the min cost flow problem failed. Solver status: " + solveStatus);
}
// [END print_solution]
}
static void Main()
{
// [START solver]
// Instantiate a SimpleMinCostFlow solver.
MinCostFlow minCostFlow = new MinCostFlow();
// [END solver]
// [START data]
// Define the directed graph for the flow.
int[] teamA = { 1, 3, 5 };
int[] teamB = { 2, 4, 6 };
// Define four parallel arrays: sources, destinations, capacities, and unit costs
// between each pair.
int[] startNodes = { 0, 0, 11, 11, 11, 12, 12, 12, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3,
3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 8, 9, 10 };
int[] endNodes = { 11, 12, 1, 3, 5, 2, 4, 6, 7, 8, 9, 10, 7, 8, 9, 10, 7, 8,
9, 10, 7, 8, 9, 10, 7, 8, 9, 10, 7, 8, 9, 10, 13, 13, 13, 13 };
int[] capacities = { 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 };
int[] unitCosts = { 0, 0, 0, 0, 0, 0, 0, 0, 90, 76, 75, 70, 35, 85, 55, 65, 125, 95,
90, 105, 45, 110, 95, 115, 60, 105, 80, 75, 45, 65, 110, 95, 0, 0, 0, 0 };
int source = 0;
int sink = 13;
// Define an array of supplies at each node.
int[] supplies = { 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4 };
// [END data]
// [START constraints]
// Add each arc.
for (int i = 0; i < startNodes.Length; ++i)
{
int arc =
minCostFlow.AddArcWithCapacityAndUnitCost(startNodes[i], endNodes[i], capacities[i], unitCosts[i]);
if (arc != i)
{
throw new Exception("Internal error");
}
}
// Add node supplies.
for (int i = 0; i < supplies.Length; ++i)
{
minCostFlow.SetNodeSupply(i, supplies[i]);
}
// [END constraints]
// [START solve]
// Find the min cost flow.
MinCostFlow.Status status = minCostFlow.Solve();
// [END solve]
// [START print_solution]
if (status == MinCostFlow.Status.OPTIMAL)
{
Console.WriteLine("Total cost: " + minCostFlow.OptimalCost());
Console.WriteLine("");
for (int i = 0; i < minCostFlow.NumArcs(); ++i)
{
// Can ignore arcs leading out of source or into sink.
if (minCostFlow.Tail(i) != 0 && minCostFlow.Tail(i) != 11 && minCostFlow.Tail(i) != 12 &&
minCostFlow.Head(i) != 13)
{
// Arcs in the solution have a flow value of 1. Their start and end nodes
// give an assignment of worker to task.
if (minCostFlow.Flow(i) > 0)
{
Console.WriteLine("Worker " + minCostFlow.Tail(i) + " assigned to task " + minCostFlow.Head(i) +
" Cost: " + minCostFlow.UnitCost(i));
}
}
}
}
else
{
Console.WriteLine("Solving the min cost flow problem failed.");
Console.WriteLine("Solver status: " + status);
}
// [END print_solution]
}
