MathModel Class

// sets
Set j = Set("j").Represents("a node of the network").HasElementsUntil(data.NumNodes);
Set i = Set("i").Represents("nodes which have an edge into node j").DependsOn(j).HasElements(j => data.TailsOf(j));
Set k = Set("k").Represents("nodes which have an edge from node j").DependsOn(j).HasElements(j => data.HeadsOf(j));
Set c = Set("c").Represents("a commodity to be transported").HasElementsUntil(data.NumCommodities);

// parameters
ParD2 capacity = Parameter("cap").Represents("capacity of arc (j,k)").HasIndices(j, k).HasValues(data.GetEdgeCapacity);
ParD2 nodeBalance = Parameter("b").Represents("equal to (negative of) demand of commodity c if j is its (source) sink node").HasIndices(c, j).HasValues(data.GetNodeBalance);
ParD3 cost = Parameter("cost").Represents("cost of unit flow of commodity c on arc (j, k)").HasIndices(j, k, c).HasValues(1);

// variables
VarD3 f = Variable("f").Represents("flow of commodity c on arc (j,k)").HasIndices(j, k, c).IsContinuous().IsNonnegative();

// constraints
Constraint conFlowBal = key("flowBal")
    | "flow balance constraint at node j"
    | forall(j)
    | sum(over(c, i), f[i, j, c]) - sum(over(c, k), f[j, k, c]) == nodeBalance[c, j];

Constraint conCapacity = key("capacity")
    | "capacity constraint of arc (j, k)"
    | forall(j, k)
    | sum(over(c), f[j, k, c]) <= capacity[j, k]; 

// objective
Objective totalCost = key("minFlowCost")
    | "minimize total flow cost"
    | minimize
    | sum(over(c, j, k), cost[j, k, c] * f[j, k, c]);

// mathematical model
var model =
    MathModel.New("multi-commodity mcnf problem")
    .Represents("multi commodity minimum cost network flow problem")
    .WithObjective(totalCost)
    .HasConstraints(conFlowBal, conCapacity);