Maximum Flow

   {  Exmpl9.5-1_MaxFlow.mpl  }

   {  Hillier and Lieberman, Introduction to Operations Research, 9th ed.  }

   {  Chapter 9.5,  Example 1, Maximum Flow,   Size: 7x14,  Page 373 }

TITLE
    MaximumFlow;

INDEX
    node := (O, A, B, C, D, E, T);

    FromNode := node;
    ToNode   := node;

    SourceNode[node] := (O);
    DestNode[node]   := (T);

DATA
    Capacity[FromNode, ToNode] :=

       [O,  A,  5,
        O,  B,  7,
        O,  C,  4,
        A,  B,  1,
        A,  D,  3,
        B,  C,  2,
        B,  D,  4,
        B,  E,  5,
        C,  E,  4,
        D,  T,  9,
        E,  D,  1,
        E,  T,  6];


VARIABLES
    Flow[FromNode, ToNode] -> x WHERE (Capacity > 0);
    Entrance[node=O];
    Destination[node=T];

MODEL

    MAX TotalFlow = Entrance[O];

SUBJECT TO

    FlowBalance[node]:

        Entrance + SUM(FromNode: Flow[FromNode,ToNode:=node])
      =
        Destination + SUM(ToNode: Flow[FromNode:=node,ToNode]);

BOUNDS
    Flow <= Capacity;

END