Minimum Cost

   {  Exmpl9.6-1_MinCost.mpl  }

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

   {  Chapter 9.6, Example 1,  Minimum cost flow,   Size: 7x7,  Page 384  }

TITLE
    MinimumCost;

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

    FromNode := node;
    ToNode := node;

DATA
    UnitCost[FromNode, ToNode] :=

      [A,  B,  2,
       A,  C,  4,
       A,  D,  9,
       B,  C,  3,
       C,  E,  1,
       D,  E,  3,
       E,  D,  2];


    Capacity[FromNode, ToNode] :=

       [A,  B,  10,
        C,  E,  80];


    SupplyDemand[node] := (50, 40, 0, -30, -60);


VARIABLES
    Ship[FromNode,ToNode] WHERE (UnitCost > 0)

MODEL

    MIN TotalCost = SUM(FromNode, ToNode: UnitCost * Ship);

SUBJECT TO

    FlowBalance[node]:

        SUM(FromNode: Ship[FromNode,ToNode:=node]) + SupplyDemand
      =
        SUM(ToNode: Ship[FromNode:=node,ToNode]);


    MaxCapacity[FromNode, ToNode] WHERE (Capacity > 0):

       Ship <= Capacity;

END