Water Conveyance

    {  Exmpl15.1-1_WaterSupply.mpl  }

    {  Applications of Optimization with Xpress-MP  }

    {  Chapter 15.1,  Water COnveyance / Water Supply Management,  Size: 10x20,  Page 311 }


TITLE
    WaterSupply;

INDEX
    node := 1..12;
    node2 := node;

DATA
    Source := 11;
    Sink   := 12;
    Pipe[node,node2] := [1,3,1,1,5,1,1,6,1,
                         2,5,1,2,6,1,
                         3,4,1,3,5,1,
                         4,8,1,4,9,1,
                         5,8,1,5,9,1,5,10,1,
                         6,7,1,
                         7,9,1,7,10,1,
                         8,12,1,
                         9,12,1,
                         10,12,1,
                         11,1,1,11,2,1];
    Cap[node,node2] := [1,3,20,1,5,15,1,6,12,
                        2,5,6,2,6,22,
                        3,4,15,3,5,10,
                        4,8,7,4,9,10,
                        5,8,10,5,9,15,5,10,15,
                        6,7,22,
                        7,9,10,7,10,10,
                        8,12,18,
                        9,12,15,
                        10,12,20,
                        11,1,35,11,2,25];

VARIABLE
    Flow[node,node2] WHERE (Pipe);

MODEL

    MAX TotalFlow = SUM(node,node2=Sink: Flow);

SUBJECT TO

    FlowBalance[node<>Source] WHERE (node<>Sink) -> FBAL:
        SUM(node2: Flow[node:=node2,node2:=node]) = SUM(node2: Flow);

BOUNDS
    Flow <= Cap;

END