Network reliability

    {  Exmpl12.1-1_NetworkReliability.mpl }

    {  Applications of Optimization with Xpress-MP  }

    {  Chapter 12.1, Network Reliability,  Size: 19x44,  Page 237 }


TITLE
    NetworkReliability;

INDEX
    node := 1..11
    node2 := node;

DATA
    Source := 10;
    Sink := 11;
    Arc[node,node2] := [1,2,1,1,3,1,1,11,1,
                        2,1,1,2,3,1,2,8,1,2,9,1,
                        3,1,1,3,2,1,3,4,1,3,9,1,3,10,1,3,11,1,
                        4,3,1,4,5,1,4,6,1,4,11,1,5,4,1,
                        5,9,1,5,11,1,
                        6,4,1,6,7,1,6,9,1,6,10,1,
                        7,6,1,7,8,1,7,10,1,
                        8,2,1,8,7,1,8,10,1,
                        9,2,1,9,3,1,9,5,1,9,6,1,9,10,1,
                        10,3,1,10,6,1,10,7,1,10,8,1,10,9,1,
                        11,1,1,11,3,1,11,4,1,11,5,1];

VARIABLE
    Flow[node,node2] WHERE (Arc > 0);

MODEL

    MAX Path = SUM(node2: Flow[node:=Source]);

SUBJECT TO

    FlowConservation[node2<>Source] WHERE (node2<>Sink) -> FCON:
        SUM(node: Flow) = SUM(node: Flow[node:=node2,node2:=node]);
    FlowConservationA[node<>Source] WHERE (node<>Sink) -> FCONA:
        SUM(node2: Flow) <= 1;

    NoReturn2Source -> NRET:
        SUM(node: Flow[node2:=Source]) = 0;

BINARY
    Flow;

END