Fly By Night

    {  Exmpl8.3-4_FlyByNight.mpl  }

    {  Winston, Operations Research, Applications and Algorithms, 4th ed.  }

    {  Chapter 8.3,  Example 4, Maximum Flow,  Size: 5x6,  Page 421 }


TITLE
    FlyByNight;

INDEX
    city  := (Juneau,Seattle,Denver,LosAngeles,Dallas);
    city2 := city;

DATA
    MaxFlights[city,city2] := [Juneau,    Seattle,   3,
                               Seattle,   LosAngeles,2,
                               Seattle,   Denver,    3,
                               LosAngeles,Dallas,    1,
                               Denver,    Dallas,    2,
                               Dallas,    Juneau,    9];

VARIABLE
    Flights[city,city2] WHERE (MaxFlights > 0);

MODEL

    MAX NumberOfFlights = SUM(city,city2=Dallas: Flights);

SUBJECT TO

    FlowBalance[city]:

        SUM(city2: Flights) = SUM(city2: Flights[city:=city2,city2:=city]);

BOUNDS
    Flights <= MaxFlights;

END