Transportation

   {  Exmpl1-4_Transportation.mpl  }

   {  Roy D. Shapiro, Optimization Models for Planning and Allocation  }

   {  Chapter 1,  Example 4,  Transportation,  Size: 6x8,  Page 24  }


TITLE
    TransportationProblem;

INDEX
    mill    :=  1..2;
    market  :=  (Northburg, Midburg, Southburg) -> (N, M, S);

DATA
    WheatAvail            := 50000;

    MillingCost[mill]     := (0.13, 0.16);

    MarketDemand[market]  := (10000, 15000, 25000);

    ShipCostMill[mill]    := (0.31, 0.33);

    ShipCostMarket[market, mill] := (0.18, 0.25,
                                     0.22, 0.23,
                                     0.27, 0.19);

VARIABLES
    ShipMill[mill];
    ShipMarket[mill, market];


MODEL

   MAX TotalCost  =  SUM(mill: MillingCost * ShipMill)
                   + SUM(mill: ShipCostMill * ShipMill)
                   + SUM(mill,market: ShipCostMarket * ShipMarket);

SUBJECT TO
    WheatToMills:

       SUM(mill: ShipMill)  =  WheatAvail;


    MillBalance[mill]:

        ShipMill  =  SUM(market: ShipMarket);

    MarketReq[market]:

        SUM(mill: ShipMarket)  =  MarketDemand;

END