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EuingGas, Example 7, Winston

   {  Exmpl9.2-7_EuingGas.mpl  }

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

   {  Chapter 9.2,  Example 7, Piecewise Linear (MIP),  Size: 5x6,  Page 492  }


TITLE    
    EuingGas;

INDEX
    gasoline  := 1..2;
    gasoline2 := gasoline;
    level     := 1..3;
    bpoint    := 1..4;

DATA
    Price[gasoline]   := (12,14);
    CurrentAvail[gasoline] := (500,1000);
    MaxPurchase  := 1500;
    PriceBreak[level] := (25,20,15);    
    LowerBreakpoint[level] := (  0,500,1000);
    UpperBreakpoint[bpoint] := (0, 500,1000,1500); 
    !MinOilConstituent[
    ExcessCostA[level] := FORMULA(LowerBreakpoint * (PriceBreak[level-1] - PriceBreak[level]));
    ExcessCost[level]  := SUM(level=1..level: ExcessCostA); 
    PurchaseCost[bpoint] := FORMULA(UpperBreakpoint * PriceBreak[level:=bpoint-1] + ExcessCost[level:=bpoint-1]);

VARIABLES
    Purchase;
    PartPurchase[bpoint];
    AmntOil[gasoline,gasoline2];    
  
BINARY VARIABLES
    AssignPiecewise[level];
    
MODEL

    MAX Profit = SUM(gasoline,gasoline2: AmntOil * Price) - SUM(bpoint: PartPurchase * PurchaseCost); 
                
SUBJECT TO

    MaxOil1Usage[gasoline=1] -> OUSG:

        SUM(gasoline2: AmntOil) <= Purchase + CurrentAvail;

    MaxOil2Usage[gasoline=2] -> TUSG:

        SUM(gasoline2: AmntOil) <= CurrentAvail;

    Oil50Constituent[gasoline2=1] -> OCON:

        AmntOil[gasoline:=2] <=  AmntOil[gasoline:=1];

    Oil60Constituent[gasoline2=2] -> OCON:

        0.6 * AmntOil[gasoline:=2] <=  0.4 * AmntOil[gasoline:=1];

    PurchaseCalc -> PrC:

        Purchase = SUM(bpoint: UpperBreakpoint * PartPurchase);

!    PurchasePriceCalc[level] -> PPC:

    !    PurchaseCost = PriceBreak * Purchase + ExcessCost;
 
    PiecewiseConA[bpoint] -> PCA:
  
        PartPurchase <= SUM(level: AssignPiecewise WHERE (level=bpoint) OR (level=bpoint-1));

    AssignOneLevel -> AOL:
  
        SUM(level: AssignPiecewise) = 1;

    AssignOnebpoint -> AOBP:
  
        SUM(bpoint: PartPurchase) = 1;

END
















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