DowPont Chemical

   {  Exmpl1-2_DowPontChemical.mpl  }

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

   {  Chapter 1,  Example 2,  Process Scheduling,  Size: 8x8,  Page 17  }


TITLE
    DowPontChemical;

INDEX
    chemical  :=  (R,A,B,C,D);
    process   :=  1..3;

DATA
    RawMatCost        := 1.00;

    ProcessCapacity[process] := (56, 25, 46);

    MarketPrice[chemical]    := (0.00, 2.40, 3.20, 6.40, 12.20);

    ProcessCost[process, chemical] := [1, R, 1.50,
                                       2, A, 3.50,
                                       3, B, 4.20,
                                       3, C, 4.20];

    ProcessOutput[process,chemical] := [1, A, 0.45,
                                        1, B, 0.55,
                                        2, C, 0.80,
                                        3, D, 0.75];
VARIABLES
   ProdSale[chemical] -> S;
   ProdUse[chemical]  -> U;


MODEL

   MAX TotalProfit  =  SUM(chemical: MarketPrice * ProdSale)
                     - RawMatCost * ProdUse[R]
                     - SUM(chemical, process: ProcessCost * ProdUse);

SUBJECT TO
    ProdUse[A] + ProdSale[A]  =  ProcessOutput[1,A] * ProdUse[R];
    ProdUse[B] + ProdSale[B]  =  ProcessOutput[1,B] * ProdUse[R];
    ProdUse[C] + ProdSale[C]  =  ProcessOutput[2,C] * ProdUse[A];
                 ProdSale[D]  =  ProcessOutput[3,D] * (ProdUse[B] + ProdUse[C]);

    ProdUse[B]  =  1.5 ProdUse[C];

    ProdUse[R]               <=  ProcessCapacity[1];
    ProdUse[A]               <=  ProcessCapacity[2];
    ProdUse[B] + ProdUse[C]  <=  ProcessCapacity[3];

END