MPL Model Library MPL Model Library



Kibbutzim, Example 3.4-2, Hillier and Lieberman


   {  Exmpl_3.4-2_Kibbutzim.mpl  }

   {  Hillier and Lieberman, Introduction to Operations Research, 7th ed.  }

   {  Chapter 3.4,  Example 2,  Product-mix/Allocation,  Size: 12x9,  Page 46  }


TITLE
    KibbutzimCropAllocation;

INDEX
    kibbutz :=  1..3;
    crop    :=  (SugarBeets, Cotton, Sorghum);
 
DATA
    UsableLand[kibbutz] :=  (400, 600, 300);               [Acres]
    WaterAlloc[kibbutz] :=  (600, 800, 375);               [AcreFeet]

    WaterUsed[crop]     :=  (3, 2, 1);                     [AcreFeet/Acre]
    NetReturn[crop]     :=  (1000.00, 750.00, 250.00);     [$/Acre]
    MaxQuota[crop]      :=  (600, 500, 325);               [Acres]
    

VARIABLES
    AllocAcre[crop,kibbutz];

MODEL

    MAX TotalProfit = SUM(crop,kibbutz: NetReturn * AllocAcre);

SUBJECT TO

    MaxLandUse[kibbutz]:

        SUM(crop: AllocAcre) <= UsableLand;

    MaxWaterAlloc[kibbutz]:

        SUM(crop: WaterUsed * AllocAcre) <= WaterAlloc;

    TotalAcreage[crop]:

        SUM(kibbutz: AllocAcre) <= MaxQuota;

    EqProp12:

        SUM(crop,kibbutz=1: AllocAcre / UsableLand)
      = 
        SUM(crop,kibbutz=2: AllocAcre / UsableLand);

    EqProp23:

        SUM(crop,kibbutz=2: AllocAcre / UsableLand)
      = 
        SUM(crop,kibbutz=3: AllocAcre / UsableLand);

    EqProp31:

        SUM(crop,kibbutz=3: AllocAcre / UsableLand)
      = 
        SUM(crop,kibbutz=1: AllocAcre / UsableLand);

END