Family Budget

    {  Exmpl13.5-1_FamilyBudget.mpl  }

    {  Applications of Optimization with Xpress-MP  }

    {  Chapter 13.5, Family Budget,  Size: 12x24,  Page 276 }


TITLE
    FamilyBudget;

INDEX
    month := 1..12;
    item := (living,rent,tel,gas,car,tax);

DATA
    Income := 1900;
    Allow := 150;
    Hmin := 165;
    Expense[item] := (550,630,135,850,340,100);
    Freq[item] := (1,1,2,6,1,4);
    sda[month] := month;
    ordm[month] := (1,2,3,4,5,6,7,8,9,10,11,12);
    PaymentTime[item,month] := [tel,2,1,tel,4,1,tel,6,1,tel,8,1,tel,10,1,tel,12,1,
                gas,6,1,gas,12,1,
                tax,4,1,tax,8,1,tax,12,1];

VARIABLE
    Hobby[month];
    Save[month];

MODEL

    MAX Leisure = SUM(month: Hobby);

SUBJECT TO

    MonthlyBalance[month] -> MBAL:
        SUM(item: Expense WHERE (Freq=1) OR (PaymentTime=1))
      + Hobby + Save
     <=
        Income + Allow + IIF(month>1, Save[month-1], 0);

BOUNDS
    Hobby >= Hmin;

END