Financing an early retirement scheme

    {  Exmpl13.4-1_Retirement.mpl  }

    {  Applications of Optimization with Xpress-MP  }

    {  Chapter 13.4, Financing an Early Retirement Scheme,  Size: 7x10,  Page 273 }


TITLE
    Retirement;

DATA
    Nt := 7;

INDEX
    bond := (sncf,fujitsu,treasury);
    year := 1..Nt;

DATA
    Dem[year]   := (1000, 600, 640, 480, 760,1020, 950);
    Value[bond] := (1.0,0.8,0.5);
    Rate[bond]  := (7.0%,7.0%,6.5%);
    Ret[bond]   := Value * Rate;
    Dur[bond]   := (5,4,6);
    Interest    := 3.2%;

INDEX
    bondi[bond,year] WHERE (Dur + 1 >= year);

VARIABLE
    Buy[bond];
    Invest[year];
    Capital;

MODEL

    MIN Capital;

SUBJECT TO

    CalcCapital -> CCP:
        Capital - SUM(bond: Value * Buy) - Invest[year:=1] = Dem[year:=1];

    AnnualBalance[year=2..Nt] -> ABAL:
        SUM(bond IN bondi: Ret * Buy + IIF(Dur + 1 = year, Value * Buy, 0)) +
        Invest[year-1] * (1 + Interest) - IIF(year<Nt,Invest, 0) = Dem;

INTEGER
    Buy;

END