Stratified Sample Design

    {  sample.mpl   }

    {  GAMS Model Library, http://www.gams.com/modlib/libhtml/sample.htm  }

    {  Stratified Sample Design,  NLP,  Size: 2x4  }

!#define reciprocal


TITLE
    Sample;

OPTIONS
    ModelType=Nonlinear
    ParserType=Extended

INDEX
    h := 1..4;
    j := (a,b);

DATA
    Pop[h] := 100000 * (4,3,2,1);
    AB[j,h]   := (25,25,25,25,
                   1, 4,16,64);
    Cost[h]:= ( 1, 1, 1, 1);
    Vmax[j] := (0.04,0.01);
    TPop   := SUM(h: Pop);
    W[h]   := FORMULA(Pop/TPop);
    K1[h,j] := FORMULA(POWER(W,2)*AB);
    K2[j]   := SUM(h: W*AB/Pop);
    NrLowBd[h] := FORMULA(1/Pop);
    InitNr[h] := FORMULA(1/NrLowBd);

VARIABLES
    N[h] INITIAL 200;
#ifdef reciprocal
    Nr[h] INITIAL InitNr;
#endif

MODEL

    MIN C = SUM(h: Cost * N);
#ifdef reciprocal
   MIN C = SUM(h: Cost/Nr);
#endif

SUBJECT TO

    Vbal[j]:  SUM(h: K1/N) - K2 <= Vmax;

#ifdef reciprocal
    Vbalr[j]: SUM(h: K1 * Nr) - K2 <= Vmax;
#endif

BOUNDS
    100 <= N <= Pop;
#ifdef reciprocal
    NrLowBd <= Nr <= 0.01;
#endif
END