MODEL:
! Stratified sampling plan design, taken from
Bracken and McCormick. Minimize the cost of
sampling from 4 strata, subject to constraints on
the variances of the sample based estimates of two
categories;
SETS:
STRATUM/1..4/: SIZE, POP, COST, WEIGHT;
CATEGORY/1..2/: VARMAX, K2;
SXC( STRATUM, CATEGORY): VAR, K1;
ENDSETS ! POP = population of each stratum.
COST = cost of sampling in each.
VARMAX = variance limits.
VAR = variance for each category in each stratum.
CFIX = a fixed cost;
DATA:
POP = 400000, 300000, 200000, 100000;
COST = 1, 1, 1, 1;
VARMAX = .043, .014;
VAR = 25 1
25 4
25 16
25 64;
CFIX = 1;
ENDDATA
[OBJ] MIN = CFIX + @SUM( STRATUM: SIZE * COST);
! Compute some parameters;
TOTP = @SUM( STRATUM( I): POP( I));
@FOR( STRATUM( I):
! Weight given each stratum;
WEIGHT( I) = POP( I)/TOTP;
@GIN( SIZE( I));
);
@FOR( CATEGORY( J):
K2( J) =
@SUM( STRATUM(I): VAR( I, J)^2 *
WEIGHT( I)/ POP( I));
);
@FOR( SXC( I, J):
K1( I, J) = VAR( I, J)^2* WEIGHT( I)^2;
);
@FOR( CATEGORY( J):
@SUM( STRATUM( I): K1( I, J) / SIZE( I))
- K2( J) <= VARMAX( J)
);
@FOR( STRATUM( I):
@BND( 0.0001, SIZE(I), POP( I) -1);
);
END
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