eps1.gms : EPS in multiplications and divisions

Description

```version 21.0 - 21.3 has a problem with EPS values in equations
those EPS can come from levels or data
```

Small Model of Type : GAMS

Category : GAMS Test library

Main file : eps1.gms

``````\$Title EPS in multiplications and divisions (EPS1,SEQ=123)
\$Ontext

version 21.0 - 21.3 has a problem with EPS values in equations
those EPS can come from levels or data

\$offtext
Sets
i   canning plants   / seattle, san-diego /
j   markets          / new-york, chicago, topeka / ;

Parameters

a(i)  capacity of plant i in cases
/    seattle     350
san-diego   600  /

b(j)  demand at market j in cases
/    new-york    325
chicago     300
topeka      275  / ;

Table d(i,j)  distance in thousands of miles
new-york       chicago      topeka
seattle          2.5           1.7          1.8
san-diego        2.5           1.8          1.4  ;

Scalar f  freight in dollars per case per thousand miles  /90/ ;

Parameter c(i,j)  transport cost in thousands of dollars per case ;

c(i,j) = f * d(i,j) / 1000 ;

Variables
x(i,j)  shipment quantities in cases
z       total transportation costs in thousands of dollars ;

Positive Variable x ;

Equations
cost        define objective function
supply(i)   observe supply limit at plant i
demand(j)   satisfy demand at market j;

cost ..        z  =e=  sum((i,j), c(i,j)*x(i,j)) ;

supply(i) ..  1*sum(j,  x(i,j) + eps)  =l=  a(i) ;

demand(j) .. (eps + sum(i, x(i,j)))/1  =g=  b(j) ;

Model transport /all/ ;

Solve transport using lp minimizing z ;

abort\$(transport.solvestat <> %solvestat.NormalCompletion% or transport.modelstat <> %modelstat.Optimal%) 'bad return codes';
abort\$(abs(z.l - 153.6750) > 1e05) 'wrong solution';
abort\$(transport.numnz <> 19) 'wrong NZ count';

``````
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