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';