$title Many free variables and restart (LP09,SEQ=88)

$onText
In this test we check how a solver behaves when there are many
free variables and if it restarts from this optimal basis.
$offText

  Sets
       i   canning plants   / seattle, san-diego /
       j   markets          / new-york, chicago, topeka /
       k                    / 1*20 /

  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        3.5           2.8          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
       xx(k)   free 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
       stuff       silly equation;

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

  supply(i) ..   sum(j, x(i,j))  =l=  a(i) ;

  demand(j) ..   sum(i, x(i,j))  =g=  b(j) ;

  stuff.. sum(k, xx(k)) =e= 0;

  Model lp09 /all/ ;

option limcol=0,limrow=0;

Solve lp09 using lp minimizing z ;
abort$( lp09.solvestat <> %solveStat.normalCompletion% or lp09.modelstat <> %modelStat.optimal%) 'wrong status codes';
abort$( sum(k, mapval(xx.m(k))=mapval(eps)) <> (card(k)-1)) 'wrong EPS';


Solve lp09 using lp minimizing z ;
abort$( lp09.solvestat <> %solveStat.normalCompletion% or lp09.modelstat <> %modelStat.optimal%) 'wrong status codes';
abort$( sum(k, mapval(xx.m(k))=mapval(eps)) <> (card(k)-1)) 'wrong EPS';
abort$( lp09.iterusd > 0) 'too many iters';