$title  'CPLEX test suite - long UEL names and large domains' (cplex03,SEQ=358)
$if not '%GAMS.lp%' == '' $set solver %GAMS.lp%
$if not set solver        $set solver cplex
$onText

This problem finds a least cost shipping schedule that meets
requirements at markets and supplies at factories where demand
exceeds supply using the Cplex feature FeasOpt.


Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions.
Princeton University Press, Princeton, New Jersey, 1963.

Contributor: Michael Bussieck
$offText

$set kkk k,k0,k1,k2,k3,k4,k5,k6,k7,k8,k9

  Sets
       i   canning plants   / seattle_in_washington_state_home_of_starbucks_coffee, san-diego /
       j   markets          / new-york, chicago, topeka /
       k   dummy            / k /
  alias (%kkk%);

  Parameters

       a(i)  capacity of plant i in cases
         /    seattle_in_washington_state_home_of_starbucks_coffee     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_in_washington_state_home_of_starbucks_coffee          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,%kkk%)  shipment quantities in cases
       z       total transportation costs in thousands of dollars ;

  Positive Variable x ;

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

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

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

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

  Model transport /all/ ;

* Lets make a MIP;

  Binary variable xb(i,j,%kkk%);
  Equation minship(i,j,%kkk%);
  Equation doship(i,j,%kkk%);

  minship(i,j,%kkk%).. x(i,j,%kkk%) + eps*xb(i,j,%kkk%) =g= 90;

  doship(i,j,%kkk%)..  x(i,j,%kkk%) =e= 0;

  model miptransport /all/;

  option lp=%solver%, mip=%solver%, limrow=0, limcol=0, optcr=0;
  Solve transport using lp minimizing z ;

  if (transport.modelstat <> %modelStat.optimal% or transport.solvestat <> %solveStat.normalCompletion%, abort 'problem solving first lp');

  file fcpx Cplex Option file / %solver%.opt /; transport.optfile=1; miptransport.optfile=1;

* Indicators
  putclose fcpx / 'indic minship(i,j,%kkk%)$xb(i,j,%kkk%) 1'
                / 'indic doship(i,j,%kkk%)$xb(i,j,%kkk%) 0';

  Solve miptransport using mip minimizing z ;
  if (transport.modelstat <> %modelStat.optimal% or transport.solvestat <> %solveStat.normalCompletion%, abort 'problem with indicators (1)');
  abort$(smin((i,j,%kkk%)$(x.l(i,j,%kkk%)>1.e-6),x.l(i,j,%kkk%)) < 90) 'problems with indicators (2)';

* Indicators and BCH
  putclose fcpx / 'indic minship(i,j,%kkk%)$xb(i,j,%kkk%) 1'
                / 'indic doship(i,j,%kkk%)$xb(i,j,%kkk%) 0'
                / 'usercutcall xxxdim.inc' / 'cuts no' / 'preind 0'
                / 'heurfreq -1' / 'mipinterval 1';

$onEcho > xxxdim.inc
Sets
     i   canning plants   / seattle_in_washington_state_home_of_starbucks_coffee, san-diego /
     j   markets          / new-york, chicago, topeka /
     k   dummy            / k /
   cut   cuts             / 1 /
alias (%kkk%);
* This cut cuts away the optimal solution of value 153.675
Parameters rhs_c(cut)     / 1 2 /
           sense_c(cut)   / 1 1 /
           numcuts        / 0 /
           xb_c(cut,i,j,%kkk%) / 1.seattle_in_washington_state_home_of_starbucks_coffee.chicago.k.k.k.k.k.k.k.k.k.k.k 1
                                 1.san-diego.new-york.k.k.k.k.k.k.k.k.k.k.k 1
                                 1.san-diego.topeka  .k.k.k.k.k.k.k.k.k.k.k 1 /;
* Only add the cut the very first time
$if %ncalls% == 0 numcuts=1;
$offEcho

  Solve miptransport using mip minimizing z ;
  if (transport.modelstat <> %modelStat.optimal% or transport.solvestat <> %solveStat.normalCompletion%, abort 'problem with indicators and BCH (1)');
  abort$(smin((i,j,%kkk%)$(x.l(i,j,%kkk%)>1.e-6),x.l(i,j,%kkk%)) < 90) 'problems with indicators and BCH (2)';
  abort$(z.l < 156) 'problems with indicators and BCH (3)';

* Sensitivity in LST file
  putclose fcpx / 'objrng all' / 'rhsrng all';
  Solve transport using lp minimizing z ;
  execute '=grep -q "LOWER *CURRENT *UPPER" "%gams.scrdir%gamsstat.%gams.scrext%"';
  abort$errorlevel 'problem with obj/rhsrng option in lst file';

* Sensitivity in data file
  putclose fcpx / 'objrng all' / 'rhsrng all' / 'rngrestart rng.txt';
  Solve transport using lp minimizing z ;
  execute '=grep -q "seattle_in_washington_state_home_of_starbucks_coffee.new-york.k.k.k.k.k.k.k.k.k.k.k" rng.txt';
  abort$errorlevel 'problem with obj/rhsrng option in rng.txt';

* Increase demand by 20% to make model infeasible
  b(j) = 1.2*b(j);

* FEASOPT
  putclose fcpx / 'feasopt 1' / 'equation.feaspref 0' / 'demand.feaspref 1'
                / "demand.feaspref('new-york','k','k','k','k','k','k','k','k','k','k','k') 0";
  Solve transport using lp minimizing z ;
  if (transport.modelstat <> %modelStat.infeasible% or transport.solvestat <> %solveStat.normalCompletion%, abort 'problem with feasopt option');
  display 'All infeasibilities should be in the demand equations', x.infeas, supply.infeas, demand.infeas;
  abort$(sum((i,j,%kkk%), x.infeas(i,j,%kkk%)) + sum((i,%kkk%),supply.infeas(i,%kkk%))) x.infeas, supply.infeas, demand.infeas;

* IIS
  putclose fcpx / 'iis 1';
  Solve transport using lp minimizing z ;
  execute '=grep -q "Number of equations in .*conflict: .*5" "%gams.scrdir%gamsstat.%gams.scrext%"';
  execute '=grep -q "Number of variables in .*conflict: .*0" "%gams.scrdir%gamsstat.%gams.scrext%"';
  abort$errorlevel 'problem with IIS option'