cplex03.gms : CPLEX test suite - long UEL names and large domains

Description

```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.
```

Small Model of Type : GAMS

Category : GAMS Test library

Main file : cplex03.gms

``````\$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'
``````
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