Sensitivity Analysis in a loop with GAMS/Cplex

> I have read the document http://www.gams.com/docs/sensitiv.htm but I don't
> see how I can do sensitivity analysis in a loop.

GAMS/Cplex writes sensitivity information to a text file (include file) and GAMS cannot read such a file at compile time. I.e. you cannot read a text file or include file to be specific inside a loop.

It would have been preferable in GAMS/Cplex would have been updated so that it can write sensitivity information to a GDX file (see also GAMS/Cplex wish list).

As a work around one can call a GAMS submodel from the GAMS main model. The submodel can then convert the include file to a GDX file, which then can be read by the main model. 

A complete example is below:

$ontext
  
 shows how to do sensitivity analysis inside a single
 GAMS job by using GDX files.
  
  
 Erwin Kalvelagen, december 2003, revised jan 2009
  
$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) ..   sum(j, x(i,j))  =l=  a(i) ;
  
demand(j) ..   sum(i, x(i,j))  =g=  b(j) ;
  
Model m /all/ ;
  
  
*
* set options to cplex writes an include file with sensitivity
* information
*
$onecho > cplex.opt
objrng all
rhsrng all
rngrestart rng.inc
$offecho
  
m.optfile=1;
m.dictfile=2;
  
option lp=cplex;
Set rnglim /lo,up/;
  
*
* three different scenarios
*
set iter /iter1*iter3/;
parameter delta(iter);
delta(iter)$(ord(iter)>1) = 100;
display delta;
  
  
*
* write gams file that reads include file rng.inc and
* writes a GDX file (specified on the command line)
*
$onecho > inc2gdx.gms
set i,j,rnglim
$gdxin sets.gdx
$load i j rnglim
$include rng.inc
$offecho
  
  
*
* save the sets i,j,rnlim to gdx file sets.gdx
*
execute_unload 'sets.gdx',i,j,rnglim;
  
  
*
* parameters to hold ranges for equation DEMAND
*
parameter demandrange(j,rnglim);
parameter alldemandrange(iter,j,rnglim);
  
  
loop(iter,
 a(i) = a(i) + delta(iter);
  
 SOLVE m USING LP minimizing z;
  
*
* store the sensitivity information in a GDX file
*
 execute '=gams.exe inc2gdx.gms lo=3 gdx=dump.gdx';
  
*
* get data from GDX file
*
 execute_load 'dump.gdx',demandrange=demandRNG;
  
 alldemandrange(iter,j,rnglim) = demandrange(j,rnglim);
);
  
display alldemandrange;