[Help-glpk] Empty Sets

[Matteo Salani]

I have a big model with sets, parameters, variables and constraints 
divided in three sections and
interacting in 1 constraint.
I would like to use empty sets to basically "remove" parts of the model 
dynamically via the data file.
The problem is that in my model some subsets are defined and this makes 
GLPK unhappy.


Without posting the entire model, the problem is exactly equivalent to 
make GLPK digest the following model:

param m, integer, >= 0;

set T := 1 .. m;
set S;

param  aParameter{s in S}, integer, >= 0;
param anotherParameter{s in S, t in T}, >= 0;

set aSubSet{s in S} within T := {t in T : t > aParameter[s]};

var aVariable{s in S}, >= 0;

s.t. aConstraint{s in S, t in aSubSet[s]}: aVariable[s] >= 
anotherParameter[s,t];


This (clearly) works when S is non empty (e.g., with the following data)

param m := 3;
set S := 1;
param aParameter := 1 2 ;
param anotherParameter :=
 1 1 10
 1 2 20
 1 3 10
;

S can be empty and the model works perfectly if I hard code this info, 
i.e. the follwing model perfectly works:

param m, integer, >= 0;
set T := 1 .. m;

set S := {};  /* Hard coding an empty set */

param  aParameter{s in S}, integer, >= 0;
set aSubSet{s in S} within T := {t in T : t > aParameter[s]};
param anotherParameter{s in S, t in T}, >= 0;
var aVariable{s in S}, >= 0;
s.t. aConstraint{s in S, t in aSubSet[s]}: aVariable[s] >= 
anotherParameter[s,t];

when I try to specify an empty set in the data file I cannot make it 
work, though it is working in the above version:

set S := {}; /* In the data file */

obtaining: syntax error in set data block

the other way round does not work either, i.e., defining an empty set in 
the model and trying to override this in the data file.

Whatever suggestion is appreciated.

Thanks!
M

--
*Matteo Salani*
IDSIA
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