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If you are talking about constraints in the optimization sense (equations + inequations), this is called disjunctive programming, it is kind of a large subtopic of optimization. Some tools: LogMIP: https://www.gams.com/latest/docs/userguides/mccarl/logmip.htm EMP: https://www.gams.com/latest/docs/us...

Does GAMS not distinguish capital and lower letters?

True. It does not.

To "populate" a set:

For more detail: You don't need to declare the domain of the variable (as in variable P(A,B)). You can just write variable p; Then, if the variable appears in the constraints, it will be part of the model. Check out this example: sets A /1*5/ A1(A) /2,3/ variable d,t; equation Q,dummy; Q(A1).. d(a1)...

I adapted the text at https://www.gams.com/latest/docs/userguides/userguide/_u_g__dynamic_sets.html#UG_DynamicSets_SetComplement to your sets "The membership of B4 is set equal to all those in Bi but not in B0. The operation above is equivalent to the following longer way of representation, B4(...

this is the correct way:

A(Year)$(ord(Year)<card(Year)) = (card(Year)-1)*card(dset) - (ord(Year)-1)*card(dset);

Besides: the loop is actually unnecesary.

C(A,A1) =ceil(B(A, A1)/2);

will just do the trick

This is GAMS code to accomplish that:

sets A,B(A);
parameter C(A);

B(A)=YES$(C(A)>0);

Q(A)$A.. is very redundant. Just with Q(A).. Equation Q will be written one time for each member of A. If A is empty, it will never be written. Remember that you can only have empty sets if you choose option $Onempty, indicate dimension and have empty bars. Take this example: $Onempty set A(*) / /; ...

Loop part is correct, declarations are not. I took the code to correct syntax (other ways are also possible):

sets
A /a,b,c/
A1 /a1,b1/;
parameter
B(A, A1) /
a.a1 1
a.b1 1
b.a1 2
b.b1 3
c.a1 2
c.b1 3/;
parameter
C(A,A1)
;
loop((A,A1),
C(A,A1) =ceil(B(A, A1)/2);
);

Display C;

Most likely you have unwillingly introduced a syntax or conceptual error using conditionals involving Variables. (Perhaps a parameter which changed to a variable ?) These are situations (I can tell from the top of my head, they may be more) where you would be prompted to switch the model to DNLP. Th...