## Wednesday, September 3, 2008

### Arithmetic on indices

>Is it possible to write an objective function as
>"obj.. PROFIT =e= sum((l,m,dig) \$(ord(l) le p and ord(m) le p and ord(dig) le digmax ), x('(1+p*(ord(l)-1))','(1+p*(ord(m)-1))',dig)*ord(dig)); "
>if I only want to add particular x's to my objective function (indexed as 1+p*(ord(l)-1) and 1+p*(ord(m)-1) where p is a constant )?

>In this case, gams gives me domain violation error for first and second index and i couldn't find a way to solve it
>(the domain is not violated mathematically for example for p=3 and digmax= 9).
>Is there a way to do arithmetic operations in indexes?

Indices are always strings in GAMS. But you can do what you want as follows:

``alias (l,i), (m,j); obj.. PROFIT =e=  sum((l,m,dig,i,j) \$(ord(l) le p and ord(m) le p and ord(dig) le digmax and ord(i)=(1+p*(ord(l)-1)) and ord(j)=(1+p*(ord(m)-1))),       x(i,j,dig)*ord(dig));``

This is somewhat messy, but we can do this better. You can simplify this by introducing extra sets:

``alias (l,i), (m,j);  set l2(l);     l2(l)\$(ord(l)<=p) = yes;set m2(m);     m2(m)\$(ord(m)<=p) = yes;set dig2(dig); dig2(dig)\$(ord(dig)<=digmax) = yes;set mapl(l,i); mapl(l2(l),i)\$(ord(i)=(1+p*(ord(l)-1))) = yes;set mapm(m,j); mapm(m2(m),j)\$(ord(j)=(1+p*(ord(m)-1))) = yes;display mapl,mapm;...equation obj;obj.. PROFIT =e= sum((mapl(l,i),mapm(m,j),dig2(dig)) , x(i,j,dig)*ord(dig));``

This way you can display the intermediate sets and debug the model more easily. The equation becomes much simpler.

For large, complex models this strategy is very helpful: move complexities from the equations to set operations. Sets can be debugged easily using display or using the gdx viewer. In addition they can be debugged before the complete model is ready to be generated.