Code if then statement by only using $ utility - gams-math

Question

How can I code this 'if' conditions in GAMS?
Set j/1*10/
S/1*6/;
Parameter
b(s,j) export this from excel
U(s,j) export from excel
M(s)/1 100,2 250,3 140,4 120,5 132/ export from excel
;
table b(s,j)
1 2 3 4 5 6 7 8 9 10
1 3 40 23 12 9 52 9 14 89 33
2 0 0 42 0 11 32 11 15 3 7
3 10 20 12 9 5 30 14 5 14 5
4 0 0 0 9 0 3 8 0 13 5
5 0 10 11 32 11 0 3 1 12 1
6 12 20 2 9 15 3 14 5 14 5
;
u(s,j)=0;
u(s,j)$(b(s,j))=1;
Variable delta(j); "binary"
After solving a model I got the value of delta ( suppose delta(1)=1, delta(5)=1). Then Set A is
A(j)$(delta.l(j)=1)=Yes; (A={1,5})
I want to calculate parameter R(s) according to the following :
If there is no j in A(j) s.t. j in u(s,j) then R(s)=M(s)
Else if there is a j in A(j) s.t. j in u(s,j) then R(s)=min{b(s,j): j in A(j) , j in u(s,j) }
Then R(1)=3, R(2)=11,R(3)=5, R(4)=120, R(5)=11,R(6)=12.
Is it possible to code this ' if then ' statement only by $ utility?
Thanks

Answer 1

Following on from the comments, I think this should work for you.
(Create a parameter that mimics your variable delta just for demonstration:)
parameter delta(j);
delta('1') = 1;
delta('5') = 1;
With loop and if/else:
Create parameter R(s). Then, looping over s , pick the minimum of b(s,A) across set A where b(s,A) is defined if the sum of b(s,A) is not zero (i.e. if one of the set is non-zero. Else, set R(s) equal to M(s).
Note, the loop is one solution to the issue you were having with mixed dimensions. And the $(b(s,A)) needs to be on the first argument of smin(.), not on the second argument.
parameter R(s);
loop(s,
if (sum(A, b(s,A)) ne 0,
R(s) = smin(A$b(s,A), b(s,A));
else
R(s) = M(s);
);
);
With $ command only (#Lutz in comments):
R(s)$(sum(A, b(s,A)) <> 0) = smin(A$b(s,A), b(s,A));
R(s)$(sum(A, b(s,A)) = 0) = M(s);
Gives:
---- 56 PARAMETER R
1 3.000, 2 11.000, 3 5.000, 4 120.000, 5 11.000, 6 12.000