How to index over specific combinations of set elements

GAMS
1

I am working on a model where I have a good that is transported from a set of producers A to a set of consumers B. However, not all combinations of A and B are feasible and I do not want the relevant equations to index over these combinations. How can I make an equation only index over specific combinations of these sets?

2

Hi @Ian_Hardman ,

You can introduce a two dimensional set that keeps track of the available combinations of A and B.

I attach an example based on the well known trnsport model but instead of allowing all combinations of plants and markets, in this example we define a two dimensional set ij(i,j) of available arcs.

Set
   i 'canning plants'      / seattle,  san-diego /
   j 'markets'             / new-york, chicago, topeka /
   ij(i,j) 'existing arcs' / seattle.new-york
                             seattle.chicago
                             san-diego.chicago
                             san-diego.topeka /

Then we use the two dimensional set ij(i,j) in the equations to make sure only available arcs are considered in the generated model instance.


cost..      z =e= sum(ij(i,j), c(i,j)*x(i,j));

supply(i).. sum(j$ij(i,j), x(i,j)) =l= a(i);

demand(j).. sum(i$ij(i,j), x(i,j)) =g= b(j);

I hope this helps!

Fred

trnsport.gms (2.0 KB)