Can you help me to write the following set of constraints?

GAMS
1

Hello everyone :smiley:
I hope you can help me out with the following case.

I’m trying to write the set of equations (20) and (21) as shown in the attached file, but I’m having a hard time understanding how to write them given the conditions “when(x(i,j,m)=0 and x(i,j,m)=1)”.

So far, I wrote 20 as:

r20(m)…sum((i,j),t(i,j)*x(i,j,m))+sum((i,N(j)), h(j)*x(i,j,m))+sum((i,F(j)),((Cm-y(i,j,m))/r)) =l=Hs;

and 21 as two equations:

r21a(F,m)…(Cm-y(i,F,m))/r =g=0; :arrow_right: Here set i is not controlled.

r21b(F,m)…(Cm-y(i,j,m))/r =l=H*sum(i,x(i,j,m)); :arrow_right: Here It is controlled in the sum but not for the y(i,j,m) variable.

The model is from this article:
https://ac.els-cdn.com/S2352146516000089/1-s2.0-S2352146516000089-main.pdf?_tid=60bf7f42-ae1b-42a2-b16b-9a08fdbac586&acdnat=1543109774_132d486a9be301e65541f677a490775b


I appreciate your help.
Sin título.png

2

Hi
You just make one constraint and multiply the number 20-part on both sides by(x(i,jm,) and the 21-part by (1 - x(i,j,m)) .
If x(i,j,m) = 1, only the 20-parts are used, if x(i,jm) = 0, only the 21-parts will be used.
CHeers
Renger

3

Hi Renger,
Could you help me to write it down?
By multiplying 20 by x(i,j,m) on both sides, doesn’t the equation becomes non-linear?