## Sunday, August 24, 2008

### Minimum downtime

>Is there a chance to increase an index in a loop in gams?
>To illustrate, a(t) variable
> loop(t,
>  if(a(t) eq 0,
>   a(t+1) =0;
>   t=t+2;);
> I want a(t) makes a(t+1) zero but dont want a(t+1) makes a(t+2) zero. Thus,I should skip t+1 step in the loop.

This approach is doomed. Remember for a MIP you need to formulate linear constraints. You need to introduce binary variables to model a construct like this. The following may work:

The general idea is to use binary variables say
x(t) = 0 if a(t) =0,
x(t) = 1 otherwise
(this is fairly simple to do) and then to forbid the x pattern
... 1 0 1 ....
e.g. by a cut of the form x(t) - x(t+1) + x(t+2) ≤ 1;

This type of construct is often used in unit commitment modeling in power planning: you don't want to turn on and off generators all the time. A minimum downtime restriction is often used to prevent this from happening.

You may want to consider hiring a consultant to speed up your modeling efforts. Someone with experience can implement these constructs quickly and reliably, while it can be a long struggle for someone who has never done this before, as you have experienced with your efforts.

Note: I suggested to use binary variables in an earlier email exchange, but based on advise from people on the GAMS-L mailing list the user stayed with the loop construct. Largely because the questions posed were too much focused on narrow loop syntax issues, nobody said: this is wrong, you need to change course. If the user would have provided more background info, he would probably have been steered to more promising and time-tested approaches.

Note 2: Don't use ifthen() to model x. That causes the model to become an MINLP with discontinuous relaxations, which is really bad! This can be done in a linear fashion. Assuming a(t)≥0 we can write:

x(t) ≤ a(t)*M;
x(t) ≥ a(t)/a.up(t);