Originally posted by: AndyHam

Dear IBM,
In semiconductor manufacturing, there is an auxiliary resource called "Reticle", which is transported to across a set of machines and requires a setup time when it is first claimed by a machine. However, the reticle stays at the same machine as long as other machines do not claim it. For instance, there are two machines in a shop. Machine 1 uses reticle 2, reticle 1 and reticle 2 in that order. Note reticle 2 is claimed twice by machine 1. Machine 2 uses reticle 1 only, which indicates reticle 2 stays at machine 1 all the time. In this instance, we don't want to charge a setup penalty for the second-use of reticle 2 on machine 1. What is the best way to model this need?  I am trying to model the auxiliary resource as State. See the figure for clarification. 
Any help will be appreciated!
Regards,

Andy

Originally posted by: PhilippeLaborie

I think that for reticle constraints, you need additional state functions that are related to the reticles, not to the machines. So for a given reticle R, you have a state function PositionR whose state represents the required position (machine) of the reticle. An activity act on a machine M requiring reticle R would post a constraint alwaysEqual(PositionR, act, M). And you have a transition distance between the positions.

If a reticle can be used by only one activity at the same time then instead of a state function, you can better use a sequence variable (the type of the interval variables in the sequence would represent the position/machine) together with a noOverlap constraint with a transition distance between positions.

Originally posted by: AndyHam

I was in right track, but I could not make it work.

Now, I found the solution from your feedback. "a noOverlap constraint with a transition distance between positions.".

The model works perfect!

Big Thanks!

It leads me to one more question. Let me open another thread.