Dynamic optimization of routing in a Semiconductor Manufacturing Plant

Abstract

We consider a semiconductor manufacturing facility with multiple products and associated routes, single servers and batch servers, job class dependant service times and external arrivals. The system is modelled as an open queueing network. The aim is to optimize routing such that cycle time constrained capacity is maximized and can be checked in reasonable computation time. We use a decomposition approach based on the connected components of a properly defined fab graph. Taking into consideration arrival rate vectors and service time matrices the routing problem for the network is formulated as a Quadratic Programming Problem (QP) involving averages and variances. The strategy for use of the manifold routing options as they typically occur in semiconductor manufacturing is to distribute load in a way such that each connected component, also called closed machine set (CMS), approaches heavy traffic resource pooling behaviour. In the presence of batch servers, mainly in the furnace area of a fab, results for the batch service queue M/D-[r,D- K]/1 with threshold server starting policy are combined with a new result for a batch service system with infinitely many job classes and Round Robin service discipline and applied along with the QP solver.