The basic definition of the re-entrant line, which constitutes the typical abstraction for the formal modeling and analysis of the fab scheduling problem, considers only the job contest for the finite processing capacity of the system workstations, while ignoring completely the effects and complications arising from additional operational issues like the finite buffering capacity of the system workstation / production units. Moreover, the operational policies developed to control these logical aspects of the system behavior introduce additional constraints to the fab scheduling problem, that complicate it even further and, more importantly, invalidate prior characterizations of its optimal solutions.

Motivated by these remarks, we consider the problem of performance modeling, analysis and control of capacitated, flexibly automated re-entrant lines. Specifically, we develop an analytical framework for the modeling, analysis and control of capacitated re-entrant lines, which is based on Generalized Stochastic Petri nets (GSPN) framework. Furthermore, the underlying scheduling problem is transformed to a Markov Decision Process (MDP) problem and finally, we suggest a systematic, efficient and scalable approximating scheme, which is based on the Neuro-Dynamic Programming (NDP) theory, for the optimal scheduling policy characterized in the GSPN / MDP framework. The quality of the obtained approximations is experimentally assessed by