A generalized stochastic Petri net model for performance analysis and control of capacitated reentrant lines

The basic definition of the reentrant line, which constitutes the typical abstraction for the formal modeling and analysis of the fabrication (fab) scheduling problem, considers only the job contest for the finite processing capacity of the system workstations, ignoring completely the effects and complications arising from additional operational issues like the finite buffering capacity of the system workstations/production units. Yet, as the semiconductor industry moves to more extensively automated operational modes, the explicit characterization and control of these additional operational features is of paramount importance for the robust and stable operation of the entire system. 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, the work presented in the paper develops an analytical framework for the modeling, analysis, and control of capacitated, flexibly automated reentrant lines, based on the class of generalized stochastic Petri nets. The proposed framework allows the seamless integration of the logical/structural and the timed-based aspects of the system behavior, provides an analytical formulation for the underlying scheduling problem, and leads to an interesting qualitative characterization of the structure of the optimal scheduling policy. Hence, it provides the analytical basis for addressing the reentrant line scheduling problem in its contemporary, more complex operational context, and it constitutes the starting point for the development of new scheduling tools and policies for it.