Performance Modeling, Analysis and Control of Capacitated Re-entrant Lines

ACKNOWLEDGEMENTS First, I would like to thank God for blessing me and allowing me such opportunities as to complete my Ph.D. I would express my sincere appreciation to my advisor, Professor Spyros A. Reveliotis for his thoughtful guidance, encouragement and support that he has generously provided throughout my Ph.D. work. Jim Dai and Magnus Egerstedt for their time and valuable comments and suggestions on this work. Much appreciation and love is extended to all of my family and friends. I would like to especially acknowledge my dear parents and parents-in-law, for their continued understanding , encouragement and love throughout all these years. Table 18 Example: The system throughput as a function of the control variables, ω 1 and ω 2 , and its maximal value, for various values of the deadlock recovery rate, Figure 22 Example: Graphing the system (total) throughput as a function of the independent variable ω 1 and for a product-mix requirement T H 1 /T H 2 = 0.9 96 x SUMMARY 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, ignoring completely the effects and complications arising from additional operational issues like the finite buffering capacity of the system workstation / 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, this thesis considers the problem of performance modeling, analysis and control of capacitated, flexibly automated re-entrant lines. Specifically, the first part of the thesis develops an analytical framework for the modeling, analysis, and control of capacitated re-entrant lines, which is based on Generalized Stochastic Petri nets framework. The corresponding scheduling problem is systematically formulated, and the structure of the optimal control policy is characterized and compared to that identified for " traditional " re-entrant lines. The second part of thesis addresses the problem of developing a systematic and com-putationally effective method for computing the optimal scheduling policy …