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

Abstract

This thesis considers the problem of performance modeling, analysis and control of capacitated 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 (GSPN) framework. The corresponding scheduling problem is systematically formulated, and the structure of the optimal 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 computationally effective method for computing the optimal scheduling policy for any given configuration of capacitated re-entrant line. Specifically, the underlying scheduling problem is transformed to a Markov Decision Process (MDP) problem and an algorithm that systematically generates the MDP formulation for any given fab configuration is developed. The third part of thesis develops an effective approximating scheme based on the Neuro-Dynamic Programming (NDP) theory. In its general definition, the NDP method seeks the approximation of the optimal relative value function of the underlying MDP formulation by a parameterized function. Hence, an approximating structure for the considered problem is proposed and the quality of the generated approximations is systematically assessed. More specifically, this part of the thesis develops a set of "feature" functions and the mathematical apparatus necessary to evaluate the considered approximating scheme through a numerical experiment. The obtained results indicate that good quality approximations can be achieved by considering a set of features that characterize the distribution of the running process instances to the various processing stages and their lower order interactions. The last part of the thesis exploits the performance models developed in its earlier parts in order to provide an analytical characterization of the optimality of various deadlock resolution strategies for Markovian resource allocation systems under the objective of maximizing throughput.