ABSTRACT
This chapter presents a hybrid system modelling framework for manufacturing systems with the express goal of control and optimization. The view of a manufacturing process as a hybrid system is a natural based on the observation that such a process typically involves production parts whose physical characteristics undergo changes at various operations described by time-driven dynamics. The basic hybrid model resulting from the abstraction process is termed a stochastic flow model (SFM). The chapter develops an SFM for the manufacturing lot-sizing problem, uses Infinitesimal Perturbation Analysis (IPA) methods to derive gradient estimators of performance metrics of interest with respect to the lot-size parameters and applies them to solve the lot-sizing problem for the original manufacturing system whose SFM is analysed. A large class of problems in managing manufacturing systems involves the control of resources allocated to users, ultimately aiming to optimize various performance metrics.
