Asymptotic Optimality of Hierarchical Controls in Stochastic Manufacturing Systems: A Review

Abstract

Most manufacturing systems are large and complex and operate in an uncertain environment. One approach to managing such systems is that of hierarchical decomposition. This paper reviews the research devoted to proving that a hierarchy based on the frequencies of occurrence of different types of events in the system results in decisions that are asymptotically optimal as the rates of some events become large compared to those of others. Manufacturing systems that are addressed include single machine systems, flowshops, and jobshops producing multiple products, incorporate random production capacity and demands, and involve such decisions as production rates, capacity expansion, and promotional campaigns. The paper concludes with a review of computational results and areas of applications.

Keywords: Production Planning, Hierarchical Controls, Stochastic Manufacturing System, Dynamic Programming, Asymptotic Optimality, Open-Loop Controls, Feedback Controls, Error Bounds, Flowshops, Jobshops, Prpmotion, Capacity Expansion

JEL Classification: C00, C61, M11, M37