Optimal and Hierarchical Controls in Dynamic Stochastic Manufacturing Systems: A Review
S. P. Sethi, H. Yan, H. Zhang, and Q. Zhang
School of Management, The University of Texas at Dallas
Richardson, TX 75083-0688, USA
sethi@utdallas.edu
Department of Systems Engineering
and Engineering Management
Chinese University of Hong Kong
Shatin, Hong Kong
yan@se.cuhk.edu.hk
Institute of Applied Mathematics
Academia Sinica, Beijing, 100080, China
hqzhang@amath3.amt.ac.cn
and
Department of Mathematics
University of Georgia, Athens, GA 30602, USA
qingz@math.uga.edu

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 systems results in decisions that are asymptotically optimal as the rates of some events become large compared to those of others. The paper also reviews the research on stochastic optimal control problems associated with manufacturing systems, their dynamic programming equations, existence of solutions of these equations, and verification theorems of optimality for the systems. Manufacturing systems that are addressed include single machine systems, flowshops, and jobshops producing multiple products. These systems may also incorporate random production capacity and demands, and decisions such as production rates, capacity expansion, and promotional campaigns. The paper concludes with a review of computational results and areas of applications.