Optimal and Hierarchical Controls in Dynamic Stochastic Manufacturing Systems: A Survey
University of Texas at Dallas - Naveen Jindal School of Management
Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management
Chinese Academy of Sciences (CAS) - Academy of Mathematics and Systems Sciences
University of Georgia - Department of Mathematics
November 4, 2008
Manufacturing & Service Operations Management, Vol. 4, No. 2, pp. 133-170, Spring 2002
ITORMS (Interactive Transactions of OR/MS), Vol. 3, No. 2, 2000
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, dynamic fowshops, and dynamic 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 are also presented.
Number of Pages in PDF File: 72
Keywords: manufacturing, hierarchical systems, dynamic programming, dynamic jobshops, optimal control, stochastic optimal control, operations and marketing, hierarchical decomposition, asymptotic optimality, averaging principle, multi time scale systems
JEL Classification: M11, M3, C61Accepted Paper Series
Date posted: November 5, 2008
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