Optimal and Hierarchical Controls in Dynamic Stochastic Manufacturing Systems: A Survey

Manufacturing & Service Operations Management, Vol. 4, No. 2, pp. 133-170, Spring 2002

ITORMS (Interactive Transactions of OR/MS), Vol. 3, No. 2, 2000

72 Pages Posted: 5 Nov 2008

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Houmin Yan

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management

Hanqin Zhang

Chinese Academy of Sciences (CAS) - Academy of Mathematics and Systems Sciences

Qing Zhang

University of Georgia - Department of Mathematics

Date Written: November 4, 2008

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, 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.

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, C61

Suggested Citation

Sethi, Suresh and Yan, Houmin and Zhang, Hanqin and Zhang, Qing, Optimal and Hierarchical Controls in Dynamic Stochastic Manufacturing Systems: A Survey (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. Available at SSRN: https://ssrn.com/abstract=1295526

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

Houmin Yan

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management ( email )

Shatin, New Territories
Hong Kong

Hanqin Zhang

Chinese Academy of Sciences (CAS) - Academy of Mathematics and Systems Sciences ( email )

Zhong-Guan-Cun-Dong-Lu 55, Haidian District
Beijing, Beijing 100080
China

Qing Zhang

University of Georgia - Department of Mathematics ( email )

Athens, GA 30602
United States
(706) 542-2616 (Phone)
(706) 542-2573 (Fax)

HOME PAGE: http://www.math.uga.edu/~qingz/

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