Hierarchical Production Control in a Stochastic N-Machine Flowshop with Long-Run Average Cost

Journal of Mathematical Analysis and Applications, No. 251, pp. 285-309, 2000

31 Pages Posted: 9 Apr 2008 Last revised: 27 Apr 2008

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Hanqin Zhang

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

Qing Zhang

University of Georgia - Department of Mathematics

Abstract

This paper presents an asymptotic analysis of stochastic manufacturing systems consisting of machines in tandem subject to breakdown and repair and facing a constant demand, as the rates of change of the machine states approach infinity. This situation gives rise to a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability. The long-run average cost for the original problem converges to the long-run average cost of the limiting problem.

A method of shrinking and entire lifting is introduced in order to construct the near optimal controls for the original problem by using near optimal controls of the limiting problem. The convergence rate of the long-run average cost for the original problem to that of the limiting problem is established. This helps in providing an error estimate for the constructed open-loop asymptotic optimal control.

Keywords: hierarchical control, manufacturing systems, stochastic dynamic programming, optimal control, long-run average cost

JEL Classification: M11, C61

Suggested Citation

Sethi, Suresh and Zhang, Hanqin and Zhang, Qing, Hierarchical Production Control in a Stochastic N-Machine Flowshop with Long-Run Average Cost. Journal of Mathematical Analysis and Applications, No. 251, pp. 285¿309, 2000. Available at SSRN: https://ssrn.com/abstract=1118317

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

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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