Hierarchical Production Control in a Stochastic Manufacturing System with Long-Run Average Cost

Journal of Mathematical Analysis and Applications, Vol. 214, No. 1, pp. 151-172, 1997

25 Pages Posted: 9 Apr 2008 Last revised: 18 Jan 2009

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 a stochastic manufacturing system consisting of parallel machines 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. Open-loop and feedback controls for the original problem are constructed from optimal controls of the limiting problem in a way that guarantees their asymptotic optimality. 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: Production Planning, Hierarchical Controls, Stochastic Manufacturing System, Long-Run Average Cost, Dynamic Programming, Ergodic Problem, Asymptotic Optimality, Open-Loop Controls, Feedback Controls

JEL Classification: M11, C61

Suggested Citation

Sethi, Suresh and Zhang, Hanqin and Zhang, Qing, Hierarchical Production Control in a Stochastic Manufacturing System with Long-Run Average Cost. Journal of Mathematical Analysis and Applications, Vol. 214, No. 1, pp. 151-172, 1997. Available at SSRN: https://ssrn.com/abstract=1118312 or http://dx.doi.org/10.2139/ssrn.1118312

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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