Hierarchical Production Control in Dynamic Stochastic Jobshops with Long-Run Average Cost

Journal of Optimization Theory and Applications, Vol. 106, No. 2, pp. 231-264, August 2000

35 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

We consider a production planning problem for a dynamic jobshop producing a number of products and subject to breakdown and repair of machines. The machine capacities are assumed to be finite state Markov chains. As the rates of change of the machine states approach infinity, an asymptotic analysis of this stochastic manufacturing systems is given. The analysis results in 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 is shown to converge to the long-run average cost of the limiting problem. The convergence rate of the long-run average cost for the original problem to that of the limiting problem together with an error estimate for the constructed asymptotic optimal control is established.

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 Dynamic Stochastic Jobshops with Long-Run Average Cost. Available at SSRN: https://ssrn.com/abstract=1118321

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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