Asymptotically Optimal Production Policies in Dynamic Stochastic Jobshops with Limited Buffers

Journal of Mathematical Analysis and Applications, Vol. 317, No. 2, pp. 398-428, 2006

31 Pages Posted: 4 Mar 2008 Last revised: 27 Apr 2008

See all articles by Yumei Hou

Yumei Hou

affiliation not provided to SSRN

Hanqin Zhang

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

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Qing Zhang

University of Georgia - Department of Mathematics

Abstract

We consider a production planning problem for a jobshop with unreliable machines producing a number of products. There are upper and lower bounds on intermediate parts and an upper bound on finished parts. The machine capacities are modelled as finite state Markov chains. The objective is to choose the rate of production so as to minimize the total discounted cost of inventory and production. Finding an optimal control policy for this problem is difficult. Instead, we derive an asymptotic approximation by letting the rates of change of the machine states approach infinity. The asymptotic analysis leads to a limiting problem in which the stochastic machine capacities are replaced by their equilibrium mean capacities. The value function for the original problem is shown to converge to the value function of the limiting problem. The convergence rate of the value function together with the error estimate for the constructed asymptotic optimal production policies are established.

Keywords: Optimal production policy, Stochastic manufacturing systems, Stochastic dynamic programming, Discounted cost, Asymptotic analysis

JEL Classification: M11, C61

Suggested Citation

Hou, Yumei and Zhang, Hanqin and Sethi, Suresh and Zhang, Qing, Asymptotically Optimal Production Policies in Dynamic Stochastic Jobshops with Limited Buffers. Journal of Mathematical Analysis and Applications, Vol. 317, No. 2, pp. 398-428, 2006 . Available at SSRN: https://ssrn.com/abstract=1099740

Yumei Hou

affiliation not provided to SSRN

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

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

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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