Hierarchical Production Planning in Dynamic Stochastic Manufacturing Systems: Asymptotic Optimality and Error Bounds

Journal of Mathematical Analysis and Applications, Vol. 181, No. 2, pp. 285-319, January 15,1994

Posted: 14 Feb 2008

See all articles by Qing Zhang

Qing Zhang

University of Georgia - Department of Mathematics

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Abstract

This paper presents an asymptotic analysis of hierarchical manufacturing systems with stochastic demand and machines subject to breakdown and repair as the rate of change in machine states approaches infinity. This situation gives rise to a limiting problem in which the stochastic machine availability is replaced by the equilibrium mean availability. The value function for the original problem converges to the value function of the limiting problem. Moreover, a control for the original problem can be constructed from the optimal control of the limiting problem in a way which guarantees its asymptotic optimality. Asymptotic properties of the system trajectories are analyzed for both feedback and open loop controls in the system. The convergence rate of the value function for the original problem is found. This helps in providing an error estimate for the constructed asymptotically optimal control.

Keywords: Hierarchical controls, Production Planning, Asymptotic Optimality, Stochastic Manufacturing Systems, error bounds

JEL Classification: C61, M11

Suggested Citation

Zhang, Qing and Sethi, Suresh, Hierarchical Production Planning in Dynamic Stochastic Manufacturing Systems: Asymptotic Optimality and Error Bounds. Journal of Mathematical Analysis and Applications, Vol. 181, No. 2, pp. 285-319, January 15,1994. Available at SSRN: https://ssrn.com/abstract=1093084

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/

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

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