Hierarchical Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost: Asymptotic Optimality and Error Bounds

32 Pages Posted: 25 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

Date Written: January 1998

Abstract

This paper deals with an asymptotic analysis of hierarchical production planning in stochastic manufacturing systems consisting of a single or parallel failure-prone machines producing a number of different products without attrition. The objective is to choose production rates over time in order to minimize the long-run average expected cost of production and surplus. As the rate of machine break-down and repair approaches infinity, the analysis results in a limiting problem in which the stochatic machine capacity is replaced by the equilibrium mean capacity. The optimal value for the original problem is proved to converge to the optimal value of the limiting problem. This suggests a heuristic to construct an open-loop control for the original stochastic problem from the open-loop control of the limiting deterministic problem. We as well as obtain error bound estimates for constructed open-loop controls.

Keywords: Stochastic manufacturing system, hierarchical control, dynamic programming, viscosity solution, convergence rate, error bound, ergodic problem, long-run average cost

JEL Classification: M11, C61

Suggested Citation

Sethi, Suresh and Zhang, Hanqin and Zhang, Qing, Hierarchical Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost: Asymptotic Optimality and Error Bounds (January 1998). Available at SSRN: https://ssrn.com/abstract=1125453 or http://dx.doi.org/10.2139/ssrn.1125453

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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