Hierarchical Production Control in a Stochastic N-Machine Flowshop with Limited Buffers

Journal of Mathematical Analysis and Applications, No. 246, pp. 28-57, 2000

32 Pages Posted: 9 Apr 2008 Last revised: 26 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

This paper is concerned with an asymptotic analysis of hierarchical production planning in a stochastic manufacturing system consisting of machines that are subject to breakdown and repair. The system produces a single product whose rate of demand over time is constant. The problem is formulated as a continuous-time dynamic programming problem in which the objective is to minimize the cost of production, inventories, and backlogs. The size of the buffer between the two adjacent machines is assumed to have lower and upper bound constraints. As the rates of change of the machine states approach infinity, the analysis results in a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability. The value function for the original problem converges to the value function of the limiting problem. A method of shrinking,'', total lifting,'' and modification'' is introduced in order to construct near-optimal controls for the original problem by using near-optimal controls of the limiting problem. The convergence rate of the value function 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: hierarchical control, manufacturing systems, stochastic dynamic programming, optimal control, discounted cost

JEL Classification: M11, C61

Suggested Citation

Sethi, Suresh and Zhang, Hanqin and Zhang, Qing, Hierarchical Production Control in a Stochastic N-Machine Flowshop with Limited Buffers. Available at SSRN: https://ssrn.com/abstract=1118346

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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