Hierarchical Production Controls in a Two-Machine Stochastic Flowshop with a Finite Internal Buffer

Proceedings of the 3lst IEEE-CDC, Tucson, AZ, Dec. 16-18, 1992, 2074-2079

Posted: 6 May 2020

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Qing Zhang

Department of Mathematics, University of Georgia

Xun Yu Zhou

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management

Date Written: 1992

Abstract

This paper presents an asymptotic analysis of hierarchical production planning in a manufacturing system with two tandem machines that are subject to breakdown and repair. The buffer between the two machines is assumed finite. Therefore, the number of parts in that buffer needs to be non-negative and bounded above by the buffer size. As the rate of change in machines states approaches infinity, the analysis results in a limiting problem in which the stochastic machine capacity is replaced by the equilibrium mean capacity. The value function for the original problem is proved to converge to the value function of the limiting problem. Moreover, controls for the original problem is constructed from near optimal controls of the limiting problem in a way which guarantees their asymptotic optimality. The convergence rate of the value function for the original problem to that of the limiting problem together with the error estimate for the constructed asymptotically optimal controls are obtained.

Keywords: asymptotic analysis, tandem machines, hierarchical production planning

JEL Classification: C61, M11, M20

Suggested Citation

Sethi, Suresh and Zhang, Qing and Zhou, Xun Yu, Hierarchical Production Controls in a Two-Machine Stochastic Flowshop with a Finite Internal Buffer (1992). Proceedings of the 3lst IEEE-CDC, Tucson, AZ, Dec. 16-18, 1992, 2074-2079, Available at SSRN: https://ssrn.com/abstract=3590797

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

Department of Mathematics, University of Georgia ( email )

Athens, GA 30602-6254
United States

Xun Yu Zhou

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management ( email )

Shatin, New Territories
Hong Kong
852 2609-8320 (Phone)
852 2603-5505 (Fax)

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