On Optimality of Stochastic N-Machine Flowshop with Long-Run Average Cost

STOCHASTIC THEORY AND CONTROL: LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES, B. Pasik-Duncan, ed., Vol. 280, pp. 399-417, Springer-Verlag, Berlin, 2002

17 Pages Posted: 29 May 2008 Last revised: 30 Mar 2014

See all articles by Ernst Presman

Ernst Presman

Russian Academy of Sciences (RAS)

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 the problem of production planning in a stochastic manufacturing system with serial machines that are subject to breakdown and repair. The machine capacities are modeled by a Markov chain. The objective is to choose the input rates at the various machines over time in order to meet the demand for the system's production at the minimum long-run average cost of production and surplus, while ensuring that the inventories in internal buffers between adjacent machines remain nonnegative. The problem is formulated as a stochastic dynamic program. We prove a verification theorem and derive the optimal feedback control policy in terms of the directional derivatives of the potential function.

Keywords: Production Planning, Optimal Controls, Stochastic Manufacturing System, Long-Run Average Cost, Dynamic Programming, Ergodic Problem, Feedback Controls, flowshop

JEL Classification: M11, C61

Suggested Citation

Presman, Ernst and Sethi, Suresh and Zhang, Hanqin and Zhang, Qing, On Optimality of Stochastic N-Machine Flowshop with Long-Run Average Cost. STOCHASTIC THEORY AND CONTROL: LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES, B. Pasik-Duncan, ed., Vol. 280, pp. 399-417, Springer-Verlag, Berlin, 2002 . Available at SSRN: https://ssrn.com/abstract=1125125

Ernst Presman

Russian Academy of Sciences (RAS) ( email )

Leninsky Ave, 14
Moscow, 119991
Russia

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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