Optimal Production Planning in a Stochastic N-machine Flowshop with Long-Run Average Cost

Mathematics and Its Applications to Industry, pp. 121-140, 2000

24 Pages Posted: 25 Apr 2008

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 as Markov chains. Since the number of parts in the internal buffers between any two the problem is inherently a state constrained problem. The objective is choose the input rates at the various machines over time in order to meet formulated as a stochastic dynamic programming problem. 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 Control, 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, Optimal Production Planning in a Stochastic N-machine Flowshop with Long-Run Average Cost. Mathematics and Its Applications to Industry, pp. 121-140, 2000 . Available at SSRN: https://ssrn.com/abstract=1124713 or http://dx.doi.org/10.2139/ssrn.1124713

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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