Average Cost Optimal Policy for a Stochastic Two-Machine Flowshop with Limited Work-in-Process

NONLINEAR ANALYSIS: THEORY, METHODS & APPLICATIONS, Vol. 47, pp. 5671-5678, 2001

7 Pages Posted: 29 Apr 2008 Last revised: 13 May 2009

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

Arnab Bisi

Purdue University - Krannert School of Management; Johns Hopkins University - Carey Business School

Abstract

We consider a production planning problem in a two-machine flowshop subject to breakdown and repair of machines and subject to nonnegativity and upper bound constraints on work-in-process. The objective is to choose machine production rates over time to minimize the long-run average inventory/backlog and production costs. For sufficiently large upper bound on the work-in-process, the problem is formulated as a stochastic dynamic program. We then establish a verification theorem and a partial characterization of the optimal control policy if it exists.

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

JEL Classification: M11, C61

Suggested Citation

Presman, Ernst and Sethi, Suresh and Zhang, Hanqin and Bisi, Arnab, Average Cost Optimal Policy for a Stochastic Two-Machine Flowshop with Limited Work-in-Process. NONLINEAR ANALYSIS: THEORY, METHODS & APPLICATIONS, Vol. 47, pp. 5671-5678, 2001 . Available at SSRN: https://ssrn.com/abstract=1126434 or http://dx.doi.org/10.2139/ssrn.1126434

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

Arnab Bisi

Purdue University - Krannert School of Management ( email )

1310 Krannert Building
West Lafayette, IN 47907-1310
United States

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

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