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

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Stochastic Theory and Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 280))

Abstract

This paper is concerned with the problem of production planning in a stochastic manufacturing system with serial machines that are subject to break-down 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.

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Author information

Authors and Affiliations

  1. Central Economics and Mathematics Institute, The Russian Academy of Sciences, Moscow, Russia

    Ernst Presman

  2. School of Management, The University of Texas at Dallas, Mail Station JO4.7, Box 830688, Richardson, TX, 75083-0688, USA

    Suresh P. Sethi

  3. Institute of Applied Mathematics, Academia Sinica, Beijing, 100080, P. R. China

    Hanqin Zhang

  4. Department of Mathematics, University of Georgia, Athens, GA, 30602, USA

    Qing Zhang

Authors
  1. Ernst Presman
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  2. Suresh P. Sethi
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  3. Hanqin Zhang
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  4. Qing Zhang
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Editor information

Editors and Affiliations

  1. Dep. of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, KS, 66045, USA

    Bozenna Pasik-Duncan

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© 2002 Springer-Verlag Berlin Heidelberg

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Presman, E., Sethi, S.P., Zhang, H., Zhang, Q. (2002). On Optimality of Stochastic N-Machine Flowshop with Long-Run Average Cost. In: Pasik-Duncan, B. (eds) Stochastic Theory and Control. Lecture Notes in Control and Information Sciences, vol 280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48022-6_27

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  • DOI: https://doi.org/10.1007/3-540-48022-6_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43777-2

  • Online ISBN: 978-3-540-48022-8

  • eBook Packages: Springer Book Archive

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