IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v47y1999i4p535-549.html
   My bibliography  Save this article

Approximating an Optimal Production Policy in a Continuous Flow Line: Recurrence and Asymptotic Properties

Author

Listed:
  • Houmin Yan

    (Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong)

  • Xun Yu Zhou

    (Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong)

  • G. Yin

    (Department of Mathematics, Wayne State University, Detroit, Michigan 48202)

Abstract

This work is concerned with manufacturing systems with two failure-prone tandem machines. The production is regulated by a continuous version of buffer control. Our goal is to obtain an optimal buffer-control policy to minimize a long-run average cost function. Concentrating on threshold type of control policies, our effort is devoted to parameter optimization problems for the continuous material produce-to-stock models. We estimate the gradients of the cost function with respect to the parameter using perturbation analysis techniques, and approximate the optimal value of the parameter via a constant step-size stochastic approximation algorithm. An analysis for error accumulation in perturbation propagation is undertaken, and a sufficient condition for breaking the propagation chain is derived. In addition, we show that the event of breaking the perturbation propagation chain is recurrent if the system has sufficient capacity, derive the consistency of the gradient estimators, and establish the convergence of the iterative algorithm. We also treat non-Markovian models with the machine repair time following an Erlang distribution, and provide numerical examples to illustrate the proposed algorithm.

Suggested Citation

  • Houmin Yan & Xun Yu Zhou & G. Yin, 1999. "Approximating an Optimal Production Policy in a Continuous Flow Line: Recurrence and Asymptotic Properties," Operations Research, INFORMS, vol. 47(4), pages 535-549, August.
  • Handle: RePEc:inm:oropre:v:47:y:1999:i:4:p:535-549
    DOI: 10.1287/opre.47.4.535
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.47.4.535
    Download Restriction: no

    File URL: https://libkey.io/10.1287/opre.47.4.535?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Chand Samaratunga & Suresh P. Sethi & Xun Yu Zhou, 1997. "Computational Evaluation of Hierarchical Production Control Policies for Stochastic Manufacturing Systems," Operations Research, INFORMS, vol. 45(2), pages 258-274, April.
    2. Michael Caramanis & George Liberopoulos, 1992. "Perturbation Analysis for the Design of Flexible Manufacturing System Flow Controllers," Operations Research, INFORMS, vol. 40(6), pages 1107-1125, December.
    3. T. Bielecki & P. R. Kumar, 1988. "Optimality of Zero-Inventory Policies for Unreliable Manufacturing Systems," Operations Research, INFORMS, vol. 36(4), pages 532-541, August.
    4. Gabriel R. Bitran & Li Chang, 1987. "A Mathematical Programming Approach to a Deterministic Kanban System," Management Science, INFORMS, vol. 33(4), pages 427-441, April.
    5. Debasis Mitra & Isi Mitrani, 1990. "Analysis of a Kanban Discipline for Cell Coordination in Production Lines. I," Management Science, INFORMS, vol. 36(12), pages 1548-1566, December.
    6. Jean-Luc Deleersnyder & Thom J. Hodgson & Henri Muller-Malek & Peter J. O'Grady, 1989. "Kanban Controlled Pull Systems: An Analytic Approach," Management Science, INFORMS, vol. 35(9), pages 1079-1091, September.
    7. Debasis Mitra & Isi Mitrani, 1991. "Analysis of a Kanban Discipline for Cell Coordination in Production Lines, II: Stochastic Demands," Operations Research, INFORMS, vol. 39(5), pages 807-823, October.
    8. Lou, S. & Sethi, S. P. & Zhang, Q., 1994. "Optimal feedback production planning in a stochastic two-machine flowshop," European Journal of Operational Research, Elsevier, vol. 73(2), pages 331-345, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. G. Yin & Q. Zhang & H. M. Yan & E. K. Boukas, 2001. "Random-Direction Optimization Algorithms with Applications to Threshold Controls," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 211-233, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kim, Ilhyung & Tang, Christopher S., 1997. "Lead time and response time in a pull production control system," European Journal of Operational Research, Elsevier, vol. 101(3), pages 474-485, September.
    2. Ou, Jihong & Jiang, Jiong, 1997. "Yield comparison of push and pull control methods on production systems with unreliable machines," International Journal of Production Economics, Elsevier, vol. 50(1), pages 1-12, May.
    3. Zhao Xiaobo & Qiguo Gong & Kenichi Nakashima, 2001. "Analysis of a production system in a general configuration," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(2), pages 128-143, March.
    4. Iwase, Masaharu & Ohno, Katsuhisa, 2011. "The performance evaluation of a multi-stage JIT production system with stochastic demand and production capacities," European Journal of Operational Research, Elsevier, vol. 214(2), pages 216-222, October.
    5. Mascolo, Maria Di, 1996. "Analysis of a synchronization station for the performance evaluation of a kanban system with a general arrival process of demands," European Journal of Operational Research, Elsevier, vol. 89(1), pages 147-163, February.
    6. Kojima, Mitsutoshi & Nakashima, Kenichi & Ohno, Katsuhisa, 2008. "Performance evaluation of SCM in JIT environment," International Journal of Production Economics, Elsevier, vol. 115(2), pages 439-443, October.
    7. S. P. Sethi & H. Yan & H. Zhang & Q. Zhang, 2002. "Optimal and Hierarchical Controls in Dynamic Stochastic Manufacturing Systems: A Survey," Manufacturing & Service Operations Management, INFORMS, vol. 4(2), pages 133-170.
    8. Zipkin, Paul, 1995. "Processing networks with planned inventories: Tandem queues with feedback," European Journal of Operational Research, Elsevier, vol. 80(2), pages 344-349, January.
    9. Cigdem Gurgur, 2013. "Optimal configuration of a decentralized, market-driven production/inventory system," Annals of Operations Research, Springer, vol. 209(1), pages 139-157, October.
    10. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    11. Askin, Ronald G. & Krishnan, Shravan, 2009. "Defining inventory control points in multiproduct stochastic pull systems," International Journal of Production Economics, Elsevier, vol. 120(2), pages 418-429, August.
    12. Herer, Yale T. & Shalom, Levi, 2000. "The Kanban assignment problem - A non-integral approach," European Journal of Operational Research, Elsevier, vol. 120(2), pages 260-276, January.
    13. Eugene Khmelnitsky & Ernst Presman & Suresh Sethi, 2011. "Optimal production control of a failure-prone machine," Annals of Operations Research, Springer, vol. 182(1), pages 67-86, January.
    14. Mark Vroblefski & R. Ramesh & Stanley Zionts, 2000. "General Open and Closed Queueing Networks with Blocking: A Unified Framework for Approximation," INFORMS Journal on Computing, INFORMS, vol. 12(4), pages 299-316, November.
    15. Mourani, Iyad & Hennequin, Sophie & Xie, Xiaolan, 2008. "Simulation-based optimization of a single-stage failure-prone manufacturing system with transportation delay," International Journal of Production Economics, Elsevier, vol. 112(1), pages 26-36, March.
    16. Cigdem Z. Gurgur & Tayfur Altiok, 2007. "Analysis of decentralized multi‐product pull systems with lost sales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 357-370, June.
    17. Albino, Vito & Dassisti, Michele & O. Okogbaa, Geoffrey, 1995. "Approximation approach for the performance analysis of production lines under a kanban discipline," International Journal of Production Economics, Elsevier, vol. 40(2-3), pages 197-207, August.
    18. Venky Nagar & Madhav V. Rajan & Richard Saouma, 2009. "The Incentive Value of Inventory and Cross‐training in Modern Manufacturing," Journal of Accounting Research, Wiley Blackwell, vol. 47(4), pages 991-1025, September.
    19. Andijani, A. A., 1998. "A multi-criterion approach for Kanban allocations," Omega, Elsevier, vol. 26(4), pages 483-493, August.
    20. S. P. Sethi & H. Zhang & Q. Zhang, 2000. "Hierarchical Production Control in Dynamic Stochastic Jobshops with Long-Run Average Cost," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 231-264, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:47:y:1999:i:4:p:535-549. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.