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Analysis of a Kanban Discipline for Cell Coordination in Production Lines, II: Stochastic Demands

Author

Listed:
  • Debasis Mitra

    (AT&T Bell Laboratories, Murray Hill, New Jersey)

  • Isi Mitrani

    (University of Newcastle, Newcastle-Upon-Tyne, United Kingdom)

Abstract

We describe and analyze a discipline called kanban for the control and coordination of cells in large-scale manufacturing facilities. There are many cells in tandem and also a process of arriving consumers; each consumer queues as long as necessary before departing with a product finished by the last cell. The coordination scheme relies on the circulation of a fixed number of cards (or kanbans) in each cell. This paper differs from our earlier paper in that here the process of consumers modulates the production process. Our results are in three parts. First, the kanban is compared to the classical production discipline and its (sample path) dominance in terms of the consumers' waiting time is proven. Second, we give an analytic scheme for approximating the performance of the stochastic kanban system by examining a single cell in isolation and then combining these through fixed-point equations. Ergodicity is equivalent in our approximation to the existence and uniqueness of a solution to the fixed-point equations and a complete, finite procedure for its resolution is obtained. Third, we report on experiments involving simulations and our method of analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:39:y:1991:i:5:p:807-823
    DOI: 10.1287/opre.39.5.807
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    Citations

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    Cited by:

    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    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. 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.
    12. 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.
    13. 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.

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