IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v25y1979i2p152-158.html
   My bibliography  Save this article

The Reversibility Property of Production Lines

Author

Listed:
  • Eginhard J. Muth

    (University of Florida)

Abstract

A production line is treated as a series arrangement of k work stations. An unlimited supply of raw production items is available at the first station, and each item passes through all of die stations in sequence. The service time for a single item at station j is assumed to be a random variable with a probability distribution peculiar to that station. In this mode of operation any station will at any time be either busy, or idle, or blocked. A measure of the productivity of such a line is its mean production rate r. It has been conjectured that the production rate remains invariant under reversal of the production line. Line reversal means that every item passes through the stations in the reverse order, that is, beginning with station k and ending with station 1. A general proof of the reversibility property is given. First it is shown that with predetermined service times the total time required to process n dissimilar items through k dissimilar stations does not change when the order of the stations and the order of the items is reversed. Then it is shown for the stochastic case that the order of the items does not affect the production rate.

Suggested Citation

  • Eginhard J. Muth, 1979. "The Reversibility Property of Production Lines," Management Science, INFORMS, vol. 25(2), pages 152-158, February.
    • Handle: RePEc:inm:ormnsc:v:25:y:1979:i:2:p:152-158
    DOI: 10.1287/mnsc.25.2.152
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.25.2.152
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.25.2.152?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
    ---><---

    Citations

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


    Cited by:

    1. O'Connell, Neil & Yor, Marc, 2001. "Brownian analogues of Burke's theorem," Stochastic Processes and their Applications, Elsevier, vol. 96(2), pages 285-304, December.
    2. Kamburowski, Jerzy, 1999. "Stochastically minimizing the makespan in two-machine flow shops without blocking," European Journal of Operational Research, Elsevier, vol. 112(2), pages 304-309, January.
    3. Liu, Liming & Yuan, Xue-Ming, 2001. "Throughput, flow times, and service level in an unreliable assembly system," European Journal of Operational Research, Elsevier, vol. 135(3), pages 602-615, December.
    4. Staley, Dan R. & Kim, David S., 2012. "Experimental results for the allocation of buffers in closed serial production lines," International Journal of Production Economics, Elsevier, vol. 137(2), pages 284-291.
    5. Cathy H. Xia & George J. Shanthikumar & Peter W. Glynn, 2000. "On the Asymptotic Optimality of the SPT Rule for the Flow Shop Average Completion Time Problem," Operations Research, INFORMS, vol. 48(4), pages 615-622, August.
    6. Benavides, Alexander J. & Vera, Antony, 2022. "The reversibility property in a job-insertion tiebreaker for the permutational flow shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 297(2), pages 407-421.
    7. 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.
    8. Yu, Tae-Sun & Pinedo, Michael, 2020. "Flow shops with reentry: Reversibility properties and makespan optimal schedules," European Journal of Operational Research, Elsevier, vol. 282(2), pages 478-490.
    9. Wai Kin (Victor) Chan & Lee Schruben, 2008. "Optimization Models of Discrete-Event System Dynamics," Operations Research, INFORMS, vol. 56(5), pages 1218-1237, October.
    10. Papadopoulos, H. T. & Vidalis, M. I., 2001. "Minimizing WIP inventory in reliable production lines," International Journal of Production Economics, Elsevier, vol. 70(2), pages 185-197, March.
    11. Jeffrey M. Alden & Lawrence D. Burns & Theodore Costy & Richard D. Hutton & Craig A. Jackson & David S. Kim & Kevin A. Kohls & Jonathan H. Owen & Mark A. Turnquist & David J. Vander Veen, 2006. "General Motors Increases Its Production Throughput," Interfaces, INFORMS, vol. 36(1), pages 6-25, February.
    12. Gultekin, Hakan, 2012. "Scheduling in flowshops with flexible operations: Throughput optimization and benefits of flexibility," International Journal of Production Economics, Elsevier, vol. 140(2), pages 900-911.
    13. Nakade, Koichi, 2000. "New bounds for expected cycle times in tandem queues with blocking," European Journal of Operational Research, Elsevier, vol. 125(1), pages 84-92, August.
    14. Hyoungtae Kim & Sungsoo Park, 1999. "Optimality of the Symmetric Workload Allocation in a Single-Server Flow Line System," Management Science, INFORMS, vol. 45(3), pages 449-451, March.
    15. Suresh Chand & Ting Zeng, 2001. "A Comparison of U-Line and Straight-Line Performances Under Stochastic Task Times," Manufacturing & Service Operations Management, INFORMS, vol. 3(2), pages 138-150, January.
    16. Xiuli Chao & Michael Pinedo, 1992. "On reversibility of tandem queues with blocking," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(7), pages 957-974, December.
    17. Steven J. Erlebacher & Medini R. Singh, 1999. "Optimal Variance Structures and Performance Improvement of Synchronous Assembly Lines," Operations Research, INFORMS, vol. 47(4), pages 601-618, August.
    18. Vincent W. Slaugh & Bahar Biller & Sridhar R. Tayur, 2016. "Managing Rentals with Usage-Based Loss," Manufacturing & Service Operations Management, INFORMS, vol. 18(3), pages 429-444, July.
    19. Kamburowski, J., 1997. "The nature of simplicity of Johnson's algorithm," Omega, Elsevier, vol. 25(5), pages 581-584, October.
    20. Xiang Zhong & Hyo Kyung Lee & Molly Williams & Sally Kraft & Jeffery Sleeth & Richard Welnick & Lori Hauschild & Jingshan Li, 2018. "Workload balancing: staffing ratio analysis for primary care redesign," Flexible Services and Manufacturing Journal, Springer, vol. 30(1), pages 6-29, June.

    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:ormnsc:v:25:y:1979:i:2:p:152-158. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.