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The Reversibility Property of Production Lines

Author

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  • 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
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    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. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Wai Kin (Victor) Chan & Lee Schruben, 2008. "Optimization Models of Discrete-Event System Dynamics," Operations Research, INFORMS, vol. 56(5), pages 1218-1237, October.
    16. 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.
    17. 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.
    18. 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.
    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.

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