IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v45y1999i3p449-451.html
   My bibliography  Save this article

Optimality of the Symmetric Workload Allocation in a Single-Server Flow Line System

Author

Listed:
  • Hyoungtae Kim

    (Machine Tool & FA Division, Daewoo Heavy Industries, 601-3 Namsan-Dong, Changwon, Kyungnam 641-090, Korea)

  • Sungsoo Park

    (Department of Industrial Engineering, Korea Advanced Institute of Science and Technology, 373-1 Gusong-Dong, Yusong-Gu, Taejon 305-701, Korea)

Abstract

This paper provides a proof of the symmetrical allocation property (SAP), conjectured in an earlier work on the workload allocation problem for a manufacturing flow line system. The system consists of N single-Erlang servers in series having a common interstation buffer capacity. SAP says a symmetric workload allocation exists among the optimal solutions. We first show the reciprocal of the throughput is increasing and jointly convex, not component-wisely, in workloads. Then we apply the line reversibility property to obtain an alternative optimal allocation symmetric for any optimal workload allocation that is asymmetric. A sufficient condition for SAP to hold is also given, which relaxes the hypothesizing assumptions on the service-time distribution and interstation buffer capacities.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:3:p:449-451
    DOI: 10.1287/mnsc.45.3.449
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.45.3.449
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.45.3.449?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. Genji Yamazaki & Takeshi Kawashima & Hirotaka Sakasegawa, 1985. "Reversibility of Tandem Blocking Queueing Systems," Management Science, INFORMS, vol. 31(1), pages 78-83, January.
    2. Frederick S. Hillier & Ronald W. Boling, 1979. "On the Optimal Allocation of Work in Symmetrically Unbalanced Production Line Systems with Variable Operation Times," Management Science, INFORMS, vol. 25(8), pages 721-728, August.
    3. Eginhard J. Muth, 1979. "The Reversibility Property of Production Lines," Management Science, INFORMS, vol. 25(2), pages 152-158, February.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. Hillier, Frederick S. & So, Kut C., 1996. "On the robustness of the bowl phenomenon," European Journal of Operational Research, Elsevier, vol. 89(3), pages 496-515, March.
    4. Kirkavak, Nureddin & Dincer, Cemal, 1999. "The general behavior of pull production systems: The allocation problems," European Journal of Operational Research, Elsevier, vol. 119(2), pages 479-494, December.
    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. 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.
    7. Federica Costa & Matthias Thürer & Alberto Portioli-Staudacher, 2023. "Heterogeneous worker multi-functionality and efficiency in dual resource constrained manufacturing lines: an assessment by simulation," Operations Management Research, Springer, vol. 16(3), pages 1476-1489, September.
    8. 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.
    9. Urban, Timothy L. & Chiang, Wen-Chyuan, 2016. "Designing energy-efficient serial production lines: The unpaced synchronous line-balancing problem," European Journal of Operational Research, Elsevier, vol. 248(3), pages 789-801.
    10. Kamburowski, J., 1997. "The nature of simplicity of Johnson's algorithm," Omega, Elsevier, vol. 25(5), pages 581-584, October.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Liming Liu & Xiaoming Liu & David D. Yao, 2004. "Analysis and Optimization of a Multistage Inventory-Queue System," Management Science, INFORMS, vol. 50(3), pages 365-380, March.
    18. Wai Kin (Victor) Chan & Lee Schruben, 2008. "Optimization Models of Discrete-Event System Dynamics," Operations Research, INFORMS, vol. 56(5), pages 1218-1237, October.
    19. Baker, Kenneth R. & Powell, Stephen G., 1995. "A predictive model for the throughput of simple assembly systems," European Journal of Operational Research, Elsevier, vol. 81(2), pages 336-345, March.
    20. 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.

    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:45:y:1999:i:3:p:449-451. 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.