IDEAS home Printed from https://ideas.repec.org/a/spr/cejnor/v21y2013i1p125-139.html
   My bibliography  Save this article

Comparing the minimum completion times of two longest-first scheduling-heuristics

Author

Listed:
  • Rico Walter

Abstract

For the basic problem of non-preemptively scheduling n independent jobs on m identical parallel machines so that the minimum (or earliest) machine completion time is maximized, we compare the performance relationship between two well-known longest-first heuristics—the LPT- (longest processing time) and the RLPT-heuristic (restricted LPT). We provide insights into the solution structure of these two sequencing heuristics and prove that the minimum completion time of the LPT-schedule is at least as long as the minimum completion time of the RLPT-schedule. Furthermore, we show that the minimum completion time of the RLPT-heuristic always remains within a factor of 1/m of the optimal minimum completion time. The paper finishes with a comprehensive experimental study of the probabilistic behavior of RLPT-schedules compared to LPT-schedules in the two-machine case. Copyright Springer-Verlag 2013

Suggested Citation

  • Rico Walter, 2013. "Comparing the minimum completion times of two longest-first scheduling-heuristics," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(1), pages 125-139, January.
  • Handle: RePEc:spr:cejnor:v:21:y:2013:i:1:p:125-139
    DOI: 10.1007/s10100-011-0217-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10100-011-0217-4
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10100-011-0217-4?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yong He & Zhiyi Tan, 2002. "Ordinal On-Line Scheduling for Maximizing the Minimum Machine Completion Time," Journal of Combinatorial Optimization, Springer, vol. 6(2), pages 199-206, June.
    2. D. K. Friesen & B. L. Deuermeyer, 1981. "Analysis of Greedy Solutions for a Replacement Part Sequencing Problem," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 74-87, February.
    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. Rico Walter & Martin Wirth & Alexander Lawrinenko, 2017. "Improved approaches to the exact solution of the machine covering problem," Journal of Scheduling, Springer, vol. 20(2), pages 147-164, April.
    2. Alexander Lawrinenko & Stefan Schwerdfeger & Rico Walter, 2018. "Reduction criteria, upper bounds, and a dynamic programming based heuristic for the max–min $$k_i$$ k i -partitioning problem," Journal of Heuristics, Springer, vol. 24(2), pages 173-203, April.

    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. Rico Walter & Martin Wirth & Alexander Lawrinenko, 2017. "Improved approaches to the exact solution of the machine covering problem," Journal of Scheduling, Springer, vol. 20(2), pages 147-164, April.
    2. Leah Epstein, 2023. "Parallel solutions for ordinal scheduling with a small number of machines," Journal of Combinatorial Optimization, Springer, vol. 46(1), pages 1-24, August.
    3. Yong He & Zhiyi Tan, 2002. "Ordinal On-Line Scheduling for Maximizing the Minimum Machine Completion Time," Journal of Combinatorial Optimization, Springer, vol. 6(2), pages 199-206, June.
    4. Leah Epstein & Hanan Zebedat-Haider, 2014. "Online scheduling with rejection and reordering: exact algorithms for unit size jobs," Journal of Combinatorial Optimization, Springer, vol. 28(4), pages 875-892, November.
    5. Yiwei Jiang & Zhiyi Tan & Yong He, 2005. "Preemptive Machine Covering on Parallel Machines," Journal of Combinatorial Optimization, Springer, vol. 10(4), pages 345-363, December.
    6. Bahram Alidaee & Haibo Wang & R. Bryan Kethley & Frank Landram, 2019. "A unified view of parallel machine scheduling with interdependent processing rates," Journal of Scheduling, Springer, vol. 22(5), pages 499-515, October.
    7. Alexander Lawrinenko & Stefan Schwerdfeger & Rico Walter, 2018. "Reduction criteria, upper bounds, and a dynamic programming based heuristic for the max–min $$k_i$$ k i -partitioning problem," Journal of Heuristics, Springer, vol. 24(2), pages 173-203, April.
    8. Leah Epstein & Asaf Levin & Rob van Stee, 2016. "A Unified Approach to Truthful Scheduling on Related Machines," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 332-351, February.

    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:spr:cejnor:v:21:y:2013:i:1:p:125-139. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.