IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v35y2018i04ns0217595918500240.html
   My bibliography  Save this article

Online Parallel-Machine Scheduling in KRT Environment to Minimize Total Weighted Completion Time

Author

Listed:
  • Wenjie Li

    (School of Mathematical Sciences, Luoyang Normal University, Luoyang 471934, Henan, P. R. China)

  • Hailing Liu

    (College of Science, Henan Institute of Engineering, Zhengzhou 451191, Henan, P. R. China)

  • Shisheng Li

    (Department of Information and Computation Science, Zhongyuan University of Technology, Zhengzhou, Henan 450007, P. R. China)

Abstract

This paper studies online scheduling on m identical parallel machines under the KRT environment, where jobs arrive over time and “KRT” means that in the online setting no jobs can be released when all of the machines are busy. The goal is to determine a feasible schedule to minimize the total of weighted completion times. When m = 1, we prove that WSPT is an optimal online algorithm. When m ≥ 2, we first present a lower bound m2−2+m4 −4m+4 2m(m−1), and then show that WSPT is a 2-competitive online algorithm for the case m = 2. For the case in which m = 2 and all jobs have equal processing times, we provide a best possible online algorithm with a competitive ratio of 1+3 2.

Suggested Citation

  • Wenjie Li & Hailing Liu & Shisheng Li, 2018. "Online Parallel-Machine Scheduling in KRT Environment to Minimize Total Weighted Completion Time," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(04), pages 1-12, August.
    • Handle: RePEc:wsi:apjorx:v:35:y:2018:i:04:n:s0217595918500240
    DOI: 10.1142/S0217595918500240
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0217595918500240
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0217595918500240?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. Edward J. Anderson & Chris N. Potts, 2004. "Online Scheduling of a Single Machine to Minimize Total Weighted Completion Time," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 686-697, August.
    2. Leslie A. Hall & Andreas S. Schulz & David B. Shmoys & Joel Wein, 1997. "Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 513-544, August.
    3. Ran Ma & Jinjiang Yuan, 2017. "Online scheduling to minimize the total weighted completion time plus the rejection cost," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 483-503, August.
    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. Ma, Ran & Guo, Sainan, 2021. "Applying “Peeling Onion” approach for competitive analysis in online scheduling with rejection," European Journal of Operational Research, Elsevier, vol. 290(1), pages 57-67.
    2. Jin Xu & Natarajan Gautam, 2020. "On competitive analysis for polling systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(6), pages 404-419, September.
    3. Ma, Ran & Tao, Jiping & Yuan, Jinjiang, 2016. "Online scheduling with linear deteriorating jobs to minimize the total weighted completion time," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 570-583.
    4. Xiaoyan Zhang & Ran Ma & Jian Sun & Zan-Bo Zhang, 0. "Randomized selection algorithm for online stochastic unrelated machines scheduling," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-16.
    5. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.
    6. Dengpan Liu & Sumit Sarkar & Chelliah Sriskandarajah, 2010. "Resource Allocation Policies for Personalization in Content Delivery Sites," Information Systems Research, INFORMS, vol. 21(2), pages 227-248, June.
    7. Sitters, R.A., 2009. "Efficient algorithms for average completion time scheduling," Serie Research Memoranda 0058, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    8. Xiaoyan Zhang & Ran Ma & Jian Sun & Zan-Bo Zhang, 2022. "Randomized selection algorithm for online stochastic unrelated machines scheduling," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1796-1811, October.
    9. Ran Ma & Jinjiang Yuan, 2017. "Online scheduling to minimize the total weighted completion time plus the rejection cost," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 483-503, August.
    10. Rolf H. Möhring & Andreas S. Schulz & Frederik Stork & Marc Uetz, 2003. "Solving Project Scheduling Problems by Minimum Cut Computations," Management Science, INFORMS, vol. 49(3), pages 330-350, March.
    11. Martin Skutella & Maxim Sviridenko & Marc Uetz, 2016. "Unrelated Machine Scheduling with Stochastic Processing Times," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 851-864, August.
    12. Ma, Ran & Guo, Sainan & Miao, Cuixia, 2021. "A semi-online algorithm and its competitive analysis for parallel-machine scheduling problem with rejection," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    13. Adam Kasperski & Paweł Zieliński, 2019. "Risk-averse single machine scheduling: complexity and approximation," Journal of Scheduling, Springer, vol. 22(5), pages 567-580, October.
    14. Zhi Pei & Mingzhong Wan & Ziteng Wang, 2020. "A new approximation algorithm for unrelated parallel machine scheduling with release dates," Annals of Operations Research, Springer, vol. 285(1), pages 397-425, February.
    15. Joseph Leung & Haibing Li & Michael Pinedo, 2008. "Scheduling orders on either dedicated or flexible machines in parallel to minimize total weighted completion time," Annals of Operations Research, Springer, vol. 159(1), pages 107-123, March.
    16. Pasquale Avella & Maurizio Boccia & Bernardo D’Auria, 2005. "Near-Optimal Solutions of Large-Scale Single-Machine Scheduling Problems," INFORMS Journal on Computing, INFORMS, vol. 17(2), pages 183-191, May.
    17. Varun Gupta & Benjamin Moseley & Marc Uetz & Qiaomin Xie, 2020. "Greed Works—Online Algorithms for Unrelated Machine Stochastic Scheduling," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 497-516, May.
    18. Robbert Fokkink & Thomas Lidbetter & László A. Végh, 2019. "On Submodular Search and Machine Scheduling," Management Science, INFORMS, vol. 44(4), pages 1431-1449, November.
    19. Dahlbeck, Mirko & Fischer, Anja & Fischer, Frank, 2020. "Decorous combinatorial lower bounds for row layout problems," European Journal of Operational Research, Elsevier, vol. 286(3), pages 929-944.
    20. Natashia Boland & Riley Clement & Hamish Waterer, 2016. "A Bucket Indexed Formulation for Nonpreemptive Single Machine Scheduling Problems," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 14-30, 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:wsi:apjorx:v:35:y:2018:i:04:n:s0217595918500240. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    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.