IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v36y2019i01ns0217595919500027.html
   My bibliography  Save this article

Semi-Online Hierarchical Scheduling on Two Machines for lp-Norm Load Balancing

Author

Listed:
  • Xianglai Qi

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P. R. China)

  • Jinjiang Yuan

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P. R. China)

Abstract

This paper investigates semi-online hierarchical scheduling problems on two identical machines, with the purpose of minimizing the lp-norm of the machines’ loads. We consider two semi-online versions with knowing the total processing time T of all jobs, or knowing the total processing time Ti of the jobs of hierarchy i for i = 1, 2 in advance. For the two semi-online versions, the best possible online algorithms are designed with competitive ratios of φ∗ and 2p+4p 2(3)p 1 p, respectively, where φ∗ is the maximum value of the function φ(x) = (x+1 2 (1−x))p+(1 2 (1−x))p xp+(1−x)p 1 p in x ∈ [1 2, 1]. When p = ∞, our results cover the known results for minimizing the makespan.

Suggested Citation

  • Xianglai Qi & Jinjiang Yuan, 2019. "Semi-Online Hierarchical Scheduling on Two Machines for lp-Norm Load Balancing," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-16, February.
    • Handle: RePEc:wsi:apjorx:v:36:y:2019:i:01:n:s0217595919500027
    DOI: 10.1142/S0217595919500027
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0217595919500027
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0217595919500027?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. Leung, Joseph Y.-T. & Li, Chung-Lun, 2008. "Scheduling with processing set restrictions: A survey," International Journal of Production Economics, Elsevier, vol. 116(2), pages 251-262, December.
    2. Jinwen Ou & Joseph Y.‐T. Leung & Chung‐Lun Li, 2008. "Scheduling parallel machines with inclusive processing set restrictions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 328-338, June.
    3. Wu, Yong & Ji, Min & Yang, Qifan, 2012. "Optimal semi-online scheduling algorithms on two parallel identical machines under a grade of service provision," International Journal of Production Economics, Elsevier, vol. 135(1), pages 367-371.
    4. Xiao Min & Jing Liu & Yanxia Dong & Ming Jiang, 2015. "Online Preemptive Hierarchical Scheduling on Two Uniform Machines with Rejection," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-15.
    5. Ming Liu & Chengbin Chu & Yinfeng Xu & Feifeng Zheng, 2011. "Semi-online scheduling on 2 machines under a grade of service provision with bounded processing times," Journal of Combinatorial Optimization, Springer, vol. 21(1), pages 138-149, January.
    6. Lee, Kangbok & Hwang, Hark-Chin & Lim, Kyungkuk, 2014. "Semi-online scheduling with GoS eligibility constraints," International Journal of Production Economics, Elsevier, vol. 153(C), pages 204-214.
    7. An Zhang & Yiwei Jiang & Lidan Fan & Jueliang Hu, 2015. "Optimal online algorithms on two hierarchical machines with tightly-grouped processing times," Journal of Combinatorial Optimization, Springer, vol. 29(4), pages 781-795, May.
    8. Kangbok Lee & Joseph Leung & Michael Pinedo, 2013. "Makespan minimization in online scheduling with machine eligibility," Annals of Operations Research, Springer, vol. 204(1), pages 189-222, April.
    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. Islam Akaria & Leah Epstein, 2023. "Bin stretching with migration on two hierarchical machines," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 111-153, August.

    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. Leung, Joseph Y.-T. & Li, Chung-Lun, 2016. "Scheduling with processing set restrictions: A literature update," International Journal of Production Economics, Elsevier, vol. 175(C), pages 1-11.
    2. Xianglai Qi & Jinjiang Yuan, 2017. "Semi-online hierarchical scheduling for $$l_p$$ l p -norm load balancing with buffer or rearrangements," 4OR, Springer, vol. 15(3), pages 265-276, September.
    3. Islam Akaria & Leah Epstein, 2023. "Bin stretching with migration on two hierarchical machines," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 111-153, August.
    4. Islam Akaria & Leah Epstein, 2022. "Online scheduling with migration on two hierarchical machines," Journal of Combinatorial Optimization, Springer, vol. 44(5), pages 3535-3548, December.
    5. Kangbok Lee & Joseph Leung & Michael Pinedo, 2013. "Makespan minimization in online scheduling with machine eligibility," Annals of Operations Research, Springer, vol. 204(1), pages 189-222, April.
    6. Jueliang Hu & Yiwei Jiang & Ping Zhou & An Zhang & Qinghui Zhang, 2017. "Total completion time minimization in online hierarchical scheduling of unit-size jobs," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 866-881, April.
    7. Ferreira, Cristiane & Figueira, Gonçalo & Amorim, Pedro, 2021. "Scheduling Human-Robot Teams in collaborative working cells," International Journal of Production Economics, Elsevier, vol. 235(C).
    8. Chuleeporn Kusoncum & Kanchana Sethanan & Richard F. Hartl & Thitipong Jamrus, 2022. "Modified differential evolution and heuristic algorithms for dump tippler machine allocation in a typical sugar mill in Thailand," Operational Research, Springer, vol. 22(5), pages 5863-5895, November.
    9. Giorgi Tadumadze & Simon Emde & Heiko Diefenbach, 2020. "Exact and heuristic algorithms for scheduling jobs with time windows on unrelated parallel machines," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 461-497, June.
    10. Karhi, Shlomo & Shabtay, Dvir, 2014. "Online scheduling of two job types on a set of multipurpose machines," International Journal of Production Economics, Elsevier, vol. 150(C), pages 155-162.
    11. André Rossi & Alexis Aubry & Mireille Jacomino, 2011. "A sensitivity analysis to assess the completion time deviation for multi-purpose machines facing demand uncertainty," Annals of Operations Research, Springer, vol. 191(1), pages 219-249, November.
    12. Lee, Kangbok & Hwang, Hark-Chin & Lim, Kyungkuk, 2014. "Semi-online scheduling with GoS eligibility constraints," International Journal of Production Economics, Elsevier, vol. 153(C), pages 204-214.
    13. An Zhang & Yiwei Jiang & Lidan Fan & Jueliang Hu, 2015. "Optimal online algorithms on two hierarchical machines with tightly-grouped processing times," Journal of Combinatorial Optimization, Springer, vol. 29(4), pages 781-795, May.
    14. Jinwen Ou & Xueling Zhong & Xiangtong Qi, 2016. "Scheduling parallel machines with inclusive processing set restrictions and job rejection," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(8), pages 667-681, December.
    15. Hans Kellerer & Joseph Y.‐T. Leung & Chung‐Lun Li, 2011. "Multiple subset sum with inclusive assignment set restrictions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(6), pages 546-563, September.
    16. Dominik Kress & Sebastian Meiswinkel & Erwin Pesch, 2018. "Mechanism design for machine scheduling problems: classification and literature overview," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(3), pages 583-611, July.
    17. Juntaek Hong & Kangbok Lee & Michael L. Pinedo, 2020. "Scheduling equal length jobs with eligibility restrictions," Annals of Operations Research, Springer, vol. 285(1), pages 295-314, February.
    18. Huiqiao Su & Michael Pinedo & Guohua Wan, 2017. "Parallel machine scheduling with eligibility constraints: A composite dispatching rule to minimize total weighted tardiness," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(3), pages 249-267, April.
    19. Wu, Yong & Ji, Min & Yang, Qifan, 2012. "Optimal semi-online scheduling algorithms on two parallel identical machines under a grade of service provision," International Journal of Production Economics, Elsevier, vol. 135(1), pages 367-371.
    20. Feifeng Zheng & Yuhong Chen & Ming Liu & Yinfeng Xu, 2022. "Competitive analysis of online machine rental and online parallel machine scheduling problems with workload fence," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1060-1076, September.

    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:36:y:2019:i:01:n:s0217595919500027. 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.