IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v98y2023i1d10.1007_s00186-023-00830-3.html
   My bibliography  Save this article

Bin stretching with migration on two hierarchical machines

Author

Listed:
  • Islam Akaria

    (University of Haifa)

  • Leah Epstein

    (University of Haifa)

Abstract

In this paper, we consider semi-online scheduling with migration on two hierarchical machines, with the purpose of minimizing the makespan. The meaning of two hierarchical machines is that one of the machines can run any job, while the other machine can only run specific jobs. Every instance also has a fixed parameter $$M \ge 0$$ M ≥ 0 , known as the migration factor. Jobs are presented one by one. Each new job has to be assigned to a machine when it arrives, and at the same time it is possible to modify the assignment of previously assigned jobs, such that the moved jobs have a total size not exceeding M times the size of the new job. The semi-online variant studied here is called bin stretching. In this problem, the optimal offline makespan is provided to the scheduler in advance. This is still a non-trivial variant for any migration factor $$M > 0$$ M > 0 . We prove tight bounds on the competitive ratio for any migration factor M. The design and analysis is split into several cases, based on the value of M, and on the resulting competitive ratio. Unlike the online variant with migration for two hierarchical machines, this case allows an online fully polynomial time approximation scheme.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:98:y:2023:i:1:d:10.1007_s00186-023-00830-3
    DOI: 10.1007/s00186-023-00830-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-023-00830-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00186-023-00830-3?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. Yiwei Jiang, 2008. "Online scheduling on parallel machines with two GoS levels," Journal of Combinatorial Optimization, Springer, vol. 16(1), pages 28-38, July.
    2. Martin Böhm & Jiří Sgall & Rob Stee & Pavel Veselý, 2017. "A two-phase algorithm for bin stretching with stretching factor 1.5," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 810-828, October.
    3. Martin Böhm & Jiří Sgall & Rob Stee & Pavel Veselý, 2017. "Erratum to: A two-phase algorithm for bin stretching with stretching factor 1.5," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 829-829, October.
    4. 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.
    5. 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.
    6. Martin Böhm & Jiří Sgall & Rob Stee & Pavel Veselý, 2017. "Online bin stretching with three bins," Journal of Scheduling, Springer, vol. 20(6), pages 601-621, December.
    7. 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.
    8. Michaël Gabay & Nadia Brauner & Vladimir Kotov, 2017. "Improved lower bounds for the online bin stretching problem," 4OR, Springer, vol. 15(2), pages 183-199, June.
    9. Peter Sanders & Naveen Sivadasan & Martin Skutella, 2009. "Online Scheduling with Bounded Migration," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 481-498, May.
    10. 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.
    11. 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.
    12. 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.
    13. Martin Skutella & José Verschae, 2016. "Robust Polynomial-Time Approximation Schemes for Parallel Machine Scheduling with Job Arrivals and Departures," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 991-1021, 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. 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.
    2. 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.
    3. 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.
    4. 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.
    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. 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.
    7. 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.
    8. Leah Epstein, 2018. "A survey on makespan minimization in semi-online environments," Journal of Scheduling, Springer, vol. 21(3), pages 269-284, June.
    9. 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.
    10. György Dósa & Armin Fügenschuh & Zhiyi Tan & Zsolt Tuza & Krzysztof Węsek, 2019. "Tight lower bounds for semi-online scheduling on two uniform machines with known optimum," 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. 27(4), pages 1107-1130, December.
    11. Berndt, Sebastian & Eberle, Franziska & Megow, Nicole, 2022. "Online load balancing with general reassignment cost," LSE Research Online Documents on Economics 114914, London School of Economics and Political Science, LSE Library.
    12. 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.
    13. Letsios, Dimitrios & Mistry, Miten & Misener, Ruth, 2021. "Exact lexicographic scheduling and approximate rescheduling," European Journal of Operational Research, Elsevier, vol. 290(2), pages 469-478.
    14. 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.
    15. Leah Epstein, 2023. "Parallel solutions for preemptive makespan scheduling on two identical machines," Journal of Scheduling, Springer, vol. 26(1), pages 61-76, February.
    16. Nasini, Stefano & Nessah, Rabia, 2022. "A multi-machine scheduling solution for homogeneous processing: Asymptotic approximation and applications," International Journal of Production Economics, Elsevier, vol. 251(C).
    17. Zhiyi Tan & An Zhang, 2010. "A note on hierarchical scheduling on two uniform machines," Journal of Combinatorial Optimization, Springer, vol. 20(1), pages 85-95, July.
    18. Bakker, Hannah & Dunke, Fabian & Nickel, Stefan, 2020. "A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice," Omega, Elsevier, vol. 96(C).
    19. Li-ying Hou & Liying Kang, 2012. "Online scheduling on uniform machines with two hierarchies," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 593-612, November.
    20. Dimitrios Letsios & Jeremy T. Bradley & Suraj G & Ruth Misener & Natasha Page, 2021. "Approximate and robust bounded job start scheduling for Royal Mail delivery offices," Journal of Scheduling, Springer, vol. 24(2), pages 237-258, April.

    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:mathme:v:98:y:2023:i:1:d:10.1007_s00186-023-00830-3. 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.