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Bin stretching with migration on two hierarchical machines

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. Peter Sanders & Naveen Sivadasan & Martin Skutella, 2009. "Online Scheduling with Bounded Migration," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 481-498, May.
    3. Yiwei Jiang, 2008. "Online scheduling on parallel machines with two GoS levels," Journal of Combinatorial Optimization, Springer, vol. 16(1), pages 28-38, July.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    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. 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.
    11. 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.
    12. 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.
    13. 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.
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