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Optimal online algorithms on two hierarchical machines with tightly-grouped processing times

Author

Listed:
  • An Zhang

    (Hangzhou Dianzi University)

  • Yiwei Jiang

    (Zhejiang Sci-Tech University)

  • Lidan Fan

    (The University of Texas at Dallas)

  • Jueliang Hu

    (Zhejiang Sci-Tech University)

Abstract

This paper considers an online hierarchical scheduling problem on two parallel identical machines. The objective is to minimize the makspan. It is assumed that all jobs have bounded processing times in between $$p$$ p and $$rp$$ rp , where $$p>0$$ p > 0 and $$r\ge 1$$ r ≥ 1 . We first improve a previous result by giving an optimal online algorithm for the non-preemptive version. For the preemptive version, we present an optimal preemptive algorithm without introducing idle time for all $$r\ge 1$$ r ≥ 1 . If the algorithm is allowed to use idle time, we show that the semi-online information that jobs are tightly-grouped cannot help improve the bound of the pure online problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:29:y:2015:i:4:d:10.1007_s10878-013-9627-7
    DOI: 10.1007/s10878-013-9627-7
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    References listed on IDEAS

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    1. Orion Chassid & Leah Epstein, 2008. "The hierarchical model for load balancing on two machines," Journal of Combinatorial Optimization, Springer, vol. 15(4), pages 305-314, May.
    2. 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.
    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. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    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, 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.
    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. 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.
    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.

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