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Optimal semi-online scheduling algorithms on two parallel identical machines under a grade of service provision

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  • Wu, Yong
  • Ji, Min
  • Yang, Qifan

Abstract

This paper investigates semi-online scheduling problems on two parallel identical machines under a grade of service (GoS) provision. We consider two different semi-online versions where the optimal offline value of the instance is known in advance or the largest processing time of all jobs is known in advance. Respectively for the two semi-online models, two algorithms with competitive ratios of 3/2 and (5+1)/2 are shown to be optimal.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:proeco:v:135:y:2012:i:1:p:367-371
    DOI: 10.1016/j.ijpe.2011.07.021
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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. Yiwei Jiang, 2008. "Online scheduling on parallel machines with two GoS levels," Journal of Combinatorial Optimization, Springer, vol. 16(1), pages 28-38, July.
    3. 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.
    4. Epstein, Leah & Levin, Asaf, 2011. "Scheduling with processing set restrictions: PTAS results for several variants," International Journal of Production Economics, Elsevier, vol. 133(2), pages 586-595, October.
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    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.

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