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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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. 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.
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