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Online Algorithms for Scheduling Unit Length Jobs on Unbounded Parallel-Batch Machines with Linearly Lookahead

Author

Listed:
  • Chengwen Jiao

    (College of Science, Zhongyuan University of Technology, Zhengzhou, Henan 450007, P. R. China)

  • Jinjiang Yuan

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P. R. China)

  • Qi Feng

    (College of Science, Zhongyuan University of Technology, Zhengzhou, Henan 450007, P. R. China)

Abstract

In this paper, we propose a new online scheduling model with linear lookahead intervals, which has the character that at any time t, one can foresee the jobs that will coming in the time interval (t,λt + β] in which λ > 1,β > 0. In this new lookahead model, the length of the lookahead intervals are variable as the time going on and the number of jobs increasing, and has the tend of steady growth. In this paper, we consider online scheduling of unit length jobs on m identical parallel-batch machines under this new lookahead model to minimize makespan. The batch capacity is unbounded, that is b = ∞. We present an optimal online algorithm for λ > 1,β ≥ λ−1 λm−1, and provide a best possible online algorithm of competitive ratio 1 + αm for λ > 1, 0 < β < λ−1 λm−1, where αm is the positive root of (1 + αm)m+1λm + (1 + β − λ)∑ i=1m(1 + α m)iλi−1 = 2 + α m.

Suggested Citation

  • Chengwen Jiao & Jinjiang Yuan & Qi Feng, 2019. "Online Algorithms for Scheduling Unit Length Jobs on Unbounded Parallel-Batch Machines with Linearly Lookahead," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(05), pages 1-8, October.
    • Handle: RePEc:wsi:apjorx:v:36:y:2019:i:05:n:s0217595919500246
    DOI: 10.1142/S0217595919500246
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    References listed on IDEAS

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    1. Xiaotie Deng & Chung Keung Poon & Yuzhong Zhang, 2003. "Approximation Algorithms in Batch Processing," Journal of Combinatorial Optimization, Springer, vol. 7(3), pages 247-257, September.
    2. Chung Keung Poon & Wenci Yu, 2005. "On-Line Scheduling Algorithms for a Batch Machine with Finite Capacity," Journal of Combinatorial Optimization, Springer, vol. 9(2), pages 167-186, March.
    3. Gouchuan Zhang & Xiaoqiang Cai & C.K. Wong, 2001. "On‐line algorithms for minimizing makespan on batch processing machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 241-258, April.
    4. Chung Poon & Wenci Yu, 2005. "A Flexible On-line Scheduling Algorithm for Batch Machine with Infinite Capacity," Annals of Operations Research, Springer, vol. 133(1), pages 175-181, January.
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    Cited by:

    1. Feifeng Zheng & Yuhong Chen & Ming Liu & Yinfeng Xu, 2022. "Competitive analysis of online machine rental and online parallel machine scheduling problems with workload fence," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1060-1076, September.
    2. Xia Qian & Zhang Xingong, 2023. "Online scheduling of two-machine flowshop with lookahead and incompatible job families," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-11, January.

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