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Online scheduling on an unbounded parallel-batch machine to minimize the weighted makespan

Author

Listed:
  • Han Zhang

    (Zhengzhou University)

  • Lingfa Lu

    (Zhengzhou University)

  • Jinjiang Yuan

    (Zhengzhou University)

Abstract

In this paper we study the online over-time scheduling on an unbounded parallel-batch machine to minimize the weighted makespan. First, we show that the general problem has a low bound 2 and then design a 4-competitive online algorithm. Furthermore, we consider a special case in which the jobs have agreeable processing times and weights. When all jobs have the same weights (the task is to minimize the makespan), an online algorithm with the best possible competitive ratio $$\frac{\sqrt{5}+1}{2}\approx 1.618$$ 5 + 1 2 ≈ 1.618 has been established in the literature. We show that, after a slightly modification, this known online algorithm also has the best possible competitive ratio $$\frac{\sqrt{5}+1}{2}\approx 1.618$$ 5 + 1 2 ≈ 1.618 for our problem. Finally, we introduce limited restarts into the above special case and present an online algorithm with a better competitive ratio $$\frac{11}{7}\approx 1.571$$ 11 7 ≈ 1.571 .

Suggested Citation

  • Han Zhang & Lingfa Lu & Jinjiang Yuan, 2025. "Online scheduling on an unbounded parallel-batch machine to minimize the weighted makespan," Journal of Combinatorial Optimization, Springer, vol. 49(1), pages 1-17, January.
    • Handle: RePEc:spr:jcomop:v:49:y:2025:i:1:d:10.1007_s10878-024-01242-7
    DOI: 10.1007/s10878-024-01242-7
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    References listed on IDEAS

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    1. Xing Chai & Lingfa Lu & Wenhua Li & Liqi Zhang, 2018. "Best-Possible Online Algorithms for Single Machine Scheduling to Minimize the Maximum Weighted Completion Time," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(06), pages 1-11, December.
    2. Oron, Daniel & Shabtay, Dvir & Steiner, George, 2015. "Single machine scheduling with two competing agents and equal job processing times," European Journal of Operational Research, Elsevier, vol. 244(1), pages 86-99.
    3. Wenjie Li, 2015. "A Best Possible Online Algorithm for the Parallel-Machine Scheduling to Minimize the Maximum Weighted Completion Time," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-10.
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    5. Yuan, Jinjiang & Ng, C.T. & Cheng, T.C.E., 2020. "Scheduling with release dates and preemption to minimize multiple max-form objective functions," European Journal of Operational Research, Elsevier, vol. 280(3), pages 860-875.
    6. 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.
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