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On-Line Single Machine Scheduling of Unit Time Jobs with Rejection: Minimizing the Maximum Quadratic Completion Time

Author

Listed:
  • Liqi Zhang

    (College of Information and Management Science, Henan Agricultural University, Zhengzhou, Henan 450003, P. R. China)

  • Lingfa Lu

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

  • Xueke Sun

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

  • Lili Zuo

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

Abstract

In this paper, we consider the on-line single machine scheduling of unit time jobs with rejection. All jobs arrive on-line over a list (one by one). For each arriving job, the on-line algorithm must decide immediately to accept or reject it. The objective is to minimize the maximum quadratic completion time of accepted jobs plus the total rejection cost of rejected jobs. For this problem, we show that 1.7299 is a lower bound on the competitive ratio and present a simple greedy algorithm with the competitive ratio 2. Furthermore, we also provide a modified greedy algorithm with a better competitive ratio 1 + 3 2 ≈ 1.86602.

Suggested Citation

  • Liqi Zhang & Lingfa Lu & Xueke Sun & Lili Zuo, 2025. "On-Line Single Machine Scheduling of Unit Time Jobs with Rejection: Minimizing the Maximum Quadratic Completion Time," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 42(05), pages 1-10, October.
    • Handle: RePEc:wsi:apjorx:v:42:y:2025:i:05:n:s0217595925500095
    DOI: 10.1142/S0217595925500095
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