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Online early work scheduling on parallel machines

Author

Listed:
  • Jiang, Yiwei
  • Wu, Mengjing
  • Chen, Xin
  • Dong, Jianming
  • Cheng, T.C.E.
  • Blazewicz, Jacek
  • Ji, Min

Abstract

We consider non-preemptive online parallel-machine scheduling with a common due date to maximize the total early work of all the jobs, i.e., the total processing time of the jobs (or parts) completed before the common due date. For the general case of m machines, we provide a parameter lower bound with respect to m. For the online algorithm, we first show that the tight competitive ratio of the classical list scheduling (LS) algorithm is 43. We then improve the upper bound on the competitive ratio for the previous algorithm, EFFm, to 1.2956. Additionally, we present a formula to compute the upper bound on the competitive ratio for any given m. For the case of three machines, we improve the lower bound to 1.1878 and propose an improved online algorithm with a tight competitive ratio of 1.2483.

Suggested Citation

  • Jiang, Yiwei & Wu, Mengjing & Chen, Xin & Dong, Jianming & Cheng, T.C.E. & Blazewicz, Jacek & Ji, Min, 2024. "Online early work scheduling on parallel machines," European Journal of Operational Research, Elsevier, vol. 315(3), pages 855-862.
    • Handle: RePEc:eee:ejores:v:315:y:2024:i:3:p:855-862
    DOI: 10.1016/j.ejor.2024.01.009
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    References listed on IDEAS

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    1. Chen, Xin & Liang, Yage & Sterna, Małgorzata & Wang, Wen & Błażewicz, Jacek, 2020. "Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date," European Journal of Operational Research, Elsevier, vol. 284(1), pages 67-74.
    2. Justkowiak, Jan-Erik & Kovalev, Sergey & Kovalyov, Mikhail Y. & Pesch, Erwin, 2023. "Single machine scheduling with assignable due dates to minimize maximum and total late work," European Journal of Operational Research, Elsevier, vol. 308(1), pages 76-83.
    3. Lee, Kangbok & Zheng, Feifeng & Pinedo, Michael L., 2019. "Online scheduling of ordered flow shops," European Journal of Operational Research, Elsevier, vol. 272(1), pages 50-60.
    4. Malgorzata Sterna & Kateryna Czerniachowska, 2017. "Polynomial Time Approximation Scheme for Two Parallel Machines Scheduling with a Common Due Date to Maximize Early Work," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 927-944, September.
    5. Leah Epstein, 2023. "Parallel solutions for preemptive makespan scheduling on two identical machines," Journal of Scheduling, Springer, vol. 26(1), pages 61-76, February.
    6. Xin Chen & Malgorzata Sterna & Xin Han & Jacek Blazewicz, 2016. "Scheduling on parallel identical machines with late work criterion: Offline and online cases," Journal of Scheduling, Springer, vol. 19(6), pages 729-736, December.
    7. Mosheiov, Gur & Oron, Daniel & Shabtay, Dvir, 2021. "Minimizing total late work on a single machine with generalized due-dates," European Journal of Operational Research, Elsevier, vol. 293(3), pages 837-846.
    8. C. N. Potts & L. N. Van Wassenhove, 1992. "Single Machine Scheduling to Minimize Total Late Work," Operations Research, INFORMS, vol. 40(3), pages 586-595, June.
    9. Györgyi, Péter & Kis, Tamás, 2020. "A common approximation framework for early work, late work, and resource leveling problems," European Journal of Operational Research, Elsevier, vol. 286(1), pages 129-137.
    10. Ma, Ran & Guo, Sainan, 2021. "Applying “Peeling Onion” approach for competitive analysis in online scheduling with rejection," European Journal of Operational Research, Elsevier, vol. 290(1), pages 57-67.
    11. Lin, Ran & Wang, Jun-Qiang & Liu, Zhixin & Xu, Jun, 2023. "Best possible algorithms for online scheduling on identical batch machines with periodic pulse interruptions," European Journal of Operational Research, Elsevier, vol. 309(1), pages 53-64.
    12. Yinfeng Xu & Rongteng Zhi & Feifeng Zheng & Ming Liu, 2022. "Competitive algorithm for scheduling of sharing machines with rental discount," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 414-434, August.
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