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An Optimal Online Algorithm for Scheduling with Learning Consideration

Author

Listed:
  • Ran Ma

    (School of Management Engineering, Qingdao University of Technology, Qingdao 266525, P. R. China2University Research Center for Smart City, Construction and Management of Shandong, Province, Qingdao 266525, P. R. China)

  • Wenwen Han

    (School of Management Engineering, Qingdao University of Technology, Qingdao 266525, P. R. China2University Research Center for Smart City, Construction and Management of Shandong, Province, Qingdao 266525, P. R. China)

  • Cuixia Miao

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, P. R. China)

  • Juan Zou

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, P. R. China)

Abstract

This paper investigates a classic online scheduling problem with learning effect on a single machine. Specifically, a number of independent jobs that arrive online over time will be processed on a single machine and learning effect implies that the real processing time of job Jj is a non-increasing function of its position h, i.e., pjh = pjαh−1, where pj is the basic processing time of job Jj and 0 < α < 1 is the learning index. Our goal is to minimize the total completion time of all jobs. For the problem, we develop a deterministic polynomial time online algorithm called Delayed Shortest Basic Processing Time (DSBPT) and state that it is an online algorithm with a competitive ratio of 2, which matches the lower bound of the online scheduling problem we focus on.

Suggested Citation

  • Ran Ma & Wenwen Han & Cuixia Miao & Juan Zou, 2021. "An Optimal Online Algorithm for Scheduling with Learning Consideration," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 38(05), pages 1-17, October.
    • Handle: RePEc:wsi:apjorx:v:38:y:2021:i:05:n:s0217595921400029
    DOI: 10.1142/S0217595921400029
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