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Online Batch Scheduling of Simple Linear Deteriorating Jobs with Incompatible Families

Author

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  • Wenhua Li

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)

  • Libo Wang

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)

  • Xing Chai

    (College of Science, Henan University of Technology, Zhengzhou 450001, China)

  • Hang Yuan

    (Department of Economics, State University of New York at Binghamton, Binghamton, NY 13902, USA)

Abstract

We considered the online scheduling problem of simple linear deteriorating job families on m parallel batch machines to minimize the makespan, where the batch capacity is unbounded. In this paper, simple linear deteriorating jobs mean that the actual processing time p j of job J j is assumed to be a linear function of its starting time s j , i.e., p j = α j s j , where α j > 0 is the deterioration rate. Job families mean that one job must belong to some job family, and jobs of different families cannot be processed in the same batch. When m = 1 , we provide the best possible online algorithm with the competitive ratio of ( 1 + α max ) f , where f is the number of job families and α max is the maximum deterioration rate of all jobs. When m ≥ 1 and m = f , we provide the best possible online algorithm with the competitive ratio of 1 + α max .

Suggested Citation

  • Wenhua Li & Libo Wang & Xing Chai & Hang Yuan, 2020. "Online Batch Scheduling of Simple Linear Deteriorating Jobs with Incompatible Families," Mathematics, MDPI, vol. 8(2), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:170-:d:315117
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    References listed on IDEAS

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