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Online scheduling with linear deteriorating jobs to minimize the total weighted completion time

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  • Ma, Ran
  • Tao, Jiping
  • Yuan, Jinjiang

Abstract

In this paper, we study the online scheduling of linear deteriorating jobs on a single machine to minimize the total weighted completion time. In the problem, a set of n independent linear deteriorating jobs arriving online over time has to be scheduled on a single machine, where the information of each job including its deterioration rate and weight is unknown in advance. Linear deterioration means that the processing time pj of a job Jj is a linear function of its starting time sj. In this paper, we assume that pj=αj(A+Bsj), where A and B are nonnegative with A+B>0 and αj ≥ 0 is the deterioration rate of Jj. The goal is to minimize the total weighted completion time, i.e., ∑wjCj. For this problem, we provide a best possible online algorithm with a competitive ratio of 1+λ(A)+αmaxB, where αmax=max1≤j≤nαj and λ(A)=0 or λ(A)=1 depending on whether A=0 or A > 0.

Suggested Citation

  • Ma, Ran & Tao, Jiping & Yuan, Jinjiang, 2016. "Online scheduling with linear deteriorating jobs to minimize the total weighted completion time," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 570-583.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:570-583
    DOI: 10.1016/j.amc.2015.10.058
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    References listed on IDEAS

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    Cited by:

    1. Ran Ma & Jinjiang Yuan, 2017. "Online scheduling to minimize the total weighted completion time plus the rejection cost," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 483-503, August.
    2. Rubing Chen & Jinjiang Yuan, 2020. "Single-machine scheduling of proportional-linearly deteriorating jobs with positional due indices," 4OR, Springer, vol. 18(2), pages 177-196, June.
    3. 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.
    4. Xing Chai & Wenhua Li & Yuejuan Zhu, 2021. "Online scheduling to minimize maximum weighted flow-time on a bounded parallel-batch machine," Annals of Operations Research, Springer, vol. 298(1), pages 79-93, March.
    5. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.

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