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Competitive analysis of online machine rental and online parallel machine scheduling problems with workload fence

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Abstract

In this paper, we introduce the concept of “workload fence" into online machine rental and machine scheduling problems. With the knowledge of workload fence, online algorithms acquire the information of a finite number of first released jobs in advance. The concept originates from the frozen time fence in the domain of master scheduling in materials management. The total processing time of the jobs foreseen, corresponding to a finite number of jobs, is called workload fence, which is irrelevant to the job sequence. The remaining jobs in the sequence, however, can only become known on their arrival. This work aims to reveal whether the knowledge of workload fence helps to boost the competitive performance of deterministic online algorithms. For the online machine rental problem, we prove that the competitiveness of online algorithms can be improved with a sufficiently large workload fence. We further propose a best online algorithm for the corresponding scenario. For online parallel machine scheduling with workload fence, we give a positive answer to the above question for the case where the workload fence is equal to the length of the longest job. We also show that the competitiveness of online algorithms may not be improved even with a workload fence strictly larger than the largest length of a job. The results help one manager to make a better decision regarding the tradeoff between the performance improvement of online algorithms and the cost caused to acquire the knowledge of workload fence.

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No datasets were generated or analysed during the current study.

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Funding

This paper was supported by the National Natural Science Foundation of China (71771048, 71832001, and 72071144) and the Fundamental Research Funds for the Central Universities (2232018H-07).

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Authors and Affiliations

  1. Glorious Sun School of Business and Management, Donghua University, Shanghai, 200051, China

    Feifeng Zheng & Yuhong Chen

  2. School of Economics and Management, Tongji University, Shanghai, 200092, China

    Ming Liu

  3. School of Management, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, China

    Yinfeng Xu

Authors
  1. Feifeng Zheng
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  2. Yuhong Chen
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  3. Ming Liu
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  4. Yinfeng Xu
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Correspondence to Feifeng Zheng.

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Zheng, F., Chen, Y., Liu, M. et al. Competitive analysis of online machine rental and online parallel machine scheduling problems with workload fence. J Comb Optim 44, 1060–1076 (2022). https://doi.org/10.1007/s10878-022-00882-x

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