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Single-server parallel-machine scheduling with loading and unloading times

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Abstract

We consider a scheduling problem in which jobs are processed on two identical parallel machines that share a common server that loads and unloads jobs on them. Each job has to be loaded by the server before being processed on one of the machines and unloaded immediately by the server after its processing. The goal is to minimize the makespan. We study non-preemptive variants of the problem where the loading and unloading times are both equal to one time unit. Since the non-preemptive variant of the problem is NP-hard, we apply two classical heuristics, namely list scheduling (LS) and longest processing time (LPT),to tackle the problem. We show that LS and LPT have tight worst-case ratios of 12/7 and 4/3, respectively.

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Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (11001242), Zhejiang Province Natural Science Foundation of China (LY13A010015), and the Humanities and Social Sciences Planning Foundation of the Ministry of Education (13YJA630034).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou , 310018, China

    Yiwei Jiang, Qinghui Zhang, Jueliang Hu & Jianming Dong

  2. School of Computer Science and Information Engineering, Zhejiang Gongshang University, Hangzhou, 310018, China

    Min Ji

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  1. Yiwei Jiang
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  2. Qinghui Zhang
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  3. Jueliang Hu
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  4. Jianming Dong
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  5. Min Ji
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Corresponding author

Correspondence to Yiwei Jiang.

Additional information

A preliminary version of this paper has been published in the Proceedings of COCOA2013, Lecture Notes in Computer Science, 8287, 106–116, 2013.

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Jiang, Y., Zhang, Q., Hu, J. et al. Single-server parallel-machine scheduling with loading and unloading times. J Comb Optim 30, 201–213 (2015). https://doi.org/10.1007/s10878-014-9727-z

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  • DOI: https://doi.org/10.1007/s10878-014-9727-z

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