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Approximation Schemes for Scheduling a Batching Machine with Nonidentical Job Size

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Abstract

In this paper we study the problem of scheduling a batching machine with nonidentical job sizes. The jobs arrive simultaneously and have unit processing time. The goal is to minimize the total completion times. Having shown that the problem is NP-hard, we put forward three approximation schemes with worst case ratio 4, 2, and \(\frac{3}{2}\), respectively.

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References

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Authors and Affiliations

  1. Department of Mathematics, Linyi Normal University, Linyi, 276000, China

    Xianzhao Zhang & Zengxia Cai

  2. College of Operations Research and Management, Qufu Normal University, Rizhao, 276826, China

    Yuzhong Zhang

  3. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Zhigang Cao

Authors
  1. Xianzhao Zhang
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  2. Yuzhong Zhang
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  3. Zhigang Cao
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  4. Zengxia Cai
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Corresponding author

Correspondence to Xianzhao Zhang.

Additional information

The research was supported by Natural Science Fundation of Shandong Province under Grant No. Y2005A04.

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Zhang, X., Zhang, Y., Cao, Z. et al. Approximation Schemes for Scheduling a Batching Machine with Nonidentical Job Size. Jrl Syst Sci & Complex 20, 592–600 (2007). https://doi.org/10.1007/s11424-007-9057-7

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  • DOI: https://doi.org/10.1007/s11424-007-9057-7

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