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Minimizing Total Completion Time of Batch Scheduling with Nonidentical Job Sizes

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Book cover Combinatorial Optimization and Applications (COCOA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10627))

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Abstract

This paper concerns the problem of scheduling jobs with unit processing time and nonidentical sizes on single or parallel identical batch machines. The objective is to minimize the total completion time of all jobs. We show that the worst-case ratio of the algorithm based on the bin-packing algorithm First Fit Increasing (FFI) lies in the interval \([\frac{109}{82}, \frac{2+\sqrt{2}}{2}]\approx [1.3293, 1.7071]\) for the single machine case, and is no more than \(\frac{6+\sqrt{2}}{4}\approx 1.8536\) for the parallel machines case.

Supported by the National Natural Science Foundation of China (11671356, 11271324, 11471286).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Rongqi Li, Zhiyi Tan & Qianyu Zhu

Authors
  1. Rongqi Li
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  2. Zhiyi Tan
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  3. Qianyu Zhu
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Corresponding author

Correspondence to Zhiyi Tan .

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Editors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Xiaofeng Gao

  2. Harbin Institute of Technology, Shenzhen, China

    Hongwei Du

  3. Kennesaw State University, Kennesaw, Georgia, USA

    Meng Han

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Li, R., Tan, Z., Zhu, Q. (2017). Minimizing Total Completion Time of Batch Scheduling with Nonidentical Job Sizes. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10627. Springer, Cham. https://doi.org/10.1007/978-3-319-71150-8_16

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  • DOI: https://doi.org/10.1007/978-3-319-71150-8_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71149-2

  • Online ISBN: 978-3-319-71150-8

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