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Applying Johnson’s Rule in Scheduling Multiple Parallel Two-Stage Flowshops

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Frontiers of Algorithmics (IJTCS-FAW 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13933))

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Abstract

It is well-known that the classical Johnson’s Rule leads to optimal schedules on a two-stage flowshop. However, it is still unclear how Johnson’s Rule would help in scheduling multiple parallel two-stage flowshops with the objective of minimizing the makespan. Thus within the paper, we study the problem and propose a new efficient algorithm that incorporates Johnson’s Rule applied on each individual flowshop with a carefully designed job assignment process to flowshops. The algorithm is successfully shown to have a runtime \(O(n \log n)\) and an approximation ratio 7/3, where n is the number of jobs. Compared with the recent PTAS result for the problem, our algorithm has a larger approximation ratio, but it is more efficient in practice from the perspective of runtime.

This work is supported by the National Natural Science Foundation of China under Grants 62072476; Natural Science Foundation of Hunan Province under Grant 2020JJ4949 and 2021JJ40791; Excellent Youth Project of Scientific Research of Hunan Provincial Education Department under Grant 19B604; the Open Project of Xiangjiang Laboratory (No. 22XJ03005).

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Authors and Affiliations

  1. College of Computer and Information Engineering, Central South University of Forestry and Technology, Changsha, People’s Republic of China

    Guangwei Wu & Fu Zuo

  2. School of Computer Science and Engineering, Central South University, Changsha, People’s Republic of China

    Guangwei Wu, Feng Shi & Jianxin Wang

  3. Xiangjiang Laboratory, Changsha, People’s Republic of China

    Feng Shi

Authors
  1. Guangwei Wu
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  2. Fu Zuo
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  3. Feng Shi
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  4. Jianxin Wang
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Corresponding author

Correspondence to Guangwei Wu .

Editor information

Editors and Affiliations

  1. City University of Hong Kong, Hong Kong SAR, China

    Minming Li

  2. Chinese Academy of Sciences, Beijing, China

    Xiaoming Sun

  3. University of Macau, Macau, China

    Xiaowei Wu

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Wu, G., Zuo, F., Shi, F., Wang, J. (2023). Applying Johnson’s Rule in Scheduling Multiple Parallel Two-Stage Flowshops. In: Li, M., Sun, X., Wu, X. (eds) Frontiers of Algorithmics. IJTCS-FAW 2023. Lecture Notes in Computer Science, vol 13933. Springer, Cham. https://doi.org/10.1007/978-3-031-39344-0_16

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  • DOI: https://doi.org/10.1007/978-3-031-39344-0_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-39343-3

  • Online ISBN: 978-3-031-39344-0

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