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Min-Max Relative Regret for Scheduling to Minimize Maximum Lateness

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Combinatorial Algorithms (IWOCA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13889))

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Abstract

We study the single machine scheduling problem under uncertain parameters, with the aim of minimizing the maximum lateness. More precisely, the processing times, the release dates and the delivery times of the jobs are uncertain, but an upper and a lower bound of these parameters are known in advance. Our objective is to find a robust solution, which minimizes the maximum relative regret. In other words, we search for a solution which, among all possible realizations of the parameters, minimizes the worst-case ratio of the deviation between its objective and the objective of an optimal solution over the latter one. Two variants of this problem are considered. In the first variant, the release date of each job is equal to 0. In the second one, all jobs are of unit processing time. In all cases, we are interested in the sub-problem of maximizing the (relative) regret of a given scheduling sequence. The studied problems are shown to be polynomially solvable.

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Acknowledgement

This research has been partially supported by the ANR Lorraine Artificial Intelligence project (ANR-LOR-AI).

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Authors and Affiliations

  1. LCOMS, University of Lorraine, Metz, France

    Imad Assayakh, Imed Kacem & Giorgio Lucarelli

Authors
  1. Imad Assayakh
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  2. Imed Kacem
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  3. Giorgio Lucarelli
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Correspondence to Imad Assayakh .

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Editors and Affiliations

  1. National Cheng Kung University, Tainan, Taiwan

    Sun-Yuan Hsieh

  2. National Taipei University of Business, Taoyuan, Taiwan

    Ling-Ju Hung

  3. National Taitung University, Taitung, Taiwan

    Chia-Wei Lee

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Assayakh, I., Kacem, I., Lucarelli, G. (2023). Min-Max Relative Regret for Scheduling to Minimize Maximum Lateness. In: Hsieh, SY., Hung, LJ., Lee, CW. (eds) Combinatorial Algorithms. IWOCA 2023. Lecture Notes in Computer Science, vol 13889. Springer, Cham. https://doi.org/10.1007/978-3-031-34347-6_5

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  • DOI: https://doi.org/10.1007/978-3-031-34347-6_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-34346-9

  • Online ISBN: 978-3-031-34347-6

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