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On the exact solution of a large class of parallel machine scheduling problems

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Abstract

This work deals with a very generic class of scheduling problems with identical/uniform/unrelated parallel machine environment. It considers well-known attributes such as release dates, deadlines, or sequence-dependent setup times and accepts any objective function defined over job completion times. Non-regular objectives are also supported. We introduce a branch-cut-and-price algorithm for such problems that makes use of non-robust cuts, i.e., cuts which change the structure of the pricing problem. This is the first time that such cuts are employed for machine scheduling problems. The algorithm also embeds other important techniques such as strong branching, reduced cost fixing and dual stabilization. Computational experiments over literature benchmarks showed that the proposed algorithm is indeed effective and could solve many instances to optimality for the first time.

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Acknowledgements

We would like to thank Dr. Artur Pessoa and Dr. Rafael Martinelli for the valuable comments and suggestions. This research was partially funded by Programa Institucional de Internacionalização CAPES PrInt UFF No. 88881. AS received Grants CNPq 305223/2015-1 and 428549/2016-0. EU received grants CNPq 313601/2018-6 and Faperj E-26/202.887/2017. Experiments presented in this paper were carried out using the PlaFRIM (Federative Platform for Research in Computer Science and Mathematics), created under the Inria PlaFRIM development action with support from Bordeaux INP, LABRI and IMB and other entities: Conseil Régional d’Aquitaine, Université de Bordeaux, CNRS and ANR in accordance with the “Programme d’Investissements d’Avenir” (see www.plafrim.fr/en/home).

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Authors and Affiliations

  1. Departamento de Computação Científica, Centro de Informática, Universidade Federal da Paraíba, Rua dos Escoteiros, s/n, Mangabeira, João Pessoa, PB, 58058-600, Brazil

    Teobaldo Bulhões

  2. Inria Bordeaux Sud-Ouest, 200 Avenue de la Veille Tour, Talence, France

    Ruslan Sadykov

  3. Institute of Mathematics (CNRS UMR 5251), University of Bordeaux, Talence, France

    Ruslan Sadykov

  4. Departamento de Sistemas de Computação, Centro de Informática, Universidade Federal da Paraíba, Rua dos Escoteiros, s/n, Mangabeira, João Pessoa, PB, 58058-600, Brazil

    Anand Subramanian

  5. Departamento de Engenharia de Produção, Universidade Federal Fluminense, Rua Passo da Pátria 156, São Domingos, Niterói, RJ, 24210-240, Brazil

    Eduardo Uchoa

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  1. Teobaldo Bulhões
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  2. Ruslan Sadykov
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  4. Eduardo Uchoa
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Correspondence to Anand Subramanian.

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Bulhões, T., Sadykov, R., Subramanian, A. et al. On the exact solution of a large class of parallel machine scheduling problems. J Sched 23, 411–429 (2020). https://doi.org/10.1007/s10951-020-00640-z

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