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A relax-and-fix with fix-and-optimize heuristic applied to multi-level lot-sizing problems

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Abstract

In this paper, we propose a simple but efficient heuristic that combines construction and improvement heuristic ideas to solve multi-level lot-sizing problems. A relax-and-fix heuristic is firstly used to build an initial solution, and this is further improved by applying a fix-and-optimize heuristic. We also introduce a novel way to define the mixed-integer subproblems solved by both heuristics. The efficiency of the approach is evaluated solving two different classes of multi-level lot-sizing problems: the multi-level capacitated lot-sizing problem with backlogging and the two-stage glass container production scheduling problem (TGCPSP). We present extensive computational results including four test sets of the Multi-item Lot-Sizing with Backlogging library, and real-world test problems defined for the TGCPSP, where we benchmark against state-of-the-art methods from the recent literature. The computational results show that our combined heuristic approach is very efficient and competitive, outperforming benchmark methods for most of the test problems.

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Acknowledgments

We would like to thank Dr. Tao Wu for providing us the code of LugNP heuristics used in the comparisons. The work conducted by the first three authors was supported by Fundação de Amparo e Pesquisa do Estado de São Paulo (FAPESP) Projects 2010/10133-0, 2011/15534-5 and 2011/15581-3 and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Projects 483474/2013-4 and 312967/2014-4.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, University of São Paulo, Avenida trabalhador são-carlense, 400, Centro, São Carlos, SP, 13566-590, Brazil

    Claudio Fabiano Motta Toledo, Márcio da Silva Arantes & Marcelo Yukio Bressan Hossomi

  2. Department of Mathematics and Computer Science, UNESP, R. Roberto Simonsen, 305, CP 266, Presidente Prudente, SP, 19060-080, Brazil

    Paulo Morelato França

  3. Department of Management Science, University of Strathclyde, 40 George Street, Glasgow, G1 1QE, UK

    Kerem Akartunalı

Authors
  1. Claudio Fabiano Motta Toledo
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  2. Márcio da Silva Arantes
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  3. Marcelo Yukio Bressan Hossomi
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  4. Paulo Morelato França
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  5. Kerem Akartunalı
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Corresponding author

Correspondence to Claudio Fabiano Motta Toledo.

Appendix

Appendix

See Tables 4, 5, 6, and 7.

Table 4 Comparison for SET1 instances (time limit =  100 s)
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Table 5 Comparison for SET2 instances (time limit =  150 s)
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Table 6 Comparison for SET3 instances (time limit =  300 s)
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Table 7 Comparison for SET4 instances (time limit =  300 s)
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Toledo, C.F.M., da Silva Arantes, M., Hossomi, M.Y.B. et al. A relax-and-fix with fix-and-optimize heuristic applied to multi-level lot-sizing problems. J Heuristics 21, 687–717 (2015). https://doi.org/10.1007/s10732-015-9295-0

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  • DOI: https://doi.org/10.1007/s10732-015-9295-0

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