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

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Toledo, Claudio Fabiano Motta and Arantes, Márcio da Silva and Hossomi, Marcelo Yukio Bressan and França, Paulo Morelato and Akartunali, Kerem (2015) A relax-and-fix with fix-and-optimize heuristic applied to multi-level lot-sizing problems. Journal of Heuristics, 21 (5). pp. 687-717. ISSN 1572-9397 (https://doi.org/10.1007/s10732-015-9295-0)

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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.

ORCID iDs

Toledo, Claudio Fabiano Motta, Arantes, Márcio da Silva, Hossomi, Marcelo Yukio Bressan, França, Paulo Morelato and Akartunali, Kerem ORCID logoORCID: https://orcid.org/0000-0003-0169-3833;
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