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

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

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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.