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

Claudio Fabiano Motta Toledo, Márcio da Silva Arantes, Marcelo Yukio Bressan Hossomi, Paulo Morelato França, Kerem Akartunali

Research output: Contribution to journalArticlepeer-review

53 Citations (Scopus)
414 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)687-717
Number of pages31
JournalJournal of Heuristics
Issue number5
Early online date2 Jul 2015
Publication statusPublished - 31 Oct 2015


  • lot-sizing
  • heuristics
  • relax-and-fix
  • fix-and-optimize
  • backlogging


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