Pricing, relaxing and fixing under lot sizing and scheduling

Luis Guimarães*, Diego Klabjan, Bernardo Almada-Lobo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


We present a novel mathematical model and a mathematical programming based approach to deliver superior quality solutions for the single machine capacitated lot sizing and scheduling problem with sequence-dependent setup times and costs. The formulation explores the idea of scheduling products based on the selection of known production sequences. The model is the basis of a matheuristic, which embeds pricing principles within construction and improvement MIP-based heuristics. A partial exploration of distinct neighborhood structures avoids local entrapment and is conducted on a rule-based neighbor selection principle. We compare the performance of this approach to other heuristics proposed in the literature. The computational study carried out on different sets of benchmark instances shows the ability of the matheuristic to cope with several model extensions while maintaining a very effective search. Although the techniques described were developed in the context of the problem studied, the method is applicable to other lot sizing problems or even to problems outside this domain.

Original languageEnglish (US)
Pages (from-to)399-411
Number of pages13
JournalEuropean Journal of Operational Research
Issue number2
StatePublished - Oct 16 2013


  • Lot sizing and scheduling Sequence-dependent setups Non-triangular setups Column generation MIP-based heuristics

ASJC Scopus subject areas

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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