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Uncapacitated lot sizing with backlogging: The convex hull

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  • KÛCÛKYAVUZ, Simge
  • POCHET, Yves

    (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

Abstract

An explicit description of the convex hull of solutions to the uncapacitated lot sizing problem with backlogging, in its natural space of production, setup, inventory and backlogging variables, has been an open question for many years. In this paper, we identify valid inequalities that subsume all previously known valid inequalities for this problem. We show that these inequalities are enough to describe the convex hull of solutions. We give polynomial separation algorithms for some special cases. Finally, we report a summary of computational experiments with our inequalities that illustrates their effectiveness.

Suggested Citation

  • KÛCÛKYAVUZ, Simge & POCHET, Yves, 2007. "Uncapacitated lot sizing with backlogging: The convex hull," LIDAM Discussion Papers CORE 2007006, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2007006
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2007.html
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    Cited by:

    1. Zhili Zhou & Yongpei Guan, 2013. "Two-stage stochastic lot-sizing problem under cost uncertainty," Annals of Operations Research, Springer, vol. 209(1), pages 207-230, October.
    2. Nadjib Brahimi & Tarik Aouam, 2016. "Multi-item production routing problem with backordering: a MILP approach," International Journal of Production Research, Taylor & Francis Journals, vol. 54(4), pages 1076-1093, February.

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