Uncapacitated lot sizing with backlogging: The convex hull

Simge Kucukyavuz*, Yves Pochet

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)151-175
Number of pages25
JournalMathematical Programming
Issue number1
StatePublished - Apr 2009


  • Backlogging
  • Computation
  • Convex hull
  • Lot sizing
  • Separation algorithms

ASJC Scopus subject areas

  • Software
  • Mathematics(all)


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