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Uncapacitated lot sizing with backlogging: the convex hull


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.

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Correspondence to Simge Küçükyavuz.

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The first author gratefully acknowledges partial financial support by a contract F49620-03-1-0477 from the AFOSR/MURI to the Department of Systems and Industrial Engineering and the Department of Management and Policy at the University of Arizona.

The work of Yves Pochet was partly carried out within the framework of ADONET, a European network in Algorithmic Discrete Optimization, contract no. MRTN-CT-2003-504438, and the text presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister’s Office, Science Policy Programming. The scientific responsibility is assumed by the authors.

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Küçükyavuz, S., Pochet, Y. Uncapacitated lot sizing with backlogging: the convex hull. Math. Program. 118, 151–175 (2009).

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

Mathematics Subject Classification (2000)

  • 90C11
  • 90C57