Annals of Operations Research

, Volume 271, Issue 2, pp 887–913 | Cite as

A perfect information lower bound for robust lot-sizing problems

  • Marcio Costa Santos
  • Michael PossEmail author
  • Dritan Nace
Original Research


Robust multi-stage linear optimization is hard computationally and only small problems can be solved exactly. Hence, robust multi-stage linear problems are typically addressed heuristically through decision rules, which provide upper bounds for the optimal solution costs of the problems. We investigate in this paper lower bounds inspired by the perfect information relaxation used in stochastic programming. Specifically, we study the uncapacitated robust lot-sizing problem, showing that different versions of the problem become tractable whenever the non-anticipativity constraints are relaxed. Hence, we can solve the resulting problem efficiently, obtaining a lower bound for the optimal solution cost of the original problem. We compare numerically the solution time and the quality of the new lower bound with the dual affine decision rules that have been proposed by Kuhn et al. (Math Program 130:177–209, 2011).


Multi-stage robust optimization Perfect information Lot-sizing problem Complexity 

Supplementary material


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Authors and Affiliations

  1. 1.Department of Computer ScienceUniversité Libre de BruxellesBrusselsBelgium
  2. 2.INOCSINRIA Lille Nord-EuropeRennesFrance
  3. 3.UMR CNRS 5506 LIRMMUniversité de MontpellierMontpellier Cedex 5France
  4. 4.UMR CNRS 7253 Heudiasyc, Université de Technologie de Compiègne, Centre de Recherches de RoyallieuSorbonne universitésCompiègneFrance

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