Ann Oper Res https://doi.org/10.1007/s10479-018-2908-x ORIGINAL RESEARCH A perfect information lower bound for robust lot-sizing problems 1,2 3 Marcio Costa Santos · Michael Poss · Dritan Nace © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract 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 opti- mal 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). Keywords Multi-stage robust optimization · Perfect information · Lot-sizing problem · Complexity B Michael Poss firstname.lastname@example.org Marcio Costa Santos email@example.com Dritan Nace firstname.lastname@example.org Department of Computer Science, Université Libre
Annals of Operations Research – Springer Journals
Published: Jun 1, 2018
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