A perfect information lower bound for robust lot-sizing problems

A perfect information lower bound for robust lot-sizing problems 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 michael.poss@lirmm.fr Marcio Costa Santos mcs.marcio@gmail.com Dritan Nace dritan.nace@hds.utc.fr Department of Computer Science, Université Libre http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Operations Research Springer Journals

A perfect information lower bound for robust lot-sizing problems

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Business and Management; Operations Research/Decision Theory; Combinatorics; Theory of Computation
ISSN
0254-5330
eISSN
1572-9338
D.O.I.
10.1007/s10479-018-2908-x
Publisher site
See Article on Publisher Site

Abstract

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 michael.poss@lirmm.fr Marcio Costa Santos mcs.marcio@gmail.com Dritan Nace dritan.nace@hds.utc.fr Department of Computer Science, Université Libre

Journal

Annals of Operations ResearchSpringer Journals

Published: Jun 1, 2018

References

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