A perfect information lower bound for robust lot-sizing problems

A perfect information lower bound for robust lot-sizing problems 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). 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 Journals
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

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).

Journal

Annals of Operations ResearchSpringer Journals

Published: Jun 1, 2018

References

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