Lexicographic α-robustness: an application to the 1-median problem

R. Kalaï; M. A. Aloulou; Ph. Vallin; D. Vanderpooten

RAIRO - Operations Research (2010)

  • Volume: 44, Issue: 2, page 119-138
  • ISSN: 0399-0559

Abstract

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In the last decade, several robustness approaches have been developed to deal with uncertainty. In decision problems, and particularly in location problems, the most used robustness approach rely either on maximal cost or on maximal regret criteria. However, it is well known that these criteria are too conservative. In this paper, we present a new robustness approach, called lexicographic α-robustness, which compensates for the drawbacks of criteria based on the worst case. We apply this approach to the 1-median location problem under uncertainty on node weights and we give a specific algorithm to determine robust solutions in the case of a tree. We also show that this algorithm can be extended to the case of a general network.

How to cite

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Kalaï, R., et al. "Lexicographic α-robustness: an application to the 1-median problem." RAIRO - Operations Research 44.2 (2010): 119-138. <http://eudml.org/doc/250861>.

@article{Kalaï2010,
abstract = { In the last decade, several robustness approaches have been developed to deal with uncertainty. In decision problems, and particularly in location problems, the most used robustness approach rely either on maximal cost or on maximal regret criteria. However, it is well known that these criteria are too conservative. In this paper, we present a new robustness approach, called lexicographic α-robustness, which compensates for the drawbacks of criteria based on the worst case. We apply this approach to the 1-median location problem under uncertainty on node weights and we give a specific algorithm to determine robust solutions in the case of a tree. We also show that this algorithm can be extended to the case of a general network. },
author = {Kalaï, R., Aloulou, M. A., Vallin, Ph., Vanderpooten, D.},
journal = {RAIRO - Operations Research},
keywords = {Robustness; 1-median location problem; minmax cost/regret; robustness},
language = {eng},
month = {4},
number = {2},
pages = {119-138},
publisher = {EDP Sciences},
title = {Lexicographic α-robustness: an application to the 1-median problem},
url = {http://eudml.org/doc/250861},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Kalaï, R.
AU - Aloulou, M. A.
AU - Vallin, Ph.
AU - Vanderpooten, D.
TI - Lexicographic α-robustness: an application to the 1-median problem
JO - RAIRO - Operations Research
DA - 2010/4//
PB - EDP Sciences
VL - 44
IS - 2
SP - 119
EP - 138
AB - In the last decade, several robustness approaches have been developed to deal with uncertainty. In decision problems, and particularly in location problems, the most used robustness approach rely either on maximal cost or on maximal regret criteria. However, it is well known that these criteria are too conservative. In this paper, we present a new robustness approach, called lexicographic α-robustness, which compensates for the drawbacks of criteria based on the worst case. We apply this approach to the 1-median location problem under uncertainty on node weights and we give a specific algorithm to determine robust solutions in the case of a tree. We also show that this algorithm can be extended to the case of a general network.
LA - eng
KW - Robustness; 1-median location problem; minmax cost/regret; robustness
UR - http://eudml.org/doc/250861
ER -

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