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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.
@article{RO_2010__44_2_119_0,
author = {Kala{\"\i}, R. and Aloulou, M. A. and Vallin, Ph. and Vanderpooten, D.},
title = {Lexicographic $\alpha $-robustness : an application to the 1-median problem},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {119--138},
publisher = {EDP-Sciences},
volume = {44},
number = {2},
year = {2010},
doi = {10.1051/ro/2010010},
mrnumber = {2666485},
zbl = {1189.90078},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2010010/}
}
TY - JOUR AU - Kalaï, R. AU - Aloulou, M. A. AU - Vallin, Ph. AU - Vanderpooten, D. TI - Lexicographic $\alpha $-robustness : an application to the 1-median problem JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2010 SP - 119 EP - 138 VL - 44 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro/2010010/ DO - 10.1051/ro/2010010 LA - en ID - RO_2010__44_2_119_0 ER -
%0 Journal Article %A Kalaï, R. %A Aloulou, M. A. %A Vallin, Ph. %A Vanderpooten, D. %T Lexicographic $\alpha $-robustness : an application to the 1-median problem %J RAIRO - Operations Research - Recherche Opérationnelle %D 2010 %P 119-138 %V 44 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro/2010010/ %R 10.1051/ro/2010010 %G en %F RO_2010__44_2_119_0
Kalaï, R.; Aloulou, M. A.; Vallin, Ph.; Vanderpooten, D. Lexicographic $\alpha $-robustness : an application to the 1-median problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 44 (2010) no. 2, pp. 119-138. doi: 10.1051/ro/2010010
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