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Long-term planning versus short-term planning in the asymptotical location problem

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Date
2009
Link to item file
http://arxiv.org/abs/math/0612718v1
Dewey
Recherche opérationnelle
Sujet
Location problem; facility location; Fermat-Weber problem; k-median problem; sequential allocation; average distance functional; optimal transportation
Journal issue
ESAIM. COCV
Volume
15
Number
3
Publication date
2009
Article pages
509-524
Publisher
Cambridge University Press
DOI
http://dx.doi.org/10.1051/cocv:2008034
URI
https://basepub.dauphine.fr/handle/123456789/12709
Collections
  • CEREMADE : Publications
Metadata
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Author
Brancolini, Alessio
Buttazzo, Giuseppe
Santambrogio, Filippo
Stepanov, Eugene
Type
Article accepté pour publication ou publié
Abstract (EN)
Given the probability measure ν over the given region $\Omega\subset \mathbb{R}^n$ , we consider the optimal location of a set Σ composed by n points in Ω in order to minimize the average distance $\Sigma\mapsto \int_\Omega \mathrm{dist}\,(x,\Sigma)\,{\rm d}\nu$ (the classical optimal facility location problem). The paper compares two strategies to find optimal configurations: the long-term one which consists in placing all n points at once in an optimal position, and the short-term one which consists in placing the points one by one adding at each step at most one point and preserving the configuration built at previous steps. We show that the respective optimization problems exhibit qualitatively different asymptotic behavior as $n\to\infty$ , although the optimization costs in both cases have the same asymptotic orders of vanishing.

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