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

dc.contributor.authorBrancolini, Alessio
dc.contributor.authorButtazzo, Giuseppe
dc.contributor.authorSantambrogio, Filippo
dc.contributor.authorStepanov, Eugene
dc.date.accessioned2014-02-20T13:58:27Z
dc.date.available2014-02-20T13:58:27Z
dc.date.issued2009
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/12709
dc.language.isoenen
dc.subjectLocation problemen
dc.subjectfacility locationen
dc.subjectFermat-Weber problemen
dc.subjectk-median problemen
dc.subjectsequential allocationen
dc.subjectaverage distance functionalen
dc.subjectoptimal transportationen
dc.subject.ddc003en
dc.titleLong-term planning versus short-term planning in the asymptotical location problemen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenGiven 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.en
dc.relation.isversionofjnlnameESAIM. COCV
dc.relation.isversionofjnlvol15en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2009
dc.relation.isversionofjnlpages509-524en
dc.relation.isversionofdoihttp://dx.doi.org/10.1051/cocv:2008034en
dc.identifier.urlsitehttp://arxiv.org/abs/math/0612718v1en
dc.relation.isversionofjnlpublisherCambridge University Pressen
dc.subject.ddclabelRecherche opérationnelleen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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