Comptes Rendus
no. 10
Asymptotique d'un problème de positionnement optimal
Guy Bouchitté1 ; Chloé Jimenez1 ; Mahadevan Rajesh1
1 Laboratoire d'analyse non linéaire appliquée, Université de Toulon et du Var, BP 132, 83957 La Garde cedex, France
Comptes Rendus. Mathématique, Volume 335 (2002) no. 10, pp. 853-858.

On considère le problème de positionnement optimal de n centres de production pour une répartition non uniforme de la population. Le critère d'optimisation est une moyenne pondérée de la fonction distance au centre de production le plus proche. Dans cette Note, on étudie le comportement asymptotique du problème quand n tend vers l'infini en le reliant à l'asymptotique d'un problème de transport de masse de type Monge–Kantorovich.

We consider the problem of optimal location of production centres to serve a non-uniform distribution of customers. The location is required to be optimal with respect to the cost of transportation which is modeled by a weighted average of the distance function to the nearest production centre. In this Note we study the asymptotic behaviour of the problem as the number of production centres increases. This is done in connection with the theory of Monge–Kantorovich for mass transportation.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02575-X

Guy Bouchitté 1 ; Chloé Jimenez 1 ; Mahadevan Rajesh 1

1 Laboratoire d'analyse non linéaire appliquée, Université de Toulon et du Var, BP 132, 83957 La Garde cedex, France 
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Guy Bouchitté; Chloé Jimenez; Mahadevan Rajesh. Asymptotique d'un problème de positionnement optimal. Comptes Rendus. Mathématique, Volume 335 (2002) no. 10, pp. 853-858. doi : 10.1016/S1631-073X(02)02575-X. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02575-X/

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