On a robustness property in single-facility location in continuous space

Marc Ciligot-Travain (1) , Sado Traoré (2)

1 LANLG - Laboratoire d'Analyse non linéaire et Géométrie
2 ISEA

We consider a single-facility location problem in continuous space, here the problem of minimizing a sum or the maximum of the possibly weighted distances from a facility to a set of points of demand. The main result of this paper shows that every solution (optimal facility location) of this problem has an interesting robustness property. Any optimal facility location is the most robust in the following sense: given a suitable highest admissible cost, it allows the greatest perturbation of the locations of the demand without exceeding this highest admissible chosen cost.

Mots clés: Single-Facility Location; Robustness; Fermat-Weber problem; 1-center problem

Domaines: Optimisation et contrôle [math.OC]

Marc Ciligot-Travain, Sado Traoré. On a robustness property in single-facility location in continuous space. 2010. ⟨hal-00633469⟩