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Title: Isodistant points in competitive network facility location
Authors: Pelegrín, Blas
Suárez Vega, Rafael Ricardo 
Cano, Saúl
UNESCO Clasification: 531004 Operaciones comerciales internacionales
Keywords: Localización de mercados
Modelos económetricos
Issue Date: 2012
Publisher: 1134-5764
Journal: TOP 
Abstract: An isodistant point is any point on a network which is located at a predetermined distance from some node. For some competitive facility location problems on a network, it is verified that optimal (or near-optimal) locations are found in the set of nodes and isodistant points (or points in the vicinity of isodistant points). While the nodes are known, the isodistant points have to be determined for each problem. Surprisingly, no algorithm has been proposed to generate the isodistant points on a network. In this paper, we present a variety of such problems and propose an algorithm to find all isodistant points for given threshold distances associated with the nodes. The number of isodistant points is upper bounded by nm, where n and m are the number of nodes and the number of edges, respectively. Computational experiments are presented which show that isodistant points can be generated in short run time and the number of such points is much smaller than nm. Thus, for networks of moderate size, it is possible to find optimal (or near-optimal) solutions through the Integer Linear Programming formulations corresponding to the discrete version of such problems, in which a finite set of points are taken as location candidates.
ISSN: 1134-5764
DOI: 10.1007/s11750-010-0148-6
Source: TOP[ISSN 1134-5764],v. 20, p. 639-660
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