Location and shape of a rectangular facility in ℝn. Convexity properties. Convexity properties

Carrizosa, Emilio; Munõz-Márquez, Manuel; Puerto, Justo

doi:10.1007/bf02680563

Cited by 12 publications

(16 citation statements)

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“…They compute the optimal solution for one specific example, but fail to give a general algorithm. More recently, Carrizosa, Muñoz-Márquez, and Puerto [7,8] use convexity properties for problems of this type to deal with the error resulting from nonlinear numerical methods for approximating solutions. It should be noted that the objective function is no longer convex when distances are computed in the presence of obstacles.…”

Section: "There Are Three Important Factors That Determine the Value mentioning

confidence: 99%

On the Continuous Fermat-Weber Problem

Fekete

Mitchell

Beurer

2005

Operations Research

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We give the first exact algorithmic study of facility location problems that deal with finding a median for a continuum of demand points. In particular, we consider versions of the "continuous k-median (Fermat-Weber) problem" where the goal is to select one or more center points that minimize the average distance to a set of points in a demand region. In such problems, the average is computed as an integral over the relevant region, versus the usual discrete sum of distances. The resulting facility location problems are inherently geometric, requiring analysis techniques of computational geometry. We provide polynomial-time algorithms for various versions of the L 1 1-median (Fermat-Weber) problem. We also consider the multiple-center version of the L 1 k-median problem, which we prove is NP-hard for large k. MSC Classification: 90B85, 68U05ACM Classification: F.2.2

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Section: "There Are Three Important Factors That Determine the Value mentioning

confidence: 99%

On the Continuous Fermat-Weber Problem

Fekete

Mitchell

Beurer

2005

Operations Research

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“…Adapting the branch and bound (in particular, the design of bounds) for the case of extensive facilities, e.g. Carrizosa et al (1998a), deserves further study.…”

Section: Discussionmentioning

confidence: 99%

Anti-covering Problems

Carrizosa

G.-Tóth

2015

Location Science

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In covering location models, one seeks the location of facilities optimizing the weight of individuals covered, i.e., those at the distance from the facilities below a threshold value. Attractive facilities are wished to be close to the individuals, and thus the covering is to be maximized, while for repulsive facilities the covering is to be minimized. On top of such individual-facility interactions, facility-facility interactions are relevant, since they may repel each other. This chapter is focused on models for locating facilities using covering criteria, taking into account that facilities are repulsive from each other. Contrary to the usual approach, in which individuals are assumed to be concentrated at a finite set of points, we assume the individuals to be continuously distributed in a planar region. The problem is formulated as a global optimization problem, and a branch and bound algorithm is proposed.

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“…In the last years the assumption that facilities are represented by isolated points has been questioned by different authors and the natural extension of considering sets rather than points has attracted the attention of the researchers Wesolowsky 2000, 2002;Carrizosa et al 1995Carrizosa et al , 1998aCarrizosa et al , 1998bChen 2001;Drezner and Wesolowsky 1980;Drezner 1986;Nickel et al 2003.…”

Section: Introductionmentioning

confidence: 99%

“…A possible way to deal with sets as demand facilities takes the average behavior into account, so that any point in the demand facility is visited according to a given probability distribution. This approach induces the minimization of expected distances (see Drezner 1986, Drezner and Wesolowsky 1980or Carrizosa et al 1995, 1998a, 1998b.…”

Section: Introductionmentioning

confidence: 99%