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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2009.12.002 Byline: Masashi Miyagawa Keywords: Location; Flow demand; Shortest distance; Nearest neighbour distance Abstract: This paper deals with the deviation distance to visit a facility from pre-planned routes. Facilities are approximated by both points and lines on a continuous plane. To see the relationship between the deviation distance and the availability of facilities, we derive the distributions of the rectilinear deviation distance for regular and random patterns of facilities. These distributions demonstrate how the shortest distance and the relative position of origin and destination affect the deviation distance. We also show that the deviation distance is a generalization of the nearest neighbour distance. Author Affiliation: Department of Ecosocial System Engineering, University of Yamanashi, 4-3-11 Takeda, Kofu, Yamanashi 400-8511, Japan Article History: Received 2 July 2009; Accepted 2 December 2009

This article examines the kth nearest neighbor distance for three regular point patterns: square, triangular, and hexagonal lattices. The probability density functions of the kth nearest distance and the average [...]

This article proposes a continuous approximation model for determining the number of hierarchical facilities when lower level facilities are subject to failures. The average distance from customers to the nearest open facility is derived for two types of customer behavior. The optimal number of facilities that minimizes the average distance is then obtained. The analytical expression for the optimal number of facilities demonstrates how the location of facilities, the failure probability, and the customer behavior affect the optimal hierarchy and the average distance. The result shows that introducing the hierarchy can reduce the average distance if the failure probability is small and the penalty for failing to use facilities is large. The model provides a fundamental understanding of the optimal hierarchy and is useful for designing hierarchical facility systems. [ABSTRACT FROM AUTHOR]

This article presents a bi-objective model for determining the number and size of finite size facilities. The objectives are to minimize both the average closest distance to facilities and the probability that a random line intersects facilities. The former represents the accessibility of customers, whereas the latter represents the interference to travelers. The average closest distance and the probability of intersecting facilities are derived for circular facilities randomly distributed in a circular city. The analytical expressions for the average closest distance and the probability of intersecting facilities demonstrate how the number and size of facilities affect the accessibility of customers and the interference to travelers. The model focuses on the tradeoff between the accessibility and interference, and the tradeoff curve provides planners with alternatives for the number and size of facilities. [ABSTRACT FROM AUTHOR]