Distributions of rectilinear deviation distance to visit a facility

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