Distribution of the Ratio of Distances to the First and Second Nearest Facilities

Abstract

This paper deals with the ratio of the distances to the first and second nearest facilities. The ratio represents the reliability of facility location when the nearest facility is closed and customers are serviced by the second nearest facility. The distribution of the ratio is derived for grid and random patterns of facilities. Distance is measured as the Euclidean and rectilinear distances. The distribution shows how the ratio is distributed in a study region, and will supply building blocks for facility location models with closing of facilities. The distribution of the ratio of the road network distances is also calculated for actual facility location.