Tour-distance Voronoi diagram and its application to location analysis

The purpose of this paper is to show tour-distance Voronoi diagrams which represent market areas of facilities under the assumption that consumers use more than one facility. Bisectors composing tour-distance Voronoi diagrams are generally curved lines, although those of higher-order Voronoi diagrams are composed of straight lines. It is osberved that contiguous facilities have larger joint market areas than scattered facilities do. Applying them to location problem of competitive facilities, it is found out that spatial concentration tends to be superior for facilities that maximize their market areas, if every consumer makes tour to obtain more than one service in a multipurpose trip.