The single-location problem is to locate a new transportation facility in a network that can serve all customers at the minimum distance or cost. There are four types of single-location problems. The absolute 1-center problem is considered in this paper. By definition, in that problem, the customers are on any vertex and the center may be a vertex or a poyn n an edge. There are two previous methods for finding the absolute 1-center: (a) the hakimi method (1965) and (b) the minieka method (1981). They considered all possible links ofa network to determine the best candidate point. Later, larson and odoni proposed a shortcut to reduce the number of links needed for calculation. In this paper, a new shortcut with a stricter bound is first proposed to find the absolute 1-center directly. The larson andodoni shortcut is then introduced and integrated with the minieka method to form a combined method. Finally, a new method is developed to find the absolute 1-center based on a spanning tree that is obtained from that of the vertex to all shortest distances. The number ofiterations needed to perform the analysis is in proportion to the number of vertices instead of edges for any given network. To make a consistent coparison four different methods have been programmed and tested with several networks. The results show that the new methodor the new shortcut is fast and powerful in finding the absolute 1-center location. They provide the same solutions and belong to polynomial time-bounded algorithms. Therefore, we recommend use of the new method or shortcut for locating a new facility if the absolute 1-center problem is considered in a network. This paper appears in transportation research record no. 1251, Transport supply analysis.
Samenvatting