| Abstract: | The objective of this paper is to formulate location-allocation models of linear facilities, such as bridges, railroad crossings, and staircases. The location-allocation models in this paper differ from existing location-allocation models in that the service provided by the facilities is consumed by trips, with associated origins and destinations. The first part of the paper shows the formulation of these location-allocation problems in one-dimensional space. It is demonstrated that these problems can also be formulated by the use of a rectilinear Voronoi diagram in two-dimensional space. The second part of the paper demonstrates fundamental relationships between the number of facilities and the total length of indirect trips and between the number of facilities and the total number of indirect trips for uniformly and independently distributed origins and destinations. |
