Interacting new facilities and location-allocation problems

This paper examines the location-allocation problems involving interacting new facilities on a plane and on a sphere. Specifically, the authors consider a situation in which flows between the existing facilities are channeled through the new facilities. The new facilities interact and the level of interactions between them is determined by the flows between the existing facilities they serve. Although special cases of this problem with one, two and three new facilities on a plane have been considered by the researchers, the general problem with p new facilities remains unsolved. In this study, the authors formulate this problem both on a plane and on a sphere. An algorithm that solves the location and the allocation phases separately in an iterative manner is formulated for the planar problem. Modifications needed in the algorithm for solving the spherical problem are discussed. Computational results with two versions of the proposed algorithm spanning a range of problem sizes are reported.