Spherical Location Under Restricted Distance

Abstract

This paper deals with the problem of locating a new facility with respect to n given demand points on earth, with upper bounds imposed on distances between the new facility and each demand points. Distances are measured as the length of the shortest arc of great circle. The proposed algorithm makes use of a Lagrangean relaxation in which the distance constraints, which are not satisfied by the associated unconstrained solution, are incorporated in the economic function. Computational results of a limited number of test problems are presented.