Big Triangle Small Triangle Method for the Weber Problem on the Sphere

Abstract

We propose the Big Triangle Small Triangle (BTST) Method for solving the Weber problem on the sphere (WPS). It can also be applied to other single facility location problems on the sphere. The WPS is a variation of the Weber problem which is a classic and well-studied location problem. We assume that the demand points are distributed on the surface of a sphere, and our problem is to find the location of a facility so as to minimize the sum of the distances from demand points to the facility. The distance is measured by the great circle distance. The objective function of the WPS is not convex, and the Weiszfeld-type algorithm is not guaranteed to find the facility’s optimal location. The BTST type algorithm divides the surface of the sphere into spherical triangles and applies a branch-and-bound method. We show that it finds the optimal solution within a short computational time.