Abstract/Summary

The optimal location of plants by a global firm is analysed for the first time using measures of distance along the spherical surface of Planet Earth. With a uniform distribution of customers an optimal location strategy will normally seek a space-filling configuration of identical areas that are as near circular as possible. The hexagonal space-filling solution for location on an infinite plane cannot be generalised to the surface of a sphere. Different spatial patterns are required for different numbers of plants; these may be based on triangles, squares or pentagons. The chapter reviews the current state of knowledge on the topic, drawing on theories of spherical geometry and regular convex polyhedra, and on applications in physics, chemistry and medicine. Overall, there appears to be no general solution to the problem; only a set of quite different solutions for various special cases. The lack of any general solution to this central problem in international business illustrates the ‘impossibility’ referred to in the title of this chapter.