A reinterpretation of Christaller's central place theory: from marketing principle to generalised maximal covering location problem

Abstract

Previous research efforts (Ishizaki, 1992) demonstrate that the marketing principle of Christaller's central place theory can be formulated as the set-covering problem. Results from this model applied to a hypothetical lattice network bring up the question of how to generate the hexagonal system of central places. Christaller required a set of six K-places, located at the median points between their neighboring B-places, to cover unsupplied areas about k-d units from B-places. However, only three K′-places will entirely serve unsupplied areas. Why are K-places located at the median points between B-places? The primary purpose of this paper is to propose a reinterpretation for solving this problem and reformulate the marketing principle using a location-allocation model. The relaxed models reflecting real assumptions are developed to expand the notions of the marketing principle. Relationships between the marketing principle with the relaxed models in this paper and well-known location-allocation models are discussed, in order to investigate the implications of the marketing principle. -English summary