Formulating Christaller's central place theory by location- allocation model

Abstract

This paper reconstructs the marketing principle of Christaller's central place theory using the location-allocation model. The model is applied to a hypothetical lattice network which is composed of two parts: an inner network where the entry of central places is possible and all nodes must be served from central places; and an outer network where nodes are not potential centre sites but demand nodes that do not have to be covered with all goods. To build the hierarchy, both the top-down method and the bottom-up method are applied. The system of central places generated by the bottom-up method is that of the K=3 system developed by Christaller. The solution result using the top-down method however, clearly does not fit Christaller's K=3 system. The system generated by the latter method reveals a complicated configuration of central places and has a number of hierarchical levels. As compared with the result by the top-down method, we notice that the system built using the bottom-up method is characterised by a concentration of functions and, therefore, shows efficient hierarchical organisation. Consequently, the above model is valid only if it is constructed by the bottom-up method. In order to generate the K=3 system by the top-down method, it is necessary to reinterpret Christaller's objective function. -from English summary