Recursive procedures for the spatial structuring of Christaller hierarchies

Previous research efforts demonstrate the use of location covering in the spatial structuring of central places within a single-good context. In a multilevel context, a mathematical programming approach is developed to the siting of central places for Christaller hierarchies. The primary model expresses the basic spatial relations between centers and hinterland locations in the form of coverage constraints. The objective function maximizes both market coverage of demand and market overlap. A unique feature of this model is the upper bound on market overlap, which allows the formation of different market structures consistent with the various K-valued central place systems. After the problem has been formulated as a hierarchical program, it is decomposed into a number of subproblems which are solved as a series of linear programs within a simple recursive algorithm. A Christaller construct which is crucial to this decomposition is the ‘range of region’. Indeed, its relationship to the nearest neighbor distances of central places on any one level of the hierarchy is what facilitates an orderly recursion process. Siting examples serve to illustrate the working of the algorithm in isotropic settings. Moreover, modifications to the primary model which are necessary for nonisotropic environments are discussed.