A Location‐Allocation Model of Lösch's Central Place Theory: Testing on a Uniform Lattice Network

Abstract

This paper develops a location-allocation model of Liisch's central place theory thatmaximizes the number of firms that can coexist in the market, subject to range, threshold, hierarchy, and other constraints. F.0.b. costs, ecofiomies of scale, and elastic demand are included. Consumer b e h a w postulates concerning the "nearest center hypothesis" and the "indifference principle" are f m u l a t e d as nonlinear constraints but not used during solution. Methods are developed for simulating the continuous, infinite plain with a discrete, bounded network by use of an outer overflow network and a symmetrical market area constraint. The model is tested b y applying it to a u n i f m lattice network and comparing the results to the expected pattern of nested hexagons. Solutions consistent with the k = 3, 4, and 7 patterns are generated b y changing threshold values. However, remaining inconsistencies appear to be due to the inability to express the consumer behavior laws as linear constraints, to the bounded and discrete nuture of the network, and to the objective function being the sum of integer variables. The long-run purpose of developing and validating a location-allocation model of a location theory is to use it to relax the theory's restrictive assumptions and to apply the theory to n o n u n i f m regions.

Geographical Analysis: Its First 40 Years

“…In addition to the early and highly significant article about location‐allocation ( p ‐median problem) by ReVelle and Swain (), GA has presented a number of solution techniques and articles devoted to computation of p ‐median results (Rosing, Hillsman, and Rosing‐Vogelaar ). However, apart from these computational concerns, the relations between transport and location are reflected in Kuby (), which makes the connection between transportation, central place theory, and location‐allocation models. Employing a different perspective, Taylor () devotes considerable attention to world city networks, emphasizing their interlocking components.…”

A Location Model for Urban Hierarchy Planning with Population Dynamics

“…One of the earliest attempts to derive the spatial distribution of productive and residential activities in a region with a location model is due to Puryear (1975). Other relevant works include those by Kohsaka (1983) and Kuby (1989). Recently, Curtin and Church (2007) applied a p-dispersion location model to generate central place systems.…”

Spatial Optimization Models

“…Christaller attempted to find the laws that determined the number, size, and distribution of towns in a region of Southern Germany. Since that time geographers, archaeologists, and anthropologists have searched for Christaller's central place patterns in other regions and in other applications and have developed spatial optimization models that solve for the optimal spatial arrangement of towns and markets (Kuby, 1989). Virtually all early location theories have some type of spatial optimization counterpart today.…”