TY - JOUR

T1 - A Location‐Allocation Model of Lösch's Central Place Theory

T2 - Testing on a Uniform Lattice Network

AU - Kuby, Michael

PY - 1989/10

Y1 - 1989/10

N2 - This paper develops a location‐allocation model of Lösch's central place theory that maximizes the number of firms that can coexist in the market, subject to range, threshold, hierarchy, and other constraints. F.o.b. costs, economies of scale, and elastic demand are included. Consumer behavior postulates concerning the “nearest center hypothesis” and the “indifference principle” are formulated 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 by applying it to a uniform 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 by 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 nature 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 nonuniform regions. 1989 The Ohio State University

AB - This paper develops a location‐allocation model of Lösch's central place theory that maximizes the number of firms that can coexist in the market, subject to range, threshold, hierarchy, and other constraints. F.o.b. costs, economies of scale, and elastic demand are included. Consumer behavior postulates concerning the “nearest center hypothesis” and the “indifference principle” are formulated 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 by applying it to a uniform 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 by 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 nature 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 nonuniform regions. 1989 The Ohio State University

UR - http://www.scopus.com/inward/record.url?scp=0024799437&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024799437&partnerID=8YFLogxK

U2 - 10.1111/j.1538-4632.1989.tb00899.x

DO - 10.1111/j.1538-4632.1989.tb00899.x

M3 - Article

AN - SCOPUS:0024799437

SN - 0016-7363

VL - 21

SP - 316

EP - 337

JO - Geographical Analysis

JF - Geographical Analysis

IS - 4

ER -