This paper presents a range of methods for computing the equilibrium configuration of shopping facility sizes. First, the presently available range of quasi-balancing factor methods is considered and built into a theoretical framework in which further algorithms may be defined. Then the use of the gradient method is considered, which is a general method of solution of nonlinear equations. Last, it is shown that a special case exists in which a closed form solution may be obtained.
Get full access to this article
View all access options for this article.
References
1.
Dixon-LewisGGreenbergJ B, 1975“Calculation of high temperature equilibrium, partial equilibrium, and quasi-steady state properties in gaseous sytems, and of flame temperature”Journal of the Institute of Fuel48132–138
2.
EilonSTilleyR P RFowlerT R, 1969“Analysis of a gravity demand model”Regional Studies3115–122
3.
HammarlingS J, 1970Latent Roots and Latent Vectors (Adams and Hilger, London)
4.
HarrisBWilsonA G, 1978“Equilibrium values and dynamics of attractiveness terms in production-constrained spatial interaction models”Environment and Planning A10371–388
5.
HeadingJ, 1958Matrix Theory for Physicists (Longman, Harlow, Essex)
6.
HuffD L, 1964“Defining and estimating a trading area”Journal of Marketing2834–38
7.
LakshmananT RHansenW G, 1965“A retail market potential model”Journal of the American Institute of Planners31134–143
8.
MarquardtD W, 1963“An algorithm for least squares estimation of non-linear parameters”Journal of the Society of Industrial and Applied Mathematics11431–441
9.
Numerical Algorithm Group, 1976Library Manual, Oxford University Computing Laboratory, Oxford
10.
WhiteR W, 1977“Dynamic central place theory: results of a simulation approach”Geographical Analysis9226–243
11.
WilkinsonJ H, 1965The Algebraic Eigenvalue Problem (Oxford University Press, London)
12.
WilsonA G, 1976“Retailers' profits and consumers' welfare in spatial interaction shopping model”London Papers in Regional Science 6. Theory and Practice in Regional Science Ed. MasserI (Pion, London) pp 42–59
13.
WilsonA GClarkeM, 1979“Some illustrations of catastrophe theory applied to urban retailing structures”London Papers in Regional Science 10. Development in Urban and Regional Analysis Ed. BrehenyM (Pion, London) pp 5–27
