Towards a dynamic aggregate shopping model and its application to retail trading hour and market area analysis

The supermarket equation is a differential equation peculiar to spatial science. The complex form of this equation is presented here and is used to study aggregate consumer shopping patterns. The focus is the relationship between trips to, and shopping within, planned shopping centres relative to retail trading hour boundaries. In this context, five malls in Sydney are studied in the period prior to the introduction of deregulated shopping hours in 1992. The space-time convergence of aggregate consumer behaviour at these retail nodes show that the gravity coefficient can be treated in a temporal context. Estimates of mean trading hours can be made from the general solution and these are compared to alternative estimates from Fourier analysis. Time corrections to the gravity coefficient allow for a dynamic market area analysis, where the primary trade area can be determined relative to the trading hours of the shopping centre. A Sydney example shows how this methodology can be applied with population census data.