Modeling retail trade areas using higher-order, multiplicatively weighted voronoi diagrams

Abstract

Voronoi (Thiessen) trade area models are geometrically based procedures for generating theoretical trade areas using store characteristics and assumptions about consumer behavior. Existing models assume that customers patronize only one facility resulting in mutually exclusive trade areas. We introduce two new Voronoi models which include the assumption that a customer selects from the k ( k = 1, 2, 3, …) nearest most attractive facilities. When the customer is indifferent between the k facilities, the trade areas are given by the order-k, multiplicatively weighted Voronoi diagram. If the customer shows a preference for nearer facilities, the trade areas are given by the ordered, order-k, multiplicatively weighted Voronoi diagram. Both models produce overlapping trade areas. The ordered, order-k, multiplicatively weighted Voronoi diagram model also enables us to examine the effects of different preference levels on the sales estimates for a facility. The new models are demonstrated using data relating to a chain of supermarkets in the twin cities of Kitchener-Waterloo in Ontario, Canada.