Competitive Neural Networks for Customer Choice Models

In this paper we propose and examine two different models for customer choices in for instance a wholesale department, given the actual sales. Both customers and products are modeled by points in a k-dimensional real vector space. Two possible strategies are discussed: in one model the customer buys the nearest option from categories of products, in the other he/she buys all products within a certain radius of his/her position. Now we deal with the following problem: given only the sales list, how can we retrieve the relative positions corresponding to customers and products? In particular we are interested in the dimension k of the space: we are looking for low dimensional solutions with a good “fit” to the real sales list. Theoretical complexity of these problems is addressed: they are very hard to solve exactly; special cases are shown to be NP-complete. We use competitive neural network techniques for both artificial and real life data, and report the results.