Modeling Dynamic Choice Behavior of Customers

A central task in operations is demand estimation, which provides high quality inputs for assortment planning and revenue management (RM). For simplicity, many models in practice assume that each product has its own independent demand stream. However, if products are substitutes, then the demand for a given product will be a function of the set of alternatives available to consumers when they make their purchase decisions, and of the subset of products that may be on sale. Such choice behavior is a topic of great interest among researchers and practitioners alike because it has significant revenue consequences. The building block for estimating customer choice is the specification of a choice model, either parametric or nonparametric. In this paper, we take a non-parametric approach. We use a simple, though quite general, non-parametric choice model in which customer types are defined by their rank ordering of all alternatives (along with the no-purchase alternative). When faced with a choice from an offer set, a customer is assumed to purchase the available product that ranks highest in her preference list – or she does not purchase at all if the no-purchase alternative ranks higher than any available product. Customers that share the same preference list constitute a type. With a finite number of alternatives, there is a finite number of rankings and hence a finite number of customer types. Demand is then described by a discrete probability mass function (pmf) on the set of customer types. This type of rank-based choice model has previously been applied in areas such as economics and psychology. One of the first applications in operational settings was the retail assortment problem studied by [4]. As they point out, several common demand processes studied in the literature can be modeled as special cases of a rank-based choice model (e.g., multinomial logit (MNL), Markovian second choice, universal backup, Lancaster demand, and the independent demand model). Recently, with the rise of business analytics and data-driven approaches, there has been an increasing interest in demand estimation and revenue predictions derived from nonparametric choice models (e.g., [2] and [5]). However, these estimation proposals work on sales transactions and product availability data, or equivalently, on revealed preferences relating pairs of products. They all assume that every data point is an independent observation coming from different customers. In this paper, we take a different perspective, and assume that a set of customers make repeated purchases from the firm. The canonical example is customers buying groceries on a weekly basis from a grocery retailer, but more broadly the setting includes any application in which customers exhibit loyalty through repeated purchases be it apparel, hotel, airline, etc. The goal of the retailer ∗SJ and GV are affiliated with IOMS, NYU Stern. email: {sjagabat, gvulcano}@stern.nyu.edu