A dynamic programming approach to customer relationship pricing

The practice of offering discounts to prospective customers represents a rudimentary form of using transaction history measures to customize the marketing mix. Furthermore, the proliferation of powerful customer relationship management (CRM) systems is providing the data and the communications channels necessary to extend this type of pricing strategy into true dynamic marketing policies that adjust pricing as customer relationships evolve. In this paper, we describe a dynamic programming-based approach to creating optimal relationship pricing policies. The methodology has two main components. The first component is a latent class logit model that is used to model customer buying behavior. The second component is a dynamic optimization procedure that computes profit-maximizing price paths. The methodology is illustrated using subscriber data provided by a large metropolitan newspaper. The empirical results provide support for the common managerial practice of offering discounts to new customers. However, in contrast to current practice, the results suggest the use of a series of decreasing discounts based on the length of customer tenure rather than a single steep discount for first-time purchasers. The dynamic programming (DP) methodology also represents an important approach to calculating customer value (CV). Specifically, the DP framework allows the calculation of CV to be an explicit function of marketing policies and customer status. As such, this method for calculating CV accounts for the value of managerial flexibility and improves upon existing methods that do not model revenue and attrition rates as functions of marketing variables.