A nonhomogeneous hidden Markov model of response dynamics and mailing optimization in direct marketing

• Allowing firms to address the dynamic implications of mailing decisions.
• Maximizing the long-term value generated by the customers.
• Endogeneity of mailings which may result in biased parameter estimates is corrected.
• Uncertainty in the parameters is considered in optimizing the mailing decisions.
• Captures the season-changing effects on state transition.

Catalog firms mail billions of catalogs each year. To stay competitive, catalog managers need to maximize the return on these mailings by deciding who should receive a mail-order catalog. In this paper, we propose a two-step approach that allows firms to address the dynamic implications of mailing decisions, and to make efficient mailing decisions by maximizing the long-term value generated by customers. Specifically, we first propose a nonhomogeneous hidden Markov model (HMM) to capture the interactive dynamics between customers and mailings. In the second step, we use the parameters obtained from the HMM to determine the optimal mailing decisions using the Partial Observable Markov Decision Process (POMDP). Both the immediate and the long-term effects of mailings are accounted for. The mailing endogeneity that may result in biased parameter estimates is also corrected. We conduct an empirical study using six years of quarterly solicitation data derived from the well-known DMEF donation data set. All metrics used suggest that the proposed model fits the data well in terms of correct predictions and outperforms all other benchmark models. The simulative experimental results show that the proposed method for optimizing total accrued benefits outperforms the usual targeted-marketing methodology for optimizing each promotion in isolation. We also find that the sequential targeting rules acquired by our proposed methods are more cost-containment oriented in nature compared with the corresponding single-event targeting rules.