On Optimal Time for Customer Retention in Non-Contractual Setting

Churn predicting is an import issue in customer relationship management. In non-contractual setting, a popular approach to indentify churn is to calculate customer’s probability of being alive based on Pareto/NBD. Customer whose probability of being alive is greater than a certain threshold is classified as alive, else is classified as dead. The problem is how to determine this cutoff threshold optimally. This paper models the churn from a retention perspective. We assume the objective of the churn analysis is to maintain profitable customers, i.e., once these customers are classified as churn, a retention action should be taken and this often concerns a cost. Therefore, only when the expected profit from customer is over the retention cost, customer can reasonably be regard as a churner. Base on this understanding of churn, we proposed two models, a basic model and an extension model. Both models can calculate a suitable threshold for churn judgment. The objective in extension model is to maximize customer lifetime value, while basic model only calculates whether the retention is profitable within single decision period. Furthermore, our extension model is suitable for churn analysis in a continuous time manner, and considers the time discount factor in the mean time. Our models show that selecting optimal threshold for retention can be a profitable strategy to influence the lifetime value of customers. Numerical examples show that the customer lifetime value is strictly concave on cutoff threshold. The optimal threshold decreases in the dropoff rate, increases in the purchase rate, the expected profit per purchase and in the winback probability. We also find the discount rate has little influence on the optimal threshold