Managing Customer Churn via Service Mode Control

We introduce a novel stochastic control model for the problem of a service firm interacting over time with one of its customers who probabilistically churns depending on the customer’s satisfaction. The firm has two service modes available, and they determine the drift and volatility of the Brownian reward process. The firm’s objective is to maximize the rewards generated over the customer’s lifetime. Meanwhile, the customer might churn probabilistically if the customer’s satisfaction, modeled as an Orstein–Uhlenbeck process controlled by the firm’s service mode, is below a certain threshold. We build upon Markov processes with spatial delay to solve this problem, and we explicitly characterize the firm’s optimal policy, which is either myopic or a sandwich policy. A sandwich policy is one in which the firm deploys the service mode with inferior reward rate when the customer satisfaction level is in a specific interval near the satisfaction threshold and uses the myopically optimal service mode for all other satisfaction levels. Specifically, we find that the firm should use the safe service mode when the customer is marginally satisfied and the risky service mode when the customer is marginally unsatisfied. We find numerically that the customer lifetime value under the optimal policy is large relative to that under the myopic policy. Our results are robust to a variety of alternative model specifications.