Managing Customer Churn via Service Mode Control
73 Pages Posted: 20 Jun 2018 Last revised: 17 Aug 2018
Date Written: June 28, 2018
We consider the problem faced by a service firm interacting over time with one of its customers. The firm has two service modes available, which differ in their expected reward rates as well as their volatilities. The firm's objective is to maximize the rewards generated over the customer's lifetime. Meanwhile, the customer is unsophisticated and might abandon the system if he is unsatisfied with recent rewards. We show that the firm's optimal policy is either myopic or a sandwich policy. A sandwich policy is one where the firm utilizes the myopically optimal service mode when the customer is either very happy or very unhappy, but that utilizes the service mode with inferior reward rate when the customer happiness is near the satisfaction threshold. Specifically, the firm becomes risk averse when the customer is marginally satisfied and risk seeking when the customer is marginally unsatisfied. We show numerically that our results are robust to different specifications of the hazard rate of customer abandonment as a function of happiness. We also demonstrate numerically that the potential value of using the optimal policy is large in comparison to the myopic one.
Keywords: Stochastic model applications, optimal control, buyer behavior, customer lifetime value, happiness, churn, goodwill model
JEL Classification: A12, D03, M31
Suggested Citation: Suggested Citation