Abstract
We introduce a novel stochastic control model for the problem of 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 (risk). The firm's objective is to maximize the rewards generated over the customer's lifetime. Meanwhile, the customer is unsophisticated and might, probabilistically, abandon the system if 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 in a specific interval near the satisfaction threshold. Specifically, the firm should be risk averse when the customer is marginally satisfied and risk seeking 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. We also show that our results are robust to a variety of alternative model specifications.
Published Version
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