Pricing in Service Systems with Rational Balking and Abandonment of Time‐Sensitive Customers

The current literature on pricing in service systems with time‐sensitive customers predominately ignores the rational abandonment of customers with mixed‐risk attitude. The goal of this study is to address this gap. We consider an unobservable queueing system with a nonlinear waiting cost function, which is concave up to a certain point and then becomes convex, capturing the mixed‐risk attitude of customers observed in empirical studies. We assume that customers are sensitive with respect to waiting time (delay) and strategic regarding their balking and abandonment decisions. We characterize the optimal pricing policy that maximizes the service provider's revenue. We show that the pricing policies studied in the literature, including the joint service and cancellation (entrance) fee policy, are suboptimal and cannot induce the socially optimal behavior. We demonstrate that while the cancellation fee can regulate a customer's balking strategy, the service fee cannot effectively control a customer's abandonment decision. We then provide conditions under which the joint service and cancellation fee policy is optimal. We finally prove that the service provider should compensate customers for their waiting in order to efficiently control the abandonment of customers. We propose a pricing policy, which includes entrance, service, and wait time (delay) fees, that maximizes the provider's revenue. We derive the optimal fees and show that, under the proposed optimal pricing policy, customers pay service and cancellation fees while they are partially compensated for the time spent waiting for service.