Lead-time quotation with ex-ante and ex-post customer reference effects

We investigate optimal dynamic lead-time quotes for a service provider by considering the reference effects of quotes on customers, both ex-ante , when customers form expectations and decide whether to join based on the quote and their prior information about waits, and ex-post , when customers compare their realized waiting times to the quote to assess satisfaction, resulting in goodwill loss for the provider. We adopt a behavioral model in which customers respond to quoted lead times but do not interact strategically. We model the system as an unobservable queue. Customers decide whether to join based on their expected waiting cost, a function of both the quote and their expected sojourn time. The provider chooses lead-time quotes to maximize its expected revenues minus a loss of goodwill associated with customer dissatisfaction, a function of the quotes and the customers’ actual sojourn times. We prove that a threshold-like policy is optimal for the provider. In the presence of a piecewise linear loss-of-goodwill function, we characterize the optimal threshold and the quotes for each number of customers in the system. We also consider endogenous arrival rates driven by goodwill and show the existence and properties of a steady-state solution. These policies can inform the design of lead-time quotation for service providers, especially small and medium-sized enterprises (SMEs).