Optimal Pricing With Impatient Customers

We investigate the optimal pricing strategy in a service-providing framework, where customers can become impatient and leave the system prior to service completion. In this setting, a price is quoted to an incoming customer based on the current number of customers in the system. When the quoted price is lower than the price the incoming customer is willing to pay (which follows a fixed probability distribution), then the customer joins the system and a reward equal to the quoted price is earned....