TR-2005-4 Pricing strategies and service differentiation in queues — A profit maximization perspective ∗

We consider the problem of pricing and scheduling the customers arriving at a service facility, with the objective of maximizing the profits of the facility, when the value of service and time-sensitivity of a customer are his private information. First we consider the ‘discrete types’ problem where each customer belongs to one of N types, type i being characterized by its value for service Ri and cost of waiting per unit time ci. For the special case when Ri ci is decreasing in ci, we characterize the structure of the optimal pricing-scheduling policy and design a polynomial-time algorithm to find it. We then analyze the same problem under the additional restriction of at most m different levels of service, characterize the optimal pricing-scheduling policy, and provide an efficient way to find it. Finally, we consider the case where the types of customers form a continuum and the customers have a generalized delay cost structure. Using the insights from the discrete types case, we characterize the conditions under which the optimal mechanism schedules the customers according to the cμ rule. This research was supported by an NSF grant DMI-0093981 Department of Industrial Engineering and Operations Research, Columbia University, New York, NY; email: ark2001@columbia.edu Department of Industrial Engineering and Operations Research, Columbia University, New York, NY; email: jay@ieor.columbia.edu