Revenue Management in Queueing Systems with Unknown Demand Characteristics

Response time is an important dimension of operational excellence in many manufacturing and service sectors. Firms in such settings may find it attractive to dynamically adjust prices based on the state of their order book and the corresponding lead times. Virtually the entire revenue management literature for queues assumes that providers know the distribution of customer demand attributes. However, such precise demand information may hardly be available. We relax this assumption and study the case of an unknown mix of patient and impatient customers who differ in their time-sensitivity. The provider has a Bernoulli prior on the customer mix which corresponds to an optimistic or pessimistic demand scenario and which she updates depending on whether customers buy or not at the posted prices. We characterize the optimal dynamic pricing policy under Bayesian updating and the resulting system performance. It has a threshold structure whereby the provider experiments with a high price as long as her posterior belief that the demand scenario is optimistic exceeds a certain positive threshold and otherwise reverts to charging a low price forever. We analytically characterize the length of the experimentation period and the probability that the provider eventually learns the underlying demand scenario. Finally, we study the provider