Pricing and capacity rationing for rentals with uncertain durations

We consider a rental firm with two types of customers. Contract customers pay fixed, prenegotiated rental fees and expect a high quality of service. Walk-in customers have no contractual relations with the firm and are ‘shopping for price’. Given multiple contract and walk-in classes, the rental firm has to decide when to offer service to contract customers and what fees to charge walk-in customers for service. We formulate this rental management problem as a problem in stochastic control and characterize optimal policies for managing contract and walk-in customers. We also consider static, myopic controls that are simpler to implement, and we analytically establish conditions under which these policies perform optimally. Complementary numerical tests provide a sense of the range of systems for which myopic policies are effective.