Pricing Time-Sensitive Services Based on Realized Performance

Services like FedEx charge up-front fees but reimburse customers for delays. However, lead time pricing studies ignore such delay refunds. This paper contributes to filling this gap. It studies revenue-maximizing tariffs that depend on realized lead times for a provider serving multiple time-sensitive customer types. We relax two key assumptions in the standard model since Naor (1969). First, customers may be risk averse (RA) with respect to payoff uncertainty, where payoff equals valuation, minus delay cost, minus payment. Second, tariffs may be arbitrary functions of realized lead times. The standard model assumes risk neutral (RN) customers and restricts attention to flat rates. Our main findings are: 1. With RN customers, flat rate pricing maximizes revenues but leaves customers exposed to payoff variability. 2. With RA customers, flat rate pricing is suboptimal. If types are distinguishable, the optimal lead time-dependent tariffs fully insure delay cost risk and yield the same revenue as under optimal flat rates for RN customers. With indistinguishable RA types, the differentiated first-best tariffs may be incentive-compatible even for uniform service, yielding higher revenues than with RN customers. 3. Under price and capacity optimization, lead time-dependent pricing yields higher profits with less capacity vs. flat rate pricing.