EXTENSION OF LITTLEWOOD’S RULE TO THE MULTI-PERIOD STATIC REVENUE MANAGEMENT MODEL WITH STANDBY CUSTOMERS

Abstract

Classical Littlewood’s rule (1972) for the two-period static revenue management of a single perishable resource is extended to a generic T-period model with monotonically increasing fixed fares, ending with standby customers with a special fare. The expected revenue in the entire period is expressed explicitly in terms of multiple definite integrals involving the distribution function of the demand in each period. The exact optimal protection level in each period is calculated successively, resulting in the maximized total expected revenue. The Brumelle-McGill’s theorem for the optimal booking limits in the T-period model is also extended to a similar model with standby customers. We show some numerical examples with comments on the effects of accepting standby customers on the optimal booking limits and the increase in the expected revenue.