Stochastic Comparisons in Airline Revenue Management

Abstract

Consider two markets of different sizes but similar costs and fare structure. All other things being equal, is an airline’s expected revenue larger in the market with larger demand? If not, under what circumstances is it possible to compare expected revenues without carrying out a detailed analysis? In this article, we provide answers to these questions by studying the relationship between the optimal expected revenue and the demand distributions when the latter are comparable according to various stochastic orders. For the two-fare class problem with dependent demand we obtain three results. We show that airlines should prefer lesser positive dependence between fare classes when marginal demand distributions are the same. We also describe particular dependence structures under which stochastically larger marginal demand distributions improve optimal expected revenue. Finally, when the dependence between effective demands in the two fare classes arises due to “sell ups,” we show that stochastically larger marginal demand distributions should be preferred. (Sell ups occur when some lower-fare-class customers buy higher-fare tickets upon finding that the former tickets are sold out.) For a problem with an arbitrary number of fare classes and independent demands, we show that stochastically larger demand distributions should be preferred. Numerical examples demonstrating the effect of parameterized demand distributions (with appropriate stochastic ordering) and dependence structures are also presented.