Mathematical programming issues related to pricing and revenue management

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This proposal is concerned with issues revolving around the theme of pricing and revenue management, currently one of the most active fields in operations research. It is best explained in the context of an airline that wishes to improve its profitability in a competitive environment, and traditionally involves four components: demand forecasting, overbooking policy, seat inventory control, and pricing. The common thread to these components is that, in contrast with stretegic issues such as aircraft purchasing or route modifications, they do not require capital investment and have a low impact on costs, although they have a direct impact on revenues. My research in this field has been motivated by earlier studies in bilevel programming, a branch of mathematics where a decision maker (a government, a firm) incorporates within its decision process the reaction of other agents (competitors, customers) to its own course of action. This approach, although natural in the revenue management context, yields mathematical formulations that are extremely challenging from the computational point of view.