Groupe d’études et de recherche en analyse des décisions

Revenue Management and Bilevel Programming

Gilles Savard Professeur titulaire, Département de mathématiques et de génie industriel, Polytechnique Montréal, Canada

The vast majority of revenue management systems currently implemented in the airline and rail industries focus on demand forecasting, overbooking and seat inventory, while neglecting the pricing issue, either from the supply side (price setting) or the demand side (customer reaction to fares set by all carriers). The aim of this presentation is to propose a unified framework for price optimization under behavioural demand models. Rather than using econometric models to modelize the demand, we consider a comprehensive and detailed optimization model to simulate customer behaviour. This leads to a bilevel program where the leader controls parameters such as prices or capacity, while customers respond by optimizing their utility over the supply set by the leader firm and its competitors. After an introduction of the bilevel programming problem, we discuss the main properties of two bilevel classes, namely the linear/linear and the bilinear/bilinear ones, and their links to well-known combinatorial problems. We illustrate the bilevel programming paradigm in the context of Revenue Management by presenting in details a model for jointly optimizing and automating the pricing and seat allocation processes of an airline.

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