Correspondence: Jay M Rosenberger, Department of Industrial and Manufacturing Systems Engineering, The University of Texas at Arlington Campus, Box 19017, Arlington, TX 76019, USA. Tel: +1 817 272 5787; Fax: +1 817 272 3406; E-mail: jrosenbe@uta.edu

¹Sheela Siddappa is a researcher at General Motors in Bangalore, India. She holds a PhD in industrial engineering from The University of Texas at Arlington. Her research interests include revenue management, statistical regression, and optimisation under uncertainty. This research was done as part of Siddappa's PhD thesis (Siddappa, 2006).

²Jay Rosenberger is an assistant professor of industrial engineering at The University of Texas at Arlington. He holds a PhD in industrial engineering from the Georgia Institute of Technology. His research interests include mathematical programming and simulation in transportation, defense, and healthcare. Dr Rosenberger's graduate research on airlines won the First Place 2003 Pritsker Doctoral Dissertation award. Prior to joining the faculty at UTA, Dr Rosenberger worked in the Operations Research and Decision Support Department at American Airlines.

³Victoria Chen is an associate professor of industrial engineering at The University of Texas at Arlington. She holds a PhD in Operations Research and Industrial Engineering from Cornell University. Dr Chen's primary research interests utilise statistical methodologies to create new methods for operations research problems appearing in engineering and science. She has expertise in the design of experiments and statistical modelling, particularly for computer experiments and stochastic optimisation. She has studied applications in inventory forecasting, airline optimisation, water reservoir networks, wastewater treatment, and air quality. Through her statistics-based approach, she has developed computationally tractable methods for continuous state stochastic dynamic programming, yield management, and environmental decision-making.

Received 16 February 2007; Revised 16 February 2007; Published online 22 February 2008.

Abstract

We develop an overbooking approach for airline revenue management. We estimate a revenue function by employing a statistical modelling approach, specifically a multivariate adaptive regression splines approximation of a stochastic network model. We develop an overbooking cost function using a binomial distribution to model the number of customers that show up for the flight. We implement a hybrid gradient algorithm that combines Newton's and a steepest ascent method to optimise profit. Finally, we compare our method to one that overbooks based on the probability that the number of customers that show up for a flight exceeds the flight capacity.