One of the most powerful and simple approaches to model a customer’s choice behavior, with the aim to predict his choice decision facing different options, is non-parametric choice modeling of demand. In this approach, each arriving customer chooses from available alternatives according to an ordered preference list of products. If the customer's most preferred product is not available, he substitutes it with the next lower rank product in his ordered preference list.
In this paper, we propose a new mathematical programming approach to compute optimal allocation of airline resources under a non-parametric choice model of demand. We develop a modified column generation algorithm to efficiently solve large scale, real world practical problems. As the complexity of the algorithm increases with the number of the ordered preference lists, we provide an aggregation algorithm to reduce the number of the ordered preference lists without degrading the quality of the solution. The computational results show that the approach outperforms alternative models.