October 21, 2001 | Kalyan Talluri, Garrett van Ryzin
This paper addresses the issue of customer choice behavior in revenue management, which is often ignored or approximated in existing methodologies. The authors develop a general and exact analysis of this problem, focusing on a single-leg yield management problem where buyers' choice behavior is explicitly modeled. The choice model specifies the probability of purchasing each fare product as a function of the set of available fare products. The control problem involves deciding which subset of fare products to offer at each point in time. The optimal policy is shown to have a simple form: it consists of identifying a sequence of "nondominated" subsets and opening one of these sets at each time point, with the optimal index increasing in the remaining capacity. The paper also shows that the optimal policy is nested if and only if the ordered sets are increasing, and provides conditions for when nesting by fare order is optimal. Two important models, the independent demand model and the multinomial logit model, are shown to satisfy these conditions, making nested-by-fare-order policies optimal in these cases. Additionally, the paper develops an estimation procedure based on the expectation-maximization (EM) method to estimate arrival rates and choice model parameters when no-purchase outcomes are unobservable. Numerical results are provided to illustrate the model and estimation procedure.This paper addresses the issue of customer choice behavior in revenue management, which is often ignored or approximated in existing methodologies. The authors develop a general and exact analysis of this problem, focusing on a single-leg yield management problem where buyers' choice behavior is explicitly modeled. The choice model specifies the probability of purchasing each fare product as a function of the set of available fare products. The control problem involves deciding which subset of fare products to offer at each point in time. The optimal policy is shown to have a simple form: it consists of identifying a sequence of "nondominated" subsets and opening one of these sets at each time point, with the optimal index increasing in the remaining capacity. The paper also shows that the optimal policy is nested if and only if the ordered sets are increasing, and provides conditions for when nesting by fare order is optimal. Two important models, the independent demand model and the multinomial logit model, are shown to satisfy these conditions, making nested-by-fare-order policies optimal in these cases. Additionally, the paper develops an estimation procedure based on the expectation-maximization (EM) method to estimate arrival rates and choice model parameters when no-purchase outcomes are unobservable. Numerical results are provided to illustrate the model and estimation procedure.