Title: Estimation and Optimization Problems in Revenue Management with Customer Choice Behavior

Advisor: Dr. Anton Kleywegt

Committee Members:

Dr. Jim Dai

Dr. David Goldberg

Dr. Brani Vidakovic

Dr. Jim Xu (College of Computing)

Date and time: Tuesday, December 6th, 1:00 PM.

Location: ISyE Groseclose Building, 226

Abstract:

Revenue management is the application of various statistical and operations research techniques to choose the price and availability of a company's products to optimize the revenue performance. To successfully achieve the goal of revenue maximization, revenue managers desire an accurate understanding of customer behavior. One important trend in revenue management is to model customer behavior using discrete choice models. This thesis deals with some of the challenges that arise with the incorporation of discrete choice models in revenue management.

The first part of the thesis studies the parameter estimation problem in revenue management with discrete choice models. Revenue management models that include customer choice behavior have among others two types of parameters: (1) customer arrival rates and (2) choice parameters. In most applications, revenue managers have access to censored arrival data only, because the data do not include potential customers who decided not to purchase, that is, no-purchase data are missing. An important question is under what conditions all the arrival rate and choice parameters are identifiable with such censored data. It has been known that if the censored data contain observed choices among alternatives in only one assortment, then models with both arrival rate and choice parameters are not identifiable, even if the arrival process is homogeneous. We consider a setting with multiple assortments, in which case arrival rate and choice parameters may or may not be identifiable. We derive the necessary and sufficient conditions for the arrival rate and choice parameters to be identifiable with censored data. When the arrival process is a non-homogeneous Poisson process, the identification of arrival rate and choice parameters is possible only when we have observed multiple sample paths with the same arrival rates. We derive the necessary and sufficient conditions for the identification of the arrival rate function and the choice parameters. Surprisingly, the identification conditions are mild and do not depend on any knowledge of the arrival rate function. Based on this observation, we propose a semiparametric estimation procedure to jointly estimate the arrival rate function and the choice parameters. Both the estimates of the cumulative arrival rate function and the choice parameters are proved to converge to the true quantities almost surely when the data increase. Numerical examples also show that the algorithm can accurately estimate the arrival process and the choice parameters.

The second part of the thesis focuses on a revenue management problem with the buy-down effect. The buy-down effect refers to the phenomenon that a product becomes more attractive if it is the cheapest available within a certain subset of the assortment, than if it is not the cheapest available within that subset. The multinomial logit (MNL) model can be modified to reflect the buy-down effect. We consider the dynamic assortment optimization problem under a discrete choice model with the buy-down effect. We propose a sales based linear programming (SBLP) formulation as a deterministic approximation to the original stochastic problem. Both the number of the decision variables and the number of constraints in the SBLP formulation are polynomial of the number of products. Thus, it is a much more efficient model than the popular choice based deterministic linear programming (CDLP) formulation. We give an efficient algorithm that converts an SBLP solution to a CDLP solution. We then consider the extreme case of the buy-down effect, where customers consider only the cheapest available product in each specified subset of the assortment. An SBLP formulation is developed and an algorithm that converts an SBLP solution to a CDLP solution is given. Last, we consider the extension where the no-purchase alternative in the choice set is random. We propose a polynomial algorithm to solve the assortment optimization problem with 100\% buy-down effect and random no-purchase alternative. We prove that if a choice model has a general buy-down effect, then an optimal solution to the static assortment optimization problem under a discrete choice model with buy-down effect and random no-purchase alternative is nested by revenue within subsets. The nesting property allows us to reduce the assortment optimization problem with general buy-down effect to the one with 100\% buy-down effect, for which our efficient polynomial algorithm can be used.