Jeff McGill

Revenue Management: Research Overview and Prospects

This survey reviews the forty-year history of research on transportation revenue management (also known as yield management). We cover developments in forecasting, overbooking, seat inventory control, and pricing, as they relate to revenue management, and suggest future research directions. The survey includes a glossary of revenue management terminology and a bibliography of over 190 references.

Airline seat allocation with multiple nested fare classes

This paper addresses the problem of determining optimal booking policies for multiple fare classes that share the same seating pool on one leg of an airline flight when seats are booked in a nested fashion and when lower fare classes book before higher ones. We show that a fixed-limit booking policy that maximizes expected revenue can be characterized by a simple set of conditions on the subdifferential of the expected revenue function. These conditions are appropriate for either the discrete or continuous demand cases. These conditions are further simplified to a set of conditions that relate the probability distributions of demand for the various fare classes to their respective fares. The latter conditions are guaranteed to have a solution when the joint probability distribution of demand is continuous. Characterization of the problem as a series of monotone optimal stopping problems proves optimality of the fixed-limit policy over all admissible policies. A comparison is made of the optimal solutions ...

Allocation of Airline Seats between Stochastically Dependent Demands

This paper examines the problem of allocating airline seats between two nested fare classes when the demands for the classes are stochastically dependent. The well known simple seat allotment formula of Littlewood which requires the assumption of statistical independence between demands is generalized to a formula which requires only a much weaker monotonic association assumption. The model employed here is also used to examine the problems of full fare passenger spillage and passenger upgrades from the discount class.

Dynamic Pricing in the Presence of Strategic Consumers and Oligopolistic Competition

We present a dynamic pricing model for oligopolistic firms selling differentiated perishable goods to multiple finite segments of strategic consumers who are aware that pricing is dynamic and may time their purchases accordingly. This model encompasses strategic behavior by both firms and consumers in a unified stochastic dynamic game in which each firms objective is to maximize its total expected revenues, and each consumer responds according to a shopping-intensity-allocation consumer choice model. We prove the existence of a unique subgame-perfect equilibrium, provide equilibrium optimality conditions, and prove monotonicity results for special cases. The model provides insights about equilibrium price dynamics under different levels of competition, asymmetry between firms, and multiple market segments with varying properties. We demonstrate that strategic behavior by consumers can have serious impacts on revenues if firms ignore that behavior in their dynamic pricing policies. Moreover, ideal equilibrium responses to consumer strategic behavior can recover only a portion of the lost revenues. A key conclusion is that firms may benefit more from limiting the information available to consumers than from allowing full information and responding to the resulting strategic behavior in an optimal fashion.

Risk in Revenue Management and Dynamic Pricing

We present a new model for optimal dynamic pricing of perishable services or products that incorporates a simple risk measure permitting control of the probability that total revenues fall below a minimum acceptable level. The formulation assumes that sales must occur within a finite time period, that there is a finite---possibly large---set of available prices, and that demand follows a price-dependent, nonhomogeneous Poisson process. This model is particularly appropriate for applications in which attainment of a revenue target is an important consideration for managers; for example, in event management, in seasonal clearance of high-value items, or for business subunits operating under performance targets. We formulate the model as a continuous-time optimal control problem, obtain optimality conditions, explore structural properties of the solution, and report numerical results on problems of realistic size.

Dynamic Pricing with Online Learning and Strategic Consumers: An Application of the Aggregating Algorithm

We study the problem faced by a monopolistic company that is dynamically pricing a perishable product or service and simultaneously learning the demand characteristics of its customers. In the learning procedure, the company observes the sales history over consecutive learning stages and predicts consumer demand by applying an aggregating algorithm (AA) to a pool of online stochastic predictors. Numerical implementation uses finite-sample distribution approximations that are periodically updated using the most recent sales data. These are subsequently altered with a random step characterizing the stochastic predictors. The companys pricing policy is optimized with a simulation-based procedure integrated with AA. The methodology of the paper is general and independent of specific distributional assumptions. We illustrate this procedure on a demand model for a market in which customers are aware that pricing is dynamic, may time their purchases strategically, and compete for a limited product supply. We derive the form of this demand model using a game-theoretic consumer choice model and study its structural properties. Numerical experiments demonstrate that the learning procedure is robust to deviations of the actual market from the model of the market used in learning.

Price Guarantees in Dynamic Pricing and Revenue Management

We present a new model for revenue management of product sales that incorporates both dynamic pricing and a price guarantee. The guarantee provides customers with compensation if, prior to a fixed future date, the price of the product drops below a level specified at the time of purchase. We consider the problem of simultaneously determining optimal dynamic price and guarantee policies for items from a fixed stock when demand depends both on the price and on the parameters of the price guarantee. The model can be used for pricing any items with limited availability over a fixed time horizon. We formulate this model as a discrete-time optimal control problem, prove the existence of its optimal solution, explore some of the structural properties of the solution, present lower-bounding heuristics for solving the problem, and report numerical results.

Censored regression analysis of multiclass passenger demand data subject to joint capacity constraints

In most passenger transportation systems, demand for seats is not recorded after all spaces for a particular trip have been sold out or after a booking limit has been reached. Thus historical booking data is comprised of ticketsales notdemand — a condition known as censorship of the data. Data censorship is particularly complex when there are multiple classes of demand since the demand in one class can influence the degree of censorship in another. This paper examines the problem of simultaneously estimating passenger demand models for two or more correlated classes of demand that are subject to a common capacity constraint. It is shown that theEM method of Dempster et al. [5] can be adapted to provide maximum likelihood estimates of the parameters of the demand model under these circumstances. The problem of modelling demand for airline flights is discussed as a typical example of this estimation problem. Numerical examples show that, with reasonable sample sizes, it is possible to obtain good estimates even when 75% or more of the data have been censored.

Network Cargo Capacity Management

We consider the problem faced by an airline that is flying both passengers and cargo over a network of locations on a fixed periodic schedule. Bookings for many classes of cargo shipments between origin-destination pairs in this network are made in advance, but the weight and volume of aircraft capacity available for cargo as well as the exact weight and volume of each shipment are not known at the time of booking. The problem is to control cargo accept/reject decisions to maximize expected profits while ensuring effective dispatch of accepted shipments through the network. This network stochastic dynamic control problem has very high computational complexity. We propose a linear programming and stochastic simulation-based computational method for learning approximate control policies and discuss their structural properties. The proposed method is flexible and can utilize historical booking data as well as decisions generated by default control policies.

Linear programming with online learning

We propose online decision strategies for time-dependent sequences of linear programs which use no distributional and minimal geometric assumptions about the data. These strategies are obtained through Vovks aggregating algorithm which combines recommendations from a given strategy pool. We establish an average-performance bound for the resulting solution sequence.