Kalyan T. Talluri

The theory and practice of revenue management

Quantity-Based RM.- Single-Resource Capacity Control.- Network Capacity Control.- Overbooking.- Price-based RM.- Dynamic Pricing.- Auctions.- Common Elements.- Customer-Behavior and Market-Response Models.- The Economics of RM.- Estimation and Forecasting.- Industry Profiles.- Implementation.

A Randomized Linear Programming Method for Computing Network Bid Prices

We analyze a randomized version of the deterministic linear programming (DLP) method for computing network bid prices. The method consists of simulating a sequence of realizations of itinerary demand and solving deterministic linear programs to allocate capacity to itineraries for each realization. The dual prices from this sequence are then averaged to form a bid price approximation. This randomized linear programming (RLP) method is only slightly more complicated to implement than the DLP method. We show that the RLP method can be viewed as a procedure for estimating the gradient of the expected perfect information (PI) network revenue. That is, the expected revenue obtained with full information on future demand realizations. The expected PI revenue can, in turn, be viewed as an approximation to the optimal value function. We establish conditions under which the RLP procedure provides an unbiased estimator of the gradient of the expected PI revenue. Computational tests are performed to evaluate the revenue performance of the RLP method compared to the DLP.

The Aircraft Maintenance Routing Problem

Federal aviation regulations require that all aircraft undergo maintenance after flying a certain number of hours. To ensure high aircraft utilization, maintenance is done at night, and these regulations translate into requiring aircraft to overnight at a maintenance station every three to four days (depending on the fleet type), and to visit a balance-check station periodically. After the schedule is fleeted, the aircraft are routed to satisfy these maintenance requirements. We give fast and simple polynomial-time algorithms for finding a routing of aircraft in a graph whose routings during the day are fixed, that satisfies both the three-day maintenance as well as the balance-check visit requirements under two different models: a static infinite-horizon model and a dynamic finite-horizon model. We discuss an implementation where we embed the static infinite-horizon model into a three-stage procedure for finding a maintenance routing of aircraft.

Swapping Applications in a Daily Airline Fleet Assignment

An airlines schedule consists of a set of flight legs that it is scheduled to fly. A fleet assignment is an assignment of equipment types (such as a 757, 767, F100 etc.) to each of the flight legs. The fleet assignment is called a daily fleet assignment if the same assignment of equipment types is used every day of the week. The daily fleet assignment has to satisfy certain coverage, balance, and equipment availability constraints. Given a daily fleet assignment, we consider the problem of changing the assignment of a specified flight leg to a different equipment type while still satisfying all the constraints. We give a simple algorithm for making this swap that will not affect the equipment type composition of aircraft overnighting at the various stations. We describe two further applications of our swapping procedure in the airline schedule development process.

Mathematical models in airline schedule planning: A survey

The schedule is an airlines primary product, having the most influence (along with price) on a passengers choice of an airline. Once an airline decides (at least tentatively) on a schedule, a host of related problems have to be resolved before it can consider the schedule feasible, and can proceed to market the schedule. Among these problems are traffic forecasting and allocation that forecasts traffic on each flight leg for use in the fleet assignment model, fleet assignment that decides the fleet type of the aircraft flying the legs in the schedule, equipment swapping to change an assigned equipment type on a leg if and when necessary, through flight selection for determining which pairs of flights to market as one-stops (without any aircraft change), maintenance routing that develops aircraft rotations to provide adequate opportunities for overnight maintenance, and flight numbering to number flights as consistently as possible with a prior schedule. Considerable methodological and computational advances have been made in the recent past in developing models and solution methods for almost all of the problems mentioned above. In this paper we survey these various models and solution techniques.

Dynamic Price Competition with Fixed Capacities

In this paper, we study price competition for an oligopoly in a dynamic setting, where each of the sellers has a fixed number of units available for sale over a fixed number of periods. Demand is stochastic, and depending on how it evolves, sellers may change their prices at any time. This reflects the fact that firms constantly, and almost costlessly, change their prices, reacting to updates in their estimates of market demand, competitor prices, or inventory levels. In a setting with demand uncertainty, we show that there is a unique subgame-perfect equilibrium for a duopoly, in which all states sellers engage in Bertrand competition and the seller with the lower equilibrium reservation value sells a unit at a price equal to the competitors equilibrium reservation value. This structure therefore extends the marginal-value concept of bid-price control, used in many revenue management implementations, to a competitive model. We give a closed-form solution to the equilibrium price paths for a duopoly and extend all the results to an n-firm oligopoly. We then study extensions to multiple customer types, uncertain valuations, and differentiated products. This paper was accepted by Martin Lariviere, operations management.

Revenue management: models and methods

Revenue management is the collection of strategies and tactics firms use to scientifically manage demand for their products and services. The practice has grown from its origins in airlines to its status today as a mainstream business practice in a wide range of industry areas, including hospitality, energy, fashion retail, and manufacturing. This article provides an introduction to this increasingly important subfield of operations research, with an emphasis on use of simulation. Some of the contents are based on excerpts from the book The Theory and Practice of Revenue Management (Talluri and van Ryzin 2004a), written by the first two authors of this article.

A Randomized Linear Programming Method for Network Revenue Management with Product-Specific No-Shows

Revenue management practices often include overbooking capacity to account for customers who make reservations but do not show up. In this paper, we consider the network revenue management problem with no-shows and overbooking, where the show-up probabilities are specific to each product. No-show rates differ significantly by product (for instance, each itinerary and fare combination for an airline) as sale restrictions and the demand characteristics vary by product. However, models that consider no-show rates by each individual product are difficult to handle because the state-space in dynamic programming formulations (or the variable space in approximations) increases significantly. In this paper, we propose a randomized linear program to jointly make the capacity control and overbooking decisions with product-specific no-shows. We establish that our formulation gives an upper bound on the optimal expected total profit, and our upper bound is tighter than a deterministic linear programming upper bound that appears in the existing literature. Furthermore, we show that our upper bound is asymptotically tight in a regime where the leg capacities and the expected demand is scaled linearly with the same rate. We also describe how the randomized linear program can be used to obtain a bid price control policy. Computational experiments indicate that our approach is quite fast, is able to scale to industrial problems, and can provide significant improvements over standard benchmarks.

A Finite-Population Revenue Management Model and a Risk-Ratio Procedure for the Joint Estimation of Population Size and Parameters

Many dynamic revenue management models divide the sale period into a finite number of periods T and assume, invoking a fine-enough grid of time, that each period sees at most one booking request. These Poisson-type assumptions restrict the variability of the demand in the model, but researchers and practitioners were willing to overlook this for the benefit of tractability of the models. In this paper, we criticize this model from another angle. Estimating the discrete finite-period model poses problems of indeterminacy and non-robustness: Arbitrarily fixing T leads to arbitrary control values and on the other hand estimating T from data adds an additional layer of indeterminacy. To counter this, we first propose an alternate finite-population model that avoids this problem of fixing T and allows a wider range of demand distributions, while retaining the useful marginal-value properties of the finite-period model. The finite-population model still requires jointly estimating market size and the parameters of the customer purchase model without observing no-purchases. Estimation of market-size when no-purchases are unobservable has rarely been attempted in the marketing or revenue management literature. Indeed, we point out that it is akin to the classical statistical problem of estimating the parameters of a binomial distribution with unknown population size and success probability, and hence likely to be challenging. However, when the purchase probabilities are given by a functional form such as a multinomial-logit model, we propose an estimation heuristic that exploits the specification of the functional form, the variety of the offer sets in a typical RM setting, and qualitative knowledge of arrival rates. Finally we perform simulations to show that the estimator is very promising in obtaining unbiased estimates of population size and the model parameters.

On Equilibria in Duopolies with Finite Strategy Spaces

We will call a game a reachable (pure strategy) equilibria game if starting from any strategy by any player, by a sequence of best-response moves we are able to reach a (pure strategy) equilibrium. We give a characterization of all finite strategy space duopolies with reachable equilibria. We describe some applications of the sufficient conditions of the characterization.