EVALUATION OF UNCONSTRAINING METHODS IN AIRLINES’ REVENUE MANAGEMENT SYSTEMS

Airline revenue management systems are used to calculate booking limits on each fare class to maximize expected revenue for all future flight departures. Their performance depends critically on the forecasting module that uses historical data to project future quantities of demand. Those data are censored or constrained by the imposed booking limits and do not represent true demand since rejected requests are not recorded. Eight unconstraining methods that transform the censored data into more accurate estimates of actual historical demand ranging from naive methods such as discarding all censored observation, to complex, such as Expectation Maximization Algorithm and Projection Detruncation Algorithm, are analyzed and their accuracy is compared. Those methods are evaluated and tested on simulated data sets generated by ICE V2.0 software: first, the data sets that represent true demand were produced, then the aircraft capacity was reduced and EMSRb booking limits for every booking class were calculated. These limits constrained the original demand data at various points of the booking process and the corresponding censored data sets were obtained. The unconstrained methods were applied to the censored observations and the resulting unconstrained data were compared to the actual demand data and their performance was evaluated

Processing of parafoveally presented words. An fMRI study.

Abstract The present fMRI study investigated neural correlates of parafoveal preprocessing during reading and the type of information that is accessible from the upcoming - not yet fixated - word. Participants performed a lexical decision flanker task while the constraints imposed by the first three letters (the initial trigram) of parafoveally presented words were controlled. Behavioral results evidenced that the amount of information extracted from parafoveal stimuli, was affected by the difficulty of the foveal stimulus. Easy to process foveal stimuli (i.e., high frequency nouns) allowed parafoveal information to be extracted up to the lexical level. Conversely, when foveal stimuli were difficult to process (orthographically legal nonwords) only constraining trigrams modulated the task performance. Neuroimaging findings showed no effects of lexicality (i.e., difference between words and pseudowords) in the parafovea independently from the difficulty of the foveal stimulus. The constraints imposed by the initial trigrams, however, modulated the hemodynamic response in the left supramarginal gyrus. We interpreted the supramarginal activation as reflecting sublexical (phonological) processes. The missing parafoveal lexicality effect was discussed in relation to findings of experiments which observed effects of parafoveal semantic congruency on electrophysiological correlates

Demand Forecasting in Revenue Management Systems

RÉSUMÉ : La gestion des revenues est l’art de développer des modèles mathématiques capables de déterminer quel produit offrir à quel segment de consommateurs à un moment précis dans le but de maximiser les profits. La prévision de la demande joue un rôle fondamental dans la gestion des revenues, car un manque de précision à cet égard engendrer une perte de profits. Dans cette thèse, nous proposons une étude systématique et approfondie de différentes méthodes qui sont employées pour prévoir la demande. Tout d’abord, nous présenterons un nouveau schéma de classification détaillant les caractéristiques de ces différentes méthodes pour déterminer en quoi elles diffèrent les unes des autres. Dans ce but, nous ferons une analyse exhaustive de la littérature existant à ce sujet pour être à même de bien catégoriser ces méthodes dans notre schéma. Par la suite, nous investiguerons à propos des systèmes de gestion des revenue qui utilisent un réseau neuronal artificiel modifié combiné à un historique des données pour prévoir le nombre de passagers, selon les heures de départ, pour une importante entreprise européenne de transport ferroviaire. Après, afin de bien cerner les effets de saisonnalité et modéliser le comportement des consommateurs, nous proposerons un nouveau modèle non paramétrique. La source de notre problématique part d’un modèle non-convexe et non linéaire composé de variables entières. Dans ce modèle, les variables représentent l’utilité de chaque produit ainsi que la demande potentielle de chaque jour et les variables binaires qui sont utilisées afin d’assigner chaque jour à chaque groupe des jours selon ses caractéristiques. Nous avons linéarisé et rendu convexe ce modèle avec succès en utilisant des techniques de linéarisation. Puis, nous avons présenté les caractéristiques de la disponibilité pour un temps donné afin d’extraire les corrélations entre les probabilités générées par ces choix. De plus, nous avons déterminé pour chaque journée un nombre prédéfini de blocs selon les caractéristiques spécifiques de la demande. Ainsi, nous avons pu déterminer une solution initiale basée sur laquelle on serre l’amplitude des variables. Ensuite, nous avons représenté un algorithme séparation et évaluation impliquant des techniques d’optimisation globale pour estimer les utilités et la demande potentielle à chaque jour. Le prétraitement des données a nécessité l’implémentation de plusieurs nœuds avant effectuer le branchement. Ce processus utilise des solveurs linéaires et non linéaires. Les résultats sont représentés par données synthétiques et données réelles. Par ailleurs, ces résultats sont comparés à deux modèles non linéaires d’optimisation globale bien connus. Le modèle que nous proposons offre une performance nettement supérieure. Dans la dernière partie de cette dissertation, nous étudierons l’impact de ce modèle de demande sur la performance des revenues générées. Les résultats sont représentés à l’aide des données synthétiques générés par une programmation linéaire déterministe basée sur les modèles de choix discret.----------ABSTRACT : A revenue management system is defined as the art of developing mathematical models that are capable of determining which product should be offered to which customer segment at a given time in order to maximize revenue. Demand forecasting plays a crucial role in revenue management. The lack of precision in demand models results in the loss of revenue. In this thesis, we provide an in-depth and systematic study of different methods that are applied to demand forecasting. We first introduce a new classification scheme for them and propose the characteristics that differentiate the methods from one another. All existing papers are reviewed and many of them have been categorized based on our classification scheme. After, we investigated a demand prediction model that uses a modified neural network method and historical data to forecast the number of passengers at the departure time for a major European railway company. Afterwards, in order to capture seasonal effects and taking customer behavior into account, we proposed a new, non-parametric mathematical model. The original problem is a nonconvex nonlinear model with integer variables. The variables in this model are the product utilities, the daily demand flow and binary assignment variables. We successfully linearized and convexified the model by using linearization techniques. Then, we used the characteristics of product availabilities for a given time to extract logical relations between choice probabilities. Moreover, we have classified each day to one of the predefined numbers of clusters based on their related daily demand flow. We represent a branch and bound algorithm, which uses global optimization techniques to find the estimated utilities and daily potential demand. Several node preprocessing techniques are implemented before branching. Both linear and nonlinear solvers are used in the branching process. The computational results are represented by using synthetic data. Also, they are compared to two well-known nonlinear and global optimizers and our proposed model outperforms both solvers. In the final part of this dissertation, we investigate the impact of the suggested demand model on revenue performance. The numerical results are presented using synthetic data produced by a modified Deterministic Choice-Based Linear Programming approach. Keywords: Revenue Management, Choice-Based Demand Modeling, Uncensoring Methods, Neural Networks, Global Optimization Approac

Demand forecasting in a railway revenue management system

The research in Revenue Management has tightly focused on airline markets and somewhat neglected other similar markets. The purpose of this thesis is to offer an extensive overview on RM in the railway context. The backgrounds and concepts of RM are discussed and the applicability of RM in railway markets is evaluated. The differences between railways and airlines are also explored. I am especially focused on the demand forecasting process and different methods that can be used to forecast uncertain demand for a specific train. I also discuss how demand forecasting relates to other RM components, such as capacity allocation. Relevant RM theories and demand forecasting methods are compiled based on the existing literature. Because of the limited availability of real demand data, I use hypothetical demand data to illustrate how different forecasting methods can be applied and how the performance of each method can be evaluated. I also compile an illustrative capacity allocation example using EMSR -model. I conclude that the applicability of RM in railway markets is evident. I find four significant differences between railways and airlines that are relevant to RM. Railways tend to have more complex networks, less price differentiation, shorter booking lead times, and less competitive markets. Illustrative demand forecasting examples indicate that the evaluation of different forecasting methods is essential, since the performance of different methods might vary substantially, depending on the available data and the time horizon of desired forecast. Capacity allocation examples suggest that it is particularly important that demand forecasts would provide the accurate predictions of total demand and demand distribution between fare classes. However, it should be taken into account that the findings of illustrative examples cannot be generalized, since the hypothetical data was used in the analysis. Thus further examination with real demand data should be required. Additionally, the issues of constrained data and network effect are omitted from the analysis

Forecast combination in revenue management demand forecasting.

The domain of multi level forecast combination is a challenging new domain containing a large potential for forecast improvements. This thesis presents a theoretical and experimental analysis of different types of forecast diversification on forecast error covariances and resulting combined forecast quality. Three types of diversification are used: (a) diversification concerning the level of learning (b) diversification of predefined parameter values and (c) the use of different forecast models. The diversification is carried out on forecasts of seasonal factor predictions in Revenue Management for Airlines. After decomposing the data and generating diversified forecasts a (multi step) combination procedure is applied. We provide theoretical evidence of why and under which conditions multi step multi level forecast combination can be a powerful approach in order to build a high quality and adaptive forecast system. We theoretically and experimentally compare models differing with respect to the used decomposition, diversification as well as the applied combination models and structures. After an introduction into the application of forecasting seasonal behaviour in Revenue Management, a literature review of the theory of forecast combination is provided. In order to get a clearer idea of under which condition combination works, we then investigate aspects of forecast diversity and forecast diversification. The diversity of forecast errors in terms of error covariances can be expressed in a decomposed manner in relation to different independent error components. This type of decomposed analysis has the advantage that it allows conclusions concerning the potential of the diversified forecasts for future combination. We carry out such an analysis of effects of different types of diversification on error components corresponding to the bias-variance-Bayes decomposition proposed by James and Hastie. Different approaches of how to include information from different levels into forecasting are also discussed in the thesis. The improvements achieved with multi level forecast combination prove that theoretical analysis is extremely important in this relatively new field. The bias-variance-Bayes decomposition is extended to the multi level case. An analysis of the effects of including forecasts with parameters learned at different levels on the bias and variance error components show that forecast combination is the best choice in comparison to some other discussed alternatives. The proposed approach represents a completely automatic procedure. It realises changes in the error components which are not only advantageous at the low level, but have also a stabilising effect on aggregates of low level forecasts to the higher level. We also identify cases in which multi level forecast combination should ideally be connected with the use of different function spaces and/or thick modelling related to certain parameter values or preprocessing procedures. In order to avoid problems occurring for large sets of highly correlated forecasts when considering covariance information, we investigated the potential of pooling and trimming for our case. We estimate the expected behaviour of our diversified forecasts in purely error variance based pooling represented by a common approach of Aiolfi and Timmermann and analyse effects of different kinds of covariances on the accuracy of the combined forecast. We show that a significant loss in the expected forecast accuracy may ensue because of typical inhomogeneities in the covariance matrix for the analysed case. If covariance information is available in a sufficiently high quality, it is possible to run a clustering directly based on covariance information. We discuss how to carry out a clustering in that case. We also consider a case (quite common in our application) when covariance information may not be available and propose a novel simplified representation of the covariance matrix which represents the distance in the forecast generation space and is only based on knowledge about the forecast generation process. A new pooling approach is proposed that avoids inhomogeneities in the covariance matrix by considering the information contained in the simplified covariance representation. One of the main advantages of the proposed approach is that the covariance matrix does not have to be calculated. We compared the results of our approach with the approach of Aiolfi and Timmermann and explained the reasons for significant improvement. Another advantage of our approach is that it leads to the generation of novel multi step, multi level forecast generation structures that carry out the combination in different steps of pooling. Finally, we describe different evolutionary approaches in order to generate combination structures automatically. We investigate very flexible approaches as well as approaches that avoid the expected inhomogeneities in the error covariance matrix based on our theoretical findings. The theoretical analysis is supported by experimental results. We could achieve an improvement of forecast quality up to 11 percent for the practical application of demand forecasting in Revenue Management compared to the current optimised forecasting system

Deep Inventory Management

We present a Deep Reinforcement Learning approach to solving a periodic review inventory control system with stochastic vendor lead times, lost sales, correlated demand, and price matching. While this dynamic program has historically been considered intractable, we show that several policy learning approaches are competitive with or outperform classical baseline approaches. In order to train these algorithms, we develop novel techniques to convert historical data into a simulator. We also present a model-based reinforcement learning procedure (Direct Backprop) to solve the dynamic periodic review inventory control problem by constructing a differentiable simulator. Under a variety of metrics Direct Backprop outperforms model-free RL and newsvendor baselines, in both simulations and real-world deployments

Single-dimensional leg-level dynamic programming with booking-time dependent cancellation probabilities for revenue management

In this paper, an optimisation method is introduced that accounts for cancellations. We do so by estimating the opportunity cost of a booking between the time of booking and the expected time of cancellation. The formulation involves an estimate of the value of the state of the system at the time of cancellation (which is in the future), found through novel heuristics we introduce. The fare that is used to determine whether a product is available for sale, is adjusted by the risk the airline faces. We introduce an example which shows that there may be cases where it is optimal to reject a higher-priced product if the risk of cancellation is high, while accepting a lower-priced product. Simulations show increases in revenues against a traditional formulations that does not explicitly models cancellations. We show our method is robust against choice of heuristic, misjudgement of cancellation probability and forecasting errors

Improving joint revenues through partner sharing of flight leg opportunity costs

Thesis (S.M. in Transportation)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 125-128).Airlines participating in alliances offer code share itineraries (with flight segments operated by different partners) to expand the range of origin-destination combinations offered to passengers, thus increasing market share at little cost. The presence of code share flights presents a problem for airline revenue management (RM) systems, which aim to maximize revenues in an airline's network by determining which booking requests are accepted. Because partners do not jointly optimize revenues on code share flights, alliance revenue gains from implementing advanced RM methods may be lower than an individual airline's gains. This thesis examines seat availability control methods that alliance partners can adopt to improve the total revenues of the alliance without formally merging. Partners share information about the opportunity costs to their network, called "bid prices", of selling a seat on their own flight leg, a mechanism termed bid price sharing (BPS). Results show that BPS methods often improve revenues and work best for networks with certain characteristics and partners with similar RM systems that exchange recently calculated bid prices as often as possible. Gains are typically only achieved if both alliance partners participate in the code share availability decision (called dual control) rather than one partner only, but implementation of dual control is more difficult for airlines in practice. In the best case scenario, gains of up to .40% where achieved, which can translate into $120 million per year for the largest airlines. In our simulations, BPS with dual control and frequent bid price calculation and exchange was the only method that produced consistently positive revenue gains in all the scenarios tested. Therefore, alliance airlines must consider the trade off between revenue gains and implementation difficulties of more frequent bid price exchange or dual control.by Alyona Michel.S.M.in Transportatio