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

Evolving Multilevel Forecast Combination Models - An Experimental Study

This paper provides a description and experimental comparison of different forecast combination techniques for the application of Revenue Management forecasting for Airlines. In order to benefit from the advantages of forecasts predicting seasonal demand using different forecast models on different aggregation levels and to reduce the risks of high noise terms on low level predictions and overgeneralization on higher levels, various approaches based on combination of many predictions are presented and experimentally compared. We propose to evolve combination structures dynamically using Evolutionary Computing approaches. The evolved structures are not only able to generate predictions representing well balanced and stable fusions of methods and levels, they are also characterised by high adaptive capabilities. The focus on different levels or methods of forecasting may change as well as the complexity of the combination structure depending on changes in parts of the input data space in different data aggregation levels. Significant forecast improvements have been obtained when using the proposed dynamic multilevel structures

Forecasting and Forecast Combination in Airline Revenue Management Applications

Predicting a variable for a future point in time helps planning for unknown future situations and is common practice in many areas such as economics, finance, manufacturing, weather and natural sciences. This paper investigates and compares approaches to forecasting and forecast combination that can be applied to service industry in general and to airline industry in particular. Furthermore, possibilities to include additionally available data like passenger-based information are discussed

Adaptive Mechanisms in an Airline Ticket Demand Forecasting System

Adaptivity is a very important feature for industrial forecast systems. In the airline industry, a reliable forecasting of a demand for tickets at different fare levels forms a crucial step in a global optimization process, the objective of which is to sell a restricted number of available seats in a plane with a maximized revenue. Due to continuously changing demand caused by seasonality, special events like holidays or fairs, changes in the flight schedules or changes of the political or cultural situation of a country, there is a need for robust, adaptive forecasting techniques able to cope with such changes. In this paper an overview of various adaptive mechanisms used in the new forecasting system of the Lufthansa Airline is presented

Dynamic Pooling for the Combination of Forecasts Generated Using Multi Level Learning

In this paper we provide experimental results and extensions to our previous theoretical findings concerning the combination of forecasts that have been diversified by three different methods: with parameters learned at different data aggregation levels, by thick modeling and by the use of different forecasting methods. An approach of error variance based pooling as proposed by Aiolfi and Timmermann has been compared with flat combinations as well as an alternative pooling approach in which we consider information about the used diversification. An 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 corresponding to the different types of diversification. We describe different evolutionary approaches in order to evolve the order of pooling of the diversification dimensions. Extensions of such evolutions allow the generation of more flexible multi level multi step combination structures containing better adaptive capabilities. We could prove a significant error reduction comparing results of our generated combination structures with results generated with the algorithm of Aiolfi and Timmermann as well as with flat combination for the application of Revenue Management seasonal forecasting

Integration of Forecasting, Scheduling, Machine Learning, and Efficiency Improvement Methods into the Sport Management Industry

Sport management is a complicated and economically impactful industry and involves many crucial decisions: such as which players to retain or release, how many concession vendors to add, how many fans to expect, what teams to schedule, and many others are made each offseason and changed frequently. The task of making such decisions effectively is difficult, but the process can be made easier using methods of industrial and systems engineering (ISE). Integrating methods such as forecasting, scheduling, machine learning, and efficiency improvement from ISE can be revolutionary in helping sports organizations and franchises be consistently successful. Research shows areas including player evaluation, analytics, fan attendance, stadium design, accurate scheduling, play prediction, player development, prevention of cheating, and others can be improved when ISE methods are used to target inefficient or wasteful areas