Integrated Airline Scheduling
4.2 Schedule Evaluation .1 Overview.1Overview
4.2.2 Market Size Estimation
4.2.2.4 Gravity Model Development
The gravity model by Grosche et al. (2007) is used as a basis from which the model used in this study is derived. This model primarily uses geo-economic variables as input and cross-sectional data for calibration, allowing an application to new mar- kets for which historical data is not available.6Statistical tests on the model show
6This set of variables is extracted from the data also available for this study.
satisfying results; in addition, the model was thoroughly validated with a formal test and by analyzing the stability of the coefficient of determination R2and the co- efficients of the independent variables for different subsets of the total number of observations.
One reason for the good performance of this gravity model is its application to ho- mogeneous data, because only routes between Germany and other European coun- tries were available for calibration. This assumption is confirmed when applying the calibrated model to all city-pairs within Europe. Because some statistical offices and industrial organizations (for example Eurostat, AEA, ICAO etc.) publish traffic figures for some selected routes, their order with regard to passenger flows can be compared with the order of the estimated passenger demand figures. A comparison unveils an overestimation by the gravity model especially for long-haul routes. The reason for this might be Germany’s central geographical position in Europe, leading to calibration data with markets representing typical medium-haul flights.
These observations support the basic requirement to apply gravity models to ho- mogeneous markets (Kanafani, 1983). For this study in which all city-pairs in Eu- rope are considered, the next step would be to build a set of gravity models and to calibrate them across the various markets within Europe, or to use European-wide data for the calibration of a more robust gravity model that then could be applied to all markets. In fact, the estimation of market sizes by airlines consists of the con- struction and calibration of many different models for individual regions or routes.
Unfortunately, reliable data needed for such a calibration is not available for this study. Thus, two strategies remain to obtain market sizes for further use:
1. Usage of observed passenger flows as market size between those city-pairs for which this information is published.
2. Construction, calibration and application of a gravity model that has been re- duced compared to the model of Grosche et al. (2007) to better reflect all mar- kets in Europe.
The first strategy provides accurate data of realized passenger flows. However, these flows represent constrained passenger demand, because they result from existing air- line services with their characteristics. For example, if there is no airline service on a market, the resulting passenger flow is zero even if demand exists. Or if capacities are small for a city-pair, the passenger flows probably underestimate the real uncon- strained demand. Also because of the lack of available data, using this strategy re- sults in a zero matrix for the demand between city-pairs with only a few cells filled.
In contrast, a gravity model produces demand estimates with traffic between many city-pairs. Thus, it better reflects the (unconstrained) demand structure, although the individual passenger numbers estimated for the city-pairs will differ from the real values and the overall model fit might be poor. The reason for this is that the gravity model is applied to heterogeneous markets, although it was calibrated with homogeneous data sets. Nevertheless, this strategy is applied to produce market size estimates, because to assess different airline schedule construction techniques, the accuracy of passenger forecasts on selected markets is less important than consider- ing more realistic demand structures across all markets. It has to be emphasized that
76 4 Integrated Airline Scheduling this reduction and the related drawbacks result from the lack of information on the demand. If market sizes are available or could be obtained with any other estimation technique, this data could be used immediately to replace the estimates used here for schedule evaluation or to calibrate better fitting gravity models.
The gravity model used for market size estimation in this study is the basic model presented by Grosche et al. (2007) without the independent variables travel time and GDP. Airports of multi-airport cities were aggregated. The final model was manually selected by ordering the markets according to their estimated market sizes and comparing this order with the order of markets with real data available. It has the following form:
Vi j=eεPi jπCi jχBβi jDδi j, (4.6) where Vi j is the total passenger volume between cities i and j, the exponents in Greek letters are used to model the impact of the input factors and are subject to the calibration process. The variables in capital letters are the independent factors influ- encing the travel volume. Table 4.2 lists the variables and their aggregate functional forms.
Table 4.2 Independent factors of the gravity model
Variable Functional Factor
Form
Pi j PiPj Population
Ci j CiCj Catchment
Bi j Bi+Bj Buying power index
Di j Geographical distance
The following items briefly describe the independent variables used in the model.
• Population: The population of a city is determined based on various statistical offices of the involved countries. In all cases the latest figures were considered.
The population refers only to the city of each airport, potential passengers from an airport’s vicinity are included in the catchment data.
• Catchment: A catchment area of an airport covers the vicinity of an airport.
Usually, the catchment area includes only those areas that are within a certain traveling distance to the airport. Consequently, the catchment area of an airport is defined as the region that is within 60 minutes driving time. The number of people living in this region are expected to use the airport for their travel pur- poses and are thus included in the catchment. The catchment data is derived from population data of the regions given on the NUTS3-level. NUTS (Nomen- clature des unit´es territoriales statistiques) are classification levels of territo- rial units of about the same population size that provide the basis for regional statistics for the European Union (see Fig. 4.4 for an example). In this model, catchment data from the year 2003 is considered.
• Buying power index: The average buying power index is constructed on the basis of an airport’s catchment area. Like the catchment, the buying power index
Fig. 4.4 NUTS3 on the northern coast of Germany
is given on the NUTS3-level with 100 as the European average. The index can be interpreted as an indicator for the size of the travel budget of the population within an airport’s catchment. The data used for calibration is from 2003.
• Geographical distance: The distance between two airports is calculated as the great circle distance in kilometers between the airports’ coordinates.
The calibration of the gravity model is conducted using the ordinary least square method. Table 4.3 presents the coefficients of the resulting model with t-statistics and standardized beta coefficients. The t-statistics indicate that the null hypothesis Table 4.3 Calibration results of the gravity model
Coefficients Pi j Ci j Bi j Di j
Values 0.357 0.203 1.722 -0.127
t-statistics 12.871 8.013 8.255 -2.047
Beta coefficients 0.350 0.229 0.222 -0.057
(the independent variables have no effect) can be rejected for each variable at the 5%-level. As discussed before, although the R2 is rather poor (R2=0.283), this model is used to calculate market size, because it better reflects demand structures across various markets in Europe.