Integrated Airline Scheduling
4.2 Schedule Evaluation .1 Overview.1Overview
4.2.4 Itinerary Market Share Estimation
4.2.4.2 Setup
The impact of attributes of itineraries on their attraction can be modeled either sep- arately for each city pair, or aggregated for all city pairs. If modeled separately for each city pair, model parameters are different between markets, whereas the aggregated calibration – as conducted here – results in method parameters appli- cable to all city pairs. Thus, the model can be used for estimation in new markets which is important for flight schedule construction. In addition, this study does not use different passenger segments or time periods resulting in group-specific or time- specific coefficients. Instead, each model is calibrated using all available data.
The total demand in one market is calculated as the sum of all bookings over all itineraries in the market. By dividing the number of passengers on one itinerary by the total number of passengers in the market, the market share of this itinerary can be calculated. By using the market share as the dependent variable, an aggregate
86 4 Integrated Airline Scheduling
Fig. 4.12 Different time preference functions aDT P(t)
0 0.2 0.4 0.6 0.8 1
00:00 06:00 12:00 18:00 23:55
Preference
Time
USA70 AXS EU86
forecasting model for all city pairs can be built and the effects of different market sizes are eliminated.
Data. In this study, the MIDT data described in Sect. 4.1.3 was used. This data mea- sures the realized passenger demand for each itinerary in a market (thus, the market share can be calculated) and provides the corresponding attributes of the itineraries.
A market consists of all itineraries available on one day between a pair of airports.
Only markets with at least two itineraries are considered in the study (if only one itinerary exists no estimation of the market share is necessary). The resulting data set contains 2,978 different city pairs with a total of 961,430 itineraries.
In principle, the number of attributes of an itinerary can be large depending on the level of detail. Table 4.5 lists the attributes (independent variables) that are used for this study to describe relevant properties of itineraries. It also presents a short de- scription of each variable, its range, and if necessary, the functional form as used in the different models. The different variables are modeled in such a way that the impact of the variable on the attraction of an itinerary increases with higher values.
The variable aDT P(t)requires further explanation. Passengers usually have pref- erences for specific departure times, thus, time preferences do not stay constant dur- ing the day. For example, standard business travelers are likely to prefer departure times in the morning and in the afternoon/evening. aDT P(t)describes how the pref- erence for a specific departure time changes throughout a day. In this study, three different aDT P(t)functions are considered, that are plotted in Fig. 4.12.
• USA70: This function is derived from a survey of domestic airline traffic con- ducted in 1969 by the US Department of Transportation (O’Connor, 1982).
• AXS: This function is used in a software used by an airline for schedule evaluation.
• EU86: This function is derived from a study in 1986 on passenger volumes on short-haul routes in Europe published by Biermann (1986).
Calibration and Evaluation. The goal of calibration is to adjust the parameters of each forecasting model so that the model reproduces the calibration data in the
Table 4.5 Description of explanatory (independent) variables representing relevant proper- ties of itineraries
Variable Values Functional form Description
Travel time ratio
[0,1] aT T Ri =max(2−timetimeshi,0) Ratio between total travel time timei
of itinerary i and travel time timeshof shortest itinerary sh in the market.
Itinerary type
{0,1} aTY Pi =
1 if i is direct flight
0 if i is connection Discrete value indicating direct flight or connection.
Shortest itinerary type
{0,1}
aST Yi =
1 if sh is connection 0 if sh is direct flight
Discrete value indicating if shortest itinerary sh in the market is direct flight or connection.
Departure time prefer- ence
[0,1] aDT P(depi) Indicates the attraction of the depar- ture time depiof itinerary i for a po- tential passenger (see Fig. 4.12).
Airline quality/
preference
[0,1] aQUAi Describes the quality of the airline
operating itinerary i as published by Skytrax (2006).
Airline presence
[0,1] aPRSi Indicates the total market share of the airline operating itinerary i in the mar- ket.
Closeness (closest itinerary)
[0,144] aCLO=144− |depi−depcl| Time difference between departure time depi of itinerary i and depar- ture time depcl of the closest (with respect to time) itinerary in the mar- ket. Time is measured in 5-minute- intervals (maximal time difference is 144 (12 hours)).
Travel time ratio (closest itinerary)
[0,2] aT RCi =2−timetimecli Ratio between total travel time timei
of itinerary i in comparison to travel time timeclof the closest itinerary in the market.
best way. In this study, the process of calibration and evaluation is the same for both models. Out of the total number of observations, a set of randomly chosen itineraries serves either as a calibration data set (CS) or as a validation data set (VS). The CS is used to calibrate each model. Then, the calibrated model is evaluated by measuring the forecasting quality using the data of the VS. The forecasting quality of each model is evaluated using the mean squared error (MSE)
MSE= ∑k(pk−tk)2
|K| , (4.8)
where|K|is the number of elements in the total set K of itineraries, pkis the market share predicted for itinerary k∈K, and tkis the observed market share.
88 4 Integrated Airline Scheduling