Integrated Airline Scheduling
4.2 Schedule Evaluation .1 Overview.1Overview
4.2.3 Itinerary Construction
4.2.3.2 Connection Building Rules and Parameters
In the following, the set of rules used in this study for connection building is pre- sented including parameters that have to be calibrated. Each paragraph focuses on one rule. To illustrate the functionality of each rule, the following Fig. 4.6 is introduced.
Fig. 4.6 Connection build- ing example
In this network, the arcs represent single flights, the solid bars represent airports and their locations. For example, there is one flight scheduled between A and G, and airport D is located approximately halfway between A and G. The bars also represent a time-line (from left to right), allowing one to specify departure and ar- rival times of flights at each airport. For example, when looking at airport E, the first flight arriving departed from A, then a flight departs heading to G, a flight ar- rives from D, and the last flight departs towards G. In the following, the connection building rules are illustrated for connections between A and G.
Detour. In general, each connection itinerary represents a detour compared to the direct route between two cities. A maximum detour factor dmaxindicates to what ex- tent the geographical distance of a connecting flight distcnxmight exceed the direct distance distdir between the origin and destination airport: distcnx≤dmax·distdir. This factor can be interpreted as an elliptical envelope around the direct route be- tween two cities in which a connecting airport has to be located (Mathaisel, 1997).
For example, in Fig. 4.7 routes via F between A and G exceed the maximum detour factor compared to the direct route between A and G.
In contrast, for example itineraries following the route via B or E are valid with regard to the detour factor.
Because it is based on geographical distance, the maximum detour factor re- duces the number of possible connection itineraries independently of the flights in the schedule. Using the factor leads to a preselection of possible routes that valid itineraries have to follow. The separation of geographical routes and itineraries of the schedule allows an efficient implementation: the route selection needs to be per- formed only once with the complete set of available airports and is independent of the schedule that has to be evaluated in each iteration of the optimization approach.
80 4 Integrated Airline Scheduling
Fig. 4.7 Maximum detour factor dmax
Minimum Connection Time. To represent a feasible connection, the departure air- port of a succeeding flight has to be the same as the arrival airport of its predecessor.
In addition, the second flight must not depart before the first one has arrived and a minimum connection time tmincnx has elapsed. The minimum connection time is nec- essary for passengers to change the flights and to process their baggage between the two aircraft. Usually, the airport specifies this time.
Fig. 4.8 illustrates the application of this rule. For example, there is no connection flight A–D–G. In addition, although using the same airport, the first flight arriving at E cannot be connected with the first flight departing from E, because the connection time would exceed the minimum connection time tmincnx.
Fig. 4.8 Minimum connec- tion time tmincnx
Number of Stops. In general, passengers want to minimize their travel time and to increase the convenience of the journey. Thus, if there are too many stops within a sequence of flights, this sequence is unlikely to be chosen by a passenger. A max- imum number of stops smax is defined that excludes connection flights with more intermediate stops than this number. If for example only one connecting airport is allowed (smax=1), in Fig. 4.9 there is no itinerary via D from A to G, since at least three intermediate stops would be required (via B, D, E).
Time Delay. In general, the shorter the travel time of an itinerary compared to competing itineraries, the more attractive it is to potential passengers. Thus, the
Fig. 4.9 Maximum number of stops smax
set of itineraries needs to be further reduced by removing itineraries with longer travel times. A possible connection is excluded if its travel time tcnx exceeds the travel time of the shortest itinerary tshortest in the market by a certain factor tdelay: tcnx≤tdelay·tshortest. It is assumed that the time delay is perceived differently de- pending on the type of the shortest itinerary (direct or connection), thus the factor differentiates between both types. The time delay factor with regard to the shortest connection itinerary is denoted as tdelaycnx , the one with regard to the shortest direct flight – if one exists – as tdelaydir .
Fig. 4.10 presents the application of the described rule. There are two connections via B from A to G. Depending on the time delay factor, the first flight between A and B is likely to be removed from the connection building, since at least the second connection itinerary promises a much faster connection.7
Fig. 4.10 Time delay factor tdelay
Maximum Connection Time. In contrast to the minimum connection time tmincnx, a maximum connection time tmaxcnx specifies the time a passenger is willing to wait for the connecting flight. A connection is only constructed, if the departure time of the second flight leg departs before tmaxcnx has elapsed.
Fig. 4.11 illustrates the application of this rule. At airport E, the time between the arrival from the flight arriving from A and the flight heading to G exceeds the maximum connection time tmaxcnx.
7The factor must also take the connection flights via C and E into account. Furthermore, tdelaydir has to be considered, since there is a direct flight between A and G. However, for simplicity reasons, these considerations are neglected in this example.
82 4 Integrated Airline Scheduling
Fig. 4.11 Maximum con- nection time tmaxcnx
Interline Connections. Usually, airlines and CRS limit the number of connections of flights conducted by different airlines. Flights of the same airline are allowed to be connected without any restrictions (online connections). Flights of different airlines (interline connections) are usually only connected if the airlines are members of the same strategic alliance or have any other sort of interline or code-share agreement.
With 210 different airlines from the OAG schedules, investigating all interline agree- ments would be beyond the scope of this work. Instead, in order to include interline connections, a parameter ninterlineis specified: if for any two airlines a number of in- terline connections exceeding this parameter could be observed in the given MIDT data, interline connections are allowed for these two airlines in future use.