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they perform much the same on the first three datasets while a substantial gap
occurs in the datasets with 14 and 25 percent connecting flights. Therefore, we
can conclude that with an increasing amount of connecting flights the application
of the simple one-leg flight models becomes intractable and the application of
network optimization models becomes inevitable.
When comparing runtimes there is no significant difference between the
datasets. Applying models QPDF and LPDF leads to a set of several small
instances, one per flight, to be solved in every optimization step of the simu-
lator. Here QPDF instances are harder to solve and it takes significantly more
time than to solve the corresponding linear LPDF instances. Applying model
LPCF all flights are optimized in a single model instance and hence the size is
considerably larger. Nevertheless, the running time of LPCF is significantly less
than the time to solve the suboptimal QPDF-model.
Fig. 6.
Optimization runtime during the booking period
Figure 6 shows another interesting difference. Over the booking period the
runtime of QPDF for reoptimizing all future flights shows a large variation and
we can observe an increase in time near the departure date. On the other hand
both linear models show a more or less constant optimization time over the
whole booking period with a decrease at the end of the booking period since
fewer flights have to be optimized.
