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simulation. Now for each future flight all historical bookings that were placed at
the same time (relative to the departure date) are selected and used as booking
requests from (virtual) customers. This method ensures that requests are fol-
lowing a realistic distribution and variation. The booking logic itself is rather
straightforward. For every booking request we assume that the customer accepts,
i.e., the booking is placed, if the offered price resulting from the optimization is
not exceeding the price paid; otherwise the booking is declined and the customer
leaves the system and will not return.
Note that when simulating model QPDF or LPDF all booking requests for
connecting flights are translated into bookings for the two related direct flights
as described in Section 3.
To evaluate the models for use in a revenue management system, total revenue
overallflightsisthemostimportantperformance indicator. Besides this measure
we count the total number of tickets sold.
Since we have simulated different and hypothetical data sets absolute revenue
values are not meaningful. Also, we only want to evaluate the relative perfor-
mance among the models on different scenarios. Therefore, we have calculated
for every dataset the revenue obtained from offering every customer the price
paid as recorded in historical data which can be used as a meaningful reference
value. Note that since we assume in our simulation that customers decline to
book if the offered price is higher than the price paid this reference value is the
highest achievable value. In Table 1 we state the revenues as well as the number
of tickets sold as percentage of this benchmark value together with the aver-
age CPU - running time in sec measured as the average time needed in every
simulation step to reoptimize all flights for one day.
As expected model QPDF performs worst on all datasets and models LPDF
and LPCF yield significant higher revenues. This is partially due to the fact
that no rounding is necessary. A closer look at the two LP models reveals that
Tabl e 1. Simulation results
Instance Model Total revenue Tickets sold Runtime
QPDF
60.17%
64.95%
24.584
0%
LPDF
66.05%
68.11%
8.328
LPCF
65.89%
68.90%
17.305
QPDF
60.12%
64.88%
24.466
4%
LPDF
66.19%
68.18%
8.189
LPCF
66.18%
69.05%
17.196
QPDF
59.78%
64.37%
24.863
8%
LPDF
65.73%
68.08%
8.465
LPCF
66.28%
69.42%
17.271
QPDF
59.37%
63.96%
24.614
14%
LPDF
65.21%
67.79%
8.211
LPCF
66.56%
69.91%
17.516
QPDF
58.69%
62.64%
24.962
25%
LPDF
64.12%
67.66%
8.293
LPCF
67.18%
70.36%
17.938
 
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