Airline Disruption Response Model Parameters

Because of the exponentially increasing nature of the cost coefficients, }_,, the impact of the seating capacity scaling is counterbalanced by the exponential delay penalty notion of flight-based equity inherent in the RBS-EP model.

4.2.6 Airline Disruption Response Model Parameters

As described in Section 4.1.2.3, the objective function for the airline disruption response model is described by the following five parameters: Þ, Ý,ß, u, and à, which we summarize as follows.

96 Þ < 0 = cost benefit per seat associated with flight cancellations;

0 < Ý < 1 = seating capacity scaling factor applied for operating costs; ß = linear operating cost threshold;

u = exponential growth rate for piecewise linear operating costs; and

à = length of each segment in the superlinear portion of the operating cost curve.

The per seat cancellation benefit Þ < 0 determines the propensity for airlines to cancel flights that are empty or nearly empty. The four parameters of the superlinear operating cost function, Ý, ß, u, and à, determine how quickly flight delays force airlines to cancel flights based on operational considerations. Each of these is in turn balanced against the re-accommodation delays associated with flight cancellations. In our results, we use Þ = −6, corresponding to negative 30 minutes of passenger delays per seat (based on 5 minute time intervals). Assuming average passenger delays of 6 hours for flight cancellations (a reasonable, low-end estimate), this parameter value suggests that all else being equal, an airline would like to cancel a flight that is less than 1/12th full. In the airline disruption model, all else is not equal, because single flight cancellations are impossible due to the flow balance constraints. Nonetheless, this seems like a subjectively reasonable threshold.

For the superlinear operating cost function, we consider two sets of parameter values, (Ý = 0.5, ß = 6, u = 1.5, and à = 3) and (Ý = 0.5, ß = 12, u = 1.25, and à = 3). The first suggests that flight operating costs grow linearly for up to 30 minutes of delay, before growing by a rate that increases exponentially by a factor of 1.5 every 15 minutes. The second suggests that flight operating costs grow linearly for up to an hour of delay, before growing by a rate that increases exponentially by a factor of 1.25 every 15 minutes. In each, the flight delay costs are scaled by 0.5 suggesting that baseline delay for an empty seat is half as costly as for a passenger. When referencing the two operating cost curves in our results, we refer to the first curve as aggressive and the second as conservative.

In Figure 4-4, we compare the two total cost curves (i.e., cancellation benefit plus operating costs plus passenger delays), based on a flight with an average 81.2% load factor (passengers divided by seats) and an average 36.4% of connecting passengers (split evenly between first leg and second leg passengers). Each of these values represents the empirical averages based on the planned passenger itineraries in our test scenarios. To simplify the presentation, we list – Þ as the fixed flight cost, which is equivalent from an optimization perspective. We assume that no other flights in the system are delayed, and therefore we estimate the number of missed connections based on an average, and therefore smooth, distribution of connection times. For example, we assume that 5.56% of the connecting passengers have a connection time of 60 minutes, regardless of whether this leads to an integral value. These percentages are again derived based on empirical averages from the test scenarios. This approach has the side-effect of

smoothing the passenger delay curve

increasing delay costs at intervals leading to missed connection disruption type, we use a constant

with the estimates from Chapter 3 listed

delay associated with disrupting all of the passengers, which we plot as a constant threshold. for the two parameter sets, the flight fixed cost

Thus, the difference between the curves is due cost functions.

Figure 4-4: Per seat costs for aggressive and conservative operating cost function parameters In Figure 4-4, we see that under the

hypothetical flight (as described above)

cancellations typically occur in pairs, a more accurate cancellation threshold is twice the cancellation cost, which is hit at approximately 2.5 hours of flight delay. Intuitively,

find that the resulting number of cancellations is actually quite reasonable as we detail further in our results. To ensure that our evaluation results are robust, we als

parameter set in our evaluation. The total cost curve based on this parameter set exceeds the threshold of cancellation indifference at just less than 3 hours, and exceeds twice the threshold of cancellation indifference at approximately 4 hours.

scenario types (historical, hypothetical, and GDP consider 60 sequential evaluation scenarios for each a

passenger delay curve. In practice, the passenger delay curve would exhibit stepwise increasing delay costs at intervals leading to missed connections. For all passengers,

constant 7.5 hours of expected re-accommodation delay, which is consistent listed in Table 3-5. The cost of canceling a flight equals the passenger delay associated with disrupting all of the passengers, which we plot as a constant threshold.

for the two parameter sets, the flight fixed costs, passenger delays, and cancellations costs are equivalent. Thus, the difference between the curves is due solely to the difference between the superlinear operating

costs for aggressive and conservative operating cost function parameters nder the aggressive parameter set, the airline is indifferent

(as described above) based on just less than 2 hours of flight delay. However, because cancellations typically occur in pairs, a more accurate cancellation threshold is twice the cancellation cost,

mately 2.5 hours of flight delay. Intuitively, this does seem aggressive

find that the resulting number of cancellations is actually quite reasonable as we detail further in our results. To ensure that our evaluation results are robust, we also consider a second, more conservative, parameter set in our evaluation. The total cost curve based on this parameter set exceeds the threshold of cancellation indifference at just less than 3 hours, and exceeds twice the threshold of cancellation rence at approximately 4 hours. Between the 10 days of historical disruptions scenarios, the 3 scenario types (historical, hypothetical, and GDP-only), and the two operating cost parameterizations, we consider 60 sequential evaluation scenarios for each allocation method.

97 In practice, the passenger delay curve would exhibit stepwise For all passengers, independent of accommodation delay, which is consistent a flight equals the passenger delay associated with disrupting all of the passengers, which we plot as a constant threshold. Note that s, passenger delays, and cancellations costs are equivalent.

to the difference between the superlinear operating

costs for aggressive and conservative operating cost function parameters

airline is indifferent to canceling the just less than 2 hours of flight delay. However, because cancellations typically occur in pairs, a more accurate cancellation threshold is twice the cancellation cost, this does seem aggressive, though we find that the resulting number of cancellations is actually quite reasonable as we detail further in our second, more conservative, parameter set in our evaluation. The total cost curve based on this parameter set exceeds the threshold of cancellation indifference at just less than 3 hours, and exceeds twice the threshold of cancellation Between the 10 days of historical disruptions scenarios, the 3 only), and the two operating cost parameterizations, we

98

4.3 Results

At the outset of the chapter, we posed three questions that we hoped to answer using the sequential evaluation procedure developed in Section 4.1.

1. What are the benefits of an optimization-based allocation approach in a CDM environment? 2. Is there significant value associated with incorporating aircraft connectivity considerations? 3. What are the impacts and how are they distributed for giving larger aircraft higher priority? In the next three sections, using the scenarios described in Section 4.2, we address each of these questions in turn. In some cases, the answers are inconclusive, suggesting opportunities for future research, but even in those cases, the results provide interesting insights into the dynamic nature of the National Air Transportation System. In Section 4.3.4, we conclude the chapter with a summary of our results and a discussion of the implications.