We have analyzed the existing booking policy of TransAtlantic Airlines and identified potential cost saving.
The implementation of the suggested new booking policy would lead to reduction of total expected costs per flight on average by £8,100.
Furthermore, the new policy would increase the predictability of total costs per flight. With 90% confidence new costs will be in a range £750 and £4,800 as compared to the current range of £1,900 to £20,300. The comparative description of the policies is presented in table 1.

Analysis of existing policy quick fix
Base case model
The foundation of current policy is based on the analysis in table 1. We observe that the total costs for both classes are £6,250. The analysis of existing model indicates that there are two controllable variables in yellow (booking level in both classes) and two uncontrollable variables in green (no-show %).
Table Foundation of existing policy
The available data indicates that current policy assumes some empty seats on the plane. As there is no immediate justification to this assumption, overbooking of the plane should be targeted to minimize the costs.
Table Quick policy fix
By increasing the booking level for both classes, £0 costs can be achieved (table 2).
Scenario analysis
TransAtlantic does not have data retention policy in place. Hence, TransAtlantic has applied the consensus of experts for the scenario analysis. The percentage of no-shows varies between 3% and 8% in economy class and 15%-30% in business.
Our calculations indicate that base case scenario is equal to the best case scenario. The main reason is that both cases of over- and under booking the company incurs costs, therefore the cost minimization is only achieved when the number of passengers in each class taking the flight is equal to the corresponding capacities (table 1).
In the worst case scenario, we assume the maximum no-show in both classes. The data in table 3 demonstrates that the cost of the missed opportunities (e.g. missed fare) is much higher than the passenger compensation costs
We have calculated that in the worst case the company can experience the loss of revenues of £23,250 per flight.
Table Worst case scenario
Sensitivity analysis
We have identified that there are two independent uncontrollable variables in our model. The best way to quantify the uncertainty without the simulation is to conduct a sensitivity analysis.
One-way sensitivity analysis allows identifying the influence of each variable on the total costs.
Expectedly, we observe that zero-cost for economy class happens at 5% of no-show and for business class is 20%, as these levels are equal to full capacity utilization in each class.
Any deviation from these levels results in the increased costs for the company. For the economy class the increase of no-shows by 1% point results
in the loss of £1,800, while a decrease of 1% point results in the loss of £600. In business the corresponding figures are £1,450 and £300 (figure 1).
In relative terms, the costs of 1% increase are 3 times and ~5 times higher than the costs of 1% decrease in no-shows for economy and business class correspondingly. The observation leads us to conclude that overbooking is a viable option for the airline. Analysis of two way sensitivity (Appendix A), helps us to identify the sweet spot of costs of no-shows (colored green).
Simulation
Policy comparison
In the simulation analysis we assumed triangular probability of no-shows based on the available data (economy: between 3%-8%, most people 5%; business: between 15%-30%, most common 20%). We have also used 5,000 iterations to calculate final results. Table 5 summarizes the results.
Table Simulation output analysis
According to our analysis the mean of the current policy equals £10,800. This value is different from £6,250 as the new estimated mean represents the expected value, which are the average costs weighted by their respective probabilities. The previous estimation indicates solely the costs at one point.
Quick look at the summary table helps us identify that the proposed quick fix is the least value destructing policy out of three policies. It has the lowest mean of total costs, the lowest probability of exceeding £10,000 as well as the narrowest range of the cost.
To be more assured, we have additionally conducted probability dominance analysis (figure 2), which tells that both current and quick fix policy have deterministic dominance (always better) then no overbooking policy (green line). Whereas the quick fix (blue line) has stochastic dominance over
currently employed policy (red line). The outcome of current policy maybe occasionally better than our proposed solution, but in the majority of cases the quick fix policy will be better.
Figure 2 Probability dominance analysis
Policy optimization
In order to identify the optimal booking policy we have conducted simulation with 40 different booking levels for business and economy. As these two variables are independent, we have conducted consequential analysis. Results for business class level booking are in (figure 3). The detailed information about tested values is in Appendix B.
Figure 3 Optimal booking policy
We have observed that the lowest expected value of total costs is achieved at 427 and 133 accepted reservations for economy and business respectively. The comparison of current policy against new policy can be found in table 6.
Table Current vs new policy comparison
Further model improvements
It has been suggested that passengers upgraded from the economy class to business class, can additionally reduce costs.
We have included this condition in the model and run the simulation with different booking levels for business and economy (see section on optimization). Expected booking levels are not affected by this change. No further adjustments to the booking levels are necessary due to overbooking in both classes,
Nevertheless, in some instances, as we consider the whole spectrum of possibilities, we observe that there are occasions at which business class
is not fully occupied. By introducing upgrade possibility we can indeed improve our overall results as seen from the following summary table 7.
Table New policy with upgrade option
Even though the improvement to the mean is limited to £200 and the range adjustments also non-significant, we almost eradicating the chance of incurring costs more than £10,000.
This result ascribes to the partial offsetting of business opportunity costs (fare of £1,450), with collected fare from economy class passengers of £450 and the omission of compensation cost of £150 to economy customers for overbooked flights. Thus, TransAtlantic airlines incurs only the cost of £850 per business passenger instead of £1,450 under the circumstance that business class passengers don’t show up and leave seats to extra passengers of economy class.

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