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Written by: Kiera Shepard

Kiera is a senior studying biomedical engineering with an emphasis in mechanical engineering, pursuing a Masters in applied biostatistics and epidemiology. As a frequent flyer between LA and her hometown of San Francisco, she is intrigued by the algorithms behind airline fares.

## Abstract

Have you ever wondered why plane ticket prices seem to jump around at random? This is actually the product of a carefully calculated algorithm that airlines use to maximize their profits by balancing individual ticket pricing and the capacity of the plane. The price of a plane ticket is constantly changing based on current demand for a flight, the number of seats available, and the timing of booking. Although the algorithm itself is quite complex, there are a few easy steps that can be taken in order to ensure you get the best possible deal for a flight.

## Bumping

Most of us are likely familiar with the idea of “bumping,” when an airline overbooks a flight and, in best case, has to “bribe” a couple of passengers with vouchers and cash to take a later flight, or, in worst case, has to physically pull them off the plane. United has been under fire lately for a couple of incidents in which passengers were forcibly removed from overbooked flights. Despite the recent news flood of bumping stories, bumping is actually quite rare, occurring to only about 0.06% of flyers every year [10]. While it may seem that bumping is the result of a mistake by the airline’s attendants or computer system, it is actually a very well calculated gamble on how to achieve maximum revenue. Airlines try to fill each aircraft to capacity to ensure there are no empty seats, or lost potential revenue, and for every flight they bet that a handful of passengers either cancel or don’t show up. Most of the time, the airlines bet correctly and the aircraft ends up nearly full and no one gets bumped. This allows airlines to fill their flights as much as possible, making sure that the load of the flight (the number of passengers that actually take the flight) is as close as possible to the capacity (the number of seats on the aircraft). The lost revenue associated with every seat left empty by a no-show is more than just the cost of the seat because it also includes all of the potential passengers willing to buy that seat who were turned away and whose business the airline has therefore lost to a competitor. These passengers who are turned away are called the “spill:” the difference between demand, the number of potential passengers interested in booking the flight, and load [5], [9]. There is often spill even when a flight is full because there are more people interested in the flight than there are seats. While airlines try their best to minimize spill by supplying enough seats to meet the demand for a flight, right now they are left to guesswork. This is because it is nearly impossible to know exactly how many people want to book a seat for each flight. Today, with new methods of internet user tracking permeating throughout many industries, this guesswork may soon become a simple formula.

## Protecting Seats

Airlines work to minimize the revenue loss from spill by trying to push low-paying passengers into the spill group instead of high-paying passengers. They do this by protecting, or reserving, a group of economy seats on every flight for “full fare” flyers. Instead of letting an entire flight fill up far in advance with lower priced tickets, airlines reserve some seats so that last minute bookers, paying the higher last-minute price, can buy these seats and increase the revenue of the airline for that flight. The tricky part comes when an airline has to decide how many seats to protect and for how long. If the airline doesn’t reserve enough seats, some high-paying flyers might be turned away as the flight is already overbooked. On the other side, if there aren’t enough last-minute bookers then the flight could be under-booked despite having a large spill of low-paying customers. Even when running predictive models to optimize revenue losses associated with under-booking (empty seats), spill (refused customers), and overbooking (bribing vouchers and customer dissatisfaction), many airlines still struggle to exceed a 5% operating margin [4].

Like many airlines, American Airlines employs the protecting method for high paying, last-minute customers. These seats are not visible to the average customer without elite status because he or she is likely to book in advance at a lower price or use miles or points to cover a portion of the fare. However, these seats are visible to customers with elite status as they are more likely to reserve seats last minute at a higher price, especially since many with elite status are business flyers who are willing to pay a higher price for certain times compared to more flexible leisure travelers. But it is worth noting that these seats become open to all flyers at check-in 24 hours before the flight [7].

## Buckets

When determining how many seats to protect for full fare economy passengers, airlines must account for not only the static capacity and load, but also a dynamic, or constantly changing, demand. This demand varies between and within each flight depending on its date, time of day, origin, and destination. For example, popular flights for commuters often have high demand a few days before the flight and thus more seats are protected, but leisure flights are more likely to have lower demand as the date of the flight grows closer. This case of higher demand is mirrored in more popular vacation destinations and in weekend flights as compared to mid-week flights [5]. Figure 1 shows how dynamic pricing (right) is able to both increase airline profits and decrease consumer fares by increasing the load factor. Figure 2 depicts the inverse relationship between load factor and fare, and that by adjusting the fares according to the real-time load factor airlines can increase their revenue.

The total demand for a flight fluctuates “cyclically,” or by day of the week and season of the year. It also varies “stochastically” and less predictably around the expected value of the flight. These two types of fluctuation are accounted for by a coefficient of variation. Leisure market flights tend to have higher coefficients than commuter market flights since leisure flights are less predictable. The total demand is extremely difficult to predict since airlines do not know how many potential customers were turned away or rejected if there was not enough space on the plane or not enough seats in their price range. However, new internet tracking methods are making these predictions easier and more accurate since airlines can now track the number of internet users who view a page and how far into the process of buying they get before not booking a ticket. So far it is not known if airlines use data from internet traffic, but it is very likely given how prevalent these marketing data and methods are becoming across all industries [5], [6], [8].

The nested booking policy is the optimal booking control structure and is widely used by airlines. It involves dropping booking fares into “buckets” based on the perceived demand, which is determined by the number of seats booked at a certain price. When lots of low fare tickets are being bought, the demand increases and the computer system will lift the seats in that group into a higher fare bucket. This means that the customers pay more for each seat, increasing the airline’s revenue. Conversely, if the demand is low, then the seats will get knocked down into a lower fare bucket, hoping to stimulate demand for a “better deal.” This method places seats into the highest possible price bucket that customers are willing to pay, thus optimizing the load and the revenue of the flight [5], [6], [8].

Nested booking policies alter the available price buckets based on the date and time of the flight and its origin and destination, as well. For example, weekend flights are blocked from entering low fare buckets even if the current demand is low because weekend flights are more valuable and in higher demand overall as compared to weekday flights. Similarly, flights to popular vacation destinations are limited to high fare buckets during the summer, tourist and vacation season, but are limited to lower buckets during non-holiday periods. In order to accommodate so many different demand factors, airlines average from 24 (American) to 28 (Southwest) to 77 (Delta) different fare buckets [15]! Figure 3 provides an example of the different demand factors that airlines consider when determining fares.

Due to the nature of nested booking and how airline websites handle group reservations, one may not see the best available price for their group. For example, if you are booking for six people and there are four seats available for \$200 and 16 seats available for \$250, the website will only show you the \$250 seats since not all members of the group can reserve \$200 seats. So, often times it can be beneficial to book separately instead of in large groups. On the other hand, booking on one reservation has a reduced likelihood of being seated separately or being bumped from a flight [16].

The best time to buy a ticket is late on Tuesday or early on Wednesday, in the time zone that the airline is based. This is because most low fare tickets are opened on Monday and few people tend to book flights early in the week so after a full 24 hours open with low demand, the fares will likely get bumped down again, hitting their weekly low sometime on Tuesday or Wednesday. Later on Wednesday and through the rest of the week, more people tend to buy or look at plane tickets, bumping the fares back up. Furthermore, demand, and therefore price, tends to be higher in the beginning of the month after everyone receives their paycheck, so consider booking on the back half of the month. The seats tend to price up into higher buckets, regardless of demand, in weekly cycles as the flight gets closer. So, starting at 21 days before the date of the flight, the prices will go up slightly, and this happens again 14 and 7 days before the flight, as well, so your best bet is to book more than three weeks in advance [11], [15], [16].

## Conclusion

With an understanding of how dynamic pricing for plane tickets works, one can be sure to buy the right tickets at the right times to avoid inflated prices. Dynamic pricing is dependent on the current demand for a flight, how many protected and unprotected seats are left, the type of flight, and when you are booking. Using an algorithm with many variables allows airlines to maximize the capacity of their flights and the profits yielded from each seated, and hopefully reducing any fallout from bumping passengers to later flights.  Although many factors play a role in deciding the price of a plane ticket, they result in fairly simple “buckets” of pricing.

References

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