A group of business leaders from South Central Minnesota is considering launching a new commuter airline providing service between the Mankato Regional Airport and Chicago. Because the most prominent member of this group is Gus Adolphson, we will use the working name GusAir to refer to the proposed airline in this document, with the understanding that a different name might actually be chosen if the airline becomes more than a feasibility study.
Although college students, staff, and visitors are not a particularly good fit to the proposed airline's target audience, there is enough potential that the college could benefit from the airline's existence to warrant a modicum of cooperation. In particular, the college has agreed to donate our services as a team of consultants to help answer a few questions concerning the pricing of tickets and the corresponding revenue that can be expected. When put together with information on costs (which lies outside our scope of work), this will be fundamental to determining the airline's viability.
Most airlines offer not only multiple cabins (such as first class and coach) but also multiple fare classes even within the coach cabin in an attempt to distinuish leisure travelers from business travelers. For example, in order to qualify for a low, leisure-oriented fare, a traveler may need to book in advance and stay over a Saturday night. Because GusAir does not expect to compete against surface transport for leisure travelers, there is no need for such restrictions and a single fare class is planned, akin to that used by discount airlines. All seats will be sold as one-way coach tickets for an individual flight. They need not be purchased in advance, but are tied to a specific flight, without any option for change or cancellation.
The simplest option would be for GusAir to advertise a fixed price for a ticket. To assess this option, we have been asked to find out what price would maximize revenues. (Too high a price will leave seats unsold.)
The GusAir founders are also seriously considering another, more complicated option, known as dynamic pricing. In dynamic pricing, each time a potential customer inquires about purchasing a ticket for a particular flight, they are offered a price determined by how many tickets for that flight GusAir still has left to sell and how many hours until flight time they still have in which to sell those tickets. If all goes as GusAir would ordinarily expect, the price will remain relatively stable. But if an unusual run of purchases depletes the supply of tickets for a particular flight, the remaining tickets for that flight will rise in price. Conversely, if tickets for the flight go unsold, then as the flight time nears, the price will drop, reflecting GusAir's increasingly desperate desire not to fly empty seats. Dynamic pricing has the potential to generate higher revenues, even without distinguishing between different categories of consumers, just by responding to demand as it actually unfolds.
(As an aside, dynamic pricing might also provide some differentiation between customers without needing explicit restrictions like Saturday stayovers. If last minute purchasers tend to be more willing to pay, then prices could rise as flight time nears. At the moment, GusAir's founders don't expect this to be a major issue for their target audience. But we should be able to take it into account if the market model changes.)
Because dynamic pricing is considerably more complex than a fixed price, GusAir doesn't want to base its business model on dynamic pricing without some idea how much more revenue they could expect to generate. Thus, we have been asked to compare the revenue expected from optimal dynamic pricing with that from an optimally chosen fixed price.
Finally, if our study of dynamic pricing is encouraging, the founders of GusAir are going to need to explain it to a lot of other people including bank loan officers, potential investors, and journalists. Therefore, we have been asked to provide some illustrative examples of how the price might vary over time as customers make their purchasing decisions. We have also been asked to provide a simple user interface that can be used to step through particular what-if scenarios.
Our clients have provided a list of assumptions we can make in our work. Those assumptions that provide the detailed model of consumer demand are listed in a separate section; the current section provides more general contextual assumptions. Some of these genuinely reflect the simple nature of GusAir's business model. Others are surely not true if taken literally, but are expected to be close enough that the deviations from reality are not expected to have a large impact on the results of our study. This list may not be complete; we may find ourselves needing to make some other similar assumptions.
GusAir will only sell one-way tickets. All itineraries will consist only of a single hop, without stops or connecting flights.
Multi-person parties are rare enough, and have little enough influence on pricing, that we can ignore them, instead considering only sales of individual tickets.
GusAir will not allow tickets to be changed to another flight or refunded.
GusAir will not engage in overbooking. That is, it will only sell as many tickets as there are seats for passengers. (The current plan is to use a 30-seat regional jet.)
GusAir will never cancel a flight even if poor ticket sales render the flight uneconomical. Cancellations for other reasons, such as bad weather, need not be considered in our analysis.
Tickets for each flight go on sale exactly 28 days before the flight time and remain on sale until the scheduled flight time (subject to availability). We need not consider the possibility of continuing to sell tickets past the scheduled flight time for delayed flights.
The fare will always be an integer number of dollars.
GusAir has given us information about the predicted demand for a "typical flight" and asked us to use that information in our analysis. Therefore, we don't need to concern ourselves with the difference in demand between different flight days or times.
Because the flights are infrequent and the customers are assumed to be flying for business reasons, we will assume the flights don't compete with each other. That is, a customer will never choose to switch to a different flight that has a lower price than their preferred flight.
GusAir's prices do not influence the prices of any competitors, and hence do not have any indirect effect on consumers' willingness to pay. (Of course, the higher the price, the less likely a consumer is to be willing, but that is a direct effect.) In part, this assumption arises because there are no directly competing airlines; Mankato Regional Airport currently has no scheduled passenger service, and none is anticipated. The other factor is that for other alternatives, such as driving to Minneapolis/St. Paul and flying from there, or driving the whole way to Chicago, the impact of GusAir is too small to be noticable. (Consider, for example, how little impact GusAir's existence would have on the overall demand for gasoline.)
Each encounter between a potential customer and GusAir is independent of any prior encounters. In each case, if the currently offered price is acceptable to the customer, the customer buys the ticket. For example, if the currently offered price is too high for a potential customer to choose to buy, that doesn't make the customer more likely to check again later (looking for improvement) or less likely (due to discouragement). Nor do customers engage in any strategic behavior such as waiting for tickets that are already acceptably priced to go down even further in price.
GusAir expects its costs to be nearly enough independent of passenger load that we can just optimize revenue, rather than having to optimize revenue minus cost. For example, if 29 of the 30 seats are taken on a flight that is about to depart, our simplified model will consider it desirable to sell the 30th seat at any price obtainable, rather than insisting that the price be enough to pay for such marginal costs as slightly increased fuel consumption.
The period over which tickets are sold is short enough that we can ignore the time value of money. That is, we don't need to take into account that revenue is more valuable the sooner it is obtained.
Our clients are only interested in maximizing the average (expected) revenue. They do not assign any value to reducing the risk (variability).
We can conduct our analysis as though the price offered to the consumer were identical to the revenue GusAir will realize on a sale, without needing to take into account such factors as commissions paid to distributors or fees paid to credit-card companies. (Those issues will be incorporated elsewhere in GusAir's overall feasibility study.)
We will be divide our model of customer behavior into two components. The first concerns the arrival of a potential customer inquiring about the price of a ticket for a particular flight. The second concerns the likelihood that the potential customer will then buy the ticket, which is of course influenced by the price they are quoted.
Regarding the arrival of a potential customer, we will assume that the probability of even one customer arriving within any particular hour is low enough that we can safely disregard the chance that two or more arrive within the same hour. As such, we can model customer arrival hour by hour, for each hour just considering the probability of a single customer arriving versus the alternative that none does. For now, we will assume that the probability of a customer arriving stays fixed at 10% for each hour of the entire period of 28 days (times 24 hours/day). However, it will be smart to structure our code so that the probability is computed as a function of the number of hours remaining until flight time, even though that function will currently return a constant value. That way we are positioned to later deal with a more realistic model that takes into account such factors as last-minute surges in demand or nightly dips in demand. (If in the course of making such changes, we wind up with some hours where the probability of two customers becomes non-negligible, we can just switch to using half-hour time increments or some other smaller time interval.)
The second component of our demand model reflects consumers' willingness to pay. That is, we need to determine the probability the potential customer will buy the ticket as a function of the offered price. Again, it would be wise to also include the time remaining until the flight as a parameter, because we might later want to incorporate an assumption that last-minute purchasers are looser with their money. But for now, the probability of purchase will be independent of time remaining and only dependent on price. The probability that a potential customer who arrives will choose to purchase the ticket is e− (price/200)3, where e is the base of natural logarithms.
This case study document for MCS-178 was written by Max Hailperin. Thanks to Kirsten Lilliness (Gustavus class of 2006 and now at Alaska Airlines) for providing some feedback on how this compares with reality.