Pricing and Revenue Management

Editor's Notes

• #2: I am an economist. Everyone thinks an economist can predict the stock market. If I could do that I would be so rich I could own Boeing Aircraft Company. Instead, it is the other way around.
• #3: As an economist, I suppose I need to justify why I am giving this talk. The best excuse is that what the airline industry lovingly calls revenue management has its most powerful revenue effect not in what it does day-to-day, but in what it allows in terms of ticket pricing. It allows selling some tickets cheaper than others. And price, at least to some degree, is something an economist IS allowed to talk about. Second, I used to be in Operations Research at American Airlines and I was fortunate to be involved in designing parts of the first-generation revenue management system. They have been kind enough to credit me with formulating the optimization rule. Then at United Airlines, I participated in developing their second-generation system. Finally, I seem to have been early in the suggestion of the bid-price approach for O&D-based revenue management, which is essentially the third-generation of systems. So I have been around revenue management issues for some time.
• #4: This is the list of topics I want to cover today. I found out in graduate school that 90% of what you learned is a course is what the words mean. By that I mean the seemingly boring definitions that take up half the class are really the ideas, and the darned equations are just the way we play with them. This talk is going to be too short to do the equations. I hope to do what I can to keep the ideas less than boring.
• #5: My key point about Revenue Management is that it is an enabling technology for pricing. By that I mean it allows the airline to charge the guy in the seat next to you less than you paid, and that whole mess makes sense to the airline, the passengers, and society as a whole.
• #6: This is an example of a flight through the week as it was viewed by US airlines back in 1970. Demand (blue) for normal full-fare tickets can be estimated from past weeks. It is different for each day. A protective “buffer” beyond the estimated demand saves space for extra high-fare demand, in case you forecast it wrong. Beyond that, the red area shows seats that might be sold at a discount. What is needed is a way of preventing the base high-fare demand from buying the discount fares. One way is to sell the discount tickets in a different place or a different way than the full-fare tickets. The other is to put requirements on the discount tickets like a 14-day advance purchase and a Saturday night stay. That way they can be easily used for vacations, but not for business trips. The Revenue management part of this is to create separate limits for the discount (red) seats sold. Without limits, the discounts would buy all the space set aside for the blue high-fare demand.
• #7: The idea of selling the red seats (otherwise wasted) to someone else at a lower fare is the idea that revenue management allows to happen. Starting from the position of selling only the blue (high-fare) seats, you go out and find new people who would love to take the trip, if only it were cheaper. They get a good deal, and the blue people (the high-fare and high-value demand) get a good deal too, because the money the red people pay can pay for some of the total costs and allow the high-fare tickets to be lower priced. Anyway, revenue management is all about doing this and being sure the blue people (the high-fare people) get all the seats they want.
• #8: Since reservations systems were already on computers, it was easy to add more complicated revenue management limits for reservations at different fare types. The full-fare ticket for a coach seat was called a “Y” ticket. D, V, K, M and other letters were used for various kinds of discount tickets. Early systems had little data and used lots of people to set levels and monitor whether flights were selling too many seats too fast and therefore leaving too little space for later high-fare demand. Some airlines created separate departments for setting prices and limiting reservations. Good ones realized the pricing department should make good rules to limit discount sales to the kinds of trips that were not high-fare already. Others tried to let the revenue management seat limits do all the work of separating full-fare and discount sales. Evolution is moving toward a single “Pricing and Revenue Management” department.
• #9: Two things happened once revenue management got started. At first, the discounts were only 20-30%. Then some discount carriers came along with 50% discounts and the majors with RM systems had to match. They found out they made more money going to higher load factors and lower discount fares than the had without. So RM really took off, and load factors really went up. At that point, RM became a hot topic and lots of consultants sprung up to help airlines learn the ideas and implement the computer stuff.
• #10: This is how it tends to work in the airline market place. This is an important idea. We will go through an example to see exactly how it works.
• #11: This is a realistic picture of the average cost per seat trip as it changes depending on airplane size. Larger airplanes are cheaper. The idea here is that an airline could, at least in the sense of long-term planning to set up their system, use any airplane size it though worked best.
• #12: This is the same data plotted as the total airplane trip cost against airplane size. Costs rise linearly with seats. However, there is a large cost of frequency that can be thought of as a high cost for the first small group of seats. This very straight line captures the trend of costs. Actual airplanes are points on the line. People who make and sell airplanes will argue that the line is not quite straight—it has some lower points representing their particular models. Maybe they are right. But for pricing purposes, this is the big picture of the cost relationship.
• #13: This is the marginal cost per seat. The first block of 50 seats is paying the cost of frequency, and the additional seats above 50 are paying the same low marginal cost. Again, the idea is that the airline is designing how it is going to do business, so it is choosing what airplane size to use. During that choice, the cost per seat for adding seats above the minimum size is constant and low. Adding seats means buying the next size up in airplanes.
• #14: This is the cost curve and a demand curve plotted with the same axis. The cost curve is the average cost per seat at various airplane sizes. The demand curve is the price-and-quantity the demand will pay. We have simplified out the problem of load factor. That is to say, we have plotted everything in seats instead of passengers. The simplifying assumption is that load factor is the same—so that 150 seats means 100 passengers and so on. We do this just to keep the discussion manageable. The point here is that the demand curve is below the cost curve. An airline would loose money trying to serve this market with only one fare, one price. No matter what the fare.
• #15: However, the two-price solution does work. If you charge the first 50 high-value seats a price of 1.5, and the rest of the lower-value demand a price of 0.75 you can gather enough revenue to pay all costs. And everybody who does travel pays less than they would be willing to pay—less than they value the trip. Notice that in this picture some of the high-value demand is paying the lower discount fare. This is realistic. The airline name for this behavior is “buy-down” or “dilution.” Some of the high-value people manage to qualify for lower fares, because they spend Saturday night, and plan ahead, or whatever it takes to dodge the restrictions. You never get all the high-value people paying the higher price. They do not “volunteer” to pay more. And they are not colored “blue” so you can tell them from the “red” discount customers at the airport. We will say more about this later.
• #16: Here is the case both fares and costs shown. The full fare people gain a lower price because the lower fare people carry some of the minimum cost of frequency. That is, they pay a fare below the cost of the first, expensive, block of seats. The discount fare people gain a lower price because the full-fare people carry most of the minimum cost of frequency. That is, they pay for most of the first, expensive but necessary, block of seats. The optimum sharing of prices is inversely proportional to the fare elasticities of each group. That maximizes the value in excess of fares paid, overall.
• #17: This idea goes under several names. People figuring out how to charge more call it “value of service” pricing. Economists call it “third-order price differentiation.” When you are the one paying the higher price, you may call it “patently unfair.” However, when there is a fixed cost to be covered in a shared way by two groups of demand, the solution which just covers the fixed cost and charges each group inversely to their price elasticity is the solution which maximizes the total consumer surplus, which is to say create the best deal for the most people.
• #18: Now I am going to talk about how RM works. What RM does is protect seats in the reservation system for the higher fare demand against the idea that the lower fare customer might buy them all up ahead of time. The little picture below are the signature pictures for what are now 4 types of customers and fares. Like all revenue management departments, we are going to pretend that there is perfect differentiation among these 4 types. No one can buy a ticket from the other one’s bin. The prices here are vaguely like a long-haul price level.
• #19: The top two categories are the “high fare” demand. The bottom two are the “low fare” demand.
• #20: Business fares are not quite a rich as they appear at first. On a per-square foot basis, business fares can be no better than average coach fares, particularly since business cabins tend to run at low load factors. When business fares apply for distinctly nicer service, the service quality itself adds to the refundability and lack of advance purchase or length-of-stay restrictions to differentiate among customers. The other high-fare is a coach seat sold with business-class convenience attributes—that is refundable and no advance purchase or stay restrictions. We will mix the two up during this discussion. On long haul, they are almost all business fares. On regional services, they are almost all coach fares. But they are both high fares.
• #21: The standard discounts are those offered all year. They are supposed to be used for price-elastic vacation trips. The picture here is supposed to be person with a camera.
• #22: Promotional discounts are used to fill up seats that will not sell at the standard discount. In boom times, few such tickets are sold. In low times, too many are sold. Back in the 1980s, airlines used to offer just the first three kinds of fares, and not “junk” discounts. When demand was low, it showed up as low load factors. The average fare and fare mix stayed the same. Now, airlines push these junk fares whenever demand is low. So now airlines achieve a pretty standard load factors. When demand is low, it shows up as more junk fares sold—that is to say a different fare mix and lower average fare. The picture here is of a starving artiste. The nose suggests he may be European. In practice, he is more often a student.
• #23: This is too much information to study. Perhaps the last line is the key point: different customers have different price elasticities. Elasticity of ½ means adding 10% to the price diminishes demand by 5%. Elasticity of 2 means subtracting 10% from the price increases the demand by 20%.
• #24: This is “real” data. Actually, it is the merger of 4 trans-Atlantic markets from some years’ back. The US government collects a sample of 10% of all airline tickets sold, including the airports and price paid. Sorting through this to find all the tickets between, say, Seattle and London, allows us to create this distribution of fares paid. The data covers a 3-month period. Notice almost no two people pay exactly the same fare. So there are not really 4 fares, but 4 groups of fares.
• #25: Elasticity really matters. If you want more money from an inelastic (business) market, you raise the fares. Provided your competitor allows you to, by matching.
• #26: Leisure markets are “elastic.” That means, if you want more money you lower the fares. You get more money in total because the increased demand more than covers the decreased fare. Provided you have enough space to carry them all. Junk fares are usually set so the demand more than fills the airplanes, and then the number of tickets sold is controlled by capacity limits in the reservations (revenue management) system. In this way the average fare changes goes up or down depending on how many junk fares are sold. It is almost humorous to note that changes in the average fare occur with no changes in fares offered—just changes in Revenue Management space granted to each. Economists often try to measure price elasticity using changes in this average price. But actual prices charged did not change at all.
• #27: The practical problem is that the various fare types are not actually clearly separate groups of people. When the differences in fares gets large enough, more and more people find ways to get into the lower fare types. For instance, business demand can buy two discount trips, or can make plans to stay Saturday night. Or (horror of horrors!) actually plan ahead and buy tickets early.
• #28: Now we are going to describe the words first and second generation RM systems use. Behind each word is an idea that organizes what is done. The word “bucket” refers to a grouping of a bunch of similar fares into one overall fare type. For instance, the “H” bucket might contain student, military, and senior discounts. In first generation systems, each letter had a meaning such as “Saturday night stay Required” or “3-day advanced purchase required.” In second generation systems, the letters just indicate the fare value ranges. The word “Authorization” is how many seats are allocated to each fare bucket. Nesting is the idea that high fares can, once they use up their own bucket, can poach seats from any bucket below them. There are actually several nesting structures with different rules of which bucket to go to first, second, and third to get a seat. By far the most common one is the one where fares access any space avialable in their own bucket, or any lower bucket.
• #29: Here is the conventional bucket nesting illustrated. A bunch of low K fares have been sold in the lowest K bucket. A bunch of medium H fares have been sold in the middle bucket. High Y fares have exhausted the Y bucket, but Y can poach seats from the H and K buckets, if it likes. In this picture, an extra Y fare has used an H space. Although the picture shows regions nested and limits totaled, the calculations actually focus on the seats “protected.” These are the steps between the buckets: 4 for Y, 80 for H, and the residual (90) for K.
• #30: Here we work through an example.
• #31: In this case the business class demand is not going to need all the business class seats, so the unused seats will be moved down to lower fare buckets. Some lucky folks will be upgraded at the gate. This happens less than you think, since if there are any empty seats due to no-shows, these can be the business seats.
• #32: Here is the flight, with finished allocations. The optimization rule is this: Imagine you have a low-fare customer on the reservations telephone line and all seats up to the one he is requesting are already sold. Would you rather take the low-fare (for sure, he is on the line), or would you rather take a chance on getting a higher fare later? When the discount is 50%, then you are willing to turn down the low fare if there is better than half a chance of needing the seat for high fare demand later.
• #33: The key to getting this right is not the optimization rule. The key is a good estimate of the late-booking high-fare demand. If you know it perfectly, you know exactly what to do. Your uncertainty creates a probability distribution for the sale of 10, 12, 14, 16, and so on high-fare seats. Here is what you can know when you make the forecast. Most systems rely heavily on items 1 and 6. Given the value of getting it right, I like using everything you can.
• #34: If you ever see a travel agents screen, RM displays as a letter, like “H” and seats available like “H05.” This would say you can sell up to 5 H tickets. Agents selling a connecting trip are shown the availability on both legs. If H is above zero on both, they can sell an H ticket connecting. To keep other airlines from knowing all about your RM system, you only send 0-7 seats of availability to the travel agent screen. Today on the internet, the airline gets the request directly to its own computer.
• #35: Modern, low-cost carriers operate a much more simple revenue management system. They usually sell only a single kind of ticket—an unrestricted one-way fare with no stay or advance purchase requirements. This seems like a business-class or full-fare ticket. In many ways, it is. Southwest airlines, the most famous and successful low-fare airline, is not a low-quality airline catering to budget trips. During the business week, its planes are full of high-value business trips. However, most low-fare airlines are not one-fare airlines. Fares are lowered on flights that would otherwise not fill due to low demand. Most markets are elastic—meaning lower the fares 10% produces maybe 25% more demand and thus 15% more revenue, if it all fits on the airplane. Fares are raised to ration demand on peak flights. And finally, fares are raised in the last two weeks before departure. Fares are raised close to departure because markets turn inelastic as the day of departure gets close. Many short-planned trips are high-value business trips, with high willingness to pay. So higher fares make for higher revenues, even if all the seats are not filled. This is not necessarily true to leisure destinations, or at leisure times of the week, but it is often the case. You will also see fares drop, if too many seats are empty and the time or market are elastic.
• #36: Low cost carriers initial fare plan for a flight has two characteristics. First, a fare they intend to offer for the long-run that should just about fill the airplane, and second, a ramp-up of that fare for the last week or two, for the hig-value top up. However, the first guess for the airplane-filling fare is often not quite right. So the carriers adjust up or down as booking roll in, depending on whether demand is higher or lower than expected. One aspect of most low cost carriers’ tickets is that they are not refundable. This is usually a restriction on leisure tickets designed to be an inconvenience only to business travelers. In this case, it keeps people who book early from switching to a lower fare, if one turns out to be offered later. It also keeps the business traveler, who needs to keep open the option of changing his ticket at the last day, booking late and paying the higher fare. He gets a good deal, anyway. As long as the airline is clever enough to have some seats available for him.
• #37: If you are responsible for a RM system, be sure to monitor how it does. Computer optimizations are only as good as the data they get. If the average results do not make sense, something needs to be changed. I recall being at one US airline when we could not figure out what our competitor was doing in RM all one summer. Since that competitor was known to be a cutting edge RM user, we thought maybe we were being out-smarted in some way. I remember being unable to figure out what we had wrong. It turned out a bug in their RM system was later admitted to have caused $50m in lost revenues.
• #38: RM systems also set the overbooking level. That is, the ratio of seats sold to seats actual.
• #39: Overbooking: Dealing with Extra Demand Sometimes more people with reservations show up at gate than seats. Airlines usually ask for "Volunteers." Volunteers receive: 1.Direct payment, usually near the price of a discount ticket 2.A reservation on the next scheduled departure 3.Sometimes phone calls, meals, and hotel room Volunteers are usually from discount fare travelers. If there are no volunteers, the last traveler is "involuntarily" denied. Compensation for involuntaries is greater Involuntary's compensation often set by industry standards These extra people are called "Oversales" or "Denied Boardings" or "DB's"
• #42: This is from a medieval prayer book (book on Kells, in Ireland). It is backdrop for questions and discussions.