Well, I can finally say I've attended an MIT lecture. Dr. Belobaba from MIT's International Center for Air Transportation (ICAT) dropped by today to give a guest lecture on the topic of airline pricing schemes and revenue management.

It was an interesting talk that did a good job of explaining why airlines feel the need to have multiple fares for the same flight and to sell tickets at different prices depending on when they're bought.

Basically, airlines want to sell as many high-priced tickets as possible, but they know that there are a lot of people who will only fly at lower costs, hence the need for differential pricing. Then of course, the people who were willing to pay more won't be quite as happy to part with their money if they know that someone else is getting the same service for the same price, which is why airlines introduced restrictions on low fare tickets including "Saturday night stay" conditions that prevent the type of quick round-trips that businesses require.

But on top of these differential pricing schemes, the airlines also use revenue management. That is, they reserve a certain number of the more expensive tickets based on statistical models for how many they believe they'll be able to sell. This is sensible enough, because if they know that they will eventually sell out a given number number of expensive tickets, they don't want those seats going to starving students who will only pay the cheap rate. Of course, they don't know how many tickets they'll be able to sell exactly, so that's where the probability comes in.

Technically, you look at the expected value of some probability function to do this, but all that means is that the cutoff for reserving a ticket of a certain class is the point at which you get the same number by multiplying the ticket's price by its probability of being sold as you do when you multiply the price of a cheaper ticket by its probability of being sold.

Anyway, what this all boils down to is that, first of all, you won't get the super cheap tickets months in advance, regardless of the probabilities, because airlines know they'll be able to unload those later relatively easily. The cheap tickets actually start appearing once the revenue management system kicks in and it realizes that the expensive tickets are being undersold. Now, if the expensive tickets are actually selling really well than you can forget about the cheap ticket and start wishing you had bought one before the prices tripled, however the upshot of all this is that given the statistical anomaly that is the current economy the model forecasts might be overshooting slightly.

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