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It's easy to think of factors that airlines take into account, and how the price will vary over time. There are no shortage of articles or medium posts about that. But how can I frame this as a regression problem?

I think this reduces to something like estimating the rate of demand, given time till takeoff, the price of the ticket, and supply of similar seats (any pricing model ought to contain these factors, bare minimum). Okay, smells a bit like Poisson regression, and at time $t$ the airline prices its flights in order to maximize expected profit over some time interval, perhaps subject to some risk constraint. But I think there are some problems with that:

  1. The Poisson's implied variance in demand is probably much too low. As far as I know, noise due to hidden variables will be hard to incorporate because of their stochastic nature (otherwise, negative binomial would do the trick).
  2. I don't see a straightforward way to update to "stochastic state changes". Suppose tickets are selling like hotcakes for a particular destination at a certain time - obviously demand for this flight is higher than our model thought, so we should raise the ticket price to reflect that. For the same reason as 1, I don't think there's a simple update rule to employ, like in a Kalman filter.
  3. This model completely neglects carrying capacity. Not many people need to fly from Wyoming to Alaska, but if the flight is almost fully booked early on, then the pool of potential customers could be exhausted. That means prices should go down, not up.

While I understand that airlines in perfect competition don't want to tell each other how they do this, I wonder if there is a simple answer I'm not thinking of, or if there's another industry with similar problems that can afford to release literature.

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  • $\begingroup$ What exactly do you want to do? Build a toy model for estimating the demand? Or you want to re-create the actual pricing? Second case may be hard up to impossible, because you don’t have their data. $\endgroup$
    – Tim
    May 3, 2021 at 5:24
  • $\begingroup$ I just want to know how they set up/handle the problem, I dont want to actually run the regression. to be honest, its because I have a job interview soon that deals with something similar I and would like to sound competent. $\endgroup$
    – goopy
    May 3, 2021 at 5:52
  • $\begingroup$ I would assume that airlines have teams of very smart people who constantly tweak their models, and that they will most likely not publicize them, because (a) they may be seen as a competitive advantage, (b) they could be gamed, e.g., by booking websites, and (c) if people can play with the models, there is no telling what kind of strange effects they could whip up into a shitstorm. ... $\endgroup$ May 3, 2021 at 6:17
  • $\begingroup$ ... If I was your interviewer, I would already be very happy with the kind of thinking you exhibit in your question. I would not expect you to already have the answers, but to have an idea of how you would go about to set up and/or refine such a model. If you came up with something like this, my next question would then be which avenue you think would be most important to pursue from a revenue/profit maximizing perspective, and watch you argue and defend your position. $\endgroup$ May 3, 2021 at 6:19
  • $\begingroup$ See many earlier posts at oper research SE and also here. Surely there must be a duplicate there! $\endgroup$ May 3, 2021 at 11:27

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