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Let us say I have daily room booking data over time. Rooms have features X like aircon, number of sleeps/person. Rooms can be booked for a number of nights (NONs) between 1 and 7. They also have a price per night and prices for shorter NONs tend to be larger to encourage longer stays. I would like to be able to predict the "conversion probability" of a room ideally at daily level:

P(Time, X, NONs, price per night)

At first, I thought this could be modelled using a multiclass/multinomial approach. However, I do not think this could work. Concerns:

  • Successive days/weeks depend on the NONs of the previous day(s)
  • A room can only be sold once but clearly (mutually exclusive at room level). However, for certain prices, there is a probability > 0 for different NONs (non mutually exclusive classification problem?).

Maybe I overthink this and there is some clever pragmatic simplification to my problem? I would appreciate any pointers on how I could tackle this please.

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The biggest, practical simplification of the problem would be splitting it into two:

  • Predict if the room is going to be booked. It's a binary prediction that can be handled by one of the many algorithms for such problems.
  • Predict the length of stay for the booked rooms. This is a regression problem where you predict time. The model is trained only on the data on rooms that got booked.
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  • $\begingroup$ Thanks. Very much appreciate your response. Let me check if I understand. Do standard regression: NONs = f(Time, X, price per night). Also fit P(Time, X, NONs, price per night), e.g. using logistic regression, of course the training data would also contain 0 NON days. One could even feed the predictions of the regression model into the second model but the reg. How would one "marry these 2 models" up, e.g. predict NONs per week, year, quarter? Also if the regression model predicts NONs=2 for a day that affects the consecutive day ... this is one of my struggles ... $\endgroup$
    – cs0815
    Commented Aug 21, 2022 at 14:45
  • $\begingroup$ @cs0815 You would predict if there's going to be booking with first model and for the cases predicted positive, you'll predict the lengths. $\endgroup$
    – Tim
    Commented Aug 21, 2022 at 14:57
  • $\begingroup$ But booking probability and NONs depend on price and many other factors of course? Also would one shift by predicted NONs and only predict probability for the next possible arrival day? $\endgroup$
    – cs0815
    Commented Aug 21, 2022 at 15:21
  • $\begingroup$ @cs0815 this is how would you make the problem more, not less, complicated. If you want to produce a realistic simulation of day-to-day hotel bookings, it's a very complicated problem. Question to ask yourself is if you need it. With predictions described above you can easily make good but approximate answers. $\endgroup$
    – Tim
    Commented Aug 21, 2022 at 15:42
  • $\begingroup$ OK thanks would the probability also have price as IV? How do you roll things up (e.g. weekly) if NONs are predicted at daily level? Thanks! $\endgroup$
    – cs0815
    Commented Aug 21, 2022 at 16:14

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