Dynamic Pricing Platform (2/5)
Let’s discuss the available heuristics for building the theory for dynamic pricing. This is the second article of the five article series. Aim of the articles will be to give technical overview of the underlying architecture of revMax, i.e. redBus’ dynamic pricing platform. But before we start with the technical details, let’s look at the problems that needs to be addressed by the new architecture. If you are reader who has travelled at different times and same locations via the flights, it is highly likely that you have paid different prices. In short for a end consumer this is dynamic pricing. There are various purpose for which the pricing is done differently and dynamically. More details can be found here in first article.
Available Classic Solutions
Now, let’s get into the technical details of Dynamic Pricing. One of the more popular revenue management heuristics existed was expected marginal seat revenue (EMSR), discovered by Peter Belobaba. It has two versions EMSRa and EMSRb. In general EMSR, can be understood as, first differentiating the seats in flights based on certain parameters of preference by end users. Let’s say even when the seats look physically same, their positions are placed such a way that one seat may be more comfortable than the other. This way, seats can be put at different level of comfort. As the word “level” comes into the picture, this becomes an ‘ordinal’ variable. So, as per EMSR if the c1 indicates the class of seats with highest comfort and c9 indicates the class with least comfort, then the fare f(c1) > f(c2)…>f(c9). Another assumption is that the demand for the lower comfort category would arrive earlier than the for the better categories. One important assumption that is made by EMSR that should be always looked in context of implementation is that demand, capacity and distributions are continuous. Implementing this for buses comes with it’s own challenge of lower data volume and seats per category, that is so, because of number of seats in aircrafts and be at scale of >200 where as buses at best 60 seats can be there.
The core of the EMSR comes with Littlewood’s Rule, below is the representation for calculating protection limit y*.
Protection limit y* provides the protection limits for higher fare category against the lower fare category. Also, another amazing outcome is the calculation of the bid prices itself:
Let us look at small simulation for same to understand the theory. Since, this is a heuristic, looking at the simulations will make more sense than relying on the mathematical representations alone.
Updating the probable fare of first category results in a different protection limit as show below:
One can observe that increasing the probable fare of the first category increases the protection limit to another optimum value. So, at some point of time even the decision on the fares becomes a problem to be solved. It makes it more interesting when it is allowed to change the fare and protection limit both. The bid price is also given that one can provide to offer to buyers.
Littlewood’s rule is limited to two category. And EMSR generalizes it. Below is the representation taken from Wikipedia page:
Let’s look at some simulation of EMSRa. One can observe the different protection limits and the final sum of all the protected categories other than the lowest one.
A different variation of the same simulation is shown below:
With change in expected price, the system reserves more seats at higher fare. This can become a challenge as well in case the expected prices that are calculated are higher or lower than the range in which market operates.
EMSRb came into effect to tackle the issues, where certain categories may have similar prices. Essentially that becomes the boundary condition of the inverse cumulative distribution. Instead of aggregating protection levels, as EMSRa does, EMSRb aggregates demand. This brings the demand prediction as core component to derive the protection levels. This opens the possibilities of good and bad forecast and prediction models. The simulations shown in, above sections stay the same as for EMSRb and the Littlewood’s rule also applies.
Next Chapter
As it may already appear that there are too many variables to get to optimal pricing. The above methodologies will be discussed in context of the bus industry.
Chapter 2: Littlewood’s rule and EMSR
Chapter 3: Technical Architecture
Chapter 4: Details & Reasoning
References:
https://www.monash.edu/business/marketing/marketing-dictionary/d/differential-pricing#:~:text=a%20pricing%20strategy%20in%20which,%2C%20Multiple%20Pricing%2C%20Variable%20Pricing.
https://en.wikipedia.org/wiki/Expected_marginal_seat_revenue
https://en.wikipedia.org/wiki/Littlewood%27s_rule
https://en.wikipedia.org/wiki/Probability_distribution#Absolutely_continuous_probability_distribution
