Skip to 0 minutes and 8 secondsSo… did you get van Ryzin’s trick? Let’s work out what happens when the number of empty seats is higher. After years of experience, van Ryzin really knows his audience very well – so well that he has been able to

Skip to 0 minutes and 23 secondsestablish this probability table: This table clearly shows that it is less and less likely that a great number of wealthy people are waiting to enter van Ryzin’s show through door A. Indeed, the probability decreases with the number of people, so the probability that there are 3 people ready to pay €100 is clearly low.

Skip to 0 minutes and 49 secondsFrom this table, can you calculate van Ryzin’s expected revenue for each seat if he opens door A or door B? Remember, van Ryzin is calculating the expected revenue for each seat, and will only open one door at a time. What can you conclude? Is opening door A always the optimal solution? In the event that he has many seats to sell before the show, how many times should van Ryzin open door A?

Skip to 1 minute and 22 secondsSince there is no uncertainty on the revenue for door B, each seat would definitely be sold for €10 and would therefore provide €10 of revenue. For door A, things are different, since the probability of having one additional customer decreases after each sale. We can calculate the expected revenue of the first seat for each option and find the best option by comparison.

Skip to 1 minute and 50 secondsSince the probability of selling a seat through door A decreases with the number of seats available, the expected revenue of the first seat is of course greater than the second, which is greater than the third, and so forth.

Skip to 2 minutes and 5 secondsThe expected revenue can also be represented with these two curves in a graph. As seen in the table, the expected revenue for door A is decreasing, while the expected revenue for door B is constant at €10.

Skip to 2 minutes and 22 secondsWe also clearly see that the revenue expected for the first 3 seats is greater for door A than for door B. This is because the price is high and the probability of selling those seats is not small.

Skip to 2 minutes and 37 secondsThis graph also confirms that the expected revenue for the fourth seat is the same for both doors, A and B.

Skip to 2 minutes and 47 secondsWe are therefore indifferent towards opening door A or B for that seat. However, it is optimal to sell the remaining seats at €10 and leave door B open for those sales. Unlike van Ryzin’s show, there is no magic here; it is just due to a clever price discrimination scheme (the two doors) and an accurate calculation of the expected revenue for each seat. This is known as Expected Marginal Seat Revenue (or EMSR).

Skip to 3 minutes and 22 secondsNow you know how van Ryzin is filling his theatre! The right sequence for optimising the show’s revenue, is

Skip to 3 minutes and 29 secondsto open the doors in the following sequence: door A, door A again, and door A, a third time, then open either door A or B, and then only open door B.

Skip to 3 minutes and 44 secondsThis week, as you may have guessed, we are going to enter into some real life problems and see how uncertainty affects revenue management decisions. In fact, revenue management is all about optimising under uncertainty, which means controlling for risks, but also taking advantage of uncertainty to sell more than the capacity through overbooking. This week, you will also take advantage of the expertise of two experienced revenue managers. They will share their little secrets and provide an overview of the revenue management techniques used in various sectors of the industry today. Finally, you will be invited to take part in a real-life case study peer assessment exercise designed for new revenue managers carrying out a consultancy diagnostic in a zoo. Exciting!

Skip to 4 minutes and 43 secondsI hope you enjoy the week!

# Towards a general rule?

What happens when the number of empty seats is higher? Can we draw a general rule from the previous situations?

In the previous situations, the reasoning was implicitly based on an accurate calculation of the expected revenue for one or two empty seats. This generalisation is an illustration of a very important notion, known as the *Expected Marginal Seat Revenue* (or EMSR).

*Check the DOWNLOADS section to access a printable version of the slides included in this video.*