1 EMSR vs. EMSU: Revenue or Utility? 2003 Agifors Yield Management Study Group Honolulu, Hawaii Larry Weatherford,PhD University of Wyoming

2 Outline of Presentation Classic EMSR Model for Seat Protection –Example Calculations New Utility Model (EMSU) –Example Calculations Comparison of Decision Rules

3 EMSR Model for Seat Protection: Assumptions Basic modeling assumptions for serially nested classes: a) demand for each class is separate and independent of demand in other classes. b) demand for each class is stochastic and can be represented by a probability distribution c) lowest class books first, in its entirety, followed by the next lowest class, etc. d) all demands arrive in a single booking period (i.e., static optimization model)

4 EMSR Model for Seat Protection: Assumptions Another key assumption: e) your company is risk-neutral (that is, you’re indifferent between a sure $100 and a 50% chance of $200 (50% chance of 0). EMSR has been used for over a decade as the industry standard for leg seat control.

5 EMSR Model Calculations Because higher classes have access to unused lower class seats, the problem is to find seat protection levels for higher classes, and booking limits on lower classes To calculate the optimal protection levels: Define P i (S i ) = probability that X i > S i, where S i is the number of seats made available to class i, X i is the random demand for class i

6 EMSR Calculations (cont’d) The expected marginal revenue of making the Sth seat available to class i is: EMSR i (S i ) = R i * P i (S i ) where R i is the average revenue (or fare) from class i The optimal protection level,  12, for class 1 from class 2 satisfies: EMSR 1 (  12 ) = R 1 * P 1 (  12 ) = R 2 Once  12 is found, set BL 2 = Capacity -  12. Of course, BL 1 = Capacity

7 Example Calculation Consider the following flight leg example : Fare Class Avg. Demand Std. Dev.Fare Y B M To find the protection for the Y fare class, we want to find the largest value of  Y for which EMSR Y (  Y ) = R Y * P Y (  Y ) > R B

8 Example (cont’d) EMSR Y (  Y ) = 500 * P Y (  Y ) > 300 P Y (  Y ) > 0.60 where P Y (  Y ) = probability that X Y >  Y. If we assume demand in Y class is normally distributed with mean, std. dev. given earlier, then we can calculate that  Y = 37 is the largest integer value of  Y that gives a probability > 0.6 and therefore we will protect 37 seats for Y class!

9 Joint Protection for Classes 1 and 2 How many seats to protect jointly for classes 1 and 2 from class 3? The following calculations are necessary:

10 Protection for Y+B Classes To find the protection for the Y and B fare classes from M, we want to find the largest value of  YB that makes EMSR YB (  YB ) =R YB * P YB (  YB ) > R M Intermediate Calculations: R YB = (40* *300)/ (40+50) =

11 Example: Joint Protection The protection level for Y+B classes satisfies: * P YB (  YB ) > 100 P YB (  YB ) >.2571 Again, we can calculate that  YB = 101 is the largest integer value of  YB that gives a probability > and therefore we will jointly protect 101 seats for Y and B class from class M!

12 Joint Protection for Y+B Suppose we had an aircraft with capacity 150 seats, our Booking Limits would be: BL Y = 150 BL B = = 113 BL M = = 49

13 New Utility Model (EMSU) What if you’re a smaller company and not willing to take as many risks? That is, instead of being risk-neutral, you are actually risk-averse. First step is to quantify how risk averse you are.

14 There are several ways to do this, but one pretty simple way is to look at the following gamble: –Situation 1: You have a chance of winning either $100 or $0. –Situation 2: A certain cash payoff of $x. –How big would x have to be to make you indifferent between the 2 situations?

15 Risk neutral vs. Risk averse If you said x would have to be $50, then you are risk-neutral. If you picked a value for x that is less than $50 (e.g., $40), then you a risk-averse. Obviously, the lower the value for x, the more risk-averse you are. If you picked a value for x that is more than $50, you are risk-seeking.

16 Utility Calculation One of the easiest ways to convert from a $ amount to a utility is to use an exponential curve U(x) = 1 - exp (-x/riskconstant)

17 Sample curves

18 EMSU Calculations The expected marginal utility of making the Sth seat available to class i is: EMSU i (S i ) = U(R i ) * P i (S i ) where U(R i ) is the utility of the average revenue (or fare) from class i The optimal protection level,  12, for class 1 from class 2 satisfies: EMSU 1 (  12 ) = U(R 1 ) * P 1 (  12 ) = U(R 2 ) Once  12 is found, set BL 2 = Capacity -  12. Of course, BL 1 = Capacity

19 Example Calculation Consider the same flight leg example from before: Fare Class Avg. Demand Std. Dev.Fare Y B M To find the protection for the Y fare class, we want to find the largest value of  Y for which EMSU Y (  Y ) = U(R Y )* P Y (  Y ) > U(R B ) Assume our risk constant is $50

20 Example (cont’d) EMSU Y (  Y ) =U(500)* P Y (  Y ) > U(300) = * P Y (  Y ) > P Y (  Y ) > where P Y (  Y ) = probability that X Y >  Y. If we assume demand in Y class is normally distributed with mean, std. dev. given earlier, then we can calculate that  Y = 11 is the largest integer value of  Y that gives a probability > and therefore we will protect 11 seats for Y class!

21 Probability Calculations Using similar joint protection logic as before yields the following: The protection level for Y+B classes satisfies: U(388.89) * P YB (  YB ) > U(100) * P YB (  YB ) > P YB (  YB ) >

22 Joint Protection for Y+B We can calculate that  YB = 70 is the largest integer value of  YB that gives a probability > and therefore we will jointly protect 70 seats for Y and B class from class M! Suppose we had an aircraft with capacity 150 seats, our Booking Limits would be: BL Y = 150 BL B = = 139 BL M = = 80

23 As you can see, these seat allocation decisions are much more conservative (more risk-averse) in that they protect many fewer seats for the upper classes and allow more to be sold to the more “sure” lower fare class.

24 Comparison of Decision Rules Now, what revenue and utility impact does this decision have? Using the 3 fare class example (data already shown), assume a plane with capacity = 150 In 10,000 iterations (random draws of demand), EMSR generated an average utility of , while EMSU generated an average utility of , for a 4.17% increase!

25 The average # booked in each class were: –EMSREMSU –Y –B –M –LF89.0%93.9% –Yld$290.01$264.21