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EMSR vs. EMSU: Revenue or Utility?

EMSR vs. EMSU: Revenue or Utility?. 2003 Agifors Yield Management Study Group Honolulu, Hawaii Larry Weatherford,PhD University of Wyoming. Outline of Presentation . Classic EMSR Model for Seat Protection Example Calculations New Utility Model (EMSU) Example Calculations

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EMSR vs. EMSU: Revenue or Utility?

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  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 Pi(Si) = probability that Xi> Si, where Si is the number of seats made available to class i, Xi 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: EMSRi(Si ) = Ri * Pi(Si ) where Ri is the average revenue (or fare) from class i • The optimal protection level, 12, for class 1 from class 2 satisfies: EMSR1(12 ) = R1 * P1(12 ) = R2 • Once 12 is found, set BL2 = Capacity - 12 . Of course, BL1 = Capacity

  7. Example Calculation • Consider the following flight leg example : Fare ClassAvg. DemandStd. Dev. Fare Y 40 10 500 B 50 15 300 M 60 20 100 • To find the protection for the Y fare class, we want to find the largest value of Y for which EMSRY(Y ) = RY * PY(Y ) > RB

  8. Example (cont’d) EMSRY(Y ) =500 * PY(Y ) > 300 PY(Y ) > 0.60 where PY (Y ) = probability that XY>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 EMSRYB(YB ) =RYB * PYB(YB ) > RM • Intermediate Calculations: RYB = (40*500 + 50 *300)/ (40+50) = 388.89

  11. Example: Joint Protection • The protection level for Y+B classes satisfies: 388.89 * PYB(YB ) > 100 PYB(YB ) > .2571 • Again, we can calculate that YB = 101 is the largest integer value of YB that gives a probability > 0.2571 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: BLY = 150 BLB = 150 - 37 = 113 BLM = 150 - 101 = 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 50-50 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: EMSUi(Si ) = U(Ri) * Pi(Si ) where U(Ri) is the utility of the average revenue (or fare) from class i • The optimal protection level, 12, for class 1 from class 2 satisfies: EMSU1(12 ) = U(R1) * P1(12 ) = U(R2) Once 12 is found, set BL2 = Capacity - 12 . Of course, BL1 = Capacity

  19. Example Calculation • Consider the same flight leg example from before: Fare ClassAvg. DemandStd. Dev. Fare Y 40 10 500 B 50 15 300 M 60 20 100 • To find the protection for the Y fare class, we want to find the largest value of Y for which EMSUY(Y ) = U(RY)* PY(Y ) > U(RB) • Assume our risk constant is $50

  20. Example (cont’d) EMSUY(Y ) =U(500)* PY(Y ) > U(300) = 0.999955 * PY(Y ) > 0.997521 PY(Y ) > 0.99757 where PY (Y ) = probability that XY>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 > 0.99757 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) * PYB(YB ) > U(100) 0.999581 * PYB(YB ) > 0.864665 PYB(YB ) > .865027

  22. Joint Protection for Y+B • We can calculate that YB = 70 is the largest integer value of YB that gives a probability > 0.865 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: BLY = 150 BLB = 150 - 11 = 139 BLM = 150 - 70 = 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 127.26, while EMSU generated an average utility of 132.79, for a 4.17% increase!

  25. The average # booked in each class were: • EMSR EMSU • Y 38.9 32.5 • B 49.2 49.5 • M 45.5 58.8 • LF 89.0% 93.9% • Yld $290.01 $264.21

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