1. Presented to AGIFORS YM Study Group Bangkok, Thailand May 2001 Larry Weatherford University of Wyoming Dispersed Fares within a Fare Class: How Can We Harness the Reality?

2. Outline of Presentation I.Introduction-Why is this Important? II.Fare Dispersion--Point Estimate III.Fare Dispersion—a New Approach IV. Summary

3. I. Introduction-Why is this Important? ·What if fares for each fare class are not fixed at the single value we give to the leg optimization engine? (i. e., instead of a single value, there is a range of fares) ·What does your fare data look like?

6. In each case, we look at several different scenarios and look at the impact on the revenues generated by 3 different common decision rules (i.e., deterministic, EMSRa, EMSRb) and compare them to a new decision rule that specifically accounts for the dispersed fares We’ll analyze these impacts with two different sets of real airline data (booking pattern, fares)--one set is more business oriented, the other has more leisure traffic. Both sets of data have 5 fare classes and 15 booking periods --> See next page for comparison of mean demands by fare class

7. In all cases, we compare the performance of the decision rules for 7 different demand/capacity ratios (0.9, 1, 1.1, 1.2, 1.3, 1.4, 1.5) --> see next page for a comparison graph

9. II.FARE DISPERSION-POINT ESTIMATE A. Introduction We provide the optimizer with a point estimate of the fare for each fare class, but what happens if the actual fares in that class are dispersed around that mean value ? We’ll look at 3 different ways the fares might be dispersed (i.e., prob. Distributions): 1. Normal 2. Uniform 3. Skewed --> see next 2 pages for illustrative graphs

11. Number of trials/iterations = 50,000 in following examples

12. B. Results from Business data 1. BASE CASE: Fares are deterministic or fixed (results are compared to no-control decision rule) -->In general, we see both EMSRa and b give significant benefit

13. 2. Fares are Normally Distributed (compared to BASE) ·Adding dispersion to the fares doesn’t seem to have any significant impact on revenues

14. 3. Fares are Uniformly Distributed (compared to BASE) --> Doesn’t look like either of these symmetric distributions has much effect on the revenue.

15. 4. Fares are Skewed Right (compared to BASE) ·Fare dispersion of all kinds seems to have no significant impact on revenues for these decision rules

16. C. Results from Leisure data 1. BASE CASE: Fares are Deterministic or Fixed (results are compared to no-control decision rule) ·Lower %’s than Business data

17. 2. Fares are Normally Distributed (compared to BASE)

18. 3. Fares are Uniformly Distributed (compared to BASE) --> Doesn’t look like either of these symmetric distributions has much effect on the revenue.

19. 4. Fares are Skewed Right (compared to BASE) ·Fare dispersion of all kinds seems to have no significant impact on revenues for these decision rules

20. D. Conclusions for Fare Dispersion using a Point Estimate Only ·These decision rules seem to generate about the same revenue with fare dispersion even though we only provide a point estimate to the optimization engine. ·NOT saying that there’s no need to improve the stratification for a given fare structure OR that a new decision rule might not do better!!

21. III.FARE DISPERSION-A NEW APPROACH A. Introduction How can we take advantage of the fact that the actual fares in each fare class are dispersed ? Assuming we’re still using leg control and that we have demand > capacity, it seems like we should be able to find some minimum fare to use as a cutoff (i.e., not accept the really low fares in a bucket) For example, if the avg. fare in Y is $275, but we get a request in Y class for $50, should we take it?

22. The “minimum fare” addition to regular leg control (EMSRa or b) should help us here Can reservation systems handle this new idea? We’ll use the same 3 approaches to the way fares might be dispersed as described earlier (i.e., Normal, Uniform, Skewed) We’ll present 2 scenarios to represent different amounts of overlap between the fare classes (narrow, wide)

23. B. Results from Business data 1. Fares are Normal (narrow  sigma/mu = 1/6) (all results are compared to deterministic decision rule) -->there is some revenue potential (0.5-1% gain) with new rule

24. 2. Fares are Uniform (narrow  +/- 20%) here the benefit is smaller (0.3-0.6%)

25. 3. Fares are Skewed Introducing a nonsymmetric distribution seems to add to the potential benefit (now exceeds 2%)

26. What happens if we widen the dispersion and increase the overlap between fare classes? For Normal, we move from sigma/mu = 1/6 to 1/3 For Uniform, we move from range of mean +/- 20% to mean +/- 50% Representative graphs on next 2 pages of wider case

29. 4. Fares are Normal with wider dispersion (all results are compared to deterministic decision rule) -->much bigger impact the more overlap/dispersion you have

30. 5. Fares are Uniform with wider dispersion same conclusion as for the Normal distribution

31. C. Results from Leisure data 1. Fares are Normal (narrow  sigma/mu = 1/6) (all results are compared to deterministic decision rule) Larger %’s than Business data (up to 1.8%)

32. 2. Fares are Uniform (narrow  +/- 20%) Larger %’s than Business data (up to 1.3%)

33. 3. Fares are Skewed --> here the potential is tremendous (up to 7%) !

34. 4. Fares are Normal with wider dispersion greater dispersion allows the revenue improvement to go from 2% (narrow) to 5%

35. 5. Fares are Uniform with wider dispersion greater dispersion allows the revenue improvement to go from 2.8% (narrow) to 4%

36. D. Conclusions for Fare Dispersion—a New Approach For Business data set, under narrow assumptions, we saw benefits of 0.3 – 1%. Assuming wider dispersion or some skew, we saw revenue gains of 2.5 - 3%. For Leisure data set, under narrow assumptions, we saw benefits of 1.2 – 1.8%. Assuming wider dispersion or some skew, we saw revenue gains of 4 - 7%.

37. IV. Summary On average, using the standard leg optimizer, we make about the same revenue whether fares in a single fare class are a fixed value (single point) or the fares are really dispersed When the optimization engine can take into account the dispersion, the revenue benefits can be quite large!

38. The benefits depend on how much dispersion there is in the data, the shape of the dispersion, and how much overlap this creates between the fare classes.  It’s worth spending some time looking at your fare data!