Presented to

AGIFORS YM Study Group

Bangkok, Thailand

May 2001

Larry WeatherfordUniversity of Wyoming

Dispersed Fares within a Fare Class: How Can We Harness the Reality?

Outline of Presentation

I. Introduction-Why is this Important?

II. Fare Dispersion--Point Estimate

III. Fare Dispersion—a New Approach

IV. Summary

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?

Normal, sigma/mu = 1/6

0

100

200

300

400

500

Y M B V Q

Fare Class

Rev

enu

e Hi

Lo

Median

Uniform, +/- 20%

0

50

100

150

200

250

300

350

Y M B V Q

Fare Class

Reven

ue

Hi

Lo

Median

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, theother 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

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

Business-Input 1 Leisure-Input 2Fare Class Demand Fares Fare ClassDemandY 20 275$ Y 5M 13 173$ M 11B 22 122$ B 19V 23 93$ V 29Q 22 66$ Q 36

Business

0

5

10

15

20

25

Y M B V Q

Fare Class

Dem

and

Leisure

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5

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20

25

30

35

40

Y M B V Q

Fare Class

Dem

an

d

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. Normal2. Uniform3. Skewed --> see next 2 pages for illustrative graphs

NORMAL

0

0.05

0.1

0.15

0.20.25

0.3

0.35

0.4

0.45

137.49725 183.3315 229.16575 275 320.83425 366.6685 412.50275

Fare Values

Pro

bab

ilit

y

UNIFORM

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

137.5 183.33 229.16 275 320.83 366.66 412.5

Fare Values

Pro

bab

ilit

y

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

Skewed

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

200 220 250 280 300 320 350 380 400 420 450 480

Different Fare Values in Y

Pro

bab

ilit

y

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

Dmd/Cap EMSRa EMSRb0.9 0.52% 0.52%

1 3.42% 3.44%1.1 9.98% 10.01%1.2 19.36% 19.36%1.3 27.73% 27.78%

Avg 12.20% 12.22%

2. Fares are Normally Distributed (compared to BASE)

·Adding dispersion to the fares doesn’t seem to have any significant impact on revenues

Dmd/Cap EMSRa EMSRb0.9 -0.05% -0.02%

1 -0.05% -0.02%1.1 -0.02% -0.04%1.2 0.16% 0.14%1.3 0.11% 0.09%

Avg 0.03% 0.03%

3. Fares are Uniformly Distributed (compared to BASE)

--> Doesn’t look like either of these symmetric distributions has much effect on the revenue.

Dmd/Cap EMSRa EMSRb0.9 -0.02% -0.01%

1 -0.05% -0.04%1.1 0.02% -0.02%1.2 0.16% 0.17%1.3 0.12% 0.14%

Avg 0.05% 0.05%

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

Dmd/Cap EMSRa EMSRb0.9 -0.05% -0.03%

1 -0.04% -0.03%1.1 0.05% 0.05%1.2 0.15% 0.12%1.3 0.01% 0.02%

Avg 0.03% 0.03%

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

Dmd/Cap EMSRa EMSRb0.9 0.33% 0.36%

1 2.05% 2.10%1.1 5.95% 5.95%1.2 10.99% 10.95%1.3 15.48% 15.46%

Avg 6.96% 6.96%

2. Fares are Normally Distributed (compared to BASE)

Dmd/Cap EMSRa EMSRb0.9 0.01% 0.00%

1 0.02% 0.03%1.1 -0.09% -0.03%1.2 0.00% 0.03%1.3 -0.03% -0.03%

Avg -0.02% 0.00%

3. Fares are Uniformly Distributed (compared to BASE)

--> Doesn’t look like either of these symmetric distributions has much effect on the revenue.

Dmd/Cap EMSRa EMSRb0.9 0.00% 0.00%

1 0.06% 0.08%1.1 -0.09% -0.05%1.2 0.04% 0.05%1.3 -0.03% -0.04%

Avg 0.00% 0.01%

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

Dmd/Cap EMSRa EMSRb0.9 0.00% 0.00%

1 0.01% 0.00%1.1 -0.10% -0.09%1.2 -0.05% 0.00%1.3 0.03% 0.01%

Avg -0.02% -0.02%

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!!

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?

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)

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

Fares are Normally Distributed (narrow)

0.00%

0.50%

1.00%

1.50%

2.00%

Demd/Cap Ratio

% I

mp

ro

vem

en

t

over D

ete

rm

. D

ec

Ru

le EMSRa

EMSRb

NewDispRule

2. Fares are Uniform (narrow +/- 20%)

•here the benefit is smaller (0.3-0.6%)

Fares are Uniform (narrow)

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

Demd/Cap Ratio

% I

mp

ro

vem

en

t o

ver

Dete

rm

. D

ec R

ule

EMSRa

EMSRb

NewDispRule

3. Fares are Skewed

•Introducing a nonsymmetric distribution seems to add to the potential benefit (now exceeds 2%)

Fares are skewed

0.00%

1.00%

2.00%

3.00%

Demd/Cap Ratio

% Im

prov

emen

t ov

er D

eter

m D

ec.

Rul

e

EMSRa

EMSRb

NewDispRule

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

Uniform, +/- 50%

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Y M B V Q

Fare Class

Reven

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Median

Normal, sigma/mu = 1/3

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Y M B V Q

Fare Class

Rev

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4. Fares are Normal with wider dispersion (all results are compared to deterministic decision rule)

-->much bigger impact the more overlap/dispersion you have

Fares are Normally Distributed (wide)

0.00%1.00%2.00%3.00%4.00%

Demd/Cap Ratio

% Im

pro

ve

me

nt

ov

er

De

term

. De

c

Ru

le

EMSRa

EMSRb

NewDispRule

5. Fares are Uniform with wider dispersion

•same conclusion as for the Normal distribution

Fares are Uniformly Distributed (wide)

0.00%

1.00%

2.00%

3.00%

0.9 1 1.1 1.2 1.3 1.4 1.5

Demd/Cap Ratio

% Im

pro

ve

me

nt

ov

er

De

term

. De

c

Ru

le

EMSRa

EMSRb

NewDispRule

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%)

Fares are Normal (narrow)

0.00%0.50%1.00%1.50%2.00%

Demd/Cap Ratio

% Im

pro

ve

me

nt

ov

er

De

term

. D

ec

Ru

le

EMSRa

EMSRb

NewDispRule

2. Fares are Uniform (narrow +/- 20%)

Fares are Uniform (Narrow)

0.00%

0.50%

1.00%

1.50%

Demd/Cap Ratio

% Im

pro

ve

me

nt

ov

er

De

term

. De

c

Ru

le

EMSRa

EMSRb

NewDispRule

•Larger %’s than Business data (up to 1.3%)

3. Fares are Skewed

--> here the potential is tremendous (up to 7%) !

Fares are Skewed

0.00%2.00%4.00%6.00%8.00%

Demd/Cap Ratio

% Im

pro

ve

me

nt

ov

er

De

term

. De

c

Ru

le

EMSRa

EMSRb

NewDispRule

4. Fares are Normal with wider dispersion

•greater dispersion allows the revenue improvement to go from 2% (narrow) to 5%

Fares are Normal (wide)

0.00%

2.00%

4.00%

6.00%

Demd/Cap Ratio

% Im

pro

ve

me

nt

ov

er

De

term

. De

c

Ru

le

EMSRa

EMSRb

NewDispRule

5. Fares are Uniform with wider dispersion

Fares are Uniform (wide)

0.00%1.00%2.00%3.00%4.00%

Demd/Cap Ratio

% Im

pro

ve

me

nt

ov

er

De

term

. De

c

Ru

le

EMSRa

EMSRb

NewDispRule

•greater dispersion allows the revenue improvement to go from 2.8% (narrow) to 4%

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%.

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!

•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!