1. Biography for William Swan
Chief Economist, Seabury-Airline Planning Group. Visiting Professor, Cranfield University. Retired Chief Economist for Boeing Commercial Aircraft Previous to Boeing, worked at American Airlines in Operations Research and Strategic Planning and United Airlines in Research and Development. Areas of work included Yield Management, Fleet Planning, Aircraft Routing, and Crew Scheduling. Also worked for Hull Trading, a major market maker in stock index options, and on the staff at MIT’s Flight Transportation Lab. Education: Master’s, Engineer’s Degree, and Ph. D. at MIT. Bachelor of Science in Aeronautical Engineering at Princeton. Likes dogs and dark beer.
I am an economist. Everyone thinks an economist can predict the stock market. If I could do that I would be so rich I could own Boeing Aircraft Company. Instead, it is the other way around.
Scott Adams

2. How Airlines Compete Fighting it out in a City-Pair Market
William M. Swan
Chief Economist
Seabury Airline Planning Group
Nov 200
Papers:
Contact:
A stylized game. To keep the mathematics as simple as possible. However, the game and the values involved are as close to realistic as we can make them.

3. A Stylized Game With Realistic Numbers
The Simplest Case, Airlines A & Z
Case 2: Airline A is Preferred
Peak and Off-peak days
Full Spill model version
Airline A is “Sometimes” Preferred
Time-of-day Games

4. Model the Fundamentals
Capture all relevant characteristics
Different passengers pay high and low fares
Different passengers like different times of day
Different passengers have less or more time flexibility
Airlines block space to accommodate higher fares
Demand varies from day to day
Demand that exceeds capacity spills
to other flights, if possible
Airlines can be preferred, one over another
Passengers have a hierarchy of decisions
Price; Time; Airline
Bigger airplanes are cheaper per seat than smaller ones

5. Example Simple but True
Example here as simple as we could devise
Covers all fundamentals
Uses simplest possible distributions
Time of day
Fares paid
Airline choices
Demand variations
Choice Hierarchy
Means and Standard Deviations are realistic
Each is a “cartoon”
Reflects industry experience with detailed models
Based on best practices at
AA; UA; Boeing; MIT
Other airlines that were Boeing customers
University contacts
I am hoping to tempt someone to write a simulation with more realistic distributions. However means and standard deviations used here are reasonable.

6. The Simplest Case: Airlines A & Z
Identical airlines in simplest case
Two passenger types:
$100, 144 passengers demand
$300, 36 passengers demand
Average fare $140
Each airline has
100-seat airplane
Cost of $126/seat
Break-even at 90% load, half the market
Of course the load is too high, at 90%. But it will lead to realistic numbers later.

7. We Pretend Airline A is Preferred
All 180 passengers prefer airline A
Could be quality of service
Maybe Airline Z paints its planes an ugly color
Airline A demand is all 180 passengers
Keeps all 36 full-fare
Fills to 100% load with 64 more discount
Leaves 80 discount for airline Z
Average A fare $172
Revenue per Seat $172
Cost per seat was $126
Profits: huge

8. Airline Z is not Preferred
Gets only spilled demand from A
Has 80 discount passengers on 100 seats
Revenue per seat $80
Cost per seat was $126
Losses: huge
“not a good thing”

9. Preferred Carrier Does Not Want to Have Higher Fares
Pretend Airline A charges 20% more
Goes back to splitting market evenly with Z
Profits now 20%
Profits when preferred were 36%
25% extra revenue from having all of full-fares
11% extra revenue from having high load factor
Airline Z is better off when A raises prices
Returns to previous break-even condition
Note that we have NOT assumed demand did not respond to prices. We have merely assumed half the demand prefers the quality of A at 20% higher price to the quality of B at the old price and quality.

10. Major Observations Average fares look different in matched case:
$172 for A vs. $80 for Z
Preferred Airline gains by matching fares
Premium share of premium traffic
Full loads, even in the off-peak
Even though discount and full-fares match Z

11. More Observations
“Preferred wins” result drives quality matching between airlines
Result is NOT high quality
Everybody knows everybody tries to match
Therefore quality is standardized, not high
Result is arbitrary quality level
add qualities that people value beyond cost?
Interesting sideline: In US non-union labor carriers have the ability to create higher quality cheaper than heritage unionized carriers. However, in general, they have sought to be cheaper, not better. In general, they have failed. Except for Southwest, America West, Jet Blue, and Continental. All of whom have tried to be above-average quality.

12. Variations in Demand Modify Answer Matters are Worse for Z
Consider 3 seasons, matched fares case
Off peak at 2/3 of standard demand (120)
Standard demand of 180 total, as before
Peak day at 4/3 of standard demand (240)
Each season 1/3 of year
Same average demand, revenue, etc.
Off-peak A gets 24 full-fare, 76 discount
Z gets only 20 discount
Peak A gets 48 full-fare, 52 discount
Z gets 100 discount, still below break-even
Z is spilling 40 discounts, lost revenues
Overall, A at $172/seat and Z at $67
Compared to $172 & $80 in simple case
Some revenue in the market is “spilled’ – all from Airline Z
This is a primitive version of the “spill model” case of continuously varying demand levels.

13. Full Spill Model Case
Spill model captures normal full variations of seasonal demand
Spill is airline industry standard model*
Spill model exercised 3 times:
Full-fare demand against A capacity
For full-fare spill, which is zero
Total demand against A capacity
Spill will be sum of discount and full-fare
Total demand against A + Z capacity
Spill will be sum of A and Z spills
K-cyclic = 0.36; C-factorA=0.7; C-factorAZ=0.7
Results
A $11/seat below 3-season case
Z $1/seat better than 3-season case
Qualitatively the same conclusions: A wins big; Z looses.
*See Swan, 1997

14. Airline A is “Sometimes” Preferred
2/3 of customers prefer airline A
1/3 of customers prefer airline Z
Full spill case (full spill model employed)
Results:
A has 85% load; $133/seat—15% above avg.
Z has 73% load; $97/seat—15% below avg.
If Z is low-cost by 15%, can break even
This could represent new-entrant case
This is realistic. Not everyone evaluates airlines the same way, or has perfect information. A good model would be tastes for various characteristics, a utility function that is the sum of tastes, an error term that captures variations in tastes, variations in values of characteristics, variations in measurements of characteristics, and uncertainty in assessment. The smaller the difference in quality, measured by the uncertainty “sigma,” the smaller the difference in share. Result is a logit model of share.
2/3 case could also simply be better time of day.

15. Time-of-Day Games
What if 2/3 preferred case was because Z was at a different time of day?
1/3 of people prefer Z’s time of day
1/3 of people prefer A’s time of day
1/3 of people can take either, prefer Airline A’s quality (or color)
Ground rules: back to simple case
No peak, off-peak spill
Back to 100% maximum load factor
System overall at breakeven revenues and costs
Simple case for clarity of exposition
Spill issues add complication without insight
Spill will merely soften differences

16. Simple Time-of-Day Model
Total Demand
Morning
Midday
Evening
Only
17.5% AM
15% PM
any
52.5% of demand is time-fussy: prefers one of morning, midday, or evening times.
15% of demand is less fussy, preferring anything except evening times.
Another 15% of demand is less fussy, preferring only not to get up too early in the morning.
A final 17.5% of demand is entirely time-flexible: any time of day is OK.
Of course, these are average. The high-fare folks lean toward time-fussy, and the low-fare folks toward flexible.

17. Both A & Z in Morning A=36F, 64D Z=0F, 80D
RAS=$ 80
RAS=$172
Full
Fare
Morn
-ing
Mid-
Day
Even
Only
25% AM
10% PM
All 5%
Dis-count
Morn
-ing
Mid-
Day
Even
Only
10% AM
20% PM
All
30%
RAS = Revenue per Available Seat (Like RASM)
Full Fare demand of 36 is 75% “only” category, 5% “any time” category, and 10% each AM/PM categories.
Discount demand is less time-fussy: 30%-30%-35%
In base case, both flights are in the morning. The dark blue sections get their “time of day.” The light blue demands have to “replan” into the morning departure. They are less happy, but they still make the trip.
Resultant loads are as we said before in the simple case: A gets all full-fare, and fills with discount. Z gets 80% discount.

18. Z “Hides” in Evening A=18.9F, 81.1D Z=17.1F, 62.9D
RAS=$138
RAS=$114
Full
Fare
Morn
-ing
Mid-
Day
Even
Only
25% AM
10% PM
All 5%
Dis-count
Morn
-ing
Mid-
Day
Even
Only
10% AM
20% PM
All
30%
Here the Blue demand regions are captive to A. The amber/orange regions are captive to Z. The green regions replan into the alternate times of day.
Z has done a wise thing: it runs away to dominate a separate time of day. It would pay to do this, even if the time were not the favorite one. On long-haul, for instance, it pays the inferior carrier to seek out the less desirable time of day, so it can “own” some traffic. However, a matched carrier does better matching times and splitting the market.
Note that is this case, Z has gone a long way towards getting half the market. And Z gets very nearly half the business traffic, because little of it is time-flexible. It share of the discount traffic is lower. It would be lower still, except A does not have capacity for all the demand that prefers it.
In this example, with the evening being just as big a peak as the morning, A would do better to move “on top of” Z in the evening slot, rather than sit in the morning alone. So A would chase Z around the times of day—if it could. Unless Z chooses a decidedly inferior time of day. The game gets even more complicated when there are 2 “A” carriers and all three start at the same time. Who moves to the smaller off-peak time? Who follows? It depends. We see this in some large international markets with two distinct times with different demands: Say daytime and overnight. Sometimes the rest of the route structure favors one or the other. Often it is the start-up who first breaks for the secondary peak time.

19. A Pursues to Midday A=22.5F, 77.5D Z=13.5F, 66.5D
RAS=$145
RAS=$107
Full
Fare
Morn
-ing
Mid-
Day
Even
Only
25% AM
10% PM
All 5%
Dis-count
Morn
-ing
Mid-
Day
Even
Only
10% AM
20% PM
All
30%
A reduces Z’s advantage by “covering” the PM demand. In this case the “morning only” demand does NOT all go on the midday flight. They “replan” their trips equally into Midday and Evening slots.

20. Demand Up 50%, A uses 200 seats A=33.7F, 166.3D Z=20.3F, 49.7D
RAS=$134, CAS=$95
RAS=$111; CAS=$126
Full
Fare
Morn
-ing
Mid-
Day
Even
Only
25% AM
10% PM
All 5%
Dis-count
Morn
-ing
Mid-
Day
Even
Only
10% AM
20% PM
All
30%
We add 50% to the traffic, to simulate Z dropping fares and stimulating demand so there is more spill. (Fares were not dropped, because we want a higher demand case to take to multiple departure time examples, next.) However A reacts by adding capacity. Appropriate marginal costs for marginal capacity are applied. These costs are somewhat below the discount revenues, so A’s profits increase. Z tanks.
CAS is “Cost per Available Seat” As in “CASM” = Cost per Available Seat Mile/Km

21. Larger Airplanes are Cheaper Per Seat
A has gone from $126/seat to $95/seat. This is realistic.

22. Demand Up 50%, Z adds Morning A=27F, 73D Z=27F, 143D
RAS=$154, CAS=$126
RAS=$112; CAS=$126
Full
Fare
Morn
-ing
Mid-
Day
Even
Only
25% AM
10% PM
All 5%
Dis-count
Morn
-ing
Mid-
Day
Even
Only
10% AM
20% PM
All
30%
Here we are back to a 100-seat airplane for A. Z is gaining access to the Morning only market, and its high-fare traffic. The amber/orange regions for Z are double before and Z’s revenue per seat is higher.

23. Demand Up 50%, A adds Morning A=40.5F, 157.4D Z=13.5F, 58.6D
RAS=$139, CAS=$126
RAS=$ 99; CAS=$126
Full
Fare
Morn
-ing
Mid-
Day
Even
Only
25% AM
10% PM
All 5%
Dis-count
Morn
-ing
Mid-
Day
Even
Only
10% AM
20% PM
All
30%
A is the airline making money, and therefore more likely to expand its business. If it goes to the Morning time, it reduces its per seat profit, but increases its total.

24. A adds Evening Instead A=54F, 146D Z=0F, 70D
RAS=$154, CAS=$126
RAS=$ 70; CAS=$126
Full
Fare
Morn
-ing
Mid-
Day
Even
Only
25% AM
10% PM
All 5%
Dis-count
Morn
-ing
Mid-
Day
Even
Only
10% AM
20% PM
All
30%
A does better to “sit” on top of Z. As before with the one-flight case.

25. Summary and Conclusions
Airlines have strong incentives to match
A preferred airline does best matching prices
A non-preferred airline does poorly unless it can match preference.
A preferred airline gains substantial revenue
Higher load factor in the off peak
Higher share of full-fare passengers in the peak
Gains are greater than from higher prices
A less-preferred airline has a difficult time covering costs
Preferred airline’s advantage is reduced by
Spill – but not much change
Partial preference – some people prefer the other
Time-of-day distribution – good time/bad airline