a multi-stakeholder evaluation of strategic slot allocation ...2011/06/03 · (vaze and barnhart,...
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A Multi-stakeholder Evaluation of Strategic Slot Allocation Schemes under Airline Frequency
Competition
Vikrant Vaze
Cynthia Barnhart
Massachusetts Institute of Technology
June 2011, Berlin Germany
Ninth USA/Europe Seminar on Air Traffic Management
Research and Development (June 2011)
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Year Number of Passengers
Number of Flights
Total Arrival Delays to Flights (Minutes)
2000 100 100 100
2001 93.34 96.47 78.15
2002 92.06 102.32 59.75
2003 97.29 119.65 75.18
2004 105.04 126.09 103.58
2005 109.62 126.98 107.80
2006 109.81 122.86 120.99
2007 113.28 124.46 138.58
2008 108.70 118.60 119.11
2009 103.07 110.73 91.82
2010 105.00 110.03 88.30
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Extent and Causes of Airport Congestion• Cost of domestic flight delays to US economy in 2007≈ $31.2 billion*
• 84.5% of National Aviation System (NAS) delays attributed to demand exceeding the realized airport capacity**
*NEXTOR, Total Delay Impact Study (Ball, et al., 2010) **Bureau of Transportation Statistics (www.bts.gov, 2008)
• Increase in number of flights much greater than that in passengers
• ~9% reduction in #passengers/flight
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• More frequent flights attract more passengers
• Higher frequency shares associated with disproportionately higher market shares
– Sigmoidal (or S-shaped) relationship
Frequency Competition
Frequency Share
Mar
ket
Shar
e
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Prior Research
a. In the absence of competition,
– existing capacity more than enough to satisfy all passenger demand, with a similar level-of-service
– over 80% reduction in congestion related delays
(Vaze and Barnhart, 2011)
b. In the presence of competition,
– level of congestion introduced by competition is directly proportional to
1. profit margin
2. number of competitors
3. curvature of the S-curve
(Vaze and Barnhart, 2010)
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1. Model of Frequency Competition
2. Solution Methodology
3. Experimental Setup
4. Computation Results
5. Sensitivity to Assumptions
6. Conclusions
Contents
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• Slot controls: common at major airports
– Five congested airports in United States
– Many major airports in Europe and Asia
AA DL USUA WN
Nash Equilibrium
Total Slots
Slot Distribution
Competition
Administrative Slot Controls at Airports
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maximize: (𝑝𝑎𝑠𝑄𝑎𝑠 − 𝐶𝑎𝑠 𝑓𝑎𝑠)
𝑠∈𝕊𝑎
subject to: 𝑄𝑎𝑠 ≤𝑓𝑎𝑠𝛼𝑠
𝑓𝑎 ′ 𝑠𝛼𝑠
𝑎 ′ ∈𝔸𝑠
𝑀𝑠 ∀𝑠 ∈ 𝕊𝑎
𝑄𝑎𝑠 ≤ 𝐿𝐹𝑚𝑎𝑥 𝑆𝑎𝑠 𝑓𝑎𝑠 ∀𝑠 ∈ 𝕊𝑎 𝑓𝑎𝑠
∀𝑠∈𝕊𝑎
≤ 𝑈𝑎
𝑓𝑎𝑠∀𝑠∈𝕊𝑎
≥ 𝐿𝑎
𝑓𝑎𝑠 ∈ ℤ+ ∀𝑠 ∈ 𝕊𝑎
Total profit = fare revenue – operating cost
S-curve relationship
Seating capacity constraint
Upper bound on total slots
Lower bound on total slots
Model of Frequency Competition
The Basic Model
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• Extension I: Fare Differentiation
– Divides passengers into segments
– Market share is a function of frequencies, fares, and airlines specific factors
– Used for markets with asymmetric competition,
• e.g. a Regional Carrier Vs. a Legacy Carrier
• Extension II: Market Entry Deterrence
– Used for markets with a single airline
– Possibility of market entry if existing frequency is not adequate
– 2-stage Stackelberg model
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Extensions to the Basic Model
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• Size of the overall strategy space ≈ 1050
• Successive optimizations heuristic:
– While there exists an airline whose current decision is not optimal: Re-optimize
• Individual optimization problems
– Solved to optimality using dynamic programming
• Structure suitable for dynamic programming because:
– slot restrictions: additive coupling constraints across markets
– objective function: additive across markets
• #stages = #markets
• #states per stage = maximum # slots
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Solution Methodology
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• All flights out of LGA airport
• Passenger demands, operating costs, fares, and seating capacities obtained from BTS website
Obtain Nash equilibrium solution for:
1. Existing slot controls (empirical validation)
2. Varying levels of slot reduction (explorative analysis)
3. 12.3% slot reduction (multi-stakeholder evaluation)
a. Proportionate allocation: slots distributed in same ratio as current slots
b. Reward-based allocation: slots distributed in same ratio as current passengers
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Experimental Setup
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Actual Daily Frequency
Esti
mat
ed D
aily
Fre
qu
en
cy
Empirical Validation
Model results provide good fit to actual frequencies
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Percentage Slot Reduction Percentage Slot Reduction
Perc
enta
ge D
ecre
ase
in P
asse
nge
rs
Perc
enta
ge In
crea
se in
Pro
fit
Explorative Analysis
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Slot Reduction with Proportionate Allocation
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Multi-Stakeholder Evaluation
Profit ($)
Avg. Delays (min.)
Passengers Carried
-41%
-2% +19% +16%
12.3% Slot Reduction
Large Reduction in Flight and Passenger Delays
Small Reduction in Passengers Carried
Considerable Increase in Airline Profits
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Profits of Individual Airlines
12.3% Slot Reduction
+14%
+24%+58%
+29%
Each airline’s profit increases under both strategies
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Sensitivity to Maximum Load Factor Assumption
0%
5%
10%
15%
20%
25%
75% 80% 85% 90% 95%
Proportionate Reward-based
-3.0%
-2.5%
-2.0%
-1.5%
-1.0%
-0.5%
0.0%
Incr
ease
in P
rofi
tC
han
ge in
Pas
sen
gers
Slot reduction impacts are NOT very sensitive to the maximum load factor assumptions
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Relaxing the Constant Aircraft Size Assumption
Impact of Limited Upgauging
Perc
enta
ge D
ecre
ase
in P
asse
nge
rs
Maximum Upgauge Percentage
Most of the reduction in passengers carried disappears
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• Slot reduction benefits passengers, airlines and airport operators– Almost all passengers carried with
• negligible increase in schedule displacement and
• large reduction in passenger delays
– All airlines benefit through • considerable increase in operating profits and
• large reduction in flight delays
– Airport operators benefit from• reduction in airport congestion
• Results not too sensitive to assumptions– Main conclusions are robust
– Often conservative: actual benefits likely even higher
Conclusions
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References
• V. Vaze and C. Barnhart, “An assessment of the impact of demand management strategies for efficient allocation of airport capacity”, International Journal of Revenue Management, Upcoming, 2011.
• V. Vaze and C. Barnhart, “Price of airline frequency competition”, Working Paper ESD-WP-2010-10, Engineering Systems Division, Massachusetts Institute of Technology, 2010.
Thank You