evaluation of an auction mechanism for allocating airport arrival slots eric j. cholankeril william...
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Evaluation of an Auction Mechanism for Allocating Airport
Arrival Slots
Eric J. CholankerilWilliam Hall
John-Paul ClarkeJune 5, 2003
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Agenda Motivation Background on Auctions, Airline Recovery Three Methods of Slot Allocation
Collaborative Decision Making Global Optimization The Auction Mechanism
Model of the Airline Recovery Problem Results Summary and Future Work
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Motivation Problem: While on-time rates have
improved, total passenger delay has increased.
Inefficient use of airport resources during Ground Delay Programs (GDPs)
A high fraction of flight cancellations is unreported (~36%), so unused slots aren’t being redistributed to other airlines
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Motivation Why aren’t airlines releasing unused
slots? Current slot allocation method may not
provide enough direct incentive for airlines to report cancellations.
Airline may fear a loss in market share if its slots are redistributed to another airline.
Airlines may be guarding against revisions to the Ground Delay Program (GDP)
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Motivation Hypothesis: An auction could
reduce overall passenger delay by allocating arrival slots more efficiently.
An auction provides direct monetary incentive for airlines to give up unneeded slots.
Objective: Test this hypothesis.
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Vickrey Auction Sealed bid, second price auction Highest bidder wins However, winner pays only the
amount of the second highest bid
This type of auction ensures that bidders bid their true valuations
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Previously Suggested Auctions for Arrival Slot Allocation
Combinatorial Auction (Rassenti) – Airlines can bid on packages of slots
Multi-Object Auction (Milner) – Airlines report value of each possible flight/slot combination, then FAA solves large assignment problem
Groves Mechanism (Hall) – Impose a fee on an airline, equal to the lost value caused to the other airlines
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Auction Design Considerations
Package bidding is complex to implement (n slots => 2n packages!)
Individual bidding may not capture true value of slot; since flights often arrive and depart in banks, slots may be more valuable when packaged together.
Charging airlines a fee to land is politically infeasible, especially if the fee seems unrelated to the bid values
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The Airline Recovery Problem
How do airlines reroute their aircraft and delay or cancel flights in response to a GDP?
Sub-problems: fleet assignment, aircraft rerouting, crew scheduling, gate assignment, slot allocation, passenger rerouting
Set-packing model (Clarke) Aircraft selection heuristic (Rosenberger) Goal in this thesis: simple airline recovery
model, quick to solve for a real-time auction
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Goal: Evaluate Auctionas Allocation Method
Auction Arrival slots are initially assigned to airlines according to original schedule of flights.Then each slot is put up for auction, in the order of the original schedule.
Collaborative
Decision Making (CDM)
Unused slots are reported and redistributed by the FAA. An airline that gives up a slot receives priority for slots that are subsequently freed.
Global Optimizati
on
All flights and slots belong to one airline.Airline computes optimal flight-slot assignment.
Slot Allocation Methods to Compare
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Collaborative Decision Making Current Slot Allocation Method Goal: Increase usage of airport resources Implemented 1998Three Steps:1. Initial slot assignment through Ration By
Schedule (RBS)2. Substitution and Cancellation3. Compression (at regular intervals)
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CDM: Ration-By-Schedule (RBS) Given a reduced arrival capacity,
the FAA issues a Ground Delay Program (GDP) that maintains the original scheduled order of flights.
For example, if the arrival capacity is 20 arrivals per hour, arrival slots are spaced every three minutes and assigned to the airlines according to the original schedule.
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CDM: Substitution/Cancellation
Slot is assigned to airline, rather than to a particular flight
Substitution: Airline is free to reassign its flights to the slots it owns, after the initial RBS assignment. Simulate this by solving airline recovery problem.
Cancellation: Airlines may decide to release unused slots back to the FAA.
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CDM: Compression At regular intervals, any released
slots are redistributed or “compressed.”
If airline A releases one of its slots back to the FAA, and the slot is reassigned to a flight for airline B, A receives priority for the slot that is freed as a result.
Provides some incentive for airlines to release unused slots
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Global Optimization Goal: determine upper bound on amount of delay
that can be reduced through allocating slots efficiently
Simulate by assigning all flights and slots to one large airline. Airline computes optimal flight-slot assignment by solving the airline recovery problem
Note: It is possible to exploit other efficiencies, e.g. by constructing routes composed of flights from different airlines. However, we are only concerned with efficiencies that result from allocating slots.
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Auction Mechanism• Sealed-bid, sequential Vickrey
auction without package bidding
1. Assign arrival slots to airlines using Ration By Schedule.
2. Auction off each slot in order of the original schedule.
How do airlines determine sell and bid amounts?
3. Auction winner pays RBS slot owner for right to slot
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Slot Valuation How does an airline decide how
much to bid on a particular slot S1, where S is the set of slots it owns?
Bid the marginal value of the slot!1. Assign flights to S U S1
2. Assign flights to S \ {S1}3. Subtract valuations
How to assign flights? Solve airline recovery problem
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Determining the Sell Price In the auction, the RBS owner can set a
reservation price, or minimum sell price. Slot is not sold unless the amount paid is
at least the reservation price. How to determine sell price? Marginal
value of the slot. Airline can decide not to sell the slot at
all by setting the reservation price very high.
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Alternative Airline Behaviors “Cautious Airline”
With some probability p, the airline sets its reservation price to infinity in the auction.
In CDM, the airline refuses to release the slot with probability p.
“Predictive Airline” The airline bids relative to a predicted
final slot allocation, instead of bidding the marginal value of the slot.
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Model of the Airline Recovery Problem
Minimize minutes of passenger delay ∑∑
∈∈
+Ff
ff
Vv
vv KdXC
•Cv = passenger delay due to assigning route v
•Xv = 1 if route v is assigned, 1 otherwise
•df = passenger delay due to cancelling flight f
•Kf = 1 if flight f is cancelled, 0 otherwise
for assigned routes for cancelled flights
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Airline Recovery Constraints
Each aircraft is assigned to exactly one route.
Each flight is either cancelled or flown on one route.
Each slot is assigned to at most one flight.
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How to Generate Routes? First, generate “unslotted” route alternatives
for each aircraft. Then, pair GDP arrivals with slots within each route to generate “slotted” routes, and calculate the resulting delay.
Constraints satisfied: Each flight arriving at the GDP airport is assigned
to some slot. Flight arrival times equal designated slot times. Flow balance is maintained: aircraft must arrive at
and take off from the same airport.
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Generating Unslotted Routeswith a GDP at LAX
Each aircraft must be assigned to its originating flight (1,6), and some terminating flight (5 or 11)
Possible A routes: (1,2,3,4,5), (1,2,9,10,11), (1,2,11)
Possible B routes: (6,7,8,9,10,11), (6,7,4,5), (6,5), (6,7,8,11)
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Reducing Route Possibilities Using Subroutes
A: (1,2,3,4,5), (1,2,9,10,11) NOT (1,2,11)
B: (6,7,8,9,10,11), (6,7,4,5), (6,5) NOT (6,7,8,11)
What happens if A is assigned (1,2,3,4,5) and B is assigned (6,7,8,11)? 9 and 10 are cancelled, but neither depart from nor arrive at LAX!
-> Combine flights that neither depart from nor arrive at GDP airport into “subroutes”
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“Slotting” Routes Idea: Generate all possible pairings of
arrival slots to GDP arrival flights To calculate Df, minutes flight f is
delayed: If f is a GDP arrival,
Df = (slot time – f’s original arrival time) Otherwise, Df = delay implied by previous
flights in the route
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Calculating Passenger Delay
What is “passenger delay”? Sum of delays to individual passengers in arriving at their
final destinations
To calculate Cv, passenger delay for assigning route v: For terminating passengers, use delay of flight For connecting passengers, determine which passengers miss
their connections, and calculate their delays if they were to be rerouted onto later connecting flights.
To calculate Df, passenger delay due to cancelling flight f:
Calculate delays for passengers if they were to be rerouted onto later flights
Impose cancellation delay cutoff of 6 hours
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Implementation Simulated on actual flight data from March 1998
(Airline Service Quality Performance database for 10 biggest airlines, OAG database for local and international airlines)
Passenger itinerary data stochastically generated using itinerary probabilities calculated from ticket samples (DB1B Market database, Bureau of Transportation)
Average passenger load factor for Q1 1998: 70% Minimum turnaround time assumed: 25 minutes GDP at BOS, default arrival rate = 60/hr
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Results: Reducible Passenger Delay Captured
Reducible Passenger Delay= Global Opt. Delay – CDM Delay
Reduced Airport Arrival Rate,
Reduction Period
Avg. Percentage of Reducible Delay
Captured By Auction
St.Dev.
0 arrivals/hr, 2 hrs 74.51% 9.54%
10 arrivals/hr, 2 hrs 69.48% 11.78%
20 arrivals/hr, 2 hrs 22.42% 21.37%
0 arrivals/hr, 1 hr 56.64% 33.29%
20 arrivals/hr, 3 hrs 36.25% 18.77%More reducible delay captured in longer, more severe GDPs
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Results: Absolute Reduction in Passenger Delay
Large variation in percentage of delay reduced However, the delay reduction is statistically
different from zero in each case
Reduced Airport Arrival Rate,
Reduction Period
Avg. Percent Delay Reduction
St. Dev.
0 arrivals/hr, 2 hrs 6.84% 4.30%
10 arrivals/hr, 2 hrs
28.80% 10.86%
20 arrivals/hr, 2 hrs
8.83% 10.2%
0 arrivals/hr, 1 hr 5.93% 4.63%
20 arrivals/hr, 3 hrs
20.48% 12.27%
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Results: Varying One Airline’s “Cautiousness”
It is unclear whether a single airline benefits from being more cautious. Results display a high degree of randomness.
Effect of Increasing One Airline's Caution Level on Its Net Delay in the Auction
-200
-150
-100
-50
0
50
100
150
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Probability p of Withholding a Slot
Change in Passenger Minutes of Delay Minus Auction
Income, from p=0
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Results: Varying Number of Cautious Airlines
Increasing the number of cautious airlines seems to increase total delay.
Effect of Increasing Number of Cautious Airlines on Overall Passenger Delay in the Auction
C 9L UA DL US AA OH
QKAC
HQ
CO
W9
HP
NW
-5000
0
5000
10000
15000
20000
25000
0 2 4 6 8 10 12 14 16
Number of Cautious Airlines (With Caution Level 0.3)
Increase in Total Passenger Minutes of Delay,
from Zero Cautious Airlines
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Results: Varying Number of “Predictive” Airlines
Increasing the number of predictive airlines seems to increase total delay, but results also display a great deal of randomness.
Effect of Increasing Number of Predictive Airlines on Overall Passenger Delay in the Auction
C 9L
US
OH QKAC
HPHQ W9
CO
DL
UA
NW
AA
-40000
-20000
0
20000
40000
60000
80000
0 2 4 6 8 10 12 14 16
Number of Predictive Airlines
Increase in Total Passenger Minutes of Delay,
from Zero Predictive Airlines
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Optimization Running Time
Time to “slot” routes, generate route delays, and solve IP
For most airlines, under a second For Business Express, with 23 disrupted
aircraft and 1809 possible route alternatives, under 4 seconds
Optimization Model is fast enough for a real-time auction, but requires much more memory for extended GDPs with many route possibilities
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Summary Use auction to allocate arrival slots more
efficiently Assign slots to airlines according to the
original schedule, then allow airlines to bid on slots
Compared passenger delay for auction method, CDM, and global optimization
For scenarios tested: Up to 75% of reducible passenger delay was captured
At least 5-7% of overall passenger delay was reduced in all scenarios
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Ideas for Future Research Simulate other auction mechanisms,
e.g. combinatorial auction Simulate effect of revising the GDP Future work on airline recovery problem
Route generation requires a lot of memory, esp. for extended GDPs
More accurate passenger rerouting model needed Add in constraints on gate assignment, crew
scheduling, etc.