Evaluation of an Auction Mechanism for Allocating Airport Arrival Slots Eric J. Cholankeril William Hall John-Paul Clarke June 5, 2003.

Evaluation of an Auction Mechanism for Allocating Airport

Arrival Slots

Eric J. CholankerilWilliam Hall

John-Paul ClarkeJune 5, 2003

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

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

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)

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.

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

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

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

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

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

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)

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.

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.

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

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.

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

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

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.

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.

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

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.

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.

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)

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”

“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

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

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

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

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%

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

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

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

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

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

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.