Evaluation of an Auction Mechanism for Allocating Airport Arrival Slots

Evaluation of an Auction Mechanism for Allocating Airport Arrival Slots Eric J. Cholankeril William Hall John-Paul Clarke June 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 Slot Allocation Methods to Compare

Collaborative Decision Making • Current Slot Allocation Method • Goal: Increase usage of airport resources • Implemented 1998 Three Steps: • Initial slot assignment through Ration By Schedule (RBS) • Substitution and Cancellation • 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 • Assign arrival slots to airlines using Ration By Schedule. • Auction off each slot in order of the original schedule. • How do airlines determine sell and bid amounts? • 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! • Assign flights to S U S1 • Assign flights to S \ {S1} • 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 for assigned routes for cancelled flights • 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

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 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

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.

Results: Varying Number of Cautious Airlines Increasing the number of cautious airlines seems to increase total delay.

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.

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.

Evaluation of an Auction Mechanism for Allocating Airport Arrival Slots