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

2. 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

3. 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 arent being redistributed to other airlines

4. Motivation Why arent 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)

5. 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.

6. 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

7. 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

8. Auction Design Considerations Package bidding is complex to implement (n slots => 2 n 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

9. 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

10. Goal: Evaluate Auction as Allocation Method AuctionArrival 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 Optimization All flights and slots belong to one airline. Airline computes optimal flight-slot assignment. Slot Allocation Methods to Compare

11. Collaborative Decision Making Current Slot Allocation Method Goal: Increase usage of airport resources Implemented 1998 Three Steps: 1. Initial slot assignment through Ration By Schedule (RBS) 2. Substitution and Cancellation 3. Compression (at regular intervals)

12. 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.

13. 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.

14. 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

15. 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.

16. 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

17. Slot Valuation How does an airline decide how much to bid on a particular slot S 1, where S is the set of slots it owns? Bid the marginal value of the slot! 1. Assign flights to S U S 1 2. Assign flights to S \ {S 1 } 3. Subtract valuations How to assign flights? Solve airline recovery problem

18. 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.

19. 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.

20. Model of the Airline Recovery Problem Minimize minutes of passenger delay C v = passenger delay due to assigning route v X v = 1 if route v is assigned, 1 otherwise d f = passenger delay due to cancelling flight f K f = 1 if flight f is cancelled, 0 otherwise for assigned routesfor cancelled flights

21. 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.

22. 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.

23. Generating Unslotted Routes with 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)

24. 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

25. Slotting Routes Idea: Generate all possible pairings of arrival slots to GDP arrival flights To calculate D f, minutes flight f is delayed: If f is a GDP arrival, D f = (slot time – fs original arrival time) Otherwise, D f = delay implied by previous flights in the route

26. Calculating Passenger Delay What is passenger delay? Sum of delays to individual passengers in arriving at their final destinations To calculate C v, 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 D f, 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

27. 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

28. 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 hrs74.51%9.54% 10 arrivals/hr, 2 hrs69.48%11.78% 20 arrivals/hr, 2 hrs22.42%21.37% 0 arrivals/hr, 1 hr56.64%33.29% 20 arrivals/hr, 3 hrs36.25%18.77% More reducible delay captured in longer, more severe GDPs

29. 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 hrs6.84%4.30% 10 arrivals/hr, 2 hrs28.80%10.86% 20 arrivals/hr, 2 hrs8.83%10.2% 0 arrivals/hr, 1 hr5.93%4.63% 20 arrivals/hr, 3 hrs20.48%12.27%

30. Results: Varying One Airlines Cautiousness It is unclear whether a single airline benefits from being more cautious. Results display a high degree of randomness.

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

32. 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.

33. 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

34. 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

35. 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.