1. Exploratory Study of Demand Management Using Auction-Based Slot Allocation L. Le, S. Kholfi, G.L. Donohue, C-H Chen Air Transportation Systems Engineering Laboratory Dept. of Systems Engineering & Operations Research George Mason University Fairfax, VA

2. Outlines  Slot auction model  Auctioneer optimization model  Airline optimization model  Illustration : a case study  Summary and future work

3. ATL – Atlanta Airport (FAA Airport Capacity Benchmark Report 2001) Problem Identification Asynchronous non-uniform scheduling Underutilization Queuing delay Safety violation Safety violation?

4. Problem Identification Small aircraft makes inefficient use of slots Cumulative Flight Share Cumulative Seat Share Aircraft Size (seats) aircraft in small category 25% flight share for 5% seat share LAX arrivals, 1998 (Mark Hansen, Berkeley)

5. Auction Model Design issues  Feasibility  package slot allocation for departure and arrival slots  incremental (time phase implementation)  Optimality  efficiency : throughput (enplanement opportunity) and delay  regulatory standards: safety, flight priorities  equity:  stability in schedule  airlines’ need to leverage investments  airlines’ competitiveness : new-entrants vs. incumbents  Flexibility  primary market at strategic level  secondary market at tactical level

6. Background on auction models  Simultaneous multiple-round auction  have discrete, successive rounds, with length of each round announced in advance. After each round closes, round results are processed and made public  Account for departure/arrival slots interdependence but subject to aggregation risks  Package bidding  bidders submit bids for multiple combinations of lots rather than just individual lots. Package biddings are either accepted or rejected in their entirety  Eliminate aggregation risks

7. Auction Model Process another time window? Call for bids for slots in the time window End auction process Submit information and bid Winners determined? Yes No Auctioneer’s action Airline’s action Incremental auction prioritizing most congested periods Determine factor weights Determine time-windows to auction off

8. Auctioneer Optimization Model S T slot vector, | S T |=AAR A airline vector W T vector of factor weights B a,s bid of airline a for slot s Ranking function: Airlines are ranked by a linear combination of :  throughput  flight OD pair  airline’s prior investment  on-time performance  monetary offer BID

9. Bidding matrix X=A.S T Auctioneer Optimization Model S T slot vector, | S T |=AAR A airline vector W T vector of factor weights B a,s bid of airline a for slot s Ranking function: Airlines are ranked by a linear combination of :  throughput  flight OD pair  airline’s prior investment  on-time performance  monetary offer BID if airline a is ranked highest for slot s after a round otherwise

10. Auctioneer Optimization Model  Objective function: Allocate slots to the highest ranked airlines Max Variables: S T slot vector, | S T |=AAR A airline vector W T vector of factor weights B a,s bid of airline a for slot s if airline a is ranked highest for slot s after a round otherwise X= A*S T bidding matrix Subject to: One slot – one aircraft Minimum bid constraint Airline constraint

11. Airline Optimization Model Objective function: Maximize revenue and ultimately maximize profit Maximize M big positive value y s binary value B o T airport threshold vector  airline threshold fraction B s ’ old bid for slot s in previous round if airline bids for slot s otherwise {B s } set of monetary bids {P s } airline expected profit by using a slot Variables: Subject to: Airlines’ package bidding constraints To bid or not to bid Upper bound for bids Lower bound for bids

12. Illustration : an example FactorsWeight Number of seats0,32 Previous airline infrastructure investment0,25 Historical on-time performance0,19 OD-Pair0,13 Bid0,11 Ranking function : Aircraft type (#seats) OD pair (Slot occupancy rate) %investment Bidding matrix, initial round Winner-determining factors

13. Illustration: an example Bid score matrix, initial round Air carrier monetary bids Round 1 Withdraw from auction for these slots

14. Illustration: an example Bid score matrix, initial round Air carrier monetary bids Round 1 Withdraw from auction for these slots

15. Illustration: an example Round 1 Bid score matrix Break ties by adding 10% of airline profit to bids Bid score matrix, initial round Air carrier monetary bids Round 1 Withdraw from auction for these slots

16. Illustration: an example Round 12 (final) Auction winners Round 12 (final) Air carrier monetary bids Bid score matrix

17. Simulation design NetworkAuction Results Analysis & Feedback Airlines Bids (Mark Hansen) Means of the calculated inter-arrival times Queuing model: runway delay calculated by separation standards w(throughput)= 0 w(flight OD pair)= 0 w(prior investment)= 0 w(on-time perf.) = 0 w(monetary offer)= 1

18. Simulation design (cont.)  Auction items: departure slots  Top-down auction proceeds by most congested hours  Airlines have the same upper bid threshold which is N (N=5) times the initial bid  Airlines break ties by randomly adding a fraction of the initial bid  Airlines’ elasticity for schedule changing  No fleet mix change original scheduled time 1 hour bids withdrawn

19. Simulation scenarios  Input:  OAG schedule of departures from ATL (1261 flights)  Actual separation scenario:  OAG schedule  Auction-produced schedule  “Theoretical separation” scenario:  OAG schedule  Auction-produced schedule 100,100 80,80

20. Actual separation scenario Baseline After auction 123456789101112131415161718192021222324

21. Actual separation scenario

22. Theoretical separation scenario Baseline After auction

23. Theoretical separation scenario

24. Summary and future work  Summary  Generic market-based approach to airport demand management allows to evaluate many alternatives by varying the weighting factors,  Legal and procedural challenges would require rigorous cost-benefit evaluation.  Future work  Modeling airlines’ behavior,  Cross-airport package bidding,  Conduct sensitivity analysis for different auction formats (with different values of factor weights)

25. back-up slides

26. Problem Identification Lack of competition  Hirschman-Herfindahl Index (HHI) is standard measure of market concentration  Department of Justice uses to measure the competition within a market place  HHI=  (100*s i ) 2 w/ s i is market share of airline i  Ranging between 100 (perfect competitiveness) and 10000 (perfect monopoly)  In a market place with an index over 1800, the market begins to demonstrate a lack of competition

27. Potential solutions  Congestion pricing  monitoring and updating constraints  Promote use of larger aircraft  airline economic constraints  Improve local infrastructure  environmental constraints  Rerouting flights  market constraints

28. Design scope  Scope:  Strategic auction for arrival slots at individual airports  Objective:  Provide an optimum fleet mix at optimum safe capacity  Ensure fair market access opportunity  Reduce queuing delay  Definitions:  Slot: The concession or the entitlement to use runway capacity of a certain airport by an air carrier on a specific date and at a specific time [CITE: EEC COM(2001)335]  Grandfather right: Air carriers having historical use rate of a slot of at least 80% will have precedence.

29. Design approach  Objective:  provide an optimum fleet mix at optimum safe arrival capacity  ensure fair market access opportunity  reduce queuing delay  Assumptions  airlines could make use of slots they bid  Auction process:  an interactive and iterative process to enable flexibility and optimization  a mixture of simultaneous auction model and package model  Auction rules: Bidders are ranked using a linear combination of:  flight OD pair  throughput  airline’s prior investment  on-time performance  monetary offer

30. Auctioneer Optimization Model Safe separation b/w leading and trailing aircraft: (Mark Hansen) Mean of the calculated inter-arrival times by aircraft weight categories M T initial monetary offer vector Objective function: Ranking function: Subject to: Max S T slot vector, | S T |=AAR A airline vector W T vector of factor weights B a,s bid of airline a for slot s X= A*S T bidding matrix if airline a is ranked highest for slot s after a round otherwise Variables:

31. Auctioneer Optimization Model Safe separation b/w leading and trailing aircraft: (Mark Hansen) Mean of the calculated inter-arrival times by aircraft weight categories M T initial monetary offer vector Objective function: Ranking function: Subject to: Max S T slot vector, | S T |=AAR A airline vector W T vector of factor weights B a,s bid of airline a for slot s X= A*S T bidding matrix if airline a is ranked highest for slot s after a round otherwise Variables:

32. Auctioneer Optimization Model Subject to: Capacity constraint: One slot allocated to one flight Ranking function: Max Objective function: Variables: S T slot vector, | S T |=AAR A airline vector W T vector of factor weights B a,s bid of airline a for slot s if airline a is ranked highest for slot s after a round otherwise X= A*S T bidding matrix

33. Auctioneer Optimization Model Subject to: Ranking function: Max Objective function: Minimum bid: At any round, monetary offers should be equal or greater than initial thresholds Variables: S T slot vector, | S T |=AAR A airline vector W T vector of factor weights B a,s bid of airline a for slot s if airline a is ranked highest for slot s after a round otherwise X= A*S T bidding matrix M T initial monetary offer vector

34. Auctioneer Optimization Model Airline constraints: Only one slot is needed in a set of adjacent slots Subject to: Ranking function: Max Objective function: Variables: S T slot vector, | S T |=AAR A airline vector W T vector of factor weights B a,s bid of airline a for slot s if airline a is ranked highest for slot s after a round otherwise X= A*S T bidding matrix M T initial monetary offer vector

35. Auctioneer Optimization Model Subject to: Ranking function: Max Objective function: Airlines’ package bidding constraints Variables: S T slot vector, | S T |=AAR A airline vector W T vector of factor weights B a,s bid of airline a for slot s if airline a is ranked highest for slot s after a round otherwise X= A*S T bidding matrix M T initial monetary offer vector

36. Airline Optimization Model Airline either bids for slot s (monetary offer greater than minimum threshold) or not. M big positive value y s binary value B o T airport threshold vector if airline bids for slot s otherwise Objective function: Maximize profit Maximize {B s } set of monetary bids {P s } airline expected profit by using a slot Variables: Subject to:

37. M big positive value y s binary value B o T airport threshold vector  airline threshold fraction if airline bids for slot s otherwise Objective function: Maximize profit {B s } set of monetary bids {P s } airline expected profit by using a slot Variables: When offering bid for slot s, monetary amount should not pass a threshold Maximize Airline Optimization Model

38. Subject to: M big positive value y s binary value B o T airport threshold vector  airline threshold fraction B s ’ old bid for slot s in previous round if airline bids for slot s otherwise Objective function: Maximize profit {B s } set of monetary bids {P s } airline expected profit by using a slot Variables: Given B s ’ the bid airline offered in the previous round, in order to be ranked highest in this round, airline has to increase at least : Maximize Airline Optimization Model

39. Subject to: M big positive value y s binary value B o T airport threshold vector  airline threshold fraction B s ’ old bid for slot s in previous round if airline bids for slot s otherwise Objective function: Maximize profit {B s } set of monetary bids {P s } airline expected profit by using a slot Variables: Given B s ’ the bid airline offered in the previous round, in order to be ranked highest in this round, airline has to increase at least : Old bidMinimum increase Maximize Airline Optimization Model

40. Subject to: M big positive value y s binary value B o T airport threshold vector  airline threshold fraction B s ’ old bid for slot s in previous round if airline bids for slot s otherwise Objective function: Maximize profit {B s } set of monetary bids {P s } airline expected profit by using a slot Variables: Old bid Minimum increase Minimum new bid Maximize Airline Optimization Model

41. Subject to: M big positive value y s binary value B o T airport threshold vector  airline threshold fraction B s ’ old bid for slot s in previous round if airline bids for slot s otherwise Objective function: Maximize profit Maximize {B s } set of monetary bids {P s } airline expected profit by using a slot Variables: Airlines’ package bidding constraints Airline Optimization Model

42. Design approach  Objective:  provide an optimum fleet mix at optimum safe arrival capacity  ensure fair market access opportunity  reduce queuing delay  Assumptions  airlines could make use of slots they bid  Auction rules: Bidders are ranked using a linear combination of:  flight OD pair  throughput  airline’s prior investment  on-time performance  monetary offer