Dynamic Airline Slot Exchange during Ground Delay Programs Thomas Vossen, University of Colorado, Boulder Michael Ball, Philippe Montebello University of Maryland, College Park Ground Delay Programs: Motivation: airline schedules “assume” good weather SFO: Scheduled Arrivals 18 Number of Arrivals 16 VMC airport acceptance rate 14 12 10 8 IMC airport acceptance rate 6 4 2 0 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Ground Delay Programs delayed departures delayed departures delayed arrivals/ no airborne holding delayed departures GDPs under CDM Resource Allocation Process: • FAA: initial “fair” slot allocation [Ration-by-schedule] • Airlines: flight-slot assignments/reassignments [Cancellations and substitutions] • FAA: periodic reallocation to maximize slot utilization [Compression] Compression Example Slot released by canceled/ 4:05 delayed flight 4:05 4:20 USA 51 UAL 234 USA 345 4:50 AAL 672 4:50 AAL 672 5:10 AAL 95 5:10 AAL 95 Earliest time of arrival = 4:20 Slot Exchange Alternatives • Compression as Reallocation – Dynamic changes to airline “demand profiles” necessitate (re)rationing • Compression as Slot Trading – e.g., Slot Credit Substitutions: “I am willing to cancel flight f1 if I can move up flight f2”. Slot Trading Opportunities 160 40 140 35 Cum. cnx (% of flts in gdp) Cum. Subs (% of flts in gdp) Airline Substitution/Cancellation Patterns 120 100 80 60 40 20 0 1 75 149 223 297 371 445 519 593 667 741 815 Cumulative minutes (from start of program) 30 25 20 15 10 5 0 1 51 101 151 201 251 301 351 401 451 501 551 601 651 701 751 Cum ulative m inutes (from start of program ) Consider potential benefits of extending slot trading framework – e.g., Increase offers submitted by airlines From 1-for-1 to 2-for-2 trades • Compression and/or slot credit substitution can be interpreted as a 1-for-1 trading system, i.e. offers involve giving up one slot and getting one in return (many offers are processed simultaneously) • What about k-for-k or k-for-n offers, e.g. 2-for-2: Trade?? Value proposition for compression & SCS Value(slot) = $0 unusable because of cancellation or flight delay usable slot Value(slot) > $0 SCS/Compression “trades” are always driven by the exchange of a slot with value 0 and a slot with value > 0!! 2-for-2 trades enable airlines to profit by exchanging pairs of usable slots that result in an increase in overall value to the carrier. Airline B Airline A B20 (low priority) A25 (high priority) s3 s1 s2 A10 (low priority) s4 B35 (high priority) A’s value proposition: valA(s3) – valA(s1) + valA(s4) – valA(s2) = 2000 - 1500 + 300 - 500 = $300 B’s value proposition: valB(s1) – valB(s3) + valB(s2) – valB(s4) = 500 - 800 + 2500 - 1800 = $400 Another view of 2-for-2 trading: generalized substitutions Normal Substitution Generalized Substitution Issues • System Design: – How do airlines represent and generate offers? – Formulation and solution of FAA mediation problem • System Evaluation: – Airline objectives and strategies – Performance Measurement: • comparison with optimal centralized solution (system efficiency) % improvement 30 25 20 15 %Improvement Compression Benefits 2-for-2 Trading Model • • compression executed after flts with excessive delay (>2hrs) are canceled Global Max. 35 10 5 5 0 0 GDP bo s0 106 -0 1 bo s0 115 -0 1 bo s0 119 -0 bo 1 s0 130 -0 1 bo s0 208 -0 1 bo s0 214 -0 bo 1 s0 221 -0 1 bo s0 226 -0 1 bo s0 310 -0 bo 1 s0 313 -0 1 bo s0 321 -0 1 bo s0 323 -0 bo 1 s0 330 -0 1 bo s0 408 -0 1 bo s0 418 -0 1 bo s0 106 -0 1 bo s0 115 -0 1 bo s0 119 -0 1 bo s0 130 -0 1 bo s0 208 -0 1 bo s0 214 -0 1 bo s0 221 -0 1 bo s0 226 -0 1 bo s0 310 -0 1 bo s0 313 -0 1 bo s0 321 -0 1 bo s0 323 -0 1 bo s0 330 -0 1 bo s0 408 -0 1 bo s0 418 -0 1 Initial Results • Airline Objective: On-time Performance proposed offers: all at-least, atmost pairs that improve on-time performance Compression Global Max GDP Trading Model 40 40 35 30 25 20 15 10 Initial Results • Airline Objectives: Passenger Delay Costs Objective Function 1 Objective Function 2 • • Imposed “Staircase” structure 80 70 70 60 60 % Im p ro v em e n t 80 50 40 30 50 40 30 20 20 10 10 0 0 1/ 6/ 20 0 1/ 13 1 /2 00 1/ 20 1 /2 00 1/ 27 1 /2 00 1 2/ 3/ 20 0 2/ 10 1 /2 00 2/ 17 1 /2 00 2/ 24 1 /2 00 1 3/ 3/ 20 0 3/ 10 1 /2 00 3/ 17 1 /2 00 3/ 24 1 /2 00 3/ 31 1 /2 00 1 4/ 7/ 20 0 4/ 14 1 /2 00 4/ 21 1 /2 00 1 % Im p ro v e m e n t “Standard” Passenger Delays GDP 0 1 0 0 1 0 0 1 0 0 1 00 1 0 0 1 0 0 1 0 0 1 00 1 0 0 1 0 0 1 0 0 1 0 0 1 00 1 0 0 1 0 0 1 20 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 6/ 1 0 /1 7 /2 4 1 7 /2 4 3 /3 1 3 /2 0 /2 7 2 /3 /1 0 3 1 4 /7 /1 4 21 1/ 3/ 2 2/ 2 1 1/ 3 3 1 3/ 4 4/ GDP Towards a practical system: offer structure high priority flights “move up” range low priority flights current position “move down” range current position Offers: • Airlines willing to accept high priority moves up in exchange for low priority moves down Data Requirements: • 1 new data item per flight -- LET: latest exchange time Towards a practical system: mediation problem • IP formulation that assigns flights to slots in a manner consistent with offers – Allows airlines to express relative per unit value of upmoves vs down-moves • Objective Function – Efficiency: maximize total distance or number of up moves – Equity: aims to distribute benefits in proportion to offers submitted Towards a Practical System: Airline Cost Function for Simulation 3.5 cancellation cost x 10 4 3 2.5 2 1.5 1 0.5 0 0 20 40 60 80 100 120 Time (delay) 140 160 180 2 to 3 hrs Towards a Practical System: Initial Results Objective: • • Maximize total distance of Up moves Maximize total distance of Up moves + sum of equity components 80% 60% 70% % Improvement 70% 50% 40% 30% 20% 60% 50% 40% 30% 20% 10% 0% 0% 0 00 01 00 00 00 00 00 -0 00 00 00 00 01 0 0 01 1- 09- 21- -03 - -21 - 21- 17- 21- 04- 21- -2 1 21- 29- 04- 031 6 6 1 6 11 6 6 1 11 1 6 1 6 -0 -0 -0 -0 -0 -0 K -0 A-0 A-0 P-0 L-0 A-0 O-0 L-0 -0 G OS OS W R W R AD AH S F H T F E V G G J I I P S M S S L B L B E E C GDP Compression VG -0 BO 1-1 S- 1-0 0 BO 1-0 0 S- 9-0 EW 06- 1 2 R 1-0 EW 01 - 0 03 R -0 -00 6 IA D 21 -0 6- 00 IA 21 H -0 -00 1 JF -1 7 K -0 -0 LG 6 -2 1 A- 1-0 0 LG 1-0 0 A- 4-0 0 M 6-2 0 S P- 1-0 0 0 PH 6-2 1L00 SE 06A- 210 0 SF 1-2 0 9O 01 -0 ST 1 -0 4 L01 -00 -0 300 10% C % Improvement Objective: GDP Trading Model Summary and Conclusions • Results illustrate potential benefits of slot trading framework • Trading benefits may be limited by carriers which operate smaller aircraft – Introducing side payments may “induce” small carriers to accept delays • Results depend significantly on airline bid generation strategies. – Best airline approach depends on internal schedule and cost structure, attitude toward risk and strategy of competitors. – Competitive simulations currently being constructed.