dh (T hr D)V T AS = mg 0 dt + mv dv T AS

Transcription

1 e-companion to Aktürk, Atamtürk, and Gürel: Aircraft Rescheduling with Cruise Speed Control ec1 Appendix EC.1. Fuel Burn Model from Base of Aircraft Data Fuel flow model of BADA (EUROCONTROL (2009)) is based on the total energy model that relates the required engine thrust of an aircraft to its drag, true air speed, mass, altitude change and acceleration as follows: where dh (T hr D)V T AS = mg 0 dt + mv dv T AS T AS dt T hr: Thrust acting parallel to the aircraft velocity vector (Newtons), D: aerodynamic drag (Newtons), m : aircraft mass (kilograms) h : geodetic altitude (m), g 0 : gravitational acceleration ( m/s 2 ), V T AS : true airspeed (m/s), d dt : time derivative. (EC.1) Furthermore, they formulate aerodynamic drag, D, on an aircraft at cruise stage as a function of speed, mass, reference wing area of the aircraft and air density. Air density can be considered as a function of the altitude. They first calculate the lift coefficient C L assuming that the flight path angle is zero. 2mg 0 C L = ρvt 2 AS S cos(φ) where ρ: air density (kg/m 3 ), S: wing reference area (m 2 ), φ: bank angle. The lift coefficient C L determines the drag coefficient, C D, under nominal conditions. (EC.2) C D = C D0,CR + C D2,CR C 2 L (EC.3) where C D0,CR and C D2,CR are drag coefficients for cruise stage. The drag force D in Newtons can then be expressed as D = C DρV 2 2 T ASS. (EC.4) In order to find the fuel burn rate, we next use the formula for thrust specific fuel consumption η (kg/min kn): ( η = C f1 1 + V ) T AS C f2 (EC.5)

2 ec2 e-companion to Aktürk, Atamtürk, and Gürel: Aircraft Rescheduling with Cruise Speed Control where C f1 : 1st thrust specific fuel consumption coefficient (kg/min kn) C f2 : 2nd thrust specific fuel consumption coefficient (knots) The cruise fuel flow f cr (kg/min) is calculated using thrust specific fuel consumption η, thrust T hr and the cruise fuel flow factor C fcr : f cr = η T hr C fcr. (EC.6) At the cruise stage of a flight for given altitude and speed, required thrust equals the drag on aircraft and we get T hr = D from equation (EC.1). Consequently, both T hr and η can be expressed as a function of V T AS, and allows one to write f cr as a function of V T AS as: f cr (V T AS ) = 1 2 C f1 C fcr ( C D0,CR ρ S V 2 T AS 4 m 2 g0 2 + C D2,CR ρ S cos 2 (φ) VT 2 AS + C D0,CR ρ S V 3 T AS C f2 ) + C D2,CR C f2 4 m 2 g 2 0 ρ S cos 2 φ V T AS True air speed is the speed in the air and ground speed can be achieved by clearing the effects of wind. For the purposes of this paper, we assume the true air speed equals the ground speed and we refer to it simply as speed (v). In summary, for a given mass and altitude, the fuel burn rate (kg/min) as function of speed can be calculated as follows: Fuel Burn Rate f cr (v) = c 1 v 3 + c 2 v 2 + c 3 v + c 4 v 2, (EC.7) where the coefficients c i, i = 1, 2, 3, 4 can be expressed in terms of aircraft specific drag and fuel consumption coefficients as well as mass of aircraft, air density at given altitude, gravitational acceleration as listed in EUROCONTROL (2012) for different aircraft types.

3 e-companion to Aktürk, Atamtürk, and Gürel: Aircraft Rescheduling with Cruise Speed Control ec3 EC.2. Computational Results EC.2.1. ORD Schedule Tail No Flight No Departure Arrival Departure Time Flight Time Arrival Time Tail No Flight No Departure Arrival Departure Time Flight Time Arrival Time N530AA 398 ORD LGA 6:15 2:14 8:29 N3ETAA 1704 ORD EWR 6:35 2:05 8: LGA ORD 9:25 2:50 12: EWR ORD 9:30 2:40 12: ORD DFW 13:35 2:35 16: ORD DCA 13:10 1:45 14: DFW ORD 17:00 2:30 19: DCA ORD 15:45 2:15 18:00 N459AA 394 ORD LGA 6:50 2:15 9: ORD LAS 19:00 4:10 23: LGA ORD 10:00 2:50 12:50 N3DYAA 1063 ORD LAX 8:50 4:35 13: ORD LGA 13:55 2:20 16: LAX ORD 14:30 4:15 18: LGA ORD 17:15 2:50 20: ORD BOS 19:45 2:15 22:00 N531AA 2303 ORD DFW 6:45 2:35 9:20 N3DRAA 1021 ORD LAS 8:30 4:05 12: DFW ORD 10:10 2:20 12: LAS ORD 13:25 3:35 17: ORD AUS 13:25 2:50 16: ORD DCA 18:00 1:45 19: AUS ORD 17:00 2:45 19:45 N5DXAA 1048 ORD MIA 7:35 3:10 10: ORD LGA 20:40 2:05 22: MIA ORD 11:55 3:20 15:15 N4XGAA 2079 ORD SAN 8:45 4:30 13: ORD MIA 16:20 3:05 19: SAN ORD 14:00 4:10 18:10 N454AA 2441 ORD ATL 6:30 2:00 8: ORD LGA 19:50 2:15 22: ATL ORD 9:15 2:15 11:30 N598AA 1341 ORD SFO 7:50 4:55 12: ORD MCO 12:25 2:40 15: SFO ORD 13:30 4:25 17: MCO ORD 15:50 3:05 18: ORD TUS 19:15 3:55 23:10 N4YMAA 1137 ORD MSY 8:20 2:25 10:45 N439AA 2455 ORD PHX 7:10 4:00 11: MSY ORD 11:30 2:30 14: PHX ORD 11:55 3:30 15: ORD PHL 15:05 2:05 17: ORD LGA 16:25 2:25 18: PHL ORD 18:00 2:35 20: LGA ORD 20:00 2:35 22:35 N467AA 1823 ORD PBI 9:20 2:55 12:15 N475AA 407 ORD STL 6:20 1:10 7: PBI ORD 13:00 3:20 16: STL ORD 8:35 1:15 9: ORD STL 17:15 1:10 18: ORD SAT 10:45 3:00 13: STL ORD 19:10 1:20 20: SAT ORD 14:30 2:40 17:10 N536AA 2305 ORD DFW 7:45 2:40 10: ORD PHL 18:05 2:05 20: DFW ORD 11:35 2:20 13:55 N3EEAA 876 ORD BOS 6:35 2:10 8: ORD STL 14:50 1:05 15: BOS ORD 9:35 3:05 12: STL ORD 17:00 1:20 18: ORD SNA 13:45 4:35 18: ORD SLC 19:15 3:40 22: SNA ORD 19:10 3:50 23:00 N420AA 1686 ORD RDU 6:50 1:50 8:40 N4YDAA 451 ORD SFO 9:45 4:55 14: RDU ORD 9:25 2:15 11: SFO ORD 15:45 4:25 20: ORD PHX 12:35 3:55 16:30 N3ERAA 496 ORD DCA 6:45 1:40 8: PHX ORD 17:15 3:25 20: DCA ORD 9:15 2:10 11:25 N546AA 1462 ORD EWR 8:00 2:20 10: ORD LAS 12:25 4:05 16: EWR ORD 11:25 2:40 14: LAS ORD 17:20 3:40 21: ORD MCO 15:00 2:40 17:40 N5CLAA 1425 ORD SNA 8:25 4:40 13: MCO ORD 18:25 2:55 21: SNA ORD 14:00 4:00 18:00 N4WPAA 2311 ORD DFW 9:05 2:35 11: ORD MIA 19:25 3:00 22: DFW ORD 12:35 2:20 14:55 N535AA 2460 ORD RSW 6:45 2:45 9: ORD STL 15:50 1:10 17: RSW ORD 10:20 3:05 13: STL ORD 18:00 1:20 19: ORD EWR 14:55 2:45 17: ORD SAN 20:15 4:30 24: EWR ORD 18:45 2:45 21:30 N5EBAA 2375 ORD EGE 8:10 2:55 11:05 N3DMAA 568 ORD FLL 7:25 2:55 10: EGE ORD 12:25 2:45 15: FLL ORD 11:10 3:15 14: ORD SNA 18:40 4:30 23: ORD SJU 15:25 4:35 20:00 N3DUAA 2099 ORD LAX 7:00 4:30 11:30 N544AA 2463 ORD MCI 6:25 1:30 7: LAX ORD 12:40 4:05 16: MCI ORD 8:40 1:30 10: ORD RDU 17:45 1:55 19: ORD DFW 11:15 2:35 13:50 N3ELAA 2057 ORD SJU 8:30 4:50 13: DFW ORD 14:40 2:20 17: SJU ORD 14:25 5:35 20: ORD DEN 17:50 2:45 20:35 N3DTAA 2363 ORD HDN 9:50 2:50 12:40 N3EBAA 1565 ORD MSP 6:40 1:30 8: HDN ORD 13:40 2:50 16: MSP ORD 9:00 1:25 10:25 N412AA 2345 ORD DFW 17:15 2:35 19: ORD SAN 11:35 4:20 15: DFW ORD 20:40 2:10 22: SAN ORD 16:45 3:55 20: ORD BOS 21:50 2:05 23:55 Table EC.1 Complete ORD Schedule EC.2.2. Experimental Results for ORD Schedule EC Summary Results for Linear Delay Costs Table EC.2 presents solution statistics and rescheduling costs achieved by each rescheduling approach. The table gives results for 6 replications. Under DP column we report delay costs caused by the disruption. For the CSC approach, we report total rescheduling cost which is the sum of delay cost and additional fuel and carbon costs incurred to repair the schedule. We also report the CPU time (sec.) required to solve

4 ec4 e-companion to Aktürk, Atamtürk, and Gürel: Aircraft Rescheduling with Cruise Speed Control the models and the cost improvement achieved by CSC against DP. For S-CSC, we report the optimum solution (Optimum), total delay (Delay), required CPU time (CPU), number of possible swaps considered in the problem, number of swaps in the solution, and the number of branch-andbound nodes opened. In the last column, we give the cost improvement achieved by S-CSC over DP.

5 e-companion to Aktürk, Atamtürk, and Gürel: Aircraft Rescheduling with Cruise Speed Control ec5 w l L N d rep Delay Cost Delay Cost Delay CPU costimp% Optimum Delay CPU # possible swaps #swap #bbnodes costimp% , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , Table EC.2 Computational Results for ORD Instance

6 ec6 e-companion to Aktürk, Atamtürk, and Gürel: Aircraft Rescheduling with Cruise Speed Control Table EC.3 presents detailed cost figures for alternative rescheduling approaches. w l L N d rep Delay Fuel Carbon Delay Total Fuel Carbon Delay #swap Deadhead Spilling Total , ,245 1, , , , ,135 3, , , , ,295 2, , , , ,635 4, , , , ,574 1, , , , ,194 3,383-1, , , , , ,251 3, , , , ,538 8, , , , , ,072 2, , , , ,214 1, , , , ,933 3, , , , , ,687 2, , , , ,576 1,982-1, , , , , ,215 4,664-1, , , , , ,019 2,381-2, , , , , ,449 4,811-2, , , , , ,947 3,456-1, , , , , ,232 6,740-1, , , , , ,089 1, , , , ,559 3, , , , ,354 1, , , , ,874 4,679-2, , ,111 1,416 4, , ,954 5, , , , ,974 12, , , , , ,080 9, , , , ,350 18, , , , , ,252 6,441-1, , , , , ,642 12,831-1, , , , , ,619 12, , , , ,991 28,881 1, , , , , ,358 2, , , , ,957 8, , , , , ,857 5, , , , ,372 12, , , , , ,595 2, , , , ,590 9, , , , , ,766 6,195-1, , , , , ,399 15,970-1, , , , , ,809 7,171-2, , , , , ,089 15,451-2, , , , , ,746 11,255-1, , , , , ,446 22,955-1, , , , , ,772 4, , , , ,579 13,099 1, , ,856 11, , ,599 6, , , , ,746 17,602-1, , ,111 1,416 16,955 Table EC.3 Detailed Cost Figures for ORD Instance

7 e-companion to Aktürk, Atamtürk, and Gürel: Aircraft Rescheduling with Cruise Speed Control ec7 w l L N d rep Delay Cost Delay Cost Delay CPU costimp% Optimum Delay CPU # possible swaps #swap #bbnodes costimp% , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , Table EC.4 Nonlinear Delay Cost - Computational Results for ORD Instance EC Results for Nonlinear Delay Costs

8 ec8 e-companion to Aktürk, Atamtürk, and Gürel: Aircraft Rescheduling with Cruise Speed Control w l L N d rep Delay Fuel Carbon Delay Total Fuel Carbon Delay #swap Deadhead Spilling Total , ,600 7, , , , ,618 27, , , , , ,768 15, , , , ,837 43, , ,498 2,576 29, , ,664 10,853-1, , , , , ,268 30,457-1, , , , , ,934 21, , , , ,929 66,819 4, , ,002 3,015 62, , ,491 3, , , , ,514 16, , , , , ,152 7, , , , ,533 24, , , , , ,048 4, , , , ,032 21, , , , , ,333 9,762-1, , , , , ,298 35,869-1, , , , , ,648 14,010-2, , , , , ,241 41,602-2, , , , , ,400 20,908-1, , , , , ,697 59,205-1, , , , , ,977 7, , , , ,697 29,217 1, , ,856 25, , ,866 9, , , , ,198 33,040-1, , ,111 1,416 32, , ,142 31, , ,567 2,912 29, , , , , ,567 2,912 65, , ,564 61, , ,498 2,576 53, , , , , ,498 2, , , ,488 42, , ,536 1,638 35, , , ,182-1, , , , , ,968 77, , , , , , ,591 4, , ,002 3, , , ,968 13, , , , ,435 63, , , , , ,101 31, , , , , , , , , , ,336 14, , , , ,928 75, , , , , ,888 35,317-1, , , , , , ,269-1, , , , , ,873 46,235-2, , , , , , ,930-2, , , , , ,889 75,398-1, , ,599 2,970 70, , , ,934-1, , ,599 2, , , ,153 24, , , , , ,776 1, , ,856 76, , ,407 39, , , , , ,771 3, , ,226 4, ,548 Table EC.5 Nonlinear Delay Cost - Detailed Cost Figures for ORD Instance

9 e-companion to Aktürk, Atamtürk, and Gürel: Aircraft Rescheduling with Cruise Speed Control ec9 w l L N d rep Delay Cost Delay Cost Delay CPU costimp% Optimum Delay CPU # possible swaps #swap #bbnodes costimp% , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , Table EC.6 Step Delay Cost - Computational Results for ORD Instance EC Results for Step Delay Costs

10 ec10 e-companion to Aktürk, Atamtürk, and Gürel: Aircraft Rescheduling with Cruise Speed Control w l L N d rep Delay Fuel Carbon Delay Total Fuel Carbon Delay #swap Deadhead Spilling Total , ,245 1, , , , ,931 4, , , , , ,451 2, , , , ,748 6, , , , , ,682 1,871-1, , , , , ,977 4,165-1, , , , , ,297 3, , , , ,793 9, , , , , ,233 2, , , , ,294 1, , , , ,548 3, , , , , ,177 2, , , , ,708 2,114-1, , , , , ,124 5,596-1, , , , , ,103 2,433-2, , , , , ,555 5,917-2, , , , , ,082 3,544-1, , , , , ,771 8,279-1, , , , , ,222 1, , , , ,133 4, , , , ,529 1, , , , ,532 5,241-2, , ,111 1,416 4, , ,995 5, , , , ,993 15, , , , , ,698 10, , , , ,844 23, , , , , ,678 6,867-1, , , , , ,739 15,927-1, , , , , ,932 12, , , , ,701 33,591 1, , , , , ,592 2, , , , ,617 9, , , , , ,226 5, , , , ,108 15, , , , , ,850 3, , , , ,475 11, , , , , ,249 6,678-1, , , , , ,841 19,411-1, , , , , ,989 7,350-2, , , , , ,843 19,204-2, , , , , ,105 11,613-1, , , , , ,976 28,484-1, , , , , ,030 4, , , , ,582 15,102 1, , ,856 13, , ,943 6, , , , ,447 20,303-1, , ,111 1,416 19,656 Table EC.7 Step Delay Cost - Detailed Cost Figures for ORD Instance

11 e-companion to Aktürk, Atamtürk, and Gürel: Aircraft Rescheduling with Cruise Speed Control ec11 EC.2.3. DFW Schedule Tail No Flight No Departure Arrival Departure Time Flight Time Arrival Time Tail No Flight No Departure Arrival Departure Time Flight Time Arrival Time N377AA 7 DFW OGG 11:30 8:15 19:45 N564AA 517 DFW SJC 7:40 3:50 11:30 6 OGG DFW 21:55 7:05 29: SJC DFW 12:15 3:25 15:40 N374AA 123 DFW HNL 11:10 8:30 19: DFW SEA 16:30 4:30 21:00 8 HNL DFW 22:05 7:25 29:30 N4YBAA 529 DFW SEA 8:15 4:35 12:50 N274AA 1099 DFW ABQ 10:30 1:55 12: SEA DFW 13:35 3:50 17: ABQ DFW 13:10 1:40 14: DFW SEA 18:30 4:10 22: DFW TUS 15:40 2:25 18:05 N559AA 530 DFW RSW 8:20 2:30 10: TUS DFW 18:50 2:10 21: RSW DFW 11:35 3:00 14: DFW BNA 21:50 1:35 23: DFW LAX 15:25 3:25 18:50 N4YHAA 334 DFW BNA 7:35 1:40 9:15 N570AA 534 DFW PHL 12:55 3:15 16: BNA DFW 10:00 2:10 12: PHL DFW 16:55 4:05 21: DFW MFE 13:00 1:30 14:30 N485AA 537 DFW MFE 16:30 1:30 18: MFE DFW 15:15 1:35 16: MFE DFW 18:45 1:35 20: DFW SJC 17:40 3:55 21: DFW TPA 21:10 2:20 23:30 N3BDAA 1701 DFW AUS 15:55 1:00 16:55 N484AA 2527 DFW SLC 14:10 2:55 17: AUS DFW 17:40 1:05 18: SLC DFW 17:50 2:35 20: DFW SNA 19:30 3:15 22: DFW SAT 21:15 1:05 22:20 N3DDAA 359 DFW SNA 7:55 3:15 11:10 N5DYAA 1106 DFW BOS 8:10 3:20 11: SNA DFW 12:00 2:50 14: BOS DFW 12:25 4:30 16: DFW MIA 15:50 2:40 18: DFW EGE 18:20 2:20 20:40 N3ALAA 536 DFW ATL 6:40 2:15 8:55 N5DAAA 2413 DFW LAX 9:45 3:20 13: ATL DFW 9:45 2:30 12: LAX DFW 14:10 3:00 17: DFW SNA 13:15 3:15 16: DFW BOS 18:00 3:20 21: SNA DFW 17:20 2:55 20:15 N580AA 1123 DFW PHX 7:25 2:45 10: DFW SNA 21:15 3:15 24: PHX DFW 10:55 2:15 13:10 N258AA 393 DFW DEN 6:30 2:05 8: DFW ORD 13:55 2:20 16: DEN DFW 9:20 2:00 11:20 N5CBAA 654 DFW BOS 11:00 3:25 14: DFW BWI 12:10 2:45 14: BOS DFW 15:20 4:30 19: BWI DFW 15:45 3:40 19:25 N476AA 1148 DFW PBI 7:55 2:35 10: DFW ATL 20:25 2:00 22: PBI DFW 11:15 3:10 14:25 N4XSAA 1331 DFW SAT 8:35 1:10 9: DFW JAX 15:15 2:10 17: SAT DFW 10:30 1:10 11: JAX DFW 18:10 2:50 21: DFW OKC 12:25 :55 13: DFW ABQ 22:25 1:45 24: OKC DFW 14:05 1:00 15:05 N477AA 688 DFW RDU 6:40 2:30 9: DFW STL 18:20 1:35 19: RDU DFW 9:55 3:15 13:10 N581AA 493 DFW BUR 11:25 3:25 14: DFW TPA 14:00 2:15 16: BUR DFW 15:35 3:00 18: TPA DFW 17:15 2:50 20: DFW STL 19:25 1:35 21: DFW COS 20:55 1:55 22:50 N4XHAA 1590 DFW EWR 6:30 3:25 9:55 N551AA 700 DFW LGA 6:10 3:19 9: EWR DFW 10:55 4:05 15: LGA DFW 10:29 4:05 14: DFW EWR 16:40 3:45 20: DFW LGA 15:20 3:25 18:45 N4WWAA 1109 DFW AUS 7:30 :55 8:25 N541AA 704 DFW LGA 7:15 3:20 10: AUS DFW 9:10 1:05 10: LGA DFW 11:30 4:15 15: DFW PHL 11:05 3:10 14: DFW LGA 16:35 3:24 19: PHL DFW 15:05 4:05 19:10 N434AA 710 DFW LGA 9:05 3:20 12: DFW BNA 20:00 1:40 21: LGA DFW 13:30 4:15 17:45 N548AA 460 DFW CMH 8:40 2:10 10: DFW LGA 18:40 3:20 22: CMH DFW 11:35 2:50 14:25 N4YPAA 736 DFW LGA 14:05 3:25 17: DFW SDF 15:15 2:00 17: LGA DFW 18:29 4:05 22: SDF DFW 18:00 2:30 20:30 N526AA 1361 DFW COS 9:15 1:55 11:10 N560AA 2284 DFW ICT 9:30 1:15 10: COS DFW 12:00 1:45 13: ICT DFW 11:30 1:20 12: DFW LGA 15:45 3:20 19: DFW BWI 21:20 2:40 24:00 N503AA 817 DFW BUR 9:15 3:25 12:40 N290AA 465 DFW SAN 12:05 3:15 15: BUR DFW 13:25 3:00 16: SAN DFW 16:10 3:00 19: DFW TUL 17:30 1:00 18:30 N208AA 1143 DFW OMA 8:30 1:45 10:15 N574AA 2042 DFW FLL 6:30 2:40 9: OMA DFW 11:00 2:00 13: FLL DFW 9:55 3:10 13: DFW SAT 13:50 1:05 14: DFW TUS 17:00 2:25 19: SAT DFW 15:40 1:10 16: DFW SAT 17:55 1:10 19:05 Table EC.8 Complete DFW Schedule-Part I

12 ec12 e-companion to Aktürk, Atamtürk, and Gürel: Aircraft Rescheduling with Cruise Speed Control Tail No Flight No Departure Arrival Departure Time Flight Time Arrival Time Tail No Flight No Departure Arrival Departure Time Flight Time Arrival Time N249AA 1536 DFW MEM 12:20 1:25 13:45 N590AA 1466 DFW BOS 6:40 3:25 10: MEM DFW 14:30 1:40 16: BOS DFW 10:55 4:35 15: DFW LAX 18:55 3:25 22: DFW BWI 16:25 2:45 19:10 N441AA 836 DFW DCA 7:55 2:40 10:35 N292AA 1512 DFW BHM 8:40 1:35 10: DCA DFW 11:20 3:35 14: BHM DFW 11:00 2:05 13: DFW ATL 15:45 2:10 17: DFW AUS 13:55 1:00 14: ATL DFW 18:45 2:30 21: AUS DFW 15:40 1:05 16: DFW LAX 22:10 3:30 25: DFW ATL 17:35 2:10 19:45 N528AA 1888 DFW JAX 7:35 2:10 9:45 N3BGAA 1916 DFW BDL 7:40 3:10 10: JAX DFW 10:30 2:55 13: BDL DFW 11:40 4:10 15: DFW XNA 14:15 1:05 15:20 N5ENAA 1434 DFW MCO 6:20 2:20 8: XNA DFW 16:05 1:15 17: MCO DFW 9:35 3:00 12: DFW ELP 18:10 1:40 19: DFW TUL 13:35 1:00 14:35 N582AA 1322 DFW DTW 6:40 2:40 9: TUL DFW 15:30 1:10 16: DTW DFW 10:10 3:10 13: DFW LAX 17:40 3:25 21: DFW MEM 14:20 1:20 15:40 N4XAAA 1630 DFW IAH 12:40 1:15 13: MEM DFW 16:30 1:45 18: IAH DFW 14:40 1:10 15: DFW BWI 19:00 2:45 21: DFW DCA 16:40 2:45 19:25 N502AA 1066 DFW TPA 10:15 2:15 12:30 N4WRAA 1776 DFW PHL 6:45 3:05 9: TPA DFW 13:15 2:50 16: PHL DFW 10:35 3:50 14: DFW TPA 17:00 2:15 19: DFW SJC 15:15 3:50 19:05 N572AA 1077 DFW SFO 7:40 4:00 11: SJC DFW 19:50 3:20 23: SFO DFW 12:25 3:35 16:00 N3BLAA 1572 DFW IAD 8:00 2:35 10: DFW SMF 16:50 3:50 20: LAX DFW 18:40 2:55 21:35 N450AA 1250 DFW ATL 7:35 2:05 9:40 N5CRAA 1887 DFW LAS 6:50 2:50 9: ATL DFW 10:25 2:35 13: LAS DFW 10:35 2:40 13: DFW ELP 13:45 1:45 15: DFW STL 14:15 1:30 15: ELP DFW 16:15 1:40 17:55 N4UBAA 2385 DFW IAH 7:15 1:10 8: DFW ORF 18:45 2:40 21: IAH DFW 9:10 1:15 10:25 N483AA 1436 DFW CLT 11:45 2:15 14: DFW FAT 11:20 3:35 14: CLT DFW 14:50 3:00 17: FAT DFW 15:40 3:15 18: DFW PIT 18:45 2:35 21: DFW HSV 19:45 1:40 21:25 N540AA 1678 DFW BWI 8:20 2:45 11:05 N4WMAA 1965 DFW SFO 8:40 4:00 12: BWI DFW 11:50 3:35 15: SFO DFW 13:25 3:35 17: DFW XNA 16:15 1:05 17:20 N5CVAA 2332 DFW ORD 9:20 2:20 11: XNA DFW 18:05 1:20 19: ORD DFW 14:55 2:30 17: DFW SAN 20:15 3:10 23:25 N618AA 2407 DFW LAX 8:00 3:20 11:20 N557AA 2324 DFW ORD 6:45 2:20 9: LAX DFW 12:40 3:00 15: ORD DFW 10:00 2:35 12:35 N344AA 2421 DFW LAX 11:35 3:23 14: DFW DEN 13:55 2:05 16: LAX DFW 15:50 2:55 18: DEN DFW 16:45 1:55 18:40 N5CJAA 2459 DFW LAX 16:40 3:15 19: DFW LAS 19:35 3:00 22: LAX DFW 20:55 2:50 23:45 N505AA 1758 DFW CLT 7:40 2:25 10: CLT DFW 10:50 3:00 13: DFW DAY 14:40 2:10 16: DAY DFW 17:35 2:45 20: DFW STL 21:10 1:35 22:45 Table EC.9 Complete DFW Schedule-Part II

13 e-companion to Aktürk, Atamtürk, and Gürel: Aircraft Rescheduling with Cruise Speed Control ec13 EC.2.4. Experimental Results for DFW Schedule w l L N d rep Delay Cost Delay Cost Delay CPU costimp% Optimum Delay CPU # possible swaps #swap #bbnodes costimp% , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , Table EC.10 Computational Results for DFW Instance

14 ec14 e-companion to Aktürk, Atamtürk, and Gürel: Aircraft Rescheduling with Cruise Speed Control w l L N d rep Delay Fuel Carbon Delay Total Fuel Carbon Delay #swap Deadhead Spilling Total , ,292 1,433-1, , , , ,822 2,962-1, , , , , ,861 3, , , , ,291 5, , , , , ,505 1, , , , ,844 3, , , , ,599 7, , , , ,085 1, , , , ,752 2, , , , ,295 2, , , , ,590 4, , , , , , , ,035 2, , , , ,391 1, , , , ,971 5, , , , , ,522 1, , , , ,737 2, , , , ,211 2, , , , ,876 4, , , , ,418 2, , , , ,883 6, , , , , ,371 3, , , , , ,797 10, , , , , ,245 5,384-1, , , , , ,455 11, , , , ,545 10, , , , ,085 20, , , , ,739 3, , , , ,439 6, , , , ,517 10, , , , ,774 25,294 3, , ,435 1,650 23, , ,864 3, , , , ,869 7, , , , ,019 8, , , , ,029 16, , , , ,843 3, , , , ,893 7, , , , ,160 5, , , , ,206 18, , , , , ,242 5, , , , ,427 9, , , , ,765 8, , , , ,155 14, , , , ,524 9, , , , , ,844 23, , , , , ,309 12, , , , , ,012 35,449 1, , , ,454 Table EC.11 Detailed Cost Figures for DFW Instance