Airline Fleet Routing and Flight Scheduling under Market Competitions. Tang and Ming-Chei

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1 Arle Fleet Routg ad Flght Schedulg uder Market Compettos Shagyao Ya, Ch-Hu Tag ad Mg-Che Lee Departmet of Cvl Egeerg, Natoal Cetral Uversty 3/12/2009 Itroducto Lterature revew The model Soluto method Numercal tests Coclusos Outle 1

2 1. Itroducto Motvato Flght schedulg factors: passeger trp demads, tcket prce, operatg costs, operatg costrats (e.g. arcraft types, fleet sze, avalable slots, arport quota), arcraft mateace ad crew schedulg Passeger demad may vary, especally compettve markets. A carrer should ot eglect the fluece of ts tmetable o ts market share. 1. Itroducto Am ad scope A model ad a soluto algorthm More accurately reflect real demads, ad be more practcal for carrer operatos Mateace ad crew costrats are excluded. 2

3 1. Itroducto Framework Geeralzed tme-space etworks wth a passeger choce model A olear mxed teger program, characterzed as NP-hard A teratve soluto method, coupled wth the use of CPLEX Lterature revew Fleet routg ad flght schedulg Lev (1969), Smpso (1969), Abara(1989), A Dobso ad Lederer(1993), Subramaa et al.(1994), Hae et al.(1995), Clarke et al.(1996), Ya ad Youg (1996), Desauler et al.(1997) Ya ad Tseg (2002) 3

4 2. Lterature revew Passeger choce models Kaafa ad Ghobral (1982), Hase (1988), Teodorovc ad Krcmar-Nozc (1989), Ghobral (1989) Proussaloglou ad Koppelma (1995), Yoo ad Ashford (1996), Proussaloglou ad Koppelma (1999),ad Dua ad Lu (1999) 2. Lterature revew Summary Fxed passeger demads lterature Varato of passegers due to market compettos was eglected Multomal logt models to formulate passeger choce behavors compettve markets Choce factors: qualty of servce, safety record, flght frequecy, travel tme, fare, passeger s s attrbutes 4

5 3. The model Fleet-flow tme-space etwork Passeger-flow tme-space etworks Passeger choce model Fleet-flow tme-space etwork 3. The model Stato-1 Stato-2 (1) (2) (3) Stato-3 (1) Stato-k 7:00 7:30 8:00 8:30 9:00 9:30 10:00 10:30 11:00 21:30 22:00 22:30 23:00 (1)Flght leg arc (2)Groud arc (3)Cycle arc 5

6 Passeger-flow tme-space etwork (OD par 1->2) 1 3. The model Stato-1 (2) (2) Stato-2 (1) Stato-3 Stato-k 7:00 7:30 8:00 (1) 8:30 9:00 9:30 10:00 10:30 11:00 21:30 22:00 (3) (3) 22:30 23:00 (1)Delvery arc (2)Holdg arc (3)Collecto arc 3. The model Passeger choce model Passeger utlty fucto V a A a F a G a 4Wt a 5 Market share fucto Pr ob a ( ) a e e d D v v d Tt a (1) (2) 6

7 u1 3. The model x1 Demostrato of the calculato of the multpler u u3 u2 j k x2, j, k, ad m : supply odes a passeger-flow etwork x1, x2, ad x3 : flghts u1, u2, ad u3:multplers of the holdg arcs (, j), (, k), ad (, m) m x3 MIN z 3. The model Model formulato (VMSFSM) C ja j X SUBJECT TO j jnf X Y jnp b V a j knf knp d v a p e e v j X T jb k Y d k 0 k j b Y j NF NP, N NP, N A a F a G a Wt a 5Tta NP, N (3) (4) (5) (6) (7) 7

8 8 N NP, N NP, N NP, AF CF j j X SA g s Q X g j j g FF j KX Y j N j OF v v CF DF TDF NFF d e e jd ja, 0, 1 N (8) (9) (10) (11) (12) (13) (14) ut X f F fr a tf k tf TF ) ( ) (,, ut X f Wt wt a tf k tf TH ) ( ) (,, tt a TFH X f Tt, A j U X j j 0 N B j UN Y j j, 0 A j INT X j (16) (17) (15)

9 3. The model Problem sze 1 type of arcraft 10 ctys 30 mutes to costruct the servce ad the delvery arcs Network Model Fleet-flow tme-space etwork 1 Passeger-flow tme-space etworks 90 Nodes 27,300 Arcs 50,905 Real varables 54,955 Iteger varables 1,660 Flow coservato costratos 27,300 Sde costrats Fleet sze costrat 1 Arport quota costrats 10 Capacty costrats 1,350 4.Soluto method Repeatedly modfyg the target arle market share each terato Solvg a fxed-demad demad flght schedulg model (FMSFSM) 9

10 4.Soluto method Soluto process Step 1: Set the market demad ad the draft tmetables of the target arle/ts compettors. Step2: Apply the passeger choce model wth the parameters related to the draft tmetables to calculate the passeger demad at each ode ad for all arc multpler u s.. The, costrats (5), (6), (7), (8), (9), (10) ad (14) ca be represeted as follows: Y j NP j U k NP k Y k B NP, N (18) 4.Soluto method Step 3: Solve FMSFSM to obta the fleet flows, cludg the tmetable, ad the fleet routes Step 4: Calculate the objectve of the real passeger flows uder the fleet flows obtaed from step 3. 10

11 4.Soluto method Step 5: Update the objectve value uder the real passeger flows ad the fleet flows Step 6: If the umber of teratos that caot fd a better soluto exceeds the preset lmt, the stop; Otherwse, retur to step 2. 4.Soluto method A flow decomposto algorthm (Ya ad Youg, 1996) to decompose the lk flows to arc chas Each represets a arplae's daly route 11

12 5. Numercal tests Data aalyss A major Tawa arle s domestc operatos durg the summer of ctes served by 19 arplaes fleet A (ArBus seres) wth 160 seats fleet B (ATR 72 ) wth 72 seats 5. Numercal tests Data aalyss The plag maxmum load factor was 0.9 demad data, cost parameters ad other puts were prmarly based o actual operatg data, wth reasoable smplfcatos 12

13 5. Numercal tests Data aalyss Four cases were tested Case (1) fleet B wth o-stop flght operatos Case (2) fleet A wth o-stop flght operatos Case (3) fleet B wth o-stop ad oe-stop flght operatos Case (4) fleet A wth o-stop ad oe-stop flght operatos 5. Numercal tests Model tests ad result aalyses Case (1) Case (2) Case (3) Case (4) VMSFSM OBJ(NT$) Number of teratos for rug CPLEX CPU tme (sec) Fleet sze Number of flghts Trasfer rate (%) N/A N/A Average load factor (%) * N/A: ot avalable 13

14 5. Numercal tests Model tests ad result aalyses Case (1) Case (2) Case (3) Case (4) VMSFSM OBJ(NT$) Lower boud of the optmal soluto (NT$) FMSFSM OBJ(NT$) WEG (%) IPP (%) Numercal tests A example of arcraft routes 14

15 5. Numercal tests Sestvty aalyses Fleet sze Watg cost for passeger trasfers Passeger s s acceptable watg tme Fare 5. Numercal tests Fleet sze (Results for fleet A) Objectve value( NT$ ) o-stop flght operatos o-stop ad oe-stop flght operatos Fleet sze 15

16 5. Numercal tests Watg cost for passeger trasfers Objectve value(nt$) Passeger watg cost (NT$/30 m) fleet A fleet B 5. Numercal tests Passeger s s acceptable watg tme Scearo The passeger s acceptable tme (m) Tape-Kaohsug flght Other flghts

17 5. Numercal tests Passeger s s acceptable watg tme (fleet B results) Objectve value(nt$) Scearo o-stop flght operatos o-stop ad oe-stop flght operatos 5. Numercal tests Fare (o-stop/oe stop/oe-stop flght operatos) Objectve value(nt$ fleet A fleet B % 80% 90% 100% 110% 120% 130% Tcket prce (%) 17

18 6. Coclusos A ew schedulg model capable of corporatg passeger choce behavor A effcet soluto algorthm to solve the proposed model computato tme oe hour, error wth 5.77% Fluctuatos betwee ±3% after a lmted umber of teratos 6. Coclusos Objectves of VDFSM were better tha FDFSM, especally for Case (3), IPP was about 4.99% Several sestvty aalyses More testg ad case studes the future Choce model be modfed other applcatos 18

19 THE END 19

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