Airline Fleet Routing and Flight Airline Fleet Routing and Flight Scheduling under Market CompetitionsScheduling under Market Competitions

Shangyao Yan, Chin-Hui Tang and Ming-Chei LeeShangyao Yan, Chin-Hui Tang and Ming-Chei Lee

Department of Civil Engineering, Department of Civil Engineering, National Central UniversityNational Central University

3/12/20093/12/2009

OutlineOutlineIntroductionIntroductionLiterature reviewLiterature reviewThe modelThe modelSolution methodSolution method

Numerical testsNumerical tests

ConclusionsConclusions

1. Introduction1. IntroductionMotivationMotivation – Flight scheduling factors: passenger trip demands, Flight scheduling factors: passenger trip demands,

ticket price, operating costs, operating constraints ticket price, operating costs, operating constraints (e.g. aircraft types, fleet size, available slots, airport (e.g. aircraft types, fleet size, available slots, airport quota), aircraft maintenance and crew scheduling quota), aircraft maintenance and crew scheduling

– Passenger demand may vary, especially in Passenger demand may vary, especially in competitive markets. competitive markets.

– A carrier should not neglect the influence of its A carrier should not neglect the influence of its timetable on its market share. timetable on its market share.

1. Introduction1. IntroductionAim and scopeAim and scope– A model and a solution algorithm A model and a solution algorithm

– More accurately reflect real demands, and be More accurately reflect real demands, and be more practical for carrier operationsmore practical for carrier operations

– Maintenance and crew constraints are Maintenance and crew constraints are excluded.excluded.

1. Introduction1. IntroductionFrameworkFramework

– Generalized time-space networks with a Generalized time-space networks with a passenger choice modelpassenger choice model

– A nonlinear mixed integer program, A nonlinear mixed integer program, characterized as NP-hard characterized as NP-hard

– An iterative solution method, coupled with An iterative solution method, coupled with the use of CPLEX 7.1the use of CPLEX 7.1

2. Literature review2. Literature review

Fleet routing and flight scheduling Fleet routing and flight scheduling

– Levin (1969) , Simpson (1969), ALevin (1969) , Simpson (1969), Abara(1989),bara(1989), DobsoDobson and Lederer(1993), n and Lederer(1993), Subramanian Subramanian et alet al.(1994), .(1994), HanHane et al.(1995), Clarke et al.(1996), e et al.(1995), Clarke et al.(1996), Yan and Young (1Yan and Young (1996), 996), Desaulnier et al.(1997) Desaulnier et al.(1997)

– Yan and Tseng (2002)Yan and Tseng (2002)

2. Literature review2. Literature review

PPassenger choice modelsassenger choice models– Kanafani and Ghobrial (1982), Hansen (1988), TeodoKanafani and Ghobrial (1982), Hansen (1988), Teodo

rovic and Krcmar-Nozic (1989), Ghobrial (1989) rovic and Krcmar-Nozic (1989), Ghobrial (1989)

– Proussaloglou and Koppelman (1995), Yoo and AshfoProussaloglou and Koppelman (1995), Yoo and Ashford (1996), Proussaloglou and Koppelman (1999),and rd (1996), Proussaloglou and Koppelman (1999),and Duann and Lu (1999) Duann and Lu (1999)

2. Literature review2. Literature reviewSummarySummary– Fixed passenger demands in literature

– Variation of passengers due to market competitions was neglected

– Multinomial logit models to formulate passenger choicMultinomial logit models to formulate passenger choice behaviors in competitive marketse behaviors in competitive markets

– Choice factors: quality of service, safety record, flight fChoice factors: quality of service, safety record, flight frequency, travel time, fare, passenger’s attributesrequency, travel time, fare, passenger’s attributes

3. The model3. The model Fleet-flow time-space networkFleet-flow time-space network

Passenger-flow time-space networksPassenger-flow time-space networks

Passenger choice modelPassenger choice model

Station-1 Station-kStation-3Station-2

(3)

(1) (2)

(1)Flight leg arc (2)Ground arc (3)Cycle arc

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3. The model3. The modelFleet-flow time-space Fleet-flow time-space

network network

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(2)

(1)Delivery arc (2)Holding arc (3)Collection arc

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3. The model3. The modelPassenger-flow time-space Passenger-flow time-space

network network (OD pair 1->2)(OD pair 1->2)

Passenger choice modelPassenger choice model– Passenger utility functionPassenger utility function

– Market share functionMarket share function

3. The model3. The model

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arcs (i, j), (i, k), and (i, m)

3. The model3. The modelDemonstration of the calculation Demonstration of the calculation

of the multiplier “u”of the multiplier “u”

3. The model3. The modelModel formulationModel formulation (VMSFSM)(VMSFSM)

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3. The model3. The modelProblem size Problem size

1 type of aircraft 1 type of aircraft 、、 10 citys10 citys 、、 30 minutes to construct 30 minutes to construct the service and the delivery arcsthe service and the delivery arcs

Fleet-flow time-space network 1 Passenger-flow time-space networks 90 Nodes 27,300

Network

Arcs 50,905 Real variables 54,955 Integer variables 1,660 Flow conservation constrations 27,300

Side constraints

Fleet size constraint 1

Airport quota constraints 10

Model

Capacity constraints 1,350

4.Solution method4.Solution method

Repeatedly modifying the target airline Repeatedly modifying the target airline market share in each iterationmarket share in each iteration

Solving a fixed-demand flight scheduling Solving a fixed-demand flight scheduling model (FMSFSM) model (FMSFSM)

4.Solution method4.Solution methodSolution processSolution process

Step 1: Set the market demand and the draft timetablesStep 1: Set the market demand and the draft timetables

of the target airline/its competitors.of the target airline/its competitors.

Step2: Apply the passenger choice model with theStep2: Apply the passenger choice model with the

parameters related to the draft timetables to calculate parameters related to the draft timetables to calculate

the passenger demand at each node and for all arcthe passenger demand at each node and for all arc

multiplier “u”s. Then, constraints (5), (6), (7), (8), (9), multiplier “u”s. Then, constraints (5), (6), (7), (8), (9),

(10) and (14) can be represented as follows:(10) and (14) can be represented as follows:

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4.Solution method4.Solution method

Step 3: Solve FMSFSM to obtain the fleet flows, Step 3: Solve FMSFSM to obtain the fleet flows,

including the timetable, and the fleet routesincluding the timetable, and the fleet routes

Step 4: Calculate the objective of the real Step 4: Calculate the objective of the real

passenger flows under the fleet flows passenger flows under the fleet flows

obtained from step 3.obtained from step 3.

4.Solution method4.Solution method

Step 5: Update the objective value under the realStep 5: Update the objective value under the real

passenger flows and the fleet flowspassenger flows and the fleet flows

Step 6: If the number of iterations that cannot findStep 6: If the number of iterations that cannot find

a better solution exceeds the preset limit, a better solution exceeds the preset limit,

then stop; Otherwise, return to step 2.then stop; Otherwise, return to step 2.

4.Solution method4.Solution methodA flow decomposition algorithm (Yan and A flow decomposition algorithm (Yan and Young, 1996) to decompose the link flows Young, 1996) to decompose the link flows into arc chains into arc chains

Each represents an airplane's daily route Each represents an airplane's daily route

5. Numerical tests5. Numerical testsData analysisData analysis– A major Taiwan airline’s domestic operations

during the summer of 2001

– 8 cities served by 19 airplanes fleet A (AirBus series) with 160 seats

fleet B (ATR 72 ) with 72 seats

5. Numerical tests5. Numerical tests

Data analysisData analysis– The planning maximum load factor was 0.9The planning maximum load factor was 0.9

– demand data, cost parameters and other inpudemand data, cost parameters and other inpu

ts were primarily based on actual operating dats were primarily based on actual operating data, with reasonable simplificationsta, with reasonable simplifications

5. Numerical tests5. Numerical tests

Data analysisData analysis– Four cases were tested Four cases were tested

Case (1) fleet BCase (1) fleet B with non-stop flight operationswith non-stop flight operations

Case (2) fleet A with non-stop flight operationsCase (2) fleet A with non-stop flight operations

Case (3) fleet BCase (3) fleet B with non-stop and one-stop flight with non-stop and one-stop flight operationsoperations

Case (4) fleet ACase (4) fleet A with non-stop and one-stop flight with non-stop and one-stop flight operations operations

5. Numerical tests5. Numerical tests Model tests and result analysesModel tests and result analyses

Case (1) Case (2) Case (3) Case (4)

VMSFSM OBJ(NT$) -15743177.63 -10356567.56 -16288829.46 -14698167.78

Number of iterations for running CPLEX

146 86 110 84

CPU time (sec) 868.985 135.969 3522.703 1438.203

Fleet size 19 19 19 19

Number of flights 276 168 244 202

Transfer rate (%) N/A N/A 13.94 27.57 

Average load factor (%) 73.871 42.253 89.929 61.081

* N/A: not available

5. Numerical tests5. Numerical testsModel tests and result analysesModel tests and result analyses

Case (1) Case (2) Case (3) Case (4)

VMSFSM OBJ(NT$) -15743177.63 -10356567.56 -16288829.46 -14698167.78

Lower bound of theoptimal solution (NT$) -16372348.26 -10690326.39 -16702579.31 -15597657.03

FMSFSM OBJ(NT$) -15279826.79 -10164653.23 -15514894.91 -14040651.84

WEG (%) 3.84 3.12 2.48 5.77

IPP (%) 3.03 1.89 4.99 4.68

5. Numerical tests5. Numerical testsAn example ofAn example of

aircraft routesaircraft routes

1 2 3 4 5 6 7 87:00

8:00

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Station

5. Numerical tests5. Numerical tests

Sensitivity analysesSensitivity analyses – Fleet sizeFleet size– Waiting cost for passenger transfersWaiting cost for passenger transfers– Passenger’s acceptable waiting timePassenger’s acceptable waiting time– Fare Fare

5. Numerical tests5. Numerical tests

Fleet size Fleet size (Results for fleet A)(Results for fleet A)

5. Numerical tests5. Numerical tests

Waiting cost for passenger transfersWaiting cost for passenger transfers

5. Numerical tests5. Numerical tests

Passenger’s acceptable waiting timePassenger’s acceptable waiting time

Scenario

The passenger’s acceptable time (min)

Taipei-Kaohsiung flight

Other flights

1 30 60

2 60 90

3 90 120

4 120 150

5. Numerical tests5. Numerical testsPassenger’s acceptable waiting timePassenger’s acceptable waiting time

(fleet B results)(fleet B results)

5. Numerical tests5. Numerical tests

FareFare (non-stop/one-stop flight operations) (non-stop/one-stop flight operations)

6. Conclusions 6. Conclusions

A new scheduling model capable of A new scheduling model capable of incorporating passenger choice behaviorincorporating passenger choice behavior

An efficient solution algorithm to solve the An efficient solution algorithm to solve the proposed modelproposed model

computation time in one hour, error within 5.77%computation time in one hour, error within 5.77%

Fluctuations between ±3% after a limited Fluctuations between ±3% after a limited number of iterationsnumber of iterations

6. Conclusions6. Conclusions

Objectives of VDFSM were better than FDFSM, Objectives of VDFSM were better than FDFSM, especially for Case (3), IPP was about 4.99%especially for Case (3), IPP was about 4.99%

Several sensitivity analysesSeveral sensitivity analyses

More testing and case studies in the futureMore testing and case studies in the future

Choice model be modified in other applications Choice model be modified in other applications

THE ENDTHE END