Airline Fleet Routing and Flight Scheduling under Market Competitions Shangyao Yan, Chin-Hui Tang and Ming-Chei Lee Department of Civil Engineering, National Central University 3/12/2009

Outline Introduction Literature review The model Solution method Numerical tests Conclusions

1. Introduction Motivation Flight scheduling factors: passenger trip demands, ticket price, operating costs, operating constraints (e.g. aircraft types, fleet size, available slots, airport quota), aircraft maintenance and crew scheduling Passenger demand may vary, especially in competitive markets. A carrier should not neglect the influence of its timetable on its market share.

1. Introduction Aim and scope A model and a solution algorithm More accurately reflect real demands, and be more practical for carrier operations Maintenance and crew constraints are excluded.

1. Introduction Framework Generalized time-space networks with a passenger choice model A nonlinear mixed integer program, characterized as NP-hard An iterative solution method, coupled with the use of CPLEX 7.1

2. Literature review Fleet routing and flight scheduling Levin (1969) , Simpson (1969), Abara(1989), Dobson and Lederer(1993), Subramanian et al.(1994), Hane et al.(1995), Clarke et al.(1996), Yan and Young (1996), Desaulnier et al.(1997) Yan and Tseng (2002)

2. Literature review Passenger choice models Kanafani and Ghobrial (1982), Hansen (1988), Teodorovic and Krcmar-Nozic (1989), Ghobrial (1989) Proussaloglou and Koppelman (1995), Yoo and Ashford (1996), Proussaloglou and Koppelman (1999),and Duann and Lu (1999)

2. Literature review Summary Fixed passenger demands in literature Variation of passengers due to market competitions was neglected Multinomial logit models to formulate passenger choice behaviors in competitive markets Choice factors: quality of service, safety record, flight frequency, travel time, fare, passenger’s attributes

3. The model Fleet-flow time-space network Passenger-flow time-space networks Passenger choice model

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

Passenger-flow time-space network (OD pair 1->2) 3. The model Passenger-flow time-space network (OD pair 1->2)

3. The model Passenger choice model Passenger utility function Market share function (1) (2)

Demonstration of the calculation of the multiplier “u” 3. The model Demonstration of the calculation of the multiplier “u” i, j, k, and m : supply nodes in a passenger-flow network x1, x2, and x3 : flights u1, u2, and u3：multipliers of the holding arcs (i, j), (i, k), and (i, m)

3. The model Model formulation (VMSFSM) MIN SUBJECT TO (3) (4) (5) (6) (7)

(8) (9) (10) (11) (12) (13) (14)

(15) (16) (17)

3. The model Problem size 1 type of aircraft 、10 citys、30 minutes to construct the service and the delivery arcs

4.Solution method Repeatedly modifying the target airline market share in each iteration Solving a fixed-demand flight scheduling model (FMSFSM)

4.Solution method Solution process Step 1: Set the market demand and the draft timetables of the target airline/its competitors. Step2: Apply the passenger choice model with the parameters related to the draft timetables to calculate the passenger demand at each node and for all arc multiplier “u”s. Then, constraints (5), (6), (7), (8), (9), (10) and (14) can be represented as follows: (18)

4.Solution method Step 3: Solve FMSFSM to obtain the fleet flows, including the timetable, and the fleet routes Step 4: Calculate the objective of the real passenger flows under the fleet flows obtained from step 3.

4.Solution method Step 5: Update the objective value under the real passenger flows and the fleet flows Step 6: If the number of iterations that cannot find a better solution exceeds the preset limit, then stop; Otherwise, return to step 2.

4.Solution method A flow decomposition algorithm (Yan and Young, 1996) to decompose the link flows into arc chains Each represents an airplane's daily route

5. Numerical tests Data 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 tests Data analysis The planning maximum load factor was 0.9 demand data, cost parameters and other inputs were primarily based on actual operating data, with reasonable simplifications

5. Numerical tests Data analysis Four cases were tested Case (1) fleet B with non-stop flight operations Case (2) fleet A with non-stop flight operations Case (3) fleet B with non-stop and one-stop flight operations Case (4) fleet A with non-stop and one-stop flight operations

5. Numerical tests Model tests and result analyses Case (1) Case (2) 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 Number of flights 276 168 244 202 Transfer rate (%) N/A 13.94 27.57  Average load factor (%) 73.871 42.253 89.929 61.081 * N/A: not available

5. Numerical tests Model tests and result analyses Case (1) Case (2) VMSFSM OBJ(NT$) -15743177.63 -10356567.56 -16288829.46 -14698167.78 Lower bound of the optimal solution (NT$) -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 tests An example of aircraft routes

5. Numerical tests Sensitivity analyses Fleet size Waiting cost for passenger transfers Passenger’s acceptable waiting time Fare

5. Numerical tests Fleet size (Results for fleet A)

5. Numerical tests Waiting cost for passenger transfers

Taipei-Kaohsiung flight 5. Numerical tests Passenger’s acceptable waiting time Scenario The passenger’s acceptable time (min) Taipei-Kaohsiung flight Other flights 1 30 60 2 90 3 120 4 150

5. Numerical tests Passenger’s acceptable waiting time (fleet B results)

5. Numerical tests Fare (non-stop/one-stop flight operations)

6. Conclusions A new scheduling model capable of incorporating passenger choice behavior An efficient solution algorithm to solve the proposed model computation time in one hour, error within 5.77% Fluctuations between ±3% after a limited number of iterations

6. Conclusions Objectives of VDFSM were better than FDFSM, especially for Case (3), IPP was about 4.99% Several sensitivity analyses More testing and case studies in the future Choice model be modified in other applications

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