1. 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

2. Outline Introduction Literature review The model Solution method
Numerical tests
Conclusions

3. 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.

4. 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.

5. 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

6. 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)

7. 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)

8. 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

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

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

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

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

13. 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)

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

15. (8)
(9)
(10)
(11)
(12)
(13)
(14)

16. (15)
(16)
(17)

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

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

19. 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)

20. 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.

21. 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.

22. 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

23. 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

24. 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

25. 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

26. 5. Numerical tests Model tests and result analyses Case (1) Case (2)
VMSFSM OBJ(NT$)
Number of iterations for running CPLEX
146 86
110 84
CPU time (sec)
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

27. 5. Numerical tests Model tests and result analyses Case (1) Case (2)
VMSFSM OBJ(NT$)
Lower bound of the
optimal solution (NT$)
FMSFSM OBJ(NT$)
WEG (%)
3.84
3.12
2.48
5.77
IPP (%)
3.03
1.89
4.99
4.68

28. 5. Numerical tests
An example of
aircraft routes

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

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

31. 5. Numerical tests
Waiting cost for passenger transfers

32. 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

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

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

35. 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

36. 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

37. THE END