Airline Fleet Routing and Flight Scheduling under Market Competitions

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

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Outline

• Introduction
• Literature review
• The model
• Solution method
• Numerical tests
• Conclusions

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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.

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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.

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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

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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)

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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)

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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,
  passengers attributes

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3. The model

• Fleet-flow time-space network
• Passenger-flow time-space networks
• Passenger choice model

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3. The model

• Fleet-flow time-space network

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3. The model

• Passenger-flow time-space network
• (OD pair 1-gt2)

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3. The model

• Passenger choice model
• Passenger utility function
• Market share function

(1)
(2)
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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 u3multipliers of the
holding arcs (i,
j), (i, k), and (i, m)
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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)

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3. The model

• Problem size
• 1 type of aircraft ?10 citys?30 minutes to
  construct the service and the delivery arcs

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4.Solution method

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

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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 us. Then, constraints
  (5), (6), (7), (8), (9),
• (10) and (14) can be represented as
  follows

(18)
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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.

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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.

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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

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5. Numerical tests

• Data analysis
• A major Taiwan airlines 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

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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

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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

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5. Numerical tests

• Model 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
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5. Numerical tests

• Model 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 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
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5. Numerical tests

• An example of
• aircraft routes

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5. Numerical tests

• Sensitivity analyses
• Fleet size
• Waiting cost for passenger transfers
• Passengers acceptable waiting time
• Fare

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5. Numerical tests

• Fleet size (Results for fleet A)

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5. Numerical tests

• Waiting cost for passenger transfers

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5. Numerical tests

• Passengers acceptable waiting time

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

• Passengers acceptable waiting time
• (fleet B results)

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5. Numerical tests

• Fare (non-stop/one-stop flight operations)

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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

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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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THE END