MODEL FOR DAILY OPERATIONAL FLIGHT SCHEDULE DESIGNING
Slavica NedeljkovićFaculty of Transport and Traffic Engineering,
University of Belgrade
Serbia and Montenegro
ICRAT 2004November 22-24 2004,
Žilina, Slovakia 1
Structure of presentation
Introduction
Problem definition
Assumptions
Mathematical model
Heuristic algorithm
Numerical example
Conclusions
ICRAT 2004November 22-24 2004,
Žilina, Slovakia 2
Flight Schedule Designing
This is a very complex, combinatorial problem
The transportation planning process for a certain route network, with the available fleet that results in the airline flight schedule is designed to fulfil passenger demand, realize a profit and satisfy different operational requirements
ICRAT 2004November 22-24 2004,
Žilina, Slovakia 3
Meteorological conditionsAircraft is out of order because of technical reasonsCrew absence or delayErrors in estimation of block or turnaround time on some airports Airport congestionAir traffic controlIrregularity during passenger boarding or baggage processing
Aditional costsPassenger’s discontent Reducing airline’s reputation
Flight schedule
perturbations
Planned flight
schedule
New daily operational
flight schedule
Delay and/or cancellation of certain flights
ICRAT 2004November 22-24 2004,
Žilina, Slovakia 4
Reference survey
Thengvall, B., Bard, J., Yu, G., (2003)
Wu, C., Caves, R., (2002)
Bard, J.F., Yu, G., Arguello, M., (2001)
Thengvall, B., Bard, J., Yu, G., (2000)
Yan, S., Lin, C., (1997)
Yan, S., Tu, Y., (1997)
Yan, S., Yang, D., (1996)
ICRAT 2004November 22-24 2004,
Žilina, Slovakia 5
Problem Definition
For a planned daily flight schedule under conditions when perturbation has occurred, one has to design a new daily operational flight schedule that will minimize additional costs (induced by perturbation) to the airline
ICRAT 2004November 22-24 2004,
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Assumptions
The airline has a fleet which consists of different aircraft types (the same aircraft types have the same capacity)Aircraft can be swapped – bigger aircraft can service the flights assigned to smaller ones, and smaller aircraft can service the flights assigned to bigger ones if the number of passengers is not greater than seat capacityFlight schedule recovery time is definedFerry flights are not allowed in the new daily operational flight schedule A set of priority flights is givenVIA principle
ICRAT 2004November 22-24 2004,
Žilina, Slovakia 7
VIA Principle
ii
A B
C
A
C
BPriority flight
ICRAT 2004November 22-24 2004,
Žilina, Slovakia 8
Assumptions
Aircraft balanceRegular maintenanceDeparture time in new flight scheduleAirport's working hoursAircraft handlingMaximal allowed delayDelay in VIA principle and its cost are not consideredAverage delay cost per time unit of an aircraft is givenAverage passenger delay cost per time unit is givenCrew constraints are not considered in this paper
ICRAT 2004November 22-24 2004,
Žilina, Slovakia 9
Objective Function
Ak kPTIPl
klbrtip
s Avj
TOjLiLipp
Lii
kjlszadklbrtipklkaz
jtehjkioikiKiputpkk
iKiTPiTPkioikF
)(
),(
1
3Pr\
2
*1
Pr
),,,(),(),(
)()()()()()(
)())()(()()(min
ICRAT 2004November 22-24 2004,
Žilina, Slovakia 10
Constraints1. k(i)>>k2(i)>>k3(j)>>kaz(l,k)>>k1>kp
2. kap(atip(j)) – kap(l)0, for zad(s,l,j,k)=13. TP(i) TP*(i), iL4. TP(rot(l,j))+t(rot(l,j),j)+a(atip(j),z(rot(l,j)))TP(rot(l+1,j)),
l=1, 2, ... , l(j)-1, jAv5. TP(i) krv(p(i)), iL 6. TP(i) + t(i,j) krv(z(i)), iL, jAv i X(i,j) 7. TP(i) TPAv(j), for jPAv i X(i,j)=18. TP(i) TPA((p(i)), for p(i)PA9. TP(i) TPA(z(i)) – t(i,j), for z(i)PA i X(i,j)=110. TP(i) – TP*(i) kaš(i), iL11. kap(atip(j)) put(i), for X(i,j)=112. kap(atip(j)) put(i) + put(i)
ICRAT 2004November 22-24 2004,
Žilina, Slovakia 11
Basic Definition
Rotation
Mini rotation
Simple segment of rotation
Rotation without priority flight
Flight delay
Flight cancellation
ICRAT 2004November 22-24 2004,
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Proposed Heuristic Algorithm
Step 1: basic feasible solution designingStep 2: attempt to assign temporarily cancelled
flights (reducing number of cancelled flights)Step 3: partial crossing of rotations (reducing
average passenger delay)Step 4: the end of algorithm
ICRAT 2004November 22-24 2004,
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Numerical example
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A/C 1
A/C 2
A/C 3
A/C 4
BEGBEG TRS
PRG BEG
BEGTIV
BNX
BEGFCO TRS ZRH BEG
SKP
VIE BEG
BEY DXBBEG
BEG BEGDUS TIV TIP
A/C 5
A/C 1
A/C 2
A/C 3
A/C 4
BEGBEG TRS
PRG BEG
BEGTIV
BNX
BEGFCO TRS ZRH BEG
SKP
VIE
BEG
BEY DXBBEG
BEG BEGDUS TIV TIP
A/C 5
BEG
Step 1
A/C 1
A/C 2
A/C 3
A/C 4
BEGBEG TRS
PRG BEG
BEGTIV
BNXBEGFCO TRS ZRH BEG
SKP
VIE
BEY DXBBEG
BEG BEGDUS TIV TIP
A/C 5
BEG
Step 2
A/C 1
A/C 2
A/C 3
A/C 4
BEGBEG TRS
PRG BEG
BEGTIV BNX
BEGFCO TRS ZRH BEG SKP
VIE
BEY DXBBEG
BEG BEGDUS TIV TIP
A/C 5
BEG
Step 3
ICRAT 2004November 22-24 2004,
Žilina, Slovakia 15
Changes of objective function value through algorithm’s steps
79100
70492
70530
4297541205
S1/1 S1/2 S1/3 S2 S3
Step
Obj
ecti
ve f
unct
ion
ICRAT 2004November 22-24 2004,
Žilina, Slovakia 16
Numerical example – consequences
Step 1/1 – total delay time is 610 min, average passenger delay is 2.82 min/pax, two flights are cancelled
Step1/2 – total delay time is 330 min, average passenger delay is 1.65 min/pax, two flights are cancelled
Step1/3 – total delay time is 310 min, average passenger delay is 2.56 min/pax, two flights are cancelled
Step 2 – total delay time is 395 min, average passenger delay is 1.52 min/pax, one flight is cancelled
Step 3 – total delay time is 340 min, average passenger delay is 1.33 min/pax, one flight is cancelled
ICRAT 2004November 22-24 2004,
Žilina, Slovakia 17
Conclusions
A mathematical model and heuristic algorithm for designing a new daily operational flight schedule due to perturbations are developed
The developed model gives a set of new operational daily flight schedules which are sorted by increasing value of objective function (additional costs)
Developed model can be used in real time
Objective function does not give a real value of costs, neither if we have real data, because penalty coefficients, which are incorporated in it, modify the real value of costs
ICRAT 2004November 22-24 2004,
Žilina, Slovakia 18
Further Research
Something that could be done in further research is to give different weights to penalty coefficients with airline employee’s help (by interview with dispatchers or through analysis of solved disturbance)Crew legislation, cost of swapping aircraft, or cost of additional flights serviced by using the VIA principle and delay cost of those additional flights could be incorporated in this model
ICRAT 2004November 22-24 2004,
Žilina, Slovakia 19
Supported by
Ministry of science and environmental protection
JAT Airways
After testing, this algorithm will be incorporated in JAT Airways` decision support system
JatJatAirwayAirwayss
ICRAT 2004November 22-24 2004, Žilina, Slovakia
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Thank you for your attention!
ICRAT 2004November 22-24 2004,
Žilina, Slovakia 21