MODEL FOR DAILY OPERATIONAL FLIGHT SCHEDULE DESIGNING Slavica Nedeljković Faculty of Transport and Traffic Engineering, University of Belgrade Serbia and

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


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


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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


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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)


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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


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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


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VIA Principle

ii

A B

C

A

C

BPriority flight


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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


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Objective Function

Ak kPTIPl

klbrtip

s Avj

TOjLiLipp

Lii

kjlszadklbrtipklkaz

jtehjkioikiKiputpkk

iKiTPiTPkioikF

)(

),(

1

3Pr\

2

*1

Pr

),,,(),(),(

)()()()()()(

)())()(()()(min


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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)



Basic Definition

Rotation

Mini rotation

Simple segment of rotation

Rotation without priority flight

Flight delay

Flight cancellation



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



Numerical example



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



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



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



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



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



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

20

Thank you for your attention!



Documents

MODEL FOR DAILY OPERATIONAL FLIGHT SCHEDULE DESIGNING Slavica Nedeljković Faculty of Transport and Traffic Engineering, University of Belgrade Serbia and