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## MODEL FOR DAILY OPERATIONAL FLIGHT SCHEDULE DESIGNING

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### MODEL FOR DAILY OPERATIONAL FLIGHT SCHEDULE DESIGNING

Slavica Nedeljković

Faculty of Transport and Traffic Engineering,

University of Belgrade

Serbia and Montenegro

November 22-24 2004,

Žilina, Slovakia

1

ICRAT 2004

Structure of presentation

- Introduction
- Problem definition
- Assumptions
- Mathematical model
- Heuristic algorithm
- Numerical example
- Conclusions

November 22-24 2004,

Žilina, Slovakia

2

ICRAT 2004

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

November 22-24 2004,

Žilina, Slovakia

3

ICRAT 2004

- Aircraft is out of order because of technical reasons
- Crew absence or delay
- Errors in estimation of block or turnaround time on some airports
- Airport congestion
- Air traffic control
- Irregularity during passenger boarding or baggage processing

- Aditional costs
- Passenger’s discontent
- Reducing airline’s reputation

Delay and/or cancellation of certain flights

New daily operational flight schedule

Planned flight schedule

Flight schedule perturbations

November 22-24 2004,

Žilina, Slovakia

4

ICRAT 2004

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)

November 22-24 2004,

Žilina, Slovakia

5

ICRAT 2004

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

November 22-24 2004,

Žilina, Slovakia

6

ICRAT 2004

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 capacity
- Flight schedule recovery time is defined
- Ferry flights are not allowedin the new daily operational flight schedule
- A set of priority flights is given
- VIA principle

November 22-24 2004,

Žilina, Slovakia

7

ICRAT 2004

Assumptions

- Aircraft balance
- Regular maintenance
- Departure time in new flight schedule
- Airport's working hours
- Aircraft handling
- Maximal allowed delay
- Delay in VIA principle and its cost are not considered
- Average delay cost per time unit of an aircraft is given
- Average passenger delay cost per time unit is given
- Crew constraints are not considered in this paper

November 22-24 2004,

Žilina, Slovakia

9

ICRAT 2004

Constraints

1. k(i)>>k2(i)>>k3(j)>>kaz(l,k)>>k1>kp

2.kap(atip(j)) – kap(l)0, forzad(s,l,j,k)=1

3.TP(i) TP*(i), iL

4. 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, jAv

5. 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), forjPAv i X(i,j)=1

8. TP(i) TPA((p(i)), forp(i)PA

9. TP(i) TPA(z(i)) – t(i,j), forz(i)PA i X(i,j)=1

10. TP(i) – TP*(i) kaš(i), iL

11.kap(atip(j)) put(i), forX(i,j)=1

12.kap(atip(j)) put(i) + put(i)

November 22-24 2004,

Žilina, Slovakia

11

ICRAT 2004

Basic Definition

- Rotation
- Mini rotation
- Simple segment of rotation
- Rotation without priority flight
- Flight delay
- Flight cancellation

November 22-24 2004,

Žilina, Slovakia

12

ICRAT 2004

Proposed Heuristic Algorithm

- Step 1: basic feasible solutiondesigning
- Step 2: attempt to assign temporarily cancelled flights (reducing number of cancelled flights)
- Step 3: partial crossing of rotations (reducingaverage passenger delay)
- Step 4: the end of algorithm

November 22-24 2004,

Žilina, Slovakia

13

ICRAT 2004

A/C 1

PRG

BEG

PRG

BEG

VIE

BEG

BEG

BNX

BNX

A/C 2

A/C 2

BEG

TRS

BEG

BEG

TRS

BEG

TIV

BEG

SKP

TIV

BEG

SKP

A/C 3

A/C 3

FCO

BEG

FCO

BEG

BEG

TRS

ZRH

BEG

TRS

ZRH

VIE

A/C 4

A/C 4

DUS

BEG

TIV

TIP

DUS

BEG

BEG

TIV

TIP

BEG

BEG

BEG

BEG

BEY

DXB

BEY

DXB

A/C 5

A/C 5

Step 1

A/C 1

A/C 1

PRG

BEG

PRG

BEG

A/C 2

A/C 2

BEG

TRS

BEG

BEG

TRS

BEG

TIV

BEG

TIV

BEG

BNX

SKP

A/C 3

A/C 3

FCO

FCO

BEG

TRS

ZRH

BEG

BEG

TRS

ZRH

BEG

SKP

BNX

VIE

VIE

A/C 4

A/C 4

DUS

BEG

BEG

TIV

TIP

DUS

BEG

BEG

TIV

TIP

BEG

BEG

BEG

BEG

BEY

DXB

BEY

DXB

A/C 5

A/C 5

Step 3

Step 2

November 22-24 2004,

Žilina, Slovakia

15

ICRAT 2004

Changes of objective function value through algorithm’s steps

November 22-24 2004,

Žilina, Slovakia

16

ICRAT 2004

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

November 22-24 2004,

Žilina, Slovakia

17

ICRAT 2004

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

November 22-24 2004,

Žilina, Slovakia

18

ICRAT 2004

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

November 22-24 2004,

Žilina, Slovakia

19

ICRAT 2004

Supported by

- Ministry of science and environmental protection
- JAT Airways
- After testing, this algorithm will be incorporated in JAT Airways` decision support system

20

November 22-24 2004,

Žilina, Slovakia

ICRAT 2004

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