1. MODEL FOR DAILY OPERATIONAL FLIGHT SCHEDULE DESIGNING Slavica Nedeljković Faculty of Transport and Traffic Engineering, University of Belgrade Serbia and Montenegro ICRAT 2004 November 22-24 2004, Žilina, Slovakia 1

2. Structure of presentation Introduction Problem definition Assumptions Mathematical model Heuristic algorithm Numerical example Conclusions ICRAT 2004 November 22-24 2004, Žilina, Slovakia 2

3. 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 2004 November 22-24 2004, Žilina, Slovakia 3

4. Meteorological conditions 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 Flight schedule perturbations Planned flight schedule New daily operational flight schedule Delay and/or cancellation of certain flights ICRAT 2004 November 22-24 2004, Žilina, Slovakia 4

5. 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 2004 November 22-24 2004, Žilina, Slovakia 5

6. 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 2004 November 22-24 2004, Žilina, Slovakia 6

7. 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 allowed in the new daily operational flight schedule A set of priority flights is given VIA principle ICRAT 2004 November 22-24 2004, Žilina, Slovakia 7

8. VIA Principle i i A B C A C B Priority flight ICRAT 2004 November 22-24 2004, Žilina, Slovakia 8

9. 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 ICRAT 2004 November 22-24 2004, Žilina, Slovakia 9

10. Objective Function ICRAT 2004 November 22-24 2004, Žilina, Slovakia 10

11. Constraints 1. k(i)>>k 2 (i)>>k 3 (j)>>kaz(l,k)>>k 1 >k p 2. kap(atip(j)) – kap(l)  0, for zad(s,l,j,k)=1 3. TP(i)  TP*(i), i  L 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, j  Av 5. TP(i)  krv(p(i)), i  L 6. TP(i) + t(i,j)  krv(z(i)), i  L, j  Av i X(i,j) 7. TP(i)  TPAv(j), for j  PAv i X(i,j)=1 8. TP(i)  TPA((p(i)), for p(i)  PA 9. TP(i)  TPA(z(i)) – t(i,j), for z(i)  PA i X(i,j)=1 10. TP(i) – TP*(i)  kaš(i), i  L 11. kap(atip(j))  put(i), for X(i,j)=1 12. kap(atip(j))  put(i) + put(i) ICRAT 2004 November 22-24 2004, Žilina, Slovakia 11

12. Basic Definition Rotation Mini rotation Simple segment of rotation Rotation without priority flight Flight delay Flight cancellation ICRAT 2004 November 22-24 2004, Žilina, Slovakia 12

13. Proposed Heuristic Algorithm Step 1: basic feasible solution designing Step 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 2004 November 22-24 2004, Žilina, Slovakia 13

14. Numerical example ICRAT 2004 November 22-24 2004, Žilina, Slovakia 14

15. A/C 1  A/C 2  A/C 3  A/C 4  BEG TRS PRGBEG TIV BNX BEG FCO TRSZRH BEG SKP VIE BEG BEYDXB BEG DUSTIVTIP A/C 5  A/C 1  A/C 2  A/C 3  A/C 4  BEG TRS PRGBEG TIV BNX BEG FCO TRSZRH BEG SKP VIE BEG BEYDXB BEG DUSTIVTIP A/C 5  BEG Step 1 A/C 1  A/C 2  A/C 3  A/C 4  BEG TRS PRGBEG TIV BNX BEG FCO TRSZRHBEG SKP VIE BEYDXB BEG DUSTIVTIP A/C 5  BEG Step 2 A/C 1  A/C 2  A/C 3  A/C 4  BEG TRS PRGBEG TIVBNX BEG FCO TRSZRHBEGSKP VIE BEYDXB BEG DUSTIVTIP A/C 5  BEG Step 3 ICRAT 2004 November 22-24 2004, Žilina, Slovakia 15

16. Changes of objective function value through algorithm’s steps ICRAT 2004 November 22-24 2004, Žilina, Slovakia 16

17. 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 2004 November 22-24 2004, Žilina, Slovakia 17

18. 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 2004 November 22-24 2004, Žilina, Slovakia 18

19. 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 2004 November 22-24 2004, Žilina, Slovakia 19

20. Supported by Ministry of science and environmental protection JAT Airways After testing, this algorithm will be incorporated in JAT Airways` decision support system JatAirways ICRAT 2004 November 22-24 2004, Žilina, Slovakia 20

21. Thank you for your attention! ICRAT 2004 November 22-24 2004, Žilina, Slovakia 21