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MODEL FOR DAILY OPERATIONAL FLIGHT SCHEDULE DESIGNING

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, Ž ilina, Slovakia. 1. ICRAT 2004. Structure of presentation. Introduction Problem definition

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MODEL FOR DAILY OPERATIONAL FLIGHT SCHEDULE DESIGNING

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  1. 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

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

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

  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 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

  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) November 22-24 2004, Žilina, Slovakia 5 ICRAT 2004

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

  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 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

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

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

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

  11. 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), 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), forjPAv 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), iL 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

  12. 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

  13. 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

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

  15. A/C 1  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

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

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

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

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

  20. JatAirways 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

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

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