Fuzzy optimization of aircraft fleet management taking into account transfer passenger flows
- Authors: Romanenko V.A.1
-
Affiliations:
- Samara National Research University
- Issue: No 117 (2025)
- Pages: 74-102
- Section: Systems analysis
- URL: https://journals.rcsi.science/1819-2440/article/view/360558
- DOI: https://doi.org/10.25728/ubs.2025.117.4
- ID: 360558
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Abstract
A variant of the problem of joint optimization of the structure and number of aircraft fleet and the distribution of aircraft by air lines for an airline planning to perform mass transfer transportation of passengers based on a hub airport has been solved. It is assumed that the task is solved by the airline at the stage preceding the performance of transportation, when the demand for transportation can be known only approximately. In this case, the projected demand levels are determined by expert assessments and should be considered as fuzzy numbers. Joint optimization according to the criterion of economic efficiency is formulated as an integer mathematical programming problem with a fuzzy criterion and crisp constraints. Using the defuzzification technique, the fuzzy problem is reduced to an ordinary mathematical programming problem that can be solved in an acceptable amount of time using available software. Based on the IBM ILOG OPL software package, a solution has been obtained for a series of model examples of a problem with demand levels specified in a fuzzy and "crisp" form. The comparison revealed significant differences between the most significant results of solving the optimization problem with fuzzy and "crisp" initial data. An attempt to replace the solution obtained taking into account the vagueness of the passenger forecast with a "crisp" solution leads to a significant deterioration in the target function. All this indicates that it is advisable to take into account the vague uncertainty of the initial data. The proposed fuzzy model can be used to increase the efficiency of decisions made at the design stage of such promising air transport systems as transfer air transportation systems based on hub airports.
About the authors
Vladimir Alekseevich Romanenko
Samara National Research University
Email: vla_rom@mail.ru
Samara
References
1. АНДРОНОВ А.М., ХИЖНЯК А.Н. Математические методы планирования и управления производственно-хозяйственной деятельностью предприятий гражданской авиации. – М.: Транспорт, 1977. – 215 с.2. «Аэрофлот» продолжает развитие авиатранспортных узлов за пределами столицы. [Электронный ресурс]. – URL: http://www.ato.ru/content/aeroflot-prodolzhaet-razvitie-aviatransportnyh-uzlov-za-predelami-stolicy (дата обращения: 26.05.2025).3. ДАНЦИГ Д.Б. Линейное программирование, его применения и обобщения. – М.: Прогресс, 1966. – 600 с.4. ОРЛОВСКИЙ С.А. Проблемы принятия решений при нечёт-кой исходной информации. – М.: Наука, 1981. – 208 с.5. ПЕГАТ А. Нечёткое моделирование и управление. – М.: БИ-НОМ. Лаборатория знаний, 2013. – 798 с.6. Приказ Министерства транспорта РФ от 12 декабря 2011 г. N 310 «Об утверждении Порядка формирования, утвержде-ния и опубликования расписания регулярных воздушных пере-возок пассажиров и (или) грузов, выполняемых перевозчика-ми, имеющими соответствующие лицензии». – URL: https://mintrans.gov.ru/documents/2/2207 (дата обращения: 10.12.2024).7. РОМАНЕНКО В.А. Оптимизация параметров системы трансферных авиаперевозок с учётом нечёткой и стохасти-ческой неопределённостей // Управление большими система-ми. – 2013. – Вып. 41. – С. 285–313.8. РОМАНЕНКО В.А. Оптимизация распределения воздушных судов по авиалиниям при нечётких исходных данных // Управ-ление большими системами. – 2025. – Вып. 115. – С. 156–182.9. САКАЧ Р.В., ПИНАЕВ Е.Г., ГЛАДЫШЕВСКАЯ Г.Н. и др. Моделирование в планировании гражданской авиации. – М.: Транспорт, 1983. – 173 с.10. ABARA J. Applying integer linear programming to the fleet as-signment problem // Interfaces. – 1989. – Vol. 19, No. 4. – P. 20–28. – doi: 10.1287/inte.19.4.20.11. BAZARGAN M., HARTMAN J. Aircraft replacement strategy: Model and analysis // J. Air Transp. Manag. – 2012. – Vol. 25. – P. 26–29. – doi: 10.1016/j.jairtraman.2012.05.001.12. BELOBABA P., ODONI A., BARNHART C. The Global Airline Industry. – John Wiley & Sons, Ltd, 2009. – 509 p.13. DANTZIG G.B., FULKERSON D.R. Minimizing the number of tankers to meet a fixed schedule // Nav. Res. Logist. Q. – 1954. – Vol. 1, No. 3. – P. 217–222. – doi: 10.1002/nav.3800010309.14. FERGUSON A.R., DANTZIG G.B. The problem of routing air-craft – a mathematical solution // Aeronaut. Engng. Rev. – 1955. – Vol. 14, No. 4. – P. 51–55.15. FERGUSON A.R., DANTZIG G.B. The allocation of aircraft to routes – an example of linear programming under uncertain de-mand // Manag. Sci. – 1956. – Vol. 3, No. 1. – P. 45–73. – doi: 10.1515/9781400884179-029.16. GEURSEN I.L., SANTOS B.F., YORKE-SMITH N. Fleet plan-ning under demand and fuel price uncertainty using actor–critic re-inforcement learning // Journal of Air Transport Management. – 2023. – Vol. 109. – DOI: https://doi.org/10.1016/j.jairtraman.2023. 102397.17. HANE C.A., BARNHART C., JOHNSON E.L. et al. The fleet assignment problem: Solving a large-scale integer program // Mathematical Programming. – 1995. – Vol. 70. – P. 211–232.18. HOFF A., ANDERSSON H., CHRISTIANSEN M. et al. Industrial aspects and literature survey: Fleet composition and routing // Computers & Operations Research. – 2010. – Vol. 37, Iss. 12. – P. 2041–2061. – DOI: https://doi.org/10.1016/j.cor. 2010.03.015.19. KIZILOGLU K., SAKALLI U.S. Integrating Flight Scheduling, Fleet Assignment, and Aircraft Routing Problems with Codeshar-ing Agreements under Stochastic Environment // Aerospace. – 2023. – Vol. 10, No. 12. – doi: 10.3390/aerospace10121031.20. LISTES O., DEKKER R. A scenario aggregation-based approach for determining a robust airline fleet composition for dynamic ca-pacity allocation // Transp. Sci. – 2005. – Vol. 39, No. 3. – P. 367–382. – doi: 10.1287/trsc.1040.0097.21. NAUMANN M., SUHL L., FRIEDEMANN M. A stochastic pro-gramming model for integrated planning of re-fleeting and finan-cial hedging under fuel price and demand uncertainty // Procedia – Soc. Behav. Sci. – 2012. – Vol. 54. – P. 47–55. – doi: 10.1016/j.sbspro.2012.09.724.22. PILLA V.L., ROSENBERGER J.M., CHEN V.C. et al. A statisti-cal computer experiments approach to airline fleet assignment // IIE Trans. – 2008. – Vol. 40, No. 5. – P. 524–537. – doi: 10.1080/07408170701759734.23. RUSHMEIER R.A., KONTOGIORGIS S.A. Advances in the op-timization of airline fleet assignment // Transportation Science. – 1997. – Vol. 31, No. 2. – P. 159–169.24. SA C.A.A., SANTOS B.F., CLARKE J.P.B. Portfolio-based air-line fleet planning under stochastic demand // Omega. Elsevier. – 2019. – Vol. 97(C). – doi: 10.1016/j.omega.2019.08. 008.25. SAFAK O., CAVUS O., AKTURK M.S. Multi-stage airline scheduling problem with stochastic passenger demand and non-cruise times // Transp. Res. Part B Methodol. – 2018. – Vol. 114. – P. 39–67. – doi: 10.1016/j.trb.2018.05.012.26. SCHICK G.J., STROUP J.W. Experience with a multi-year fleet planning model // J. Manage. Sci. – 1981. – Vol. 9, No. 4. – P. 389–396. – doi: 10.1016/0305-0483(81)90083-9.27. WYATT J.K. Optimal fleet size // Oper. Res. Q. – 1961. – Vol. 12, No. 3. – P. 186. – doi: 10.2307/3006775.
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