Оптимізація складу повітряного парку авіакомпанії методами комбінаторики та регресійного аналізу

Abstract

Представлений підхід до прогнозування ефективності операційної діяльності авіакомпанії з використанням методів комбінаторики та регресійного аналізу з метою знаходження оптимального складу повітряного парку для забезпечення мінімальної вартості авіаперевезень за умови максимального задоволення попиту на транспортування з урахуванням обмежень на кількість літаків різних типів. When organizing new airways or when the demand for existing routes changes after the end of the COVID-19 coronavirus pandemic, airlines may encounter problems with optimization of the air fleet composition and redistribution of aircraft on certain flights to maximize the existing demand for air transportation while minimizing the costs of the air transport company. Mathematical apparatus, which should be used to calculate the optimal composition of the airline's fleet, is combinatorial methods and regression analysis, for the optimal distribution of aircraft in the established directions of air transportation – the transport model. In carrying out the research, scientists focus on the optimal organization of passenger and cargo flows for maximum satisfaction of the demand for transportation with minimal costs, but do not take into account the impact on the cost of transportation by the combination of aircraft types. The purpose of the research is to determine the optimal composition of the airline's air fleet to minimize the cost of air transportation, provided maximum demand for transportation with taking into account the number of aircraft of different types using methods of combinatorics and regression analysis. The formalization of the problem of determining the maximum efficiency in the case of different numbers of aircraft of different types is presented. An example of finding the optimal composition of the air fleet of airline, which has aircraft types B-737-200, B-737-300, B-737-400, B-737-500 and performs flights on routes Kyiv-Athens, Kyiv-Ashgabat, Kyiv-Budapest, Kyiv-Warsaw, is considered. The efficiency of air transportation with the different combination of aircraft types is predicted by regression analysis. For each combination, the actual (target function) and expected (regression) minimum cost of transportation is obtained. The maximum efficiency of air transportation in the case of a combination of the same number of different types of aircraft is expected in the presence of three aircraft of four different types and in the case of the combination of the different numbers of different types of aircraft – two aircraft of four different types. The number of possible combinations of aircraft of different types under the conditions of permission and prohibition on the difference of the order of location and repetitions of aircraft in the group is determined by the methods of factorials and combinations. It is proved that the methods of combinatorics and regression analysis should be used to predict the efficiency of the airline's operational activities due to their ability to find the optimal composition of the aircraft fleet to ensure the minimum cost of air transportation provided maximum satisfaction of transportation demand with restrictions on the number of aircraft of different types.