MATHEMATICAL ASPECTS AND FEATURES OF CALCULATION OF THE OPTIMAL SCHEDULE OF AIRCRAFT MOVEMENT

Abstract

The cycle of researches on methods of formation of the schedule of movement of aircrafts (PS) on the basis of the classical theory of schedules as the theory of multistage systems proceeds in work. It is shown that the movement of the aircraft is a process without interruptions, because each specific flight at a given time is performed by only one aircraft. In contrast to previous work on the theory of schedules, this study takes into account random factors of influence due to meteorological conditions on the flight path. According to the theory of schedules, the problem of stochastic optimisation of the final sequence of requirements serviced by systems with several devices, with different assumptions about the random nature of their maintenance. It is shown that the weakest assumption about the possibility of implementing a generalized operator, which theoretically translates many requirements into many agreed and executed plans, is the monotonic and unimodal kind of the corresponding functionality of the generated plans under small random influences. The potential of the theory of multistage systems in creating an optimal schedule for medium or large airlines as systems of critical application is researched. The basic requirements for the construction of a mathematical schedule in the form of a process controlled by random events are established. Using mathematical models of scheduling based on the basic data of the current movement of aircraft in the area of the airport or air cluster, we established that when the base airports change their purpose and act as terminal airports of arrival, the corresponding elements of the matrix are inversely symmetric. Additional studies of the properties of inversely symmetric matrices and the influence of additive random components on the stability of optimal solutions are carried out. Based on the method of Saaty analytic hierarchy process, the most suitable indicators of the efficiency of forming the optimal schedule in case of coincidences in the consistency indices of partial priorities, taking into account the advantages of arrival and departure times of passenger flights, are selected and substantiated. The expression for the resulting decomposition efficiency functional as a solution of the problem of multi criteria optimisation by the method of quasi-linear convolution of criteria is derived