The Algorithm of Rational Planning and Resource Allocation in Preparing a Group of Aircraft for Use in Conditions of Uncertainty

Abstract

The article considers the algorithm of rational planning of work on preparing a group of aircraft for departure, provided that the duration of each of the work is random. The work is carried out by specialists of different profiles with restrictions — it is not allowed to simultaneously perform two or more work on one aircraft and the simultaneous work of a specialist on two or more aircraft. To evaluate the preparation plan for a group of aircraft for departure, the following indicators are taken: the time required to complete all work with a given guaranteed probability and the probability of all work being completed within a given time. To conduct a probabilistic analysis of the sequence of events that determine the progress of work, at the first stage a graph of work is built. When constructing the work graph, the restrictions imposed during the statement of the problem are taken into account by introducing fictitious works. At the second stage, on the basis of the constructed graph of work performance, a stochastic model is developed in which the duration of each work is modeled in accordance with a given distribution law. For many implementations, a distribution function of a random variable is constructed — the total time of preparation of a group of aircraft for departure, by which the values of the required performance indicators are determined. Peculiarities of constructing a graph of work performance are analyzed on the example of preparation for the departure of four aircraft. A detailed probabilistic analysis of a rational plan in conditions of uncertainty — with a random duration of work — was carried out on the example of a rational plan of work on a group of two aircraft. As a result of stochastic modeling, the distribution functions of the time moment of the end of each of the work, the delay time of the start of work and the time of the end of all work on the group of aircraft are constructed. Based on the obtained distribution laws, the dependences of the numerical characteristics of random variables — the number of completed work on the aircraft — on the current time were found. The obtained values of the performance indicators allow us to assess the acceptability of the checked rational plan. If, with rational planning of work by a team of a given composition, the guaranteed time to complete work on a group of aircraft is greater than the required value, then the composition of the team will increase. An algorithm has been developed to justify the composition of the minimum number of crews, which can provide training of a group of aircraft with a given reliability for a given time with a random duration of work.