All human activity is planned in time: without this, the coordinated work of enterprises and production sites is impossible, the construction of large factories and playgrounds, children's playgrounds, strictly time-bound studies, even the time of leaving home to work for a worker and an employee, are determined according to the schedule urban transport, suburban train traffic. Obviously, the better the schedule, the higher the productivity, the less costs associated with a particular activity, the better the results. So you need to be able to schedule schedules, and most optimally. However, to do this, you must first set the task of making an optimal schedule as a mathematical problem. Tasks for scheduling, which are strictly ordered in some papers, are called priority tasks. Priority tasks include the following simple and primitive tasks, based on which complex problems are considered. There are different ways of formally presenting the tasks of the order – it is enough to mention the so-called schedules, football calendar or television program, schedules of work of urban transport or movement of suburban trains. But it should be noted that the condition of the priority task is difficult to represent in the form of a formula. Therefore, there is a method for solving them, called the method of selection. Simple problems and, at the same time, comparatively new ones for mathematics, methods of solving them, based on elementary ideas, are considered. These problems are related to the theory of optimal sequence – the section of mathematics, which is of great applied importance. The application of the method of selection to the solution of the priority tasks is considered, that is, the tasks for composing permutations that reduce the ordering of some works. Tasks that are solved by the simple method of selection often include the tasks of designing communication lines, transport lines, tasks that ask the task of establishing the order of processing of various details, the task of the distribution of products between these stores, etc. After proper formalization, the task of priority is reduced to finding the optimal permutation. The tasks and methods of solving them, proposed in the article, are not as difficult as complex, and they are solved by non-standard, non-traditional methods. Each of them requires a unique approach to solving. Their solution is based on the permutation sorting method. However, such tasks can lead us to the broad path of studying the theory of discrete optimization. Keywords : priority task, orderly rearrangement, method of selection, method of optimal selection.
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