**APPROACH TO MATHEMATICAL MODELING OF THE DISTRIBUTION OF THE ACADEMIC LOAD OF THE TEACHING STAFF OF THE DEPARTMENT BASED ON SET THEORY**

UDC 004.02; 004.942; 378.1

DOI:10.26102/2310-6018/2020.28.1.035

T.I. Kasatkina, E.V. Bolgova, L.V. Rossikhina, R.V. Kuzmenko

*The purpose of the research is to develop an approach to modeling the distribution of educational load, taking into account the features and specifics of each Department and the requirements of the educational organization. The model built on the basis of this approach can be used as an auxiliary tool when compiling the load for each of the departments. The distinctive features of the proposed approach to modeling are such features as the ability to adapt the subject area, which provides the search and implementation of the optimal ratio of discipline-employee of the Department from among the teaching staff; compliance of the report structure with the requirements of the reporting documentation instructions on labor rationing of teaching staff or similar documents of departmental educational organizations; the possibility of using the model for any number of employees staff of the Department and any number of types (number of subjects) and types (classes lecture-type class-type seminars, practical classes, etc.) teaching load of the Department, as well as the possibility of changes outside the classroom and extracurricular load PPP. As research methods and criteria for optimal load distribution, we used the weight coefficients of teaching staff, depending on the type and type of educational work and the matrix of personal weight coefficients of employees. The possibility of using set theory methods in load modeling was also shown. Based on the results of the research, an approach to the representation of the academic load of the Department in the form of sets of sets is proposed. It is shown that the load distribution problem can be reduced to solving an unbalanced modeling problem. A lot of “teaching load of the Department” consisting of many “types of Cathedral work,” many “types of academic work” and many “workers of the faculty of the Department.” The structure of the set of ” types of educational work “is represented as a combination of a subset of” classroom contact work “and a subset of”extracurricular work”. A relational scheme of relations in the load distribution model and its structural units, which are sets, is proposed. The direct and feedback relationships between structural units are shown. A set of weighting factors for the level of professional competence of an employee has been developed and a method for calculating its elements has been developed. At the same time, the method of determining the level of competence of the employee of the teaching staff of the Department by type of work is clearly demonstrated in the form of diagrams. A model for implementing the optimal distribution of academic load between the teaching staff of the Department is proposed based on a comparison of the levels of competence of teaching staff in each discipline from the set of “types of Cathedral work”. As a result of research and development, an approach to the distribution of educational load was proposed, which makes it possible to present the educational load of the Department in the form of sets of sets, and allows to distribute the educational load taking into account the features and specifics of each Department of an educational organization. Calculations of employee competence levels were performed, the results of which are presented in the form of diagrams. As a result, it is concluded that the proposed approach to distribution will allow higher education organizations to significantly reduce the burden on the teaching and administrative staff of the organization, and thus make it possible to increase the time resources for making managerial decisions and performing teaching duties.
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**Keywords:** mathematical model, educational organization, load distribution, discipline, educational load, set, report, department.

**Full text:**

KasatkinaSoavtors_1_20_1.pdf