Optimization of the structure of the learning process under the given constraints

Abstract

The article is devoted to the study of ways to optimize the mathematical model of the structure of the educational process. Formalization of the structure of the educational process was carried out in the form of setting an objective function, including the sum of the number of hours provided by the curriculum for various types of training sessions. At the same time, for each type of occupation, a weighting coefficient is provided, which characterizes the relative effectiveness of each type of occupation. The numerical values of the weight coefficients are proposed to be determined by applying the method of analyzing hierarchies based on expert assessments, which are set by appointed specialists. The task is to maximize the objective function that characterizes the overall effectiveness of the educational process. As restrictions imposed on the structure of the educational process, a system of inequalities is considered, presented in a linear form and taking into account restrictions on the budget of study time allocated for the study of the academic discipline, financial restrictions on the remuneration of teaching and teaching staff, financial restrictions associated with the content educational and material base, purchase of software and other expenses. Thus, the task of optimizing the educational process is reduced to a linear programming problem, which in this case is solved using the simplex method using a standard program implemented in various computer environments. At the same time, a dual task is formulated to determine the required time and financial resources for a given distribution of teaching hours by type of occupation. The example given in the article, implemented in the Mathcad computer environment, clearly showed the efficiency of the developed methodology.