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MATHEMATICAL MODELING IN SOCIAL AND ECONOMIC SYSTEMS
Mikhail I. Grachev, St. Petersburg University of the Ministry of Internal Affairs of Russia, St. Petersburg, Russia, mig2500@mail.ru
Vyacheslav G. Burlov, Peter the Great St. Petersburg Polytechnic University (SPbPU), St. Petersburg, Russia, burlovvg@mail.ru
Abstract
In the modern rapidly changing world, there are constant changes in all spheres of human activity, including in the social and economic systems, such as education, law, health care. All areas require study for improving management and decision-making mechanisms in order to increase the efficiency of their functioning and further logic of action improving the process of functioning of processes in social and economic systems. The introduction of the sites of educational organizations into educational institutions of higher education (UHE) has led to the need for the person in charge of the site (LOU) of the organization to have a mathematical model of management decisions to counter emerging threats. In this paper, we will consider the process of forming a mathematical model of an administrative decision, which is obtained on the basis of synthesis from the transition states of the system using the Kolmogorov differential equations, by further transforming them into a system of linear algebraic equations (SLAE) and solving them by the Gauss method. Mathematical modeling is based on synthesis processes using the law of preserving the integrity of the object (ZSCO) and the natural science approach (ESA). The use of the synthesis method allows you to achieve the control goal based on the required performance indicators. The proposed mathematical model helps in solving three processes aimed at monitoring the occurrence of a problem in a controlled system, the process of recognizing the problem and the process of implementing a managerial decision to eliminate the problem. The final obtained mathematical solution for modeling the situation in the social and economic system helps to establish a model of LOU behavior depending on the current situation, which will lead to saving time resources and the possibility of its redistribution for solving other problems. The resulting mathematical model can be further complicated by adding new variables and conditions for the implementation of the control process.
Keywords: mathematical model, modeling, management, social and economic system, manager’s qualifications, managerial decisions, educational institution, person in charge, network models, Gaus’s method, differential equations.
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Information about authors:
Mikhail I. Grachev, St. Petersburg University of the Ministry of Internal Affairs of Russia, Senior Engineer of the Information Center, St. Petersburg, Russia
Vyacheslav G. Burlov, Peter the Great St. Petersburg Polytechnic University (SPbPU), Professor at the Higher School of Technosphere Safety, Doctor of Technical Sciences, Professor, St. Petersburg, Russia