Mathematical Model of Optimal Development Enterprise Economics
Authors: Kasatkina E. V. , Vavilova D. D. 
Published: April 2020

Purpose of the study. The production sphere of the enterprise is a dynamic system of cash, material and information flows, in the framework of which the final product is formed, distributed between investments in production capital and own consumption. The task of choosing the optimal proportions of the distribution of the final product is relevant and practically significant for corporations in developing economies. The purpose of this work is, using mathematical modeling, to identify strategy for the optimal development of commercial enterprise, based on the volume of investment in factors of production and consumption norms and the accumulation profit of the enterprise.Materials and methods. To obtain scientific results, general scientific and specific research methods were used: analysis, synthesis, comparison, system analysis, parametric analysis, economic, mathematical and statistical research methods. The theoretical basis of the study is the fundamental work and publications of Russian and foreign scientists in the field of research of optimal management of the economic system of the enterprise. The authors proposed a methodological approach that distinguishes their research from others – a mathematical model of the balanced development of the economy of an economic entity is presented, where production capital, labor resources and intellectual capital are considered as factors of socio-economic development. The information base of the study is the data of the financial and accounting statements of the Public Joint Stock Company Rosneft Oil Company for the period 2006-2018.Results. The factors of development of the enterprise economy are highlighted, among which, in addition to the traditional approach, which includes capital and labor, intellectual capital is introduced into the main production factor. As a valuation of the intellectual capital of the enterprise, the costly method is used. Based on the cycle of reproduction of the enterprise’s activity, a balance equation of the enterprise’s activity model has been formed taking into account capital investments in production factors and consumption and profit accumulation rates. The criterion functional in the optimal management problem is the discounted profit of the enterprise. As a control, a function was selected that characterizes the share of investment in fixed assets, and as a state of the system, the ratio of the value of fixed assets to intellectual capital. The mathematical model of optimal development is applied to the economic system of the enterprise of PJSC NK “Rosneft”.Conclusion. Modeling the dynamics of production capital, labor resources and intellectual capital of PJSC NK “Rosneft” and the results of solving their optimal management problem show that to keep a production enterprise on a balanced growth path, 55% of net profit will be spent on developing the intellectual capital of the enterprise, 35% of net profit – to improve the state of production capital of Rosneft. Given the optimal management in the future for 2019-2022. projected annual revenue growth rate of 19.9%, fixed assets – 16.2% and annual net profit of the company –9.7%.