In the article the basic directions of development of innovative activity at mega- and microlevels are considered. The key tasks of scientific and technical policy have been studied with the purpose of determining the most effective innovation strategy that allows introducing the latest technologies into production. The main means for successful development of an enterprise in uncertain and rapidly changing environmental conditions is an effective integrated approach that ensures the formation and implementation of such an innovative activity option that will ensure the best results in the current situation. In these conditions, along with the important role of the production, resource and technological potential of the enterprise, the synergetic effect becomes crucial. The proposed methodology for determining the synergistic effect will link the directions of development of innovation activity using four groups of indicators (equipment, technology, management, sales). It is universal by definition not only of certain directions and projects at the enterprise level, but can be used at the level of the region and the country.

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The subject of research is the enterprise innovative activity. The purpose of the work is the formation of a methodological approach to assess the innovation activity development. The article systematizes the problem of assessing the effectiveness of industrial enterprise innovative activities. As a result of the study, the following tasks are solved: the need to assess the effectiveness of enterprise innovative activities is considered and substantiated; the essence of innovative activities and innovation is disclosed; theoretical provisions that justify the modern methodology for assessing the development of enterprise innovative activities are formulated; main categories are clarified; a general methodology for assessing the enterprise innovative activity is proposed and the main stages of its implementation are formulated; a comprehensive assessment of the industrial enterprise innovative activity is carried out on JSC Concern Constellation in order to determine the level of its development. The proposed methodological approach to assess the development of innovative activities of the organization, based on a comprehensive assessment of the main areas of innovation, allows identifying the most promising areas (types) of innovative activity of the enterprise in accordance with development priorities. The practical significance of the research results lies in the possibility for state authorities to use the methodology to assess the development and forecast the trends of innovative development of enterprises in the region.

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Modern scientific research in economics cannot be imagined without the use of economic and mathematical models and their subsequent analysis. Foreign economic literature contains a significant proportion of articles of both theoretical and applied nature, dominated by mathematical models used to substantiate the assumptions made and the most accurate calculation of economic efficiency. A number of economists very convincingly confirm that the recognition of any theoretical study of an economic nature is determined by the measure of the mathematical formalization of the problem, the adequacy of the mathematical apparatus used and the effectiveness of the final results obtained as a result of the study. In this regard, the article discusses the urgent problem of developing a mathematical model of optimal enterprise management. The authors propose an approach to the selection of the most appropriate modeling, taking into account the restrictions imposed on the boundary states of the system that describes the economic component of the enterprise. The use of classical mathematical approaches with their subsequent adaptation to modern conditions is given and substantiated..