Systematization of approaches to mathematical modeling of industrial enterprises’ innovative activity

Mathematical modeling use is necessary when finding optimal or most effective solutions. When implementing innovative activities in an industrial enterprise, a large number of problems arise requiring the use of accurate mathematical calculations and the correct choice of methods by which they can be implemented. Because of wide variety and uniqueness of the problems arising in the course of the innovation process, there is a need to find the mathematical methods which are the most convenient to use and can be quickly implemented in the conditions of industrial practice. In this regard, the purpose of the article is to systematize and structure the knowledge about economic and mathematical modeling, which will contribute to the speedy implementation of tasks and solving problems arising in the course of innovation in an industrial enterprise. In accordance with the stages of the innovation process the most suitable areas of mathematical modeling successfully coping with innovative ideas ranking, optimizing the output program and forecasting the implemented innovations profit are analyzed. The selected areas of mathematical modeling include decision trees, mathematical programming, game theory, econometric forecasting. As part of the innovative activities’ implementation, their features, conditions of use and disadvantages are presented. In addition, the R&D stage is highlighted in the innovation process chain. According to the scientific direction it is carried out in, the R&D stage may have a very specific and unique approach for its solution and accordingly is not included in the universal algorithm for the innovation implementation. This article may be useful for those involved in the innovative projects’ implementation at the level of specific enterprises or localized production.