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..

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This paper provides an overview of the economic state of the market, taking into account objective risks affecting economic security. The possibility of constructing simulation models using systems of nonlinear equations is considered and justified. The understanding of global and local sustainability is substantiated. By using mathematical apparatus, the possibility of the existence of a negative impact of competing players operating in a particular market sector is considered. We define the conditions necessary for the existence of civilized competition, taking into account the peculiarities of matrix calculus. The possibility of presenting the described conditions of local stability of the stationary state of the system using a parametric approach is substantiated, and the conditions of stable competitive equilibrium of the system are formulated.

The creation of highly productive forests should be based on the use of high quality seedlings. Those machines and technologies that have been used for cleaning and subsequent sorting of coniferous seeds with their subsequent sowing in the nursery do not fully provide the forestry complex with good-quality planting material. The reason for this is the use of seeds of unsorted fractions in nurseries, the failure to observe conditions during sowing that ensure the amicable emergence of seedlings and conditions in the sowing rows for the normal development of plants, excluding their large mortality and obtaining non-standard seedlings. It should be noted that modern requirements for silvicultural production largely depend on the quality of planting material. Seedlings obtained by growing them without overshooting give a high silvicultural effect if they meet the intended purpose of the cultivated area, have biometric parameters determined by GOST, which make it possible to grow high-quality planting material without overshooting in two growing seasons. The use of innovations in the restoration of forest landscapes is necessary for the cooperation of engineers and researchers. The integration of scientific and technical research and engineering design contributes to the speedy achievement of stringent environmental requirements for vehicle engines and tools. Obtaining high-quality seed is possible while maintaining the sowing qualities of seeds, reducing the degree of injury and treatment cycles, reducing losses during processing and sowing in the nursery. Based on this, there is a need to develop a device for sorting seeds of coniferous species, which will ensure the quality and efficiency of the technological process, as well as obtaining high-quality seed material in a minimum number of processing cycles.

The paper deals with the use of special (expanded) branch and bound method, which allows to significantly increase the dimension of the problem, also shows the comparative characteristics of the traditional approach and proposed.