The concept of sustainable development considers environmental, social and economic issues in general. And the goals of resource conservation and socio-economic development do not contradict each other, but contribute to mutual reinforcement. The purpose of this study is to build and test an economic and mathematical model for the formation of strategies for the behavior of an economic entity with an increase in the impact of negative environmental factors. The proposed strategies and their models are based on the income-expenditure balance equation, which takes into account both quantitative and qualitative characteristics. The constructed models are considered in the state space. The research methodology is based on building models in the form of linear combinations of functions of a homogeneous external impact and various spatial combinations of economic sources (sinks). The study makes it possible to assess the dependence of the amount of resources used for life support on the chosen adaptive strategy. Within the framework of the proposed model, it was found that the criterion for the effectiveness of the applied strategy can be an indicator of satisfaction with the state, the preservation of which, simultaneously with the preservation of the size of resources used, corresponds to the direction of optimization. This approach is consistent with the concept of sustainable development.

The purpose of the study is to develop an economic-mathematical model of the socio-economic system, which takes into account its logistical structure and ecological viability. This allows for optimal budget planning for the new project. The methodology of the study is based on the method of J. Forster, who proposed to consider the logistics system of any enterprise as a system of reservoirs linked by material, financial and information flows. The main result of the study is as follows. The methodology is designed and developed a mathematical program that allows estimating the relative value of fixed assets of production and the number of costs for creating a retail network with the impact of the environmental components. It is shown that this ratio is determined by the value of all key parameters of the enterprise logistics system. This result was obtained through careful modeling of structural changes in the logistics system of the enterprise. All basic communications (flows) between the elements of the logistics system were also considered. Calculations were conducted for the system of the equations which have been written down in shape with discrete-time. At the same time modeling was carried out so that there were no "not physical" phenomena (such as overflow of warehouses, etc.). As a result of calculations, optimum values for all basic characteristics of the new project have been specified. The most actual has separately been considered for practice as a case of optimum planning of storage facilities. The practical importance of research consists that scientific representations about interrelation of the capacity of the enterprise with key parameters of the logistic system can form a basis for more effective planning and management budgetary and production processes at the enterprise, namely: it is more reasonable to plan scales of production and expenses on logistics creation.

Constantly increasing the level of competition requires manufacturers of goods and services to individualize their products. Considering this factor, the brand takes on a new level of perception, a level of the strategic asset of the company, which allows evaluating the value of the company. With the pursuit of competitiveness and modernity, domestic companies have only in the last few years begun to view the brand as an integral part of their business, capable of generating additional profits at the expense of increased consumer loyalty. However, there are currently no standard methods for evaluating brand value, and there are some disadvantages to applying them. The article deals with modern research methods of the Interbrand and V-RATIO brand. It is revealed that the results of the calculations by different methods differ depending on the set goal: long-term or short-term costs. 19 brand evaluation criteria are considered. We propose our conceptual model of brand value estimation based on a closed system of factor analysis and modeling. The impact of the criteria on the choice of alternatives for choosing brand value strategies is suggested to be found by the Saati hierarchy analysis method. To enhance the adaptive properties of the selected criteria, it is proposed to use the mechanism of alternative strategies for increasing brand value by incorporating the Kohonen neural network process algorithm. The structure of hierarchies of influence of defined criteria on the brand development scenarios was constructed. Calculations were made by the method of analysis of hierarchies in the author's developed system, and it was found that having the resources to increase only one criterion of brand development would be the best development of leadership or internationality of the company. Based on the calculations neural network in the MATLAB, it was found that enterprise, which was researched, needed to pay attention to advertising costs or to increase brand value.

Ukraine has a relative drawback in the economic defense capabilities, which needs to be addressed by raising the indicators of macroeconomic development, innovation, and economic potential, social health of the population of the state, and the support of the Armed Forces of Ukraine, by the state. The estimation of the defense capability of states like Ukraine, Poland, Russia and Turkey is made on the basis of the developed methodological approach to the overall representation of the health of the economies of the states and their defense capabilities using the method of constructing petal diagrams with the definition of their effective areas, which became indicators of economic status and defense capability. The article analyses the dependence of the development level of the countries’ economies and the state of development of the armed forces of these countries in the conditions of resource constraints and existing risks on the basis of macroeconomic data and indicators. This article uses the indicators for the determination of the level of defense capability and the data of petal diagrams and the scenario modeling of the development strategies of the Armed Forces of Ukraine with the aim of constructing the most optimal forecast in this area.

The study is devoted to solving the scientific problem of optimizing the retail trade in the production and sale of two types of products, taking into account the change in potential demand for products. The economic and mathematical model of the production activity of the enterprise was developed taking into account logistics and market demand. The logistics scheme takes into account all the main links of the logistics system, as well as the connections between them. The considered scheme makes it possible to take into account the diversification of products manufactured by the enterprise. The mathematical model is designed for discrete time. A numerical optimization method has been developed for this mathematical model. The optimal solutions for several cases are found and investigated. The dynamics of the main characteristics of drugs was calculated for all considered cases. A comparative analysis of economic efficiency for the studied cases has been performed. The economic efficiency of retail network optimization is proved.

Throughout its existence, the Ukrainian state has always suffered from political, economic and military harassment by neighboring states from ancient times to the present day. Whether its geographical location, which determines the center of Europe, or ineffective leadership, has always forced Ukraine to uphold its legitimate interests, territorial integrity and independence. Under such conditions, the Armed Forces of Ukraine (the Armed Forces) are the key to protecting the territorial integrity and inviolability of Ukraine entrusted to them by the Constitution of the state. Ukraine has a relative backwardness in the economic defense capabilities, which needs to be addressed by raising the indicators of macroeconomic development, innovation and economic potential, social health of the population of the state, and the support of the Armed Forces of Ukraine, by the state. The estimation of the defense capability of the states of Ukraine, Poland, Russia and Turkey is made on the basis of the developed methodological approach to the overall representation of the health of the economies of the states and their defense capabilities using the method of constructing petal diagrams with the definition of their effective areas, which became indicators of economic status and defense capability. The results of the assessment of the developed and applied indices of defense capabilities of the states of Ukraine, Poland, Russia and Turkey indicate some deviations of the ratings of the states according to the MCI military potential index in comparison with the GFI global fire strength indexes and the Credit Suisse (СS) institute for the states Ukraine and Poland. According to GFI, the global fire strength index is inferior to Poland, and the MCI military capability index is the opposite. This suggests that these states have almost one level of defense, if not take into account that Poland is a member of NATO. As to the economic status of the defense capability of Turkey and Russia, Russia is ahead of and has a second world level after the United States. But they also have significant economic problems that, in the long run, give Ukraine, with proper planning of defense capabilities and the availability of significant intellectual capital, to reach their level and to ensure the inviolability of the borders from possible encroachment.

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As a result of research, the concept of a flexible evolutionary model is proposed, which with the help of machine learning allows obtaining the most successful strategy for the development of human capital. The proposed conceptual and methodological approach to machine learning of the process of assessing human capital of enterprises, taking into account the cognitive psychology of man and reflective attitudes in the human environment, can increase the effectiveness of decision-making in the field of human capital development management. The training involves indicators of return on investment in the individual, in the types of components of human capital, which are characterized by properties (creativity, competence, purposefulness, communication, motivation), where between their varieties there are appropriate reflective relationships. The main difficulty of this approach to the choice of alternative solutions for finding options for the use of human capital is the correct selection of indicators of significance (return) of contributions to the development of types of human capital, on the basis of which cycles occur of systemic learning. This approach can simplify the search for and developments of human capital development strategies, present alternative ways, and simplify management decisions.