Determining the economic sustainability reserve of economic entities in modern operating conditions

In complex socio-economic and political conditions, economic entities must have a sufficient level of economic stability and its reserve for normal life activities. Therefore, the problems of assessment and analysis of economic stability and its reserve are urgent and require immediate solution. The purpose of the article was to study the determination of economic sustainability of economic entities, its reserve, substantiation of the logic of the stages of this determination, and the formation of an appropriate analytical tool. In the research process, general scientific and special research methods were used: abstract-logical method, systematic approach, methods of analysis and synthesis, graphic method, method of building an integral taxonomic indicator of development, multi-criteria optimisation, multi-factor regression analysis, genetic algorithm, marginal utility method, cluster analysis. The article presents the selection of a system of economic sustainability indicators for economic entities of the state sector of Ukraine across regions from the point of view of their legislative basis. In order to determine the reserve of economic sustainability of public sector economic entities across the regions, an economic-mathematical model of multi-criteria optimisation of economic sustainability indicators was developed and solved using a genetic algorithm, which is a new analytical support in economics in solving this problem. A new result in economic-mathematical modelling is the method of forming partial criteria in multi-criteria regression dependency optimisation. The article provides a procedure for implementing the marginal utility method for justifying the final single optimal solution of the multi-criteria optimal problem of determining the optimal values of economic sustainability indicators. It has been proven that it is advisable to determine the absolute value of economic sustainability reserve for economic entities in the regions by their clusters, which were obtained on the basis of the system of indicators of economic sustainability and regional gross product per person. The practical significance lies in the fact that such a scientific-methodical approach to determining economic sustainability and its reserve allows for the objective development of management decisions at industrial enterprises to ensure their normal life activities in difficult war and post-war conditions