Effective management system, high competitiveness and investment attractiveness of the enterprise ensure effective development of any enterprise. It is also noted that one of the ways to effectively search for directions for the development of the enterprise management system is the use of managerial diagnostics in the management system, taking into account the diagnostics of the effectiveness of the organizational structure of the enterprise management. It has been determined that today a relevant and important issue is the need to form new and improve existing provisions (both theoretical and practical) regarding the effectiveness of the organizational structure of enterprise management under risk conditions, using mathematical modeling. In view of this, the purpose of the study is to develop an economic-mathematical model for diagnosing the effectiveness of the organizational structure of enterprise management under risk conditions. Based on the results of the research, in the article proposes a new economic-mathematical model and, on its basis, optimization criteria and ratios are formed, that ensure the effective functioning and development of the enterprise, taking into account the characteristics, role and importance of the effectiveness of the organizational structure of enterprise management under risk conditions. The scientific novelty of the obtained results lies in the improvement of the economic-mathematical model for the system of management diagnostics of the enterprise, which is based on the functional connection and compromise function between business risks and the characteristics of the effectiveness of the organizational structure of the enterprise management, as well as the corresponding set of economic values (parameters, criteria) and factors, that ensure the transfer of management information from the primary form to a form convenient for storage, transmission and processing, which will contribute to the quality adoption of management decisions aimed at the effective functioning and development of the enterprise, in view of the the process and result, strategic goals and tactical tasks , which are decided at a specific enterprise. It is advisable to conduct further research in the direction of improving the management diagnostics system of the enterprise in conditions of risk and uncertainty.

The structural components (main) of the diagnosis of the competitiveness of the business structure, supporting the opinion of scientists and enterprise managers, are the competitiveness of the products of the business structure, the concentration of the market in which the business structure functions, as well as the effectiveness of the functioning of the business structure under risk conditions, which includes financial-economic, production and commercial efficiency. It is also stated that information technology is an effective management tool for solving economic problems in the field of management and administration. It was determined that today a relevant and important issue is the need to form new and improve existing provisions (both theoretical and practical) regarding the effectiveness of the use of information technologies in the management of a business structure under risk conditions, with the use of mathematical modeling. In view of this, the purpose of the study is to develop an economic-mathematical model for diagnosing the effectiveness of the use of information technologies in the management of the business structure under risk conditions. Based on the results of the research, the article proposes a new economic-mathematical model, and based on it, a set of parameters, criteria and ratios are formed, which ensure the effective functioning and development of the business structure, taking into account the introduction (rational use) of information technologies in the management of the business structure under risk conditions. The basis of this model is the functional relationship between profits, the level of efficiency of the business structure and business risks. The scientific novelty of the obtained results lies in the improvement of the economic-mathematical model for diagnosing the competitiveness of a business structure, which is based on the functional relationship between profits, risks and the level of efficiency of the business structure, which is one of the structural components of diagnosing the competitiveness of a business structure. This model takes into account an expanded set of economic parameters and factors and, unlike the existing ones, it includes the function of a compromise between the level of efficiency of the business structure and business risks, taking into account the peculiarities, role and significance of the use of information technologies in the management of the business structure. This type of approach makes it possible to reduce the number of inaccurate and inadequate results in the context of optimizing methods of using information technologies for making reasonable and effective management decisions (both current and prospective) in the business structure management system under risk conditions. It is advisable to conduct further research in the direction of studying practical issues regarding the formation of a quality and effective management system of the business structure in conditions of risk and uncertainty.

In the conditions of the need to increase the costs of ensuring the safety of products for business structures, the need to develop a monitoring system that would allow identifying, analyzing and forecasting phenomena and trends that are critically important for avoiding bankruptcy is actualized. The article revealed that the choice of monitoring indicators and methods depends on information needs, which encourage the search for satisfaction and take the form of an information request. It has been proven that from the standpoint of a structural approach, the subjects of the monitoring system are drivers for identifying promising directions for the development of the business structure monitoring system. This is due to the fact that in a dynamic competitive environment, the information needs of management subjects are constantly changing. As a result, under the influence of the accumulation of experience and as new methods of processing and interpretation of management information are mastered, the demand for its significance and speed of obtaining objectively increases. The appropriate level of values of financial stability and profitability of a business structure characterizes its resistance to bankruptcy. Identification of the critical value of the solvency ratio by the monitoring system is a direct indication that the business structure is on the verge of bankruptcy. The task of the monitoring system is to detect signs of a decrease in the resilience of the business structure to bankruptcy. The performance of this task is possible on the basis of monitoring those indicators that characterize financial stability and profitability. It is substantiated that the presence of individual specifics of the work of each business structure, their individual resistance to bankruptcy, which is formed under the influence of certain factors, differs among themselves. In view of this, there is a need to determine the value of the average values of the factor indicators and their standard error.

The object of the research is the peculiarities of the formation, use and improvement of the model of integral assessment of the economic potential of the enterprise in accordance with modern economic conditions and changes. The success of any enterprise in conditions of uncertainty and risk directly depends on various influencing factors and is determined by the potential, the assessment of which is necessary at all levels of preparation and management decision-making, in order to expand the information base within the management system. Practice shows the presence of theoretical and practical problems related to the formation and use of applied mechanisms for assessing the economic potential of enterprises on the basis of operations research and economic diagnostics, and based on the application of economic and mathematical modeling. It is noted that under the economic potential of the enterprise it is appropriate to understand the capabilities, resources, stocks, means of the enterprise that are used and/or can be used to achieve the goals (strategic or tactical) of the enterprise. And the model of integrated evaluation of the efficiency of the use and growth of the enterprise's potential is based on the system of evaluation of the effectiveness of the functioning of its components in the financial-economic, production and commercial sphere, based on parameters (indicators) taking into account priorities, criterion values and the utility function. According to the results of the conducted research, an improved multi-criteria model of the integral assessment of the enterprise potential using the additive utility function is proposed, which, unlike the existing ones, makes it possible not only to calculate the integral indicator of the enterprise potential, to evaluate and monitor the enterprise potential, but also allows to some extent to compare with each other competing enterprises. It is advisable to carry out further research in the direction of determining the ways of effective use and growth of the enterprise's potential.

Global changes that take place in the external and internal environment are characterized by high dynamism, unpredictability and uncertainty, which is why it is important to solve the problem of improving the innovation management system in e-business. Existing e-business management systems are becoming ineffective, so e-business enterprises are facing a rather difficult period, that is, the stage of attracting innovations. An effective response of the e-business management system, with the involvement of innovations, should play an important role in increasing competitive advantages and maintaining the existing position of the enterprise in the market. Building an effective e-business innovation management system is able to timely adapt the enterprise to changes that occur in the environment of its functioning. A special role in this is played by identifying the factors that can most affect the financial and economic activities of the enterprise in the field of e-business. Successful identification of factors influencing the innovation management system will be the key to sustainable enterprise development. The article analyzes the theoretical material on the classification of factors influencing the innovation management system, as well as identifies the classification criteria by which these factors are determined. According to the conducted research, based on empirical data from e-business enterprises, the factors that have an impact on the innovation management system of an enterprise in the coordinate system of its organizational development have been identified. The identified factors are of practical importance only when they can be used by managers of e-business enterprises when making and implementing innovative decisions. It is proposed to use the method of expert assessments to evaluate these factors for their relative importance. The results obtained, and especially the gradation of these factors by the level of relative importance, are important management information at the stages of making decisions on the management of innovations in e-business enterprises, in particular when choosing management decisions.