Mathematical methods for studying risks (resumptive article)

We define risk as an unwanted opportunity and divide risk theory into three stages — risk analysis, risk estimation, risk management. Safety and risk are directly related to each other, being like a «mirror image» of each other which necessitates developing both the general theory of risk and particular theories of risk in specific areas. General risk theory allows for a uniform approach to the analysis, estimation and management of risks in specific situations. Currently, three main approaches to accounting for the uncertainty and describing risks are used — probabilistic and statistical approach, fuzzy sets, and the approach based on interval mathematics. The methods of risk estimation primarily based on probabilistic and statistical models are considered. The mathematical apparatus for estimating and managing risks is based on nonparametric formulations, limit relations, and multi-criteria optimization. Asymptotic nonparametric point estimates and confidence limits for the probability of a risk event are constructed on the base of binomial distribution and the Poisson distribution. Rules for testing statistical hypotheses regarding the equality (or difference) of two probabilities of risk events are proposed. An additive-multiplicative risk estimation model based on a hierarchical risk system based on a three-level risk system has become widespread: private risks — group risks — final risk. For this model, the role of expert estimation is revealed. The prospects of using (in the future) the theory of fuzzy sets are shown. The article deals with the main components of the mathematical apparatus of the theory of risks, in particular, the mathematical support of private theories of risks related to the quality management, innovations and investments. The simplest risk assessment in a probabilistic-statistical model is the product of the probability of a risk event and the mathematical expectation of the accidental damage. Mathematical and instrumental methods for studying global economic and environmental risks are discussed.

Devising a method for identifying the model of multi-criteria expert estimation of alternatives

An approach to constructing mathematical models of individual multicriterial estimation was proposed based on information about the ordering relations established by the expert for a set of alternatives. Structural identification of the estimation model using the additive utility function of alternatives was performed within axiomatics of the multi-attribute utility theory (MAUT). A method of parametric identification of the model based on the ideas of the theory of comparative identification has been developed. To determine the model parameters, it was proposed to use the midpoint method that has resulted in the possibility of obtaining a uniform stable solution of the problem. It was shown that in this case, the problem of parametric identification of the estimation model can be reduced to a standard linear programming problem. The scalar multicriterial estimates of alternatives obtained on the basis of the synthesized mathematical model make it possible to compare them among themselves according to the degree of efficiency and, thus, choose "the best" or rank them. A significant advantage of the proposed approach is the ability to use only non-numerical information about the decisions already made by experts to solve the problem of identifying the model parameters. This enables partial reduction of the degree of expert’s subjective influence on the outcome of decision-making and reduces the cost of the expert estimation process. A method of verification of the estimation model based on the principles of cross-validation has been developed. The results of computer modeling were presented. They confirmed the effectiveness of using the proposed method of parametric model identification to solve problems related to automation of the process of intelligent decision making.

Methodological peculiarities of probability estimation of bankruptcy of agrarian enterprises in Ukraine

Purpose. The purpose of the study is to develop the concept of complex estimation of bankruptcy probability of agrarian enterprises in Ukraine, taking into account the specifics of agricultural activities. Methodology / approach. To achieve the purpose, the following research methods were used: abstract-logical (at disclosing the essence of the concept of “bankruptcy”); dialectical (for theoretical generalizations on determining the problems and ways to overcome them, drawing conclusions); expert estimations, comparative analysis, analysis and synthesis (at developing the concept of estimating the probability of bankruptcy); relative indicators-coefficients (at studying models for estimating the probability of bankruptcy occurrence); monographic (for in-depth study of separate types of factors affecting the probability of bankruptcy); graphical and tabular (at presenting the research results). Results. It has been proven that the discriminant analysis for estimating the probability of bankruptcy (the construction of multifactor models that summarize the most important financial indicators in the integrated index) does not take into account the industry characteristics of agrarian enterprises. The concept of bankruptcy diagnostics is proposed, which combines discriminant analysis and expert estimation of qualitative signs of a possible crisis of an agrarian enterprise. The indicators selected for expert examination cover non-financial factors – the risks and threats to agricultural production in Ukraine, and their generalization may specify the risk of bankruptcy occurrence. The scoring model has been derived by the method of expert estimations, the scale has been developed, which is combined with the discriminant one that will enable to bring the results of the research into the interval of the indicator for estimating the occurrence of bankruptcy. Originality / scientific novelty. The definition of the term “bankruptcy” has been improved: the author’s definition combines the economic and legal approaches to it. The main risks of agricultural activities in Ukraine have been specified and their impact on the probability of bankruptcy of agrarian enterprises has been outlined. It has been developed the methodological concept for estimating the probability of bankruptcy of agrarian enterprises, which takes into account informal factors. For the first time, in order to predict the bankruptcy of agrarian enterprises, it has been proposed to combine discriminant analysis and expert estimation of qualitative indicators that increase its risk in agriculture. Practical value / implications. The application of the developed methodology provides an opportunity for the agrarian enterprise of timely responding to the threats of financial crisis and bankruptcy in order to prevent them. The proposed approach can be used as an element of estimating the insurance risk or investment attractiveness of agricultural enterprises. In case of its adaptation, the methodology can be used in foreign practice.

Specifics and Vulnerabilities of the Timing Control in Cyber-Physical Systems

Cyber-physical systems integrate powerful computing (real-time embedded system, operating system, applications, and Internet networking) and physical environment (advanced manufacturing cells, medical platforms, energetics aggregates, social and educational control). The reliable functionality depends extremely on the correct timing. Wrong timing because of buried malfunction or external tampering could be critical. The paper is some analysis of the vulnerable timing parameters that influence the precise processing. Expert estimation of the criticality of different timing parameters is given to support fault-tolerant design considering possible failures.

Evaluating the Prospects for the Development of Own Trademarks of Trade Enterprises

The article presents the results of the research on determining the prospects for the introduction and development of own trademarks (OTM) of the trade enterprise. The strategies of own trademarks of the trade enterprise are provided. The peculiarities of formation and implementation of dumping strategies, replacement of a competitor, brand expansion are specified. To determine the prospects for the introduction and development of own trademarks of the trade enterprise, a methodical approach is substantiated, which is formed using matrix methods, scorecard methods, and additive convolution. The developed methodical approach provides for the implementation of interrelated stages of evaluation of competitive positions of activity in relation to own trademarks compared to other types of current activities, favorable external environment and readiness of the trade enterprise for the implementation of this type of activity. To evaluate the competitive positions of the OTM-related activities in comparison with other types of current activities, the use of the Dibb –Symkin matrix and the modified BCG matrix is proposed; to assess the favorability of the external environment – PEST analysis; to assess the readiness of the trade enterprise for the introduction and development of its own trademarks – the method of scorecard according to the characteristics of organizational, technological and resource aspects of the trade enterprise’s activities regarding OTM. In order to ensure the validity of managerial decisions on optimizing the portfolio of own trademarks, a scientific-methodical approach to the ranking of assortment groups of goods that are part of own trademark is developed. The methodical basis of the developed approach is matrix methods (Dibb–Symkin matrix, modified BCG matrix), coefficient method, expert estimation method and additive convolution. The sequence of determining the competitiveness of the assortment of goods is presented, which involves grouping the assortment according to the indicators of quality, price, latitude of the assortment of goods compared to the range of products on the part of the trademark of competing enterprises and manufacturers.

The Benefits of Applying the Green Purchasing

Research background: Globalisation brings both opportunities and challenges. It affects relationships in various areas of business, including the wood processing industry. The EU seeks to make the most of globalisation for citizens and businesses while reducing its negative effects. Green purchasing is one of the tools that helps to eliminate the negative effects of globalisation. To increase the competitiveness in the wood processing industry through green purchasing is not only about reducing the direct environmental impact of business activities but also about bringing social and health as well as economic and political benefits. Green purchasing is intelligent purchasing, which increases the efficiency of procurement of goods and services with the lowest possible negative impact on the environment and thus replaces goods or services that would be purchased by default to perform the same function but with a worse impact on the environment. Purpose of the article: The aim of this paper is to determine the benefits of applying green purchasing in wood processing companies. By identifying the internal and external environment, it is possible to determine the benefits of green purchasing in terms of economic, environmental, political, and social and health aspects. Methods: Using the methods of expert estimation, SWOT analysis and Fuller’s triangle, the paper evaluates the benefits of green purchasing, and defines appropriate measures with possible strategies for its application in the wood processing industry. Findings & Value added: The main economic benefit is the reduced costs, social is the education of employees, and ecological benefit is the protection of forest resources.

WEB-system for the level of regional development evaluation

This article focuses on the automation tools development for evaluating the socio-economic development of Ukraine regions. In this work we present a method for automated determination of integral indicators based on factor analysis and expert estimation methods is presented. The method application improved the calculation results reliability and the opportunity provided to analyze the relationships between indicators in terms of their impact on the general regional socio-economic situation. The information-analytical Web-based system for evaluating the socio-economic development of Ukraine regions has been developed and implemented. The Web-based system has a three-level architecture of technical tools and intended for processes automation of socio-economic level development evaluating of Ukraine regions based on expert-statistical method. The Web-based application is designed to work with three user groups and provides access to control elements depending on the access level of user.

Estimation of professionals’ conformity for oil production cut (in the order of discussion)

The oil industry of Azerbaijan passed a long way of development. With the execution of the Contract of the Century at the end of XX century, new perspectives for the development of the economy of the country opened. However, since the beginning of COVID-19 pandemic, as an OPEC+ member Azerbaijan has assumed corresponding responsibilities on the oil production cut. As a result, oil production cut is planned from the beginning of the middle of 2020 for 96 thousand barrels through May-June, for 63 thousand barrels through July-December, as well as 30 thousand barrels during January 2021 – April 2022. According to this, SOCAR has developed strategic approaches on the measures including oil production cut, capital investment and well suspension. To prevent unexpected risks in the stage of rate decline of oil production, it is necessary to choose a mechanism of making-decision with leading professionals of the field, who should consider the complex of technical, geological and organizational measures, as well as the consistency of their execution in pandemic and after it ends. It is also significant to consider such qualities as their professional competence, far-sightedness, which, therefore, should play an important role in reviewed issue. Using the “Method of expert estimation” the professionals’ conformity with the fulfillment of evaluation calculation are reviewed.