No abstract

No abstract

Purpose is to develop a unified mathematical model to assess energy efficiency of a water inflow-drainage process as the real variant of stochastic method for water pumping from underground workings of iron-ore mines. Methods. The research process was based upon the methods of probability theory as well as stochastic modelling methods. The stochastic function integration has been reduced to summation of its ordinates and further transition to a proper boundary. Findings. A mathematical model of a water inflow-drainage system as a stochastic process has been developed in terms of input parameters of a standard operating iron-ore mine. The abovementioned has made it possible to assess realistically, substantiate, and obtain possibilities for a specific production facility as well as for generalization of the results involving determination of stochastic characteristics of drainage process. Originality. For the first time, a mathematical model of drainage from underground levels of iron-ore mines has been developed as a stochastic process. The process characteristics have been identified relying upon randomness of a water pumping technique. In contrast to the available settings, the new model parameters characterize their dispersion. Possibility to obtain complete characteristics of energy consumption has been obtained: for drainage; for water accumulation volume in underground water collectors; for water pumping from the specified mine depths over the specific period as random processes. A number of drainage features have been analyzed and differentiated being determined with the help of nor-mal law of water accumulation velocity in the underground water collectors in iron-ore mines. Practical implications. In terms of operating iron-ore mine, a generalized drainage mathematical model has been developed as a stochastic process using statistical data concerning water accumulation velocity in the underground water collectors. It has been proved that if the ordinates of water accumulation velocity in the underground water collectors obey the normal distribution law then it is expedient to characterize drainage as a stochastic process. The developed methods, studying drain-age as a stochastic process, help expand the research boundaries involving other auxiliary operations performed during underground mining of iron ore raw materials.

Purpose. To build economic and mathematical model of impacts of investment from internal sources on the profit of an industrial enterprise. Methodology. An economic and mathematical model of enterprise operations is built to enable development of methods for analyzing the impact of the internal investment amount on the profit of an industrial enterprise through considering specific features of its operation. The research involves methodological principles of economic cybernetics, namely the representation of the enterprise as a multipolar object with an unknown structure. Application of the systemic approach enables comprehensive investigation of the process of the amount of internal investment impacting profits of this enterprise. The use of structural synthesis underlies determination of the type of economic and mathematical model without considering its parameters. Findings. Mathematical modeling of operation of an industrial enterprise as a complex object enables numerical determination of the impact of the internal investment amount on the profit of an industrial enterprise. This approach makes it possible to use regression models to obtain an analytical dependence of the enterprise profit on the size of its internal investment. Theoretical research results in the determined sequence of building an economic and mathematical model of internal investment amount impacts on profits. It is proved expedient to divide the process of building a model of an industrial enterprise operation into two stages: structural synthesis and identification of model parameters. Originality. For the first time, an economic and mathematical model of operation of an industrial enterprise in the form of a black box has been used to analyze the impact of internal investment of an industrial enterprise on its profits. Practical value. Analysis of results of economic and mathematical modeling of the PJSC PivdHZK operation proves expediency of estimating the statistical dependence of the profit on the amount of internal investment. It is recommended to introduce the developed system-logical scheme in the investment practice of enterprises.

Purpose. Improvement of regression economic-mathematical models taking into account the influence of residual error as a random variable. Methodology. Methods of economic-mathematical modeling, regression analysis are used. The real conditional law of distribution of residual error as a complete characteristic of a random variable is applied. Findings. A scientific and practical approach to economic and mathematical modeling based on the study on residual error, to improve the construction of regression equations. Originality. For the first time, the application of residual error analysis as a random variable has been proposed in order to construct its conditional differential distribution function, which allows improving the quality of economic-mathematical modeling in the form of regression equations. The use of the proposed method of taking into account the residual error allows eliminating the negative impact of the violation of the conditions of the properties of the residual error in the implementation of economic and mathematical modeling using regression equations. Practical value. The analysis of the obtained results of economic-mathematical modeling of economic activity of Inhulets Mining and Processing Plant on significant statistical material with the use of the developed algorithm of residual error research confirmed the effectiveness of the proposed approach. It is recommended to include the developed algorithm taking into account the properties of the residual error in the practice of managing the financial activities of mining enterprises.