Logistic Function as a Tool of Planning

The goal of the paper is to study the role and assess the innovation impact on the economic development of the region. Methodology. Theoretical and methodological foundations of the research draw the works of scientists on the problems of economic development of regions. In the process of scientific research, a complex of such methods was used: content analysis, generalization, systematization – in order to specify the conceptual-categorical apparatus and identify features of innovation; dynamic, statistical, comparative analysis – when identifying the innovation influence features on the economic development of the region, mathematical modelling in economics – to develop a methodology for assessing the innovation impact on the economic development of the region. Results. Features of an innovative approach to the economic development of regions in the context of obtaining sustainable competitive advantage and strengthening of positions of regions on the international arena. The analysis of the innovativeness level of the regions’ development was carried out and the methodical approach for determining the degree of innovation effectiveness in a hierarchical regional section was proposed, which is based on the use of tools of the multidimensional statistical analysis. At the same time, the effectiveness of regional innovation involves the implementation of these stages: formation of the statistical data matrix on the basis of the regional innovation factors by types of INPUT and OUTPUT, defying the degree of innovation of each region, determining the innovation effectiveness measure in the hierarchical regional context. It is established that the semantic interpretation of the regional innovation effectiveness requires clarification of the classification procedure of regions taking into account the chosen methodology for the correlation of INPUT and OUTPUT indices. It is substantiated that the innovation efficiency definition should take into account interregional differentiation, as a result of which the measure of the effectiveness of regional innovation, which takes into account: the ties between the country and regions forming a hierarchical structure, the connections between the innovation index of the region of INPUT type, and the innovation index of the region of OUTPUT type. Practical importance. It is established that the use of a single combined indicator and the rating table does not allow you to track the complexity of the innovation process itself, with innovation indicators shifting in favour of those countries specializing in high-tech industries, in particular, in high-tech manufacturing. The significance of the influence on innovation, in addition to financial, economic, and educational factors is substantiated, as well as technological, organizational and managerial, and especially social and psychological factors. On the basis of calculating the innovation efficiency of regions for the different values of the given index, it is established that its magnitude affects the place of the region in the classification of regions taking into account the chosen methodology of the correlation of INPUT and OUTPUT indices. In determining the degree of innovation effectiveness in the national context, it is proposed to use the regional innovation multiplier. Its value directly determines the position of the country with regard to the effectiveness of the use of innovations in a regional context and, therefore, can serve as a benchmark for national policy in this aspect. Importance/originality. On the basis of the conducted research, a methodical approach is proposed to evaluate the effectiveness of regional innovation on fundamentally new principles, which add an opportunity to reproduce the innovative potential and increase the technological and the information level of all spheres of economic activity of the region, to achieve a high level of competitiveness of its activity.

Mathematical Models in Economics and Management

Mathematical modeling plays a major role in various disciplines. The contribution of mathematical modeling is not only attached to the concepts of general sciences, such as conventional economics and finance, but also includes Islamic sciences, such as Islamic economics and finance. This study aims to reveal the role of mathematics in the development of Islamic economics and finance. This study uses a qualitative approach in the form of library research. The results of the discussion are expressed through the ideas described in two general information, namely: (1) The results of the analysis of mapping studies on mathematical models in Islamic economics and finance, and (2) an explanation of several examples of mathematical models applied in economic theories and Islamic finance. From the results of this study, it was found that the number of publications on the development of mathematical models in Islamic economics and finance research from 1980-2020 experienced a significant increase and also began to have a high impact on other research. In addition, the development of mathematical models in solving Islamic economic and financial problems is also a trend in current research. An example is research on the development of mathematical models on the concept of profit-sharing financing and the concept of zakat.

In the modern educational space, improving the effectiveness of teaching the basics of economics is becoming a priority, especially given the increasing complexity of economic processes and the need to train competent specialists capable of analyzing and solving real economic problems. In this context, the development and implementation of mathematical modeling methods have acquired special importance as an innovative educational technique that allows students to improve their practical knowledge, analytical skills and critical thinking. Mathematical modeling in economics is a powerful tool that formalizes theoretical concepts, simulates complex relationships between economic variables, and allows predicting market behavior, assessing the effects of various economic policies, and making informed management decisions. As part of the training, models serve as a bridge between abstract theory and practical activities, making the learning process more visual, interactive and task-oriented. The article discusses the main methods and approaches to the application of mathematical modeling in educational activities: from the construction of analytical equations to modern computer software systems such as Excel, R, Python, MATLAB and specialized educational platforms. Practical examples of using models in the study of supply and demand, analysis of macroeconomic policy, evaluation of the effectiveness of production solutions, modeling of economic growth and market mechanisms are analyzed. Special attention is paid to the aspects of integrating mathematical modeling into the educational process, developing students’ skills in working with models, the ability to interpret results, as well as methods to increase motivation to study economics through the practical application of digital technologies and simulations. The article also highlights the advantages and limitations of implementing modeling, as well as the types of possible problems and ways to solve them. Summarizing, we can say that the use of mathematical modeling in teaching the basics of economics contributes to the formation of systematic thinking, analytical competencies and readiness for professional activity in a rapidly changing economy. In the context of digitalization and globalization, the integration of modeling methods into the educational process is an urgent and effective way to improve the quality of training for future economists, managers and analysts.

Purpose of this study is advancing of scientificmethodological and applicative tools which are designed to enable management of logistics costs borne by enterprise-participant of Russia-China goods exchange and which is integrating additive technologies. The authors made up the economic-mathematic model which is demonstrating the impact of particular factors causing structural change of China's costs -logistic, currencyrelated and investment. Modeling was performed with the use of multiple regression analysis method based on 2008-2017 data package. "Quandl" aggregator was used in capacity of data source. The authors brought to light priorities in the sphere of logistics costs management exercised by the company fulfilling additive technologies integration; it was demonstrated that production-logistics costs as well as costs associated with information-related processes and supply chains management are to a greater extent exposed to transformation under the impact of additive technologies integration. The authors have examined and made up two possible forms of conventional supply chain structural transformation caused by the impact of additive technologies: supply chains "3D shop" and "Home print" both of which were developed with active use of digital technologies. The authors have also developed (i) a matrix of logistics costs of an enterprise which is integrating additive technologies and maintaining single-part and small-batch production as well and (ii) a model enabling the user to calculate logistics costs of an enterprise which is integrating additive technologies and maintaining single-part and small-batch production at preproduction phase. Use of proprietary technology enables the enterprise to forecast (1 month in advance) the percent of unsecured logistic costs and compensate them at the expense of currently fulfilled orders and thus allows to considerably improving efficiency of logistics costs calculation for the enterprise which is integrating additive technologies, and, therefore, ramp up efficiency of management thereof.

The article deals with peculiarities of application of mathematical methods and models in management of agrarian enterprises. Mathematical modeling is found to be a universal and effective tool for studying the internal laws of certain phenomena and processes. It has been stated that since the solution of economic and mathematical models it is necessary to take into account certain system characteristics and a close connection of qualitative system parameters and how they are resolved. It is noted that a specialist who develops a particular model should have a thorough knowledge of agrarian economics and modeling theory and perfect to have mathematical tools. It is proved that the application of mathematical modeling methods economic and manufacturing processes make efficient use existing resource base in the process of achieving the agrarian strategic goals businesses and take into account significant sources of uncertainty and minimize them negative economic consequences. The arsenal of economic and mathematical methods and models has been systematized used in marketing management decisions business processes. The features by which the economic and mathematical models are classified are presented used in agricultural production. The ways of constructing the optimization models used in agriculture. The process of making managerial decisions on business processes is considered agricultural production using the optimization model fertilizer application. It is noted that, from a mathematical point of view, some economic processes in agribusinesses are the same and can be described using typical models. It is established that by means of economic-mathematical modeling it is possible to solve specific economic problems and practical problems in the field management of agricultural production and economic activity enterprises. It is concluded that the application of mathematical tools methods and models make it possible to substantiate the adoption process better management decisions when planning and finding promotion reserves efficiency of agricultural enterprises in crisis conditions and dynamic changes in the environment.

Advances in information technology have contributed to increased transport efficiency. The use of the latest information technologies allows automating all the information technology activities of transport enterprises that take part in the processes of organising freight traffic. Automation of transport logistics provides increased efficiency and optimisation of transportation. Due to the introduction of automated routing, accounting and planning systems at transport enterprises, transport logistics is reaching a new level. The purpose of the study is to develop an automated control system for the operation of the production and transport complex, based on the use of the latest information technology – Embarcadero RAD Studio XE10 visual programming system. It will help to optimise the transportation of mineral construction materials using the road, railway, and water modes of transport, the change of which occurs at the goods transshipment points. To solve this problem, a mathematical economic model and an automated control system for the operation of the production and transport complex have been developed. The proposed method would take into account the technical and technological capabilities of land and water modes of transport and the capacity of transshipment points, at which the cost of transporting goods will be minimal. Using the software package, the base for the transportation of mineral construction materials was calculated. The obtained initial transportation plan for each type of delivery was optimised, taking into account the production capacities of manufacturers and the needs of customers. The results of the optimal distribution of goods between different modes of transport are given (taking into account their production capacities), their change takes place in transshipment points. The results obtained allow optimal use of the technical and technological capabilities of vehicles and handling mechanisms. Based on the mathematical economic model, an automated control system for the operation of the production and transport complex has been developed, it has the form of a software package. The calculation of the initial (reference) freight traffic plan was carried out and the optimisation of the initial plan for these transportations was performed for each of the delivery options. The operability of the developed software package has been confirmed experimentally, which gives reason to offer it for the use in industrial production associated with the movement of sizable freight traffic.

The theory of optimization has a long history in mathematics, The oldest problem known to me is the 27th Theorem of the Sixth Book of Euclid, However, the first real surge of interest came in the 17th century with the discovery of the calculus (and even before, with the work of Fermat), The applications of the techniques of the differential calculus and the calculus of variations were, in large part, to mathematics, physical sciences, and engineering. The last 30 years have seen the growth of Mathematical Programing, The problems which are considered in this area may be roughly classified as problems in economics, since when broadly defined, mathematical programming is concerned with the allocation of scarce resources so as to fulfill certain requirements while optimizing some objective function. As Neustadt has indicated in the opening ceremonies of this Summer School, it has had an impressive record of practical success in solving real problems. This has been due to three influences: (1) an intellectual readiness for mathematical models in economics and industrial application; (2) a succession of good algorithms, starting with the Simplex Method; (3) the simultaneous growth of large scale electronic computers.

Cournot duopoly has now been an inspiration for mathematical modelling in economics for almost two Centuries. As the principles are very simple to grasp one needs not have a lifetime of indoctrination with economic theory to be convinced. Once nonlinear science took the stage it was mathematicians such as Rand, and Poston and Stewart, who started using applications to duopoly. Not altogether surprising, after all Cournot was a mathematician. The aim then was to create iterative processes in the style of the logistic map. Cases where both reaction functions were in this style were suggested, which, of course, could produce up to four different fixed points. Unfortunately, these were not based on economic principles, i.e., were not derived from demand functions that emerged from utility maximization. In 1991 the present author proposed the case of Cobb-Douglas utility where the resulting demand functions are always reciprocal to commodity price. Budget shares for the consumers, and hence also aggregate revenues for the producers then became constant. Dana and Montrucchio had proposed a similar case as an example 5 years before, though without fully appreciating the potential of the idea. This “isoelastic” demand function easily lends itself to explorations of dynamics. Yet, it also has its snags, above all the constancy of revenues, which leads to the absurd situation that a single supplier can reduce output to zero and sell it at an infinite price, which does not affect revenues at all. On the other hand costs can be reduced to zero by cancelling production, so the best choice is to produce nothing. This, of course, is absurd and makes the model unsuitable to deal with monopoly or collusion. The problem persists in duopoly, despite the fact that the intersection of the reaction curves in the origin is totally unstable; the curves at this intersection even have infinite slopes. Nevertheless we need some mechanism that pushes the system away from the origin if it lands there. This may sound simple, but it is not! Any such repulsion mechanism tends to take over the show, and blur the essential dynamics we want to analyze. As the reaction curves intersect the axes whereas outputs cannot be negative, it is inevitable that an occasional dropping out from production makes the system land in the origin. Once one firm chooses zero output, the other will do it as well. We need something to prevent the system from ever visiting the origin, which will be done through assuming adaptation. This means that the firms never move to the calculated best reply, just part of the way, which may be 99.99%. Given this, the assumption seems to be quite innocuous.

Our study commemorates this event by presenting a retrospective of the publications related to the use of mathematical tools for the analysis of economic, ecological, and environmental phenomena. We analyzed 1257 scientific publications using bibliometric techniques to examine the most productive and influential authors and their contributions in the economic, ecological, and environmental fields. Co-authorship among the top authors and countries, co-occurrence of the keywords, bibliographic coupling of the documents and authors, and author co-citation were analyzed by applying network analysis techniques using VOSviewer software, identifying the intellectual structure of the research and the collaborative networks in the fields. The results show that mathematics has grown impressively in terms of publication and citation. The contributions come from all over the world, but the majority are from the People’s Republic of China and Spain. The results also show themes and trends in the economic, environmental, and ecological fields and a predominant use of mathematical tools in optimization processes in order to rigorously substantiate the decisions of investors and policymakers. Thus, our study offers support for any researcher to understand the current state of the art and develop a comprehensive understanding of journal publications.

Subject. The article considers the reasons for low development pace of servitization in Russia within the context of the continuing growth of the domestic services market as a whole. Objectives. The aim of the study is to review a scenario of possible development of professional services at the regional level, the factors promoting servitization of the regional economics and possible outcomes of this process. Methods. To analyze the specifics of interaction between the industrial and tertiary sector of the regional economy, we employed the method of mathematical modelling in economics (based on the system-synergetic and project-process approaches), structural analysis of potential resources of the given model. Results. Distribution of the selected growth zones is correlated with the prospects for the formation of distribution points of the regional servitization model in the Rostov Oblast. The cities of the region may serve as supporting centers (if they are considered drivers of innovative development of the regioin’s production and service sectors). Conclusions. The task of providing competitive ability to service firms, resilience and economic stability of a given territory, as well as its social and economic progress are generally defined by the ability of local manufacturers and service firms to efficiently cooperate, offering their partners package servitization-based solutions.

This paper supports the literature which argues that derivational robustness can have epistemic import in highly idealized economic models. The defense is based on a particular example from mathematical economic theory, the dynamic Walrasian general equilibrium model. It is argued that derivational robustness first increased and later decreased the credibility of the Walrasian model. The example demonstrates that derivational robustness correctly describes the practices of a particular group of influential economic theorists and provides support for the arguments of philosophers who have offered a general epistemic justification of such practices.

This article presents the model of balanced water resources management and uses correlation analysis to examine the relationship between water resources and economic indicators in 11 divisions and cities of Shaanxi Province for the period from 2012 to 2021. In this work, the method of correlation analysis is applied to digitize the management of water resources use and recovery in Shaanxi Province over a considerable observation period. The visualization results of water resources management in var-ious cities of Shaanxi Province were obtained through an economic mathematical model.

To calculate the demographic load factor in this work, the forecasting of the working-age population of Russia was carried using the polynomial regression equation of the fourth degree with an accuracy of 0.227% and forecasting the number of people older than working age using the Verhulst equation (prediction accuracy of 1.084%) for the period from 2023 to 2031 (9 years). An economic and mathematical model was developed for calculating pension income and expenses for the implementation of individual (personalized) pension accounts of citizens and a stress analysis of the model was carried out based on an assessment of the impact of the pension contribution rate, average monthly salary, average investment income rate for transactions with pension funds of citizens (rate of return) and growth rates salaries, ensuring a balance between pension income and pension expenses of citizens. The practical implementation of the developed economic and mathematical model shows that the minimum value of the rate of return, ensuring balance between pension income and pension expenses of citizens, is 1.408%. The minimum average monthly salary is 22,949.39 rubles; the contribution rate to the Pension fund is estimated at 18.813%.

The author discusses the development of an economic-mathematical model for assessing the impact of regional budget expenditures on the average wage for solving the problems of analyzing macroeconomic indicators and forming strategic planning tools for the development of the regional socioeconomic system. The Object of the Study - expenses of the regional budget of the constituent entity of the Rossiyskaya Federatsiya, aimed at developing and maintaining the infrastructure contributing to the provision of comfortable working conditions for citizens. The Subject of the Study - methods of economic and mathematical modelling, processes of formation of the average wage. The Purpose of the Study. Development of an economic and mathematical model for assessing the impact of regional budget expenditures on the average wage level for quantitative and qualitative assessment of the effectiveness of the totality of measures arising in the process of its implementation. The Main Provisions of the Article. The labour market is the basis of a market economy and indicator, the importance of which makes it possible to draw conclusions both about the state of the economy as a whole and about the success of the reforms and transformations, in particular. His condition directly affects the performance indicators of the socio-economic system of the region: productivity, profitability, growth, etc. Research and identification of factors that have a significant impact on the processes of formation and functioning of the labor market is of not only theoretical, but practical interest. The following tasks have been solved: the economic and mathematical models are formalized; the layout of the indices characterizing the object of study; the corresponding mathematical apparatus is selected; software application developed; the proof of model performance is performed. As a methodological apparatus, methods of regression and correlation analysis were used. As a result, an economic-mathematical model of the category «labour market efficiency» was obtained, the functionality of which is sufficient to substantiate causal relationships between indicators that determine the nature of its functioning. Using the obtained results in practice, it is possible to reasonably form a system of priority long-term guidelines for the development of the socio-economic system of the region, drawn up in the form of relevant program documents. The developed software can be used as a module of a decision support system in the formation and development of a strategy for the region’s accelerated development.