Математичне моделювання в економіці: моделювання і системний аналіз

Abstract

У статті розглядаються необхідні історичні відомості про розвиток математичного моделювання. Визначено суть математичного моделювання та роз’яснено деякі його філософські проблеми. Проаналізовано основні поняття моделей та їх видів, поняття системи та її структурної схеми. Обгрунтовано доцільність застосування і наведено конкретні приклади застосування моделей і моделювання в економічних досліджен-нях. Детально проаналізовано поняття «чорної скриньки», структурної схеми системи та системного аналізу. Ключові слова: модель, математична модель, моделювання, математичне моделювання, система, входи системи, виходи системи, структурна схема системи, «чорна скринька», системний аналіз.

This paper considers the necessary historical data on the development of mathematical modeling. It de-fines the essence of mathematical modeling and clari-fies some of its philosophical problems. It analyzes the basic concepts of models and their types, the concept of the system and its structural scheme. The expedien-cy of application of models and modelling in economic research has been proved and specific examples of such usage have been demonstrated. The concept of "black box", system block diagram and system analysis have been analyzed in detail. Modelling is very goal-oriented. To achieve the goal of modeling only at the expense of object’s own capabilities or external means, present at the moment, is possible very rarely. This set of circumstances is called a problematic situation and activity that would contribute to the solving of this problem should be aimed at achieving the set goal. The means for achiev-ing this goal are called a system. Therefore, the system can be represented as a non-transparent "box" excreted from the external environment but not completely iso-lated from it. Then the goal that should be achieved by this system, pre-planned changes in the environment, some of the results of the operation of the system, used outside of it. In other words, the system is connected with the environment and through these ties affects it. These connections are called the outputs of the system. Outputs of the system correspond to the word "target" in the verbal system model. In addition, in the defini-tion the links of the second type have been mentioned: the system is the means, and therefore there must be ways to use these tools, the ability to influence the sys-tem, that is links that are directed from outside, from the environment to the system. These links are called inputs of the system. The described system model is called a "black box". The inside of the 'box', generally speaking, is not uniform, which makes it possible to distinguish its components. In turn, some system parts can also be split into parts, etc. Those components of the system that are considered by us as indivisible, are called the elements of this system; the parts which consist of more than one element are called the subsystems of the system. As a result of such selection of elements and subsystems the composition model of the system is based, which is a description of subsystems and ele-ments, which it is composed of. The term “system analysis” is often understood as a systematic approach, a defined sequence of actions, which is an important means of the development of practical activities. Here the notion of “system analy-sis” is applied in the narrow sense - as the analysis of the system. Analysis of the system is its division into elements while defining the properties of each, as well as the ties with each other and the environment. The purpose of the analysis is to separate the essential properties and relations of the system from non-essential ones and move on to a deeper study of it. Analysis of the system is closely linked with its synthe-sis. Synthesis of the system is an integration of separate elements, properties and relationships into one, in order to obtain a more complete representation of it in the form of the model. Keywords: model, mathematical model, modeling, mathematical modeling, system, system inputs, system outputs, block diagram of the system, "black box", sys-tem analysis.