Modeling is one of the most important tools in modern life when one wants to foresee the future. And this is not surprising, because the accuracy of this method is very high. Let us consider in this article what a deterministic model is.
general information
Deterministic models of systems have the peculiarity that can be studied analytically if they are sufficiently simple. In the opposite case, when using a significant number of equations and variables for this purpose, electronic computers can be used. Moreover, the help of computers, as a rule, boils down solely to their solution and finding answers. Because of this, it is necessary to change the system of equations and use a different discretization. And this entails an increased risk of error in the calculations. All types of deterministic models are characterized by the fact that knowledge of the parameters in a certain studied interval allows us to fully determine the dynamics of development of known indicators abroad.
Features
Deterministic mathematical models do not simultaneously determine the influence of many factors, and also do not take into account their interchangeability in the feedback system. What is their functionality built on? It is based on mathematical laws that describe the physical and chemical processes of an object. Thanks to this, the behavior of the system is predicted quite accurately.
For construction, generalized equations of thermal and material balances, determined by the macrokinetics of the process, are also used. For greater accuracy of forecasting, the deterministic model should have the maximum possible amount of initial information about the past of the object in question. It can be applied with respect to those technical problems where for one reason or another it is allowed to neglect the real fluctuations of the parameter values and the results of their measurement. Also one of the indications for use is that random errors can have a negligible effect on the final calculation of the system of equations.
Types of deterministic models
They may be non / periodic. Both species can be continuous in time. They are also represented as a sequence of discrete pulses. They can be described using the Laplace image or thanks to the Fourier integral.
Deterministic factor models have certain relationships between input and output process parameters. Models are defined by means of logical, differential and algebraic equations (although their solutions, presented as a function of time, can be used). Also, experimental data obtained under natural conditions or during accelerated corrosion tests can serve as the basis for calculations. Any deterministic model provides for a certain averaging of system characteristics.
Use in the economy
Let's look at a practical application. Deterministic inventory
management models are suitable for this. It should be noted that they are formalized in the class of linear programming problems.
So, for calculations, it is necessary to determine the following indicators: resource costs and output using various production methods, each of which has its own intensity; variables describing all the characteristics in the ongoing processes (including raw materials). Everything must be worked out. Each individual resource, product, service - all this is included in the material balance.
Also, for completeness of decisions, it is necessary to give an objective assessment of the quality of decisions made. Thus, deterministic economic models are ideal for describing the processes on which the initial state of the system depends. When working with electronic computers, it must be borne in mind that computers can only work with fixed factors.
Model building
According to the method of presenting the main parameters of ongoing technological processes, two types can be divided:
- Approximation models. In them, individual production units are presented as a set of fixed vectors of boundary options for their functioning.
- Models with variable parameters. In this case, certain ranges of variation are established, and additional equations are introduced to correspond to the vectors of the boundary variants.
These deterministic factor models will allow the person applying them to determine the effect of specific provisions on individual characteristics. But obtaining calculated expressions for the separation curves does not work. If dynamic optimization of continuous production is calculated, then the probabilistic nature of the information on how the processes are proceeding should not be taken into account .
Factor modeling
References to this could be seen throughout the article, but we have not yet discussed what it is. Factor modeling implies that the main provisions for which a quantitative comparison is needed are highlighted. To achieve these goals, the study produces a transformation of the form.
If a rigidly determined model has more than two factors, then it is called multifactorial. Its analysis can be carried out through various techniques. As an example, we give mathematical statistics. In this case, she considers the tasks from the point of view of previously established and developed a priori models. The choice among them is carried out according to a meaningful presentation.
For the qualitative construction of the model, it is necessary to use theoretical and experimental studies of the essence of the technological process and its cause-effect relationships. This is precisely the main advantage of the subjects we are considering. Models of deterministic factor analysis allow accurate forecasting in many areas of our lives. Thanks to their quality parameters and versatility, they have become so widespread.
Cybernetic deterministic models
They are of interest to us thanks to the transient processes based on the analysis that occur during any, even the most insignificant, changes in the aggressive properties of the external environment. For simplicity and speed of calculations, the current state of affairs is being replaced by a simplified model. It is important that it satisfies all basic needs.
The integrity of all the necessary parameters determines the efficiency of the automatic control system and the effectiveness of its decisions. It is necessary to solve the following problem: the more information is collected, the higher the probability of error and the longer the processing time. But if you limit the collection of your data, then you can count on a less reliable result. Therefore, it is necessary to find a middle ground that will allow obtaining information of sufficient accuracy, and at the same time it will not be unnecessarily complicated by unnecessary elements.
Multiplicative Deterministic Model
It is built by dividing factors into many. As an example, we can consider the process of formation of the volume of manufactured products (PP). So, for this it is necessary to have manpower (RS), materials (M) and energy (E). In this case, the PP factor can be divided into a set (RS; M; E). This option displays the multiplicative view of the factor system and the possibility of its separation. In this case, one can use the following transformation methods: expansion, formal decomposition, and elongation. The first option is widely used in analysis. It can be used to calculate the effectiveness of an employee, and so on.
When lengthening, one value is replaced by other factors. But in the end, the same number should come out. An example of elongation was considered by us above. Only formal decomposition remains. It involves the use of lengthening the denominator of the original factor model by replacing one or more parameters. Consider this example: we calculate the profitability of production. To do this, the amount of profit is divided by the size of the costs. When animating, instead of a single value, we divide by the summed expenses for material, personnel, taxes, and so on.
Probabilities
Oh, if everything went exactly as intended! But this is rare. Therefore, in practice, deterministic and probabilistic models are often used together . What can be said about the latter? Their peculiarity is that they also take into account various probabilities. Take, for example, the following. There are two states. The relationship between them is very bad. A third party decides whether to invest in enterprises in one of the countries. After all, if war breaks out, then profits will suffer. Or we can cite as an example the construction of a plant in a zone with high seismic activity. Here, after all, there are natural factors that cannot be precisely taken into account; this can only be done approximately.
Conclusion
We considered what constitute deterministic analysis models. Alas, in order to fully understand them and be able to put into practice, you should learn very well. Theoretical foundations already exist. The article also presented some simple examples. Further, it is better to follow the path of gradually complicating the working material. You can simplify your task a bit and begin to study software that can carry out appropriate modeling. But whatever the choice, understand the basics and be able to answer questions about what, how and why, is still necessary. To begin with, you should learn how to select the correct input data and choose the necessary actions. Then the program will be able to successfully complete their tasks.