Deterministic model: definition. The main types of factor deterministic models

Modeling is one of the most important tools in modern life when they want to foresee the future. And this is not surprising, because the accuracy of this method is very high. Let us, in the framework of this article, consider what the deterministic model is.

general information

Deterministic models of systems have the feature that they can be analytically investigated if they are sufficiently simple. In the opposite case, when using a significant number of equations and variables, electronic computers can be used for this purpose. And the computer help, as a rule, boils down to their solution and finding answers. Because of this, we have to change the system of equations and use another discretization. And this entails an increased risk of inaccuracy in the calculations. All types of deterministic models are characterized by the fact that knowledge of the parameters at a certain investigated interval allows us to fully determine the dynamics of the development of known indicators abroad.

Features

Deterministic mathematical models do not allow simultaneous determination of the influence of many factors, and also do not take into account their interchangeability in the feedback system. On what is their functional built? It is based on mathematical laws, which describe the physical and chemical processes of the object. Due 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 prediction, the deterministic model should possess the maximum possible amount of initial information about the past of the object under consideration. It can be applied to those technical problems where it is allowed for one reason or another to neglect the actual fluctuations in the values of the parameters and the results of their measurement. Also one of the indications to use is that random errors can have an insignificant effect on the final calculation of the system of equations.

Types of deterministic models

They can be non-periodic. Both types can be continuous in time. They are also represented as a sequence of discrete pulses. They can be described using an Laplace image or a Fourier integral.

Deterministic factor models have certain relationships between the input and output parameters of the process. Models are defined by means of logical, differential and algebraic equations (although their solutions, represented as a function of time, can also be used). Also, experimental data that were obtained under natural conditions or accelerated corrosion tests can serve as a basis for calculations. Any deterministic model provides for a certain averaging of the characteristics of the system.

Use in the economy

Let's look at practical application. For this, deterministic models of inventory management are suitable. It should be noted that they are formalized in the class of linear programming problems.

So, for calculations it is necessary to define the following indicators: resource costs and output by means of different production methods, each of which has its own intensity; Variables describing all the characteristics in the ongoing processes (including raw materials with materials). Everything should be worked out. Every single resource, product, service - all this is brought into 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 ideally suited to describe the processes on which the initial state of the system depends. When working with electronic computers, it must be taken into account that computers can only work with fixed factors.

Building models

By way of presenting the main parameters of the technological processes that occur, two types can be divided:

1. Approximation models. In them, individual production units are represented as a set of fixed vectors of boundary variants of their functioning.
2. Models with variable parameters. In this case, certain ranges of variation are established, and additional equations are introduced to match the vectors of the boundary variants.

These deterministic factor models will allow the person using them to determine the impact of specific positions on individual characteristics. But we can not get the calculated expressions for the separation curves. If the dynamic optimization of continuous production is to be calculated, then the probabilistic nature of information about how technological processes occur should not be taken into account .

Factor Modeling

References to this could be seen throughout the article, but what it is, we have not discussed. Factor modeling implies that the main points for which quantitative comparison is needed are highlighted. To perform the set goals, the study transforms 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 methods. As an example, we give mathematical statistics. In this case, she considers the tasks posed from the point of view of pre-established and elaborated a priori models. The choice among them is based on 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 the main advantage of the subjects we are considering. Models of deterministic factor analysis allow accurate prediction in many areas of our lives. Due to their qualitative parameters and universality, they have received such wide distribution.

Cybernetic deterministic models

They are of interest to us due to the transient processes based on the analysis, which occur in any, even the most insignificant, changes in the aggressive properties of the external environment. For simplicity and speed of calculations, the existing state of affairs is replaced by a simplified model. It is important that it meets all the basic requirements.

From the unity of all the necessary parameters depends on the efficiency of the automatic control system and the effectiveness of its decisions. At the same time, it is necessary to solve this 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, you can rely on a less reliable result. Therefore, it is necessary to find a golden mean which will allow obtaining information of sufficient accuracy, and at the same time this will not be unnecessarily complicated by unnecessary elements.

Multiplicative deterministic model

It is built by dividing the factors into their many. As an example, you can consider the process of forming the volume of products (PP). So, for this it is necessary to have manpower (PC), materials (M) and energy (E). In this case, the PP factor can be decomposed into a set (PC; M; E). This option displays the multiplicative form of the factor system and the possibility of its separation. In this case, you can use such transformation methods: expansion, formal decomposition and lengthening. The first variant found wide application in the analysis. It can be used to calculate the efficiency of an employee's activity, and so on.

With elongation, one value is replaced by other factors. But in the end you should get the same number. An example of elongation was considered above. There remains only a formal decomposition. It involves using the denominator extension of the original factor model by replacing one or more parameters. Consider this example: we calculate the profitability of production. For this purpose, the amount of profit is divided by the amount of expenses. In the case of multiplication, instead of a single value, we divide by the summed spending on material, personnel, taxes, and so on.

Probabilities

Oh, if everything went exactly as planned! But this happens rarely. Therefore, in practice, deterministic and probabilistic models are often used together. What can you say about the latter? Their peculiarity is that they take into account also different probabilities. Take, for example, the following. There are two states. The relationship between them is very bad. The third party decides whether to invest in the enterprises of one of the countries. After all, if the war breaks out, the profit will suffer greatly. Or you can give an example of building a plant in a zone with high seismic activity. Here, after all, there are natural factors that can not be accurately taken into account, you can only do this approximately.

Conclusion

We have examined what the models of deterministic analysis are. Alas, but to fully understand them and be able to apply in practice, it is very good to learn. Theoretical basis already exists. Also, within the framework of the article, some simple examples were presented. Further it is better to follow the path of gradual complication of the working material. You can simplify your task a bit and start learning software that can do the corresponding simulation. But whatever the choice, understand the basics and be able to answer the questions about what, how and why, it is still necessary. You must learn to pick the right input and choose the right actions for the beginning. Then the programs can successfully perform their tasks.