2024 Author: Howard Calhoun | [email protected]. Last modified: 2023-12-17 10:16
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's take a look at what a deterministic model is in this article.
General information
Deterministic system models have the feature that they can be analyzed analytically if they are simple enough. Otherwise, when using a significant number of equations and variables for this purpose, electronic computers can be used. Moreover, computer assistance, as a rule, comes down solely to solving them and finding answers. Because of this, it is necessary to change the systems of equations and use a different discretization. And this entails an increased risk of errors in the calculations. All types of deterministic models are characterized by the fact that the knowledge of the parameters on a certain interval under study allows us to fully determine the dynamicsoverseas well-known indicators development.
Features
Deterministic mathematical models do not allow simultaneously determining the influence of many factors, and also do not take into account their interchangeability in the feedback system. What is their functionality based 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.
Generalized equations of thermal and material balances, determined by the macrokinetics of the process, are also used for construction. For greater prediction accuracy, a deterministic model should have 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 for use is that random errors can have an insignificant effect on the final calculation of the system of equations.
Types of deterministic models
They may not be/periodic. Both types can be continuous in time. They are also represented as a sequence of discrete pulses. They can be described using the Laplace image or the Fourier integral.
Deterministic factorial models have certain connections between the input and output parameters of the process. Models are setthrough logical, differential and algebraic equations (although their solutions presented as a function of time can also be used). Also, experimental data that were obtained in natural conditions or during accelerated corrosion tests can serve as the 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 the 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 the calculations it is necessary to determine the following indicators: the cost of resources and the output of products using various production methods, each of which has its own intensity; variables that describe all the characteristics in ongoing processes (including raw materials with materials). Everything must be worked out. Each individual resource, product, service - all this is entered into the material balance.
Also, for the completeness of decisions, it is necessary to give an objective assessment of the quality of the 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 taken into account that computers can only work with fixed factors.
Building Models
According to the way of presenting the main parameters of the ongoingtechnological processes can be divided into two types:
- 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 set, and additional equations are introduced to match the vectors of boundary options.
These deterministic factor models will allow the person applying them to determine the impact of specific provisions on individual characteristics. But it will not be possible to obtain calculated expressions for the separation curves. If the dynamic optimization of continuous production is calculated, then the probabilistic nature of information about how technological processes proceed 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 are highlighted, for which a quantitative comparison is necessary. To achieve the goals set, the study produces a form transformation.
If a rigidly deterministic model has more than two factors, then it is called multifactorial. Its analysis can be carried out through various methods. Let's use mathematical statistics as an example. In this case, it considers the assigned tasks from the point of view of predetermined and developed a priori models. Choiceamong 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-and-effect relationships. This is precisely the main advantage of the subjects we are considering. Deterministic factor analysis models 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 due to the analysis-based transient processes that occur with 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 replaced by a simplified model. The important thing is that it satisfies all the basic requirements.
The efficiency of the automatic control system and the efficiency of its decisions depend on the unity of all the necessary parameters. At the same time, 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 deterministicmodel
It is built by dividing the factors into their set. As an example, we can consider the process of forming the volume of manufactured products (PP). So, for this it is necessary to have labor (PC), materials (M) and energy (E). In this case, the PP factor can be divided into a set (RS; M; E). This option reflects the multiplicative form of the factor system and the possibility of its separation. In this case, you can use the following transformation methods: expansion, formal decomposition and lengthening. The first option has found wide application in the analysis. It can be used to calculate the performance of an employee, and so on.
When lengthening, one value is replaced by other factors. But the end result should be the same number. An example of extension was considered by us above. Only the formal expansion remains. It involves the use of lengthening the denominator of the original factorial model due to the replacement of one or more parameters. Consider this example: we calculate the profitability of production. To do this, the amount of profit is divided by the amount of costs. When multiplying, 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 planned! But this rarely happens. 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 variousprobabilities. Take, for example, the following. There are two states. Relations between them are very bad. The third party decides whether to invest in the enterprises of one of the countries. After all, if a war breaks out, profits will suffer greatly. Or you can cite the example of building a plant in an area with high seismic activity. Here, after all, there are natural factors that cannot be taken into account exactly, it can only be done approximately.
Conclusion
We have considered what are models of deterministic analysis. Alas, in order to fully understand them and be able to put them into practice, you should learn very well. The theoretical foundations are already in place. Also, within the framework of the article, separate 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 about software that can perform the appropriate simulation. But whatever the choice may be, understand the basics and be able to answer questions about what, how and why, is still necessary. You should learn to start with choosing the right input data and choosing the right actions. Then the programs will be able to successfully perform their tasks.
Recommended:
A fashion model is Features of the profession and the most famous fashion models in the world
Walking down the catwalk in chic outfits, showcasing the works of great designers and catching admiring glances - isn't this the ultimate dream of most young girls? After all, a fashion model is beauty, fashion, luxury and glamour. But is everything as easy as it seems from the outside?
Main types and types of business plans, their classification, structure and application in practice
Each business plan is unique, because it is developed for certain specific conditions. But you need to familiarize yourself with the features of various types of business plans in order to understand their key features. Experts recommend doing this before compiling your own similar document
Types of online stores. Types and models of online stores
Almost all progressive businessmen, literally in any field, thought about selling their own products through the worldwide web. The online store is a website that provides the opportunity for the consumer and the merchant to conclude a transaction remotely
Intensification is a new round in the economy. Definition and main types
Intensification of production involves a complete overhaul of the old methods of increasing output. A creative and non-standard approach will allow the company to "survive" in any, even the most difficult conditions, when economic disasters destroy competitors
Business model - what is it? What are the business models?
Business model is a new tool for designing and planning business processes. They are aimed at finding the most effective solutions in making a profit. The process of building business models received a powerful impetus with the massive development of e-commerce. Today, these tools are used not only in the online sphere, but also in traditional business industries. Let's talk about what a business model of an enterprise is, what types of it exist and why they are needed at all
