Modeling and forecasting. Modeling

MOSCOW STATE SOCIAL UNIVERSITY

HIGHER EDUCATION

V.M. SAFRONOVA

FORECASTING AND MODELING

IN SOCIAL

Educational and methodological association of Russian universities

in Social Work Education

as a teaching aid for students

institutions of higher education

UDC 303.733.4

The publication was published within the framework of the State program of scientific and methodological support for the specialty “Social work”

Scientific adviser - V.I.Zhukov

Reviewers:

Doctor of Historical Sciences, Professor L.G. Zakharov;

Doctor of Historical Sciences, Professor A.N.Khoroshilov

Safronova V.M.

C 21 Forecasting and modeling in social work: Textbook. Benefit

for students higher schools, institutions - M.: Publishing center "Academy",

ISBN 5-7695-0834-5

The manual examines basic issues of methodology, theory and organization of scientific forecasting and modeling of social processes, various types and types of forecasts and models. Particular attention is paid to developing the skills to implement the theoretical and methodological principles of forecasting and modeling in social practice. Extensive experimental material is provided to illustrate the theoretical principles.

The book can be useful to scientists and practitioners, as well as to anyone interested in the problems of forecasting social processes.

UDC 303.733.4

ISBN 5-7695-0834-5© Safronova V.M., 2002

© Publishing center "Academy", 2002

Recent social transformations in our country have actualized the problem of predictive research and modeling in the social sphere.

Russia's recovery from the crisis, the justification of the social development strategy, the definition of immediate and long-term programs require innovative actions and broad modern thinking based on the integration of sciences. Forecasting and modeling occupy a particularly important place here as high-tech methods of scientific analysis and foresight.

The essence of this scientific and educational direction is the systematic analysis of social processes through the prism of theoretical and methodological principles to identify problems and trends in social development, and determine ways to solve social problems.

In modern conditions, the ability to foresee and predict the future, and therefore influence social processes, is also becoming one of the most valuable qualities of a young specialist.

The university system of the Russian Federation is now acquiring both the right and the opportunity to teach social forecasting and modeling as a general professional discipline for specialists of any profile. At the Moscow State Social University 10 years ago, the department “Social Forecasting and Modeling” was first created under the leadership of the author of this textbook, which acts as a scientific and methodological center for departments being created in universities of the Russian Federation, teaching courses, lecture cycles through a system of electives, courses for training, retraining and advanced training of personnel.

The learning process is built according to the following scheme: study of theory - analysis of practice -> experimental testing -> implementation. In close cooperation with the Ministry of Labor and Social Development (Department of Analysis and Forecasting of Social and Economic Development of the Russian Federation), with other federal structures, employees of the department participate in federal research programs, which contributes to enriching the educational process and a deeper study of problems during social transformations in society. Often, forecasts and models developed by undergraduate and graduate students become commercial products and help graduates more actively adapt to market conditions, increasing their competitiveness and relevance.

For the theoretical development of a new scientific direction, the department has an international certificate and was awarded first place in a university scientific competition among researchers of social practice.

The main goal of this manual is not only to introduce students to the basics of scientific forecasting and modeling of social processes, various types and types of forecasts and models, but also to consider a number of current theoretical and practical problems. Some of them involve identifying the role of forecasting and modeling in substantiating conceptual approaches to the prospects for social development and equipping everyone interested in the methodology of forecasting research to identify trends, “fields of opportunity” in social transformations, and optimal ways to achieve social results in accordance with the goals set.

The second part of the tasks provides knowledge in the field of developing forecasts and models, develops the ability to implement the theoretical and methodological principles of forecasting and modeling in social practice, and contributes to mastering the skills of development, experimental testing and implementation of the most modern modeling and forecasting technologies.

Solving these problems is aimed at creating a prognostic culture of personnel as an indispensable and important condition for increasing the efficiency of their activities, ensuring the competitiveness of specialists of any profile, at any level.

The methodology for presenting the material is based on the principle of “acquisition through simplification.” Sections of the book indicate conceptual boundaries: methodologies, technologies, methods, scenario-game modeling. At the same time, each chapter, subsections, and paragraphs include specific and visual material that is of practical importance for a wide range of readers, including practical social workers.

A list of references for in-depth study and a dictionary of basic terms increase the practical significance of the publication. A large amount of experimental material is provided as illustrations.

The appendices contain auxiliary and educational material.

When analyzing the problems of socio-economic development of the Russian Federation, materials from the Ministry of Labor and Social Development (Department of Analysis and Forecasting of Socio-Economic Development of the Russian Federation) were used to develop a forecast for the period up to 2004.

Some technologies for modeling and forecasting socio-ecological problems are the result of research by A. S. Gosporyan, who has been developing this topic for several years.

The use of certain provisions of A. V. Markova’s scientific research in the textbook enriched the content of the textbook with relevant information and analytical material at the federal level.

In the third section of the manual, in the development of the main provisions of the system-functional approach, fragments of research from the scientific school led by the author “XXI Century: Forecasts and Models” are used.

When analyzing demographic processes, various technological modeling and forecasting approaches used by other researchers (T.V. Kuzminova, A.I. Panteleev, E.A. Nazarova) were used, which allows readers to compare existing methods and determine their own attitude towards them.

All comments and suggestions sent will be gratefully accepted and taken into account by the author.

Section I

BASICS OF FORECASTING AND

SIMULATION

Methodological aspects of forecasting

and modeling of social processes

A distinctive feature of the modern world, despite the measures and efforts taken, is its imbalance, the increase in economic, political, religious, and social cataclysms. The international community and the states of the world have come to the conclusion that the existing paradigm for the development of civilization is flawed and disastrous for the future; humanity needs a change in the conceptual approach. But in order to decide which, most humane, development model to choose, it is necessary to see some general picture of technological transformations, driving forces, and cultural consequences. There are still more questions than answers to the most pressing problem: what is the information society, to which there are supposedly no alternatives? And which seemed designed to resolve the most pressing social issues.

Yes, these are global problems (including international terrorism), the study of which is the subject of interdisciplinary and international scientific research, but without their forward-looking vision and understanding, the most energetic practical activities in any country, in various aspects of the social sphere, at all levels are futile management.

For Russian society, which is experiencing an acute socio-economic and spiritual-moral crisis, ensuring the effectiveness of managing social processes, the need to develop a forecast vision of development and prospects has become one of the urgent tasks in the field of both theoretical research and scientific substantiation of social practice and one of the most important conditions of survival, recovery and development.

Nowadays, scientists and practitioners face the need to realize the possibilities of human influence on the development of society and the world as a whole; to clarify the relationship between objective processes, on the one hand, and human influence on them, on the other. The conceptual vision of the future and its forecasting depend on this: either it is just a designation of developing trends and a forecast based on them, or it is a forecast taking into account the possibilities and necessity of human influence on the emerging development trends in accordance with modern ideas and beliefs.

Time allows us to answer many questions, based on the achievements of science, and instills some optimism in our views on the future. However, the awareness of more and more new limitations is becoming more and more obvious, which, in turn, is also an achievement of science and indicates complex contradictions.

In this regard, we will further consider the following questions: Can everything be predicted? With what degree of reliability? Are the approaches to forecasting global and local systems and situations the same? What processes and phenomena can we attribute to linear dynamics, and therefore, make a forecast with a greater degree of reliability, identify trends and propose solutions? And which ones are related to nonlinear dynamics, due to which the role of random factors increases? And how, in what way will this be reflected in social practice?

This is a wide range of issues of theory and methodology.

Methodology rightfully considered as general system of principles and regulations of human activity- processes of cognition and philosophical justification of methods and techniques for organizing the entire variety of types of human activity - and how teaching about this system. Its basis is dialectics, which performs heuristic, axiological, ideological and orienting functions. The methodological aspect is objectively inherent, in principle, in any activity, leadership, management, social work due to the organic and multifaceted interconnection of various spheres of public life, as well as the continuous strengthening of interaction between them.

The concept of forecasting and modeling (social processes) that we propose is based on two main methodological principles. The first of them is the recognition of the objective nature of social processes. The second principle is the recognition of the prevailing role in the social development of the subjective factor, i.e., the reasonable purposeful activity of people, based on accumulated scientific potential and certain ethical and moral values, and in connection with this - their ability to choose, determine guidelines for social development and ways to achieve the designated goals.

Today, more than ever, an integrated system analysis of social development is needed, allowing us to see and trace trends, the course and dynamics of social processes, while trying to separate real events from subjective reactions, emotions, intentions, and assumptions. The most important aspect of this problem is to identify the role and importance of leaders in politics and social life, their understanding of the depth of social processes and their ability to influence the course of events; explore ideals and the means by which they imply the achievement of social results.

All attempts to realize and understand the world only through our own experience, at the level of everyday practice, are futile, and if we are talking about public administration, they are detrimental to the country, since the outside world (“visible”) has another side, hidden from us, requiring deep scientific analysis, forecasting of social processes, based on taking into account many factors and presupposing a certain level of philosophical, intellectual, methodological culture.

It is necessary to take into account the totality of the immediate and long-term consequences of the decisions made, not only in this study area, but also in related areas; otherwise, when it comes to social processes, as a result of interference in them, such negative phenomena may arise, a kind of chain reaction, which will negatively affect the state of affairs both in other spheres of social life and on society as a whole.

In order to look into the future, you also need to know the past. The lack of an objective analysis of the past entails both an incorrect interpretation of the present and an inability to “look” into the future, much less predict it. The past, present, and future are organically interconnected: in the name of the future, one cannot reject everything that not only predetermines it, but also ensures its stability and reliability.

In particular, many of the problems that have arisen during the current reform of Russian society cannot be considered in terms of the inevitable replacement of “old forms” with more advanced, “new” ones - as a movement forward. After all, society has been thrown back half a century; the majority of the population is below the poverty line. A tendency towards spiritual degradation of society has also emerged. It is these problems that should become the main ones; efforts should be directed towards their scientific and practical constructive solution.

Prognostics How system of scientific knowledge about the future close is connected and interacts with history and mathematics, philosophy and sociology, psychology and jurisprudence.

Forecasting- This social theory of knowledge. It is in specific interaction with a number of theoretical doctrines, concepts, systems, which to one degree or another consider the future as the main object, carry out research on the problems of the near and distant future at different levels - theoretical, psychological-intuitive, practical - and try to penetrate into the unknown.

Forecasting is fruitful only if and only if it is based on scientific systems of knowledge that make it possible to foresee the course of processes, social phenomena, development trends and the social consequences of practical measures taken.

Forecasting, which is widely used for political purposes, is often biased; the truth here is sacrificed to the proclaimed political views and concepts. Thus, the very possibility of a successful scientific forecast is largely discredited.

It should also be taken into account that for successful forecasting and modeling of social processes a certain level of theoretical thinking and a culture of thinking is required. Otherwise, it is impossible to correctly build the logic of practical actions, model options for the development of social situations, predict trends in their development, and take into account all the possible consequences of the actions taken for a particular subsystem of the social sphere and for society as a whole.

We will begin to consider the problem with the basic concepts of the course: “prognostics”, “forecast”, “forecasting”, principles of “social forecasting”, “forecasting in social practice”, etc.

Prognostics- the science of the system of our thinking about the future, of the ways and methods of studying the future. The methodology of prognostic research is based on the most valuable theoretical achievements of many sciences: historical, mathematical, philosophy, sociology. Forecasting - This scientific research method, aiming to provide possible options for those processes and phenomena that are chosen as the subject of analysis.

The forecast research methodology is based on the principle of a holistic, systematic, comprehensive consideration of the object, taking into account its hierarchical subordination, its interrelations both vertically (by level) and horizontally (with adjacent areas), dependence on external factors and internal changes.

No less important the principle is a clear definition of the status and features of the object forecasting research, a preliminary theoretical analysis of its essence based on the existing level of scientific knowledge, which will allow at all stages of the study to adhere to uniformity in the categorical conceptual apparatus and terminology, and in the process of generalizing the results to achieve the highest possible objectivity, reliability and accuracy.

The practical purpose of forecasting is the preparation of substantiated proposals, projects, programs, recommendations and assessments about:

In what direction is it desirable to develop objects in the area under study (social protection, culture, healthcare, education, youth problems, spiritual and moral processes, etc.);

How development can actually proceed;

What is the mechanism for overcoming negative trends.

In general terms, we can talk about two types of tasks: defining and motivating development goals; determination of means, methods, ways to achieve goals.

Full cycle of predictive research includes: studying the problem situation in theory and practice; analysis of pre-forecast and forecast background; defining goals and objectives; putting forward hypotheses; selection of research methods and techniques that have the necessary predictive potential; conducting experimental testing of hypotheses and verification of research results; formulating conclusions and proposals.

Forecast There is a multivariate hypothesis about possible results and development paths of the object under study (sphere, industry, type of activity, etc.).

For example, when developing a forecast for the activities of social services at the local government level to ensure targeted social protection of the population, the main hypotheses can be:

a) extensive development of social infrastructure and a corresponding increase in full-time social workers with this professional training. This is the most likely way to ensure targeted social protection of the population;

b) creating the necessary conditions for self-sufficiency of those in need of social protection who have the necessary creative and physical potential. This can help change the dynamics of the transition of this category of citizens from those in need to the level of social sufficiency.

The purpose of the forecast is to strive to provide answers to the range of questions that constitute the essence of the problem.

Social Forecasting(“social” from Latin “public, connected with society, with social relations”) - forecasting everything social, everything connected with society, with social relations, at the center of which is a person.

Foreign experience (in particular, the USA) indicates that forecasting social systems occupies a leading place (53%) among other areas of research.

In terms of time parameters, the percentage of research is as follows: for 5-10 years - 52%; for 5 -25 years - 64%; for 10 - 25 or more years - 26%.

Depending on the time period for which the forecast is made, forecasts are:

short-term (with a lead time from 1 month to 1 year);

medium-term (from 1 year to 5 years);

long-term (from 5 years to 15 years);

long-term (over 15 years).

The forecasting process itself involves:

Conducting a brief retrospective analysis of the predicted object;

Description of the current state of the object (comparative analysis of observed trends in domestic and foreign experience);

Troubleshooting:

already solved, but their implementation and implementation is just beginning;

those problems that have been solved but have not found practical use;

expert assessments of leading scientific research in this field.

Predictive research can rely on a range of methods. For example, in a predictive study of educational problems, various methods are used to identify trends: mathematical modeling, the Delphi method, the “naive extrapolation” method, etc.

Due to the multifactorial nature and exceptional complexity of the research object, prognostic recommendations are of a variant nature. The education strategy takes into account various development scenarios for society as a whole.

Therefore, when predicting education, the basis is the principle of variability, multi-criteria assessment of strategic decisions, various technologies of organizational forms are used on a competitive basis, allowing for an alternative vision of emerging problems and ways to overcome them. In this case, public expertise is of particular importance.

The essence of these studies in the most general form is to anticipate:

“socio-economic, scientific and technical conditions in which the education system will develop in the future;

The changing role and place of the human personality in social progress;

The dynamics of the development of educational needs of the population, the prestige of relevant professions and specialties;

The study of interethnic conflicts can also be carried out using a number of forecasting methods: the widespread use of analytical methods and computers, the use of simulation models, deep retrospection and pre-forecast background, the use of scenarios for the probable presentation of forecast information.

When conducting any prognostic study, the following factors are taken into account and carefully developed: methodological And organizational characteristics, and specific features of the prognosis and recommendations for borrowing its positive features.

Each of the provisions can be specified. Methodological aspects include, for example, the use of a systematic approach, analysis of the problem based on a retrospective study of historical analogies.

The basic experimental models of social protection of the population created by a team of MGSU scientists and social work practitioners in the context of society’s transition to market relations are one of the local approaches to research and practical implementation activities in this area in modeling and forecasting. An example could be: systemic modeling of social protection of the population in individual regions, in particular in the South-Western District of Moscow - in the Ramenki microdistrict with a population of 54 thousand people, in the Khanty-Mansiysk Autonomous District with a population of 1.5 million people, in Astrakhan and other regions. The creation of basic models and the development of forecasts is preceded by a hypothesis about the possibility of using experimentally verified models, their broad expert assessment and testing.

Basic tasks, logic analysis of the situation and development of forecasts in social processes in the regions are as follows:

Contribute to the optimal functioning of government structures;

Develop predictive support for management decisions in the field of social protection of the population;

Prevent the occurrence of adverse events and processes;

Explore the development of the social consequences of the transition to the market for families of different types (young, large, single-parent, refugees, military personnel, the elderly), contribute to the development of positive changes;

Develop scenarios and models for the development of such families and recommendations to the government of Russia and the administrations of the constituent entities of the Federation on their social protection and support;

Conduct forecast studies of the socio-demographic composition of youth, social problems of adolescents, the socio-economic situation of working youth, interethnic relations among youth and develop practical recommendations for the social protection of youth;

Research the social consequences of privatization (in the regions of Moscow, in a number of other cities of Russia), develop forecasts and recommendations on this basis.

An integral part of forecasting is its organizational issues, such as:

Creation of a temporary creative team (TCT) and determination of the functions of it and each member individually;

Determination of methods, objects of research;

Development of forecasting methods;

Determination of computer research methods, sociological research.

Each predictive study has its own specific characteristics.

Characteristic features may include: the presence of a large array of factual material; forms of presentation of initial information; using a set of scenarios before forecasting; clear visual presentation of forecast information; widespread use of modeling and the possibility of using the original model for assessments in management activities.

Questions and tasks for self-test

1. What are the essence, content and features of prognostics as a science? What is its role and place in the system of other sciences?

2. Name the basic principles of “social forecasting”.

3. Expand the content of the basic categories of the subject: “forecasting”, “forecasting methodology”, “forecast”.

4. Determine the range of social phenomena that require long-term forecasts and give your justification.

Literature

Khukov V. I. Russia: state, prospects, contradictions. - M., 1995.

Zagladin V., Frolov I. Global forecasting of modern times: Scientific and social aspects. - M., 1981.

Kapitsa S. P., Kurdyumov S. P., Malinetsky G. G. Synergetics and future forecasts. - M., 1997.

Safronova V. M. On trends in social development in the 21st century: Through the prism of forecast: Sat. public lectures. - M., 2001.

Social forecasting and modeling / Ed. V.M. Safronova: Textbook. - M., 1995.

Optimization methods allow you to find the best options for economic solutions according to the selected optimality criterion. Based on them, it is possible to determine the optimal profit of the enterprise, the volume of output of various types of products, the number of employees, the volume of consumed resources and other indicators.

A model is a convenient, simplified representation of the essential characteristics of an object or situation.

Models must meet the following requirements:

1. The model must reflect the characteristic, essential features of the object.

2. This mapping must be expressed in a simplified form.

3. The model should allow you to change some of its parameters for the purpose of research.

4. The model should be more convenient for experiments and cheaper to manufacture than the object.

1. Sequence of constructing an economic-mathematical model

When building an economic model, a number of steps are usually followed:

1. The subject and goals of the study are formulated.

2. In the economic system under consideration, structural or functional elements are identified and their most important characteristics are determined.

3. A verbal description of the relationships between the elements of the model is given.

4. Symbolic notations are introduced for the considered characteristics of the modeling object and the relationships between them are formalized. Thus, a mathematical model is built.

5. Calculations are carried out using a mathematical model, and the resulting solution is analyzed.

1. Main types of models

Mathematical models used in economics can be divided into classes according to a number of characteristics related to the characteristics of the object being modeled, the purpose of the modeling and the tools used:

Depending on the type of object being modeled, models can be macro and microeconomic.

Macroeconomic models describe the economy as a single whole, connecting its aggregated indicators: GDP, investment, labor productivity, employment, interest rate and other indicators.

Microeconomic models describe the interaction of structural and functional components of the economy, or the behavior of one such component in a market environment. Due to the diversity of types of economic elements and forms of their interaction in the market, microeconomic modeling occupies the main part of economic and mathematical theory.

Depending on the purposes of modeling, theoretical and applied models can be developed.

Theoretical models make it possible to study the general properties of the economy and its characteristic elements. Applied models make it possible to evaluate the functioning parameters of a specific economic object and formulate recommendations for making practical decisions.

In the modeling of a market economy, a special place is occupied by equilibrium models that describe the state of the economy when the resultant of all forces tending to bring it out of this state is equal to zero, for example, models of equilibrium of supply and demand.

Optimization models in a market economy are usually built at the micro level, such as profit maximization or cost minimization in corporate planning.

Depending on the tools used and the nature of the processes being studied, all types of modeling can be divided into deterministic and stochastic, discrete and continuous, static and dynamic, linear and nonlinear.

Deterministic modeling represents deterministic processes, i.e. processes in which the absence of any random influences is assumed.

Stochastic modeling depicts probabilistic processes and events. In this case, a number of realizations of a random process are analyzed, and the average characteristics of the process are estimated.

Discrete modeling is used to describe processes that are assumed to be discrete, i.e. discontinuous, consisting of separate parts.

Continuous modeling allows you to depict continuous processes in systems.

Based on time, models can be static and dynamic. Static models describe the state of an economic entity at a specific moment or period of time, while dynamic models include relationships among variables over time (for example, over a five-year period).

According to the degree of coarsening of the forms of structural relations of the object under study, models are divided into linear and nonlinear models. In linear models, all the desired variables are written to the first degree, and on graphs they can be represented as straight lines.

Depending on the form of representation of the object, mental and real modeling can be distinguished.

Mental modeling is often the only way to model objects that are practically unrealizable in a given time interval, or exist outside the conditions possible for physical contemplation. Mental modeling can be implemented in the form of visual and mathematical ones.

With visual modeling, based on human ideas about real objects, various visual models are created that reflect the phenomena and processes occurring in the object.

The basis of hypothetical modeling by the researcher is a certain hypothesis about the patterns of the process in a real object, which reflects the researcher’s level of knowledge about the object and is based on cause-and-effect relationships between the input and output of the object being studied.

Analog modeling is based on the use of analogies at various levels. The highest level is complete analogy, which occurs only for fairly simple objects.

A mental model can be used in cases where the processes occurring in a real object cannot be physically modeled.

Symbolic modeling can be linguistic or symbolic. Language modeling is based on a certain thesaurus, i.e. a dictionary cleared of the ambiguity inherent in a regular dictionary (for example, the word "KEY").

Sign modeling allows you to use signs to display a set of concepts, creating chains of words and sentences and thus give a description of a real object.

Mathematical models are sets of mathematical dependencies that reflect the essential characteristics of the phenomenon being studied. In many cases, mathematical models most fully reflect the modeled object. At the same time, mathematical models are more dynamic; they are better used to find the optimal parameters of an object. To model economic phenomena, models other than economic-mathematical ones, as a rule, cannot be used. Economic and mathematical models, in turn, are of two types: analytical and simulation.

For analytical modeling, functioning processes are written in the form of certain functional relations (algebraic, finite-difference, etc.). In simulation modeling, elementary phenomena that make up the process are simulated while preserving their logical structure and sequence of events over time.

Real modeling is the most adequate, but its capabilities, taking into account the complexity of objects, are very limited.

Forecasting in decision making

The uncertainty of the external environment puts the organization in such conditions that when making decisions, forecasting becomes necessary.

Definition 1

Forecasting– this is the development of forecasts (scientifically based judgments about the future states of the object under study, development alternatives, life spans, etc.).

Forecasting when making decisions means assessing the prospects for the development of the situation that may arise after the implementation of the decision. Forecasting is based on an analysis of the current situation in the organization and in the external environment. The purpose of forecasting is to identify trends that impact the organization and the market. Depending on the area of ​​consideration, forecasting is divided into the following types:

• economic(describe the general state of the economy for a certain period);
• technological(describe future technologies, innovations in terms of efficiency, labor intensity, cost-effectiveness, etc.);
• competitive(describe the strategy of competitors’ behavior in the market, their market share, sales level, new products, etc.);
• about the state of the commodity market(describe the market situation in terms of the influence of politics, economics, ecology, consumer income level, demographics, etc.);
• social(describes the attitude of consumers towards the organization, product).

Definition 2

Sources for making forecasts are information obtained from financial statements, statistical data, operational data, scientific and technical documentation, licenses, patents, external sources of information (mass media, Internet).

Main stages of forecasting are presented in the diagram.

Picture 1.

There are many types of forecasting; all existing methods are usually divided into three groups:

• quantitative;
• quality;
• informal.

Figure 2.

Quantitative methods include:

• mathematical methods (extrapolation, time series analysis, time series analysis),
• Causal modeling.

Qualitative methods are used when there is no complete information about the situation. The basis of this group of methods is expert assessments. These include:

• heuristic, expert methods;
• forecasting by analogy;
• logical forecasting;
• functional-logical forecasting.

Expert methods are applied in all categories of management. Experts are professionals in a particular field and evaluate a situation based on their experience and intuition.

Forecasting by analogy used very often. If there is an analogy between the current situation and the previous one, you can predict how the current situation will develop.

Informal methods forecasting is based on information that is collected in different ways: verbal, written, obtained as a result of espionage.

Modeling during decision making

Simulation of situations is a widely used method to help make management decisions. Modeling involves studying a problem by building a model, studying its properties and behavior. After a comprehensive analysis of the model, the information obtained is transferred to the real situation. A model is an abstract object that is brought into line with the situation being studied.

When making decisions, use the following types of modeling:

• conceptual (models are diagrams that reflect ideas about which variables in a situation are most significant for decision making and how they interact, what are the connections between them);
• mathematical (the situation is presented in the form of a formula, a set of mathematical symbols and expressions; such models are convenient for quantitative analysis, they show the influence of elements within the situation on the final decision);
• imitation (with the help of a computer, the algorithm of operation of complex systems or objects is reproduced in time, their behavior and constituent elements are imitated; at the same time, the structure of the object is preserved, the sequence of processes is also observed).

The construction of any model includes several stages:

1. Description of the object. This is a preliminary description that is as close as possible to real parameters. This stage is the basis for subsequent descriptions.
2. Formalization of the object. Based on the description, the most important characteristics of the object that affect its operation are identified. Then the controllable parameters and those that cannot be controlled are determined. A system of constraints is identified, a diagram or mathematical function is constructed. Thus, the verbal description is replaced by an abstract (formal) and ordered one. 3. Adequacy check. Calculations are carried out, and based on their results, a decision is made on whether to apply the model in practice or to adjust the model.
3. Adjustment. Information about the object is clarified and the parameters of the abstract model are adjusted. Then the adequacy assessment is carried out again.
4. Optimization. While maintaining the adequacy parameters, they try to simplify the model. In this way, you can get a simpler model, but working on the same principles. The form of the model changes, but not the content. Main indicators for optimization: resource costs, time for research, time to make a decision using the model.

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Game theory. One of the most important variables on which the success of an organization depends is competitiveness.

Obviously, the ability to predict the actions of competitors means an advantage for any organization. Game theory is a method for modeling the impact of a decision on competitors.

Game theory was originally developed by the military so that the strategy could take into account the possible actions of the enemy. In business, game models are used to predict how competitors will react to price changes, new sales support companies, additional service offerings, modifications, and new product introductions. If, for example, management determines through game theory that competitors will not do the same if they raise prices, it may have to forgo this step to avoid being put at a competitive disadvantage.

Game theory is not used as often as other models. Unfortunately, real-world situations are often very complex and change so quickly that it is impossible to accurately predict how competitors will react to a change in a firm's tactics. However, game theory is useful when it comes to identifying the most important factors to consider in a competitive decision-making situation. This information is important because it allows management to consider additional variables or factors that may affect the situation, thereby increasing the effectiveness of the decision.

Queuing theory model. The queuing theory model or optimal service model is used to determine the optimal number of service channels in relation to the demand for them. Situations in which queuing theory models can be useful include people calling an airline to reserve a seat and obtain information, waiting in line for machine data processing, equipment repair technicians, a line of trucks to be unloaded at a warehouse, and bank customers waiting for an available teller. . If, for example, customers have to wait too long for a teller, they may decide to transfer their accounts to another bank. Likewise, if trucks have to wait too long to unload, they won't be able to complete as many trips in a day as they should. Thus, the fundamental problem is balancing the costs of additional service channels (more people to unload trucks, more cashiers, more clerks to pre-sell airline tickets) against the losses of suboptimal service (trucks will not be able to make an extra stop due to for delays in unloading, consumers go to another bank or turn to another airline due to slow service).

Queue models provide management with a tool to determine the optimal number of service channels to have to balance the costs of too few and too many service channels.

Inventory management models.

The inventory management model is used to determine the timing of placing orders for resources and their quantities, as well as the mass of finished products in warehouses.

Any organization must maintain some level of inventory to avoid delays in production and distribution.

The purpose of this model is to minimize the negative consequences of stockpiling, which is expressed in certain costs. These costs come in three main types: ordering, storage, and losses associated with insufficient inventory levels. In this case, the sale of finished products or the provision of services becomes impossible, and losses also arise from downtime of production lines, in particular due to the need to pay workers, although they are not working at the moment.

Maintaining a high level of inventory eliminates losses caused by shortages. Purchasing large quantities of materials needed to create inventories in many cases minimizes ordering costs, since the company can receive appropriate discounts and reduce the amount of paperwork. However, these potential benefits are offset by additional costs such as storage costs, reloading, interest payments, insurance costs, losses from damage, theft, etc.

Linear programming model. Used to determine the optimal way to allocate scarce resources in the presence of competing needs. Linear programming is usually used by headquarters specialists to resolve production difficulties.

Typical applications of linear programming in production management:

Integrated production planning (drawing up production schedules that minimize total costs, taking into account costs due to changes in interest rates, specified restrictions on labor resources and inventory levels);

Product range planning (determining the optimal product range, in which each type has its own costs and resource requirements);

Routing of product production (determining the optimal technological route for manufacturing a product, which must be sequentially passed through several processing centers, with each center operation characterized by its own costs and productivity);

Technological process control (minimizing the yield of chips when cutting steel, waste leather or fabric in a roll or panel);

Inventory regulation (determining the optimal combination of products in a warehouse or storage);

Production scheduling (drawing up schedules that minimize costs, taking into account the costs of maintaining inventories, paying for overtime work and external orders);

Product distribution planning (drawing up an optimal shipment schedule, taking into account the distribution of products between production plants and warehouses, warehouses and retail stores);

Determining the optimal location of a new plant (determining the best location by estimating the costs of transportation between alternative locations for the new plant and its supply and distribution locations);

Transport scheduling (minimization of costs of supplying trucks for loading and transport vessels to loading berths);

Distribution of workers (minimizing costs when distributing workers among machines and workplaces);

Materials handling (minimizing costs when routing the movement of materials handling equipment, for example, forklifts, between plant departments and delivering materials from an open warehouse to places of their processing on trucks of different carrying capacities with different fuel characteristics).

Simulation modeling. All of the models described above imply the use of simulation in a broad sense, since all are substitutes for reality. However, as a modeling technique, simulation specifically refers to the process of creating a model and its experimental application to determine changes in a real situation. The main idea of ​​simulation is to use some device to simulate a real system in order to explore and understand its properties, behaviors and characteristics. A wind tunnel is an example of a physically tangible simulation model used to test the performance of aircraft and automobiles under development. Manufacturing and finance professionals can develop models to simulate the expected productivity and profit gains that will result from new technology or changes in the composition of the workforce.

Simulation is used in situations that are too complex for mathematical methods such as linear programming. This may be due to an excessively large number of variables, difficulty in mathematically analyzing certain relationships between variables, or a high level of uncertainty.

So, simulation is often a very practical way of substituting a model for a real system or natural prototype. Experiments on real or prototype systems are expensive and time consuming, and the relevant variables cannot always be controlled. By experimenting on a model of a system, it is possible to establish how it will react to certain changes or events, while it is not possible to observe this system in reality. If the results of experimentation using a simulation model indicate that the modification leads to improvement, the manager can make the decision to implement the change in the real system with greater confidence.

Economic analysis. Almost all managers perceive simulation as a modeling method. However, many of them never thought that economic analysis - obviously the most common method - is also a form of model building. Economic analysis includes almost all methods for assessing costs and economic benefits, as well as the relative profitability of an enterprise. A typical “economic” model is based on break-even analysis, a decision-making method that determines the point at which total revenue equals total costs, i.e. the point at which the enterprise becomes profitable.

The break-even production volume can be calculated for almost every product or service if the associated costs can be determined. This could be the number of seats on an airplane that must be occupied by passengers, the number of customers in a restaurant, or the sales volume of a new type of car.

In addition to modeling, there are a number of methods that can assist a manager in finding an objectively justified decision to select from several alternatives the one that most contributes to achieving goals.

Payment matrix. The essence of every decision made by management is the choice of the best of several alternatives according to specific criteria established in advance. The payment matrix is ​​one of the methods of statistical decision theory, a method that can assist a manager in choosing one of several options. It is especially useful when a manager must determine which strategy will most contribute to achieving goals. A payoff represents a monetary reward or utility resulting from a specific strategy in combination with specific circumstances. If payments are presented in the form of a table (or matrix), we obtain a payment matrix. The words “in conjunction with the particular circumstances” are very important to understand when a payment matrix can be used and to assess when a decision made based on it is likely to be reliable. In its most general form, a matrix means that payment depends on certain events that actually occur. If such an event or state of nature does not actually occur, the payment will inevitably be different. In general, a payment matrix is ​​useful when:

There are a reasonably limited number of alternatives or strategy options to choose between;

What may happen is not known with complete certainty;

The results of a decision depend on which alternative is chosen and what events actually take place.

In addition, the manager must be able to objectively assess the probability of relevant events and calculate the expected value of such probability. A leader rarely has complete certainty, but he also rarely acts in conditions of complete uncertainty. In almost all decision-making situations, a manager must evaluate the likelihood or possibility of an event. Probability can be determined objectively, just like a roulette player does when betting on odd numbers. The choice of its value may be based on past trends or the subjective assessment of the manager, who proceeds from his own experience of acting in similar situations.

Decision tree. This is a diagrammatic representation of a decision making problem. Like the payoff matrix, the decision tree allows the manager to consider different courses of action, relate financial results to them, adjust them according to the probability assigned to them, and then compare alternatives. The concept of expected value is an integral part of the decision tree method.

A decision tree can be built for complex situations where the results of one decision affect subsequent decisions. Thus, a decision tree is a useful tool for making sequential decisions.

Many of the assumptions a manager makes relate to future conditions over which the manager has little or no control. However, these types of assumptions are necessary for many planning operations. It is clear that the better a manager can predict external and internal conditions in relation to the future, the higher the chances of drawing up feasible plans.

Forecasting. It is a method that uses both accumulated experience and current assumptions about the future to determine it.

Types of forecasts:

Economic forecasts (used to predict the general state of the economy and sales volume for a specific company or for a specific product);

Forecasts of technology development (will allow us to predict the development of what new technologies can be expected, when this can happen, how economically acceptable they can be);

Forecasts of competition development (allow you to predict the strategy and tactics of competitors);

Forecasts based on surveys and research (provide the ability to predict what will happen in complex situations using data from many areas of knowledge. For example, the future market for automobiles can only be estimated by taking into account impending changes in the state of the economy, social values, political conditions, technology and environmental standards environment from pollution);

Social forecasting (currently practiced by only a few large organizations) is used to predict changes in people's social attitudes and the state of society.

Time series analysis. Sometimes called trend projection, time series analysis is based on the assumption that what happened in the past provides a fairly good approximation of the future.

This analysis is a method of identifying patterns and trends from the past and extending them into the future. This method of analysis is often used to assess the demand for goods and services, assess the need for inventories, forecast the sales structure characterized by seasonal fluctuations, or personnel requirements.

Causal (cause-and-effect) modeling. Causal modeling is the most sophisticated and mathematically complex quantitative forecasting method used today. It is used in situations with more than one variable. Causal modeling is an attempt to predict what will happen in similar situations by examining the statistical relationship between the factors under consideration and other variables.

When the amount of information is insufficient or management does not understand a complex method, or when a quantitative model is prohibitively expensive, management may resort to qualitative forecasting models. At the same time, forecasting the future is carried out by experts who are turned to for help. The four most common qualitative forecasting methods are jury opinion, aggregate marketer opinion, consumer expectation model, and expert pricing method.

Consumer expectation model. Forecast based on the results of a survey of the organization's clients. They are asked to evaluate their own needs in the future, as well as new requirements. By collecting all the data obtained in this way and making adjustments for over- or underestimation based on his own experience, the manager is often able to accurately predict aggregate demand.

Method of expert assessments. This method is a procedure that allows a group of experts to reach consensus. Experts fill out detailed questionnaires about the problem at hand. They also write down their opinions about her. Each expert then receives a compilation of the other experts' responses and is asked to reconsider his prediction and, if it does not agree with the others' predictions, is asked to explain why this is so. The procedure is usually repeated three or four times until the experts come to a consensus. It should be noted that the same object can be represented using different models. Let's consider the most common models of management decision making.

Multiplicative factor models. Their purpose is to develop characteristics of the influence of the main factors on the development of the management decision-making situation.

Descriptive models. This type is used to describe the properties and parameters of the decision-making process in order to predict its course in the future. Its effectiveness depends on the accuracy of the description of the patterns of functioning of the control object.

Normative models. The scope of their application is the management of the decision-making process, the formation of its essential elements. They assume the activity of all participants in the decision-making process in its modeling.

Inductive models. Their peculiarity is the development of a model based on generalization of observation results on individual particular facts considered important for the decision-making process.

Deductive models. This type of model is based on a simplified system of hypothetical situations. The model is formed through the transition from an abstract management situation to its concrete manifestation. managerial economic competitiveness

Problem-oriented models. The main task in developing a model is to adapt new modeling methods to specific management processes and situations.

Decision models. This type of models is developed taking into account the possibility of conducting experiments with them and using modern management technologies. The area of ​​their application is solving the most important management problems. One is target models. They are used when there is one clearly defined goal. In this case, the goal can be either simple or complex, aggregated from several goals that are simple in structure. Multi-purpose models. The situation of their use is characterized by the presence of several independent goals that cannot be reduced to one comprehensive goal.

Single-period models. When forming them, they proceed from the fact that the totality of optimal individual decisions in individual periods of making management decisions as a whole for the entire period of solving a management problem also provides an optimal solution. However, it should be taken into account that winning at a single stage does not always lead to winnings over the entire decision-making period.

Multi-period models. These models assume a comprehensive solution to a management problem, taking into account the entire period of making a management decision.

Stochastic models. These models contain an element of uncertainty; the possible probabilistic distribution of the values ​​of factors and parameters that determine the development of the situation is taken into account.

Deterministic models. Their peculiarity lies in the unambiguous determination of all factors influencing the development of the decision-making situation at the moment of their adoption. Being simplified models, they do not allow the element of uncertainty to be taken into account fully enough. At the same time, with their help many additional factors that are not available to stochastic models can be taken into account.

When choosing one or another model for making management decisions, it should be taken into account that not a single model can take into account all the factors of the external and internal environment of the organization that influence the formation and development of the problem situation. One of the significant factors in the internal environment of an organization is its established practice of developing and making management decisions.

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Course project

Subject: “Modeling of production and economic processes”

On the topic: “Statistical modeling and forecasting”

Completed by the student

gr. No. programmer

Checked by the teacher:

INTRODUCTION

I. BASIC CONCEPTS OF THE THEORY OF MODELING ECONOMIC SYSTEMS AND PROCESSES

1Classification characteristics of modeling

1.2 Effectiveness of system modeling

II. statistical modeling and forecasting

2.1 The essence of statistical modeling

2. The essence of statistical forecasting

PRACTICAL PART

3.1 Problem statement

3.2 Problem solution

CONCLUSION

APPLICATION

INTRODUCTION

In the practice of modeling systems, we most often have to deal with objects that, in the process of their functioning, contain elements of stochasticity or are subject to stochastic influences from the external environment. Therefore, the main method for obtaining results using simulation models of such stochastic systems is the method of statistical modeling on a computer, using limit theorems of probability theory as a theoretical basis.

At the stage of research and design of systems, when constructing and implementing machine models (analytical and simulation), the statistical testing method (Monte Carlo) is widely used, which is based on the use of random numbers, i.e., possible values ​​of a certain random variable with a given probability distribution. Most economic and mathematical models are characterized by a static approach to the study of the economy, when its state is studied at a given point in time. A static economic system is understood as a system whose coordinates over the period of time being studied can be considered constant. Accordingly, when formulating a static economic-mathematical model, it is assumed that all dependencies relate to one point in time, and the modeled system is constant over time. In this case, possible (and sometimes even inevitable) changes are completely ignored, since their consideration is not required to achieve the modeling goal. In addition, it is assumed that all processes of interest occurring in the system do not require deployment in time in their description, since they can be characterized with a sufficient degree of accuracy by time-independent quantities, both known and unknown. Therefore, in the static model, time is not introduced explicitly. Static models characterize the simulated system at any fixed point in time. Such a moment can represent an entire time interval, usually as its end, middle or starting point, during which the system is assumed to remain unchanged.

In static models, a group of macroeconomic models can be distinguished. These include national-economic level models, which are designed to describe large sectors of the economy or the economy of the country as a whole. The purpose of macroeconomic modeling is to study economic laws that connect the most important and meaningful indicators. In general, the mathematical models of the national economy developed to date can be divided into two large groups:

models of economic growth (often these are dynamic models);

interindustry balance models.

Models of the 1st group operate with large-aggregate indicators (gross social product, national income, volume of fixed assets, accumulation fund, consumption fund). These models are designed to study the main trends in economic development over long periods of time (on the order of several decades). These models are often represented by production functions.

.Basic concepts of the theory of modeling economic systems and processes

1.1 Classification characteristics of modeling

Modeling (in a broad sense) is the main method of research in all fields of knowledge and a scientifically based method for assessing the characteristics of complex systems, used for decision making in various fields of engineering activity. Existing and designed systems can be effectively studied using mathematical models (analytical and simulation), implemented on modern computers, which in this case act as an experimenter’s tool with a system model.

Modeling is based on the theory of similarity, which states that absolute similarity can only occur when one object is replaced by another exactly the same. When modeling, absolute similarity does not exist and one strives to ensure that the model sufficiently well reflects the aspect of the object’s functioning under study.

The purpose of modeling at the stage of implementation and operation of complex systems is to play out possible situations in order to make informed and promising decisions on the management of an object. As one of the first signs of classification of types of modeling, you can select the degree of completeness of the model and divide the models in accordance with this sign into:

full,

·incomplete

· close associates.

The basis of complete modeling is complete similarity, which manifests itself both in time and in space.

Incomplete modeling is characterized by incomplete similarity of the model to the object being studied.

Depending on the nature of the processes being studied in system S, all types of modeling can be divided:

· deterministic;

stochastic;

· static and dynamic;

· discrete;

continuous;

· discrete-continuous.

Deterministic modeling represents deterministic processes, i.e. processes in which the absence of any random influences is assumed.

Stochastic modeling depicts probabilistic processes and events. In this case, a number of realizations of a random process are analyzed, and the average characteristics, i.e., a set of homogeneous realizations, are estimated.

Static modeling is used to describe the behavior of an object at any point in time, while dynamic modeling reflects the behavior of an object over time.

Discrete modeling is used to describe processes that are assumed to be discrete, respectively, continuous modeling allows us to reflect continuous processes in systems, and discrete-continuous modeling is used for cases when they want to highlight the presence of both discrete and continuous processes.

Depending on the form of representation of the object (system S), mental and real modeling can be distinguished.

Mental modeling is often the only way to model objects that are either practically unrealizable in a given time interval or exist outside the conditions possible for their physical creation. For example, on the basis of mental modeling, many situations in the microworld that are not amenable to physical experiment can be analyzed.

Mental modeling can be implemented as:

visual;

symbolic;

· mathematical.

With visual modeling, based on human ideas about real objects, various visual models are created that display the phenomena and processes occurring in the object.

) The basis of hypothetical modeling by the researcher is a certain hypothesis about the patterns of the process in a real object, which reflects the researcher’s level of knowledge about the object and is based on cause-and-effect relationships between the input and output of the object being studied. Hypothetical modeling is used when knowledge about an object is not enough to build formal models.

) Analog modeling is based on the use of analogies at various levels. The highest level is complete analogy, which occurs only for fairly simple objects. As the object becomes more complex, analogies of subsequent levels are used, when the analog model displays several or only one side of the object’s functioning.

) A significant place in mental visual modeling is occupied by prototyping. A mental model can be used in cases where the processes occurring in a real object are not amenable to physical modeling, or can precede other types of modeling.

The construction of mental models is also based on analogies, but usually based on cause-and-effect relationships between phenomena and processes in an object. If you introduce a conventional designation for individual concepts, i.e., signs, as well as certain operations between these signs, then you can implement sign modeling and, using signs, display a set of concepts - create separate chains of words and sentences. Using the operations of union, intersection and addition of set theory, it is possible to give a description of some real object in separate symbols.

The basis of language modeling is a thesaurus. The latter is formed from a set of incoming concepts, and this set must be fixed. It should be noted that there are fundamental differences between a thesaurus and a regular dictionary.

A thesaurus is a dictionary that is cleared of ambiguity, i.e. in it, each word can correspond to only a single concept, although in a regular dictionary several concepts can correspond to one word.

Symbolic modeling is an artificial process of creating a logical object that replaces the real one and expresses the basic properties of its relationships using a certain system of signs or symbols.

Math modeling. To study the characteristics of the process of functioning of any system S using mathematical methods, including machine methods, a formalization of this process must be carried out, i.e., a mathematical model must be built.

By mathematical modeling we mean the process of establishing a correspondence between a given real object and a certain mathematical object, called a mathematical model, and the study of this model, which makes it possible to obtain the characteristics of the real object under consideration. The type of mathematical model depends both on the nature of the real object and the tasks of studying the object and the required reliability and accuracy of solving this problem. Any mathematical model, like any other, describes a real object only with a certain degree of approximation to reality. Mathematical modeling for studying the characteristics of the process of functioning of systems can be divided into:

·analytical,

·imitation,

· combined.

Analytical modeling is characterized by the fact that the processes of functioning of system elements are written in the form of certain functional relationships or logical conditions. The analytical model can be studied using the following methods:

a) analytical, when they strive to obtain, in a general form, explicit dependencies for the desired characteristics;

b) numerical, when, not being able to solve equations in general form, they strive to obtain numerical results with specific initial data;

2 Effectiveness of system modeling

Providing the required indicators of the quality of functioning of large systems, associated with the need to study the flow of stochastic processes in the systems under study and design S, allows for a complex of theoretical and experimental studies that complement each other.

The efficiency of experimental studies of complex systems turns out to be extremely low, since conducting full-scale experiments with a real system either requires large material costs and considerable time, or is practically impossible. The effectiveness of theoretical research from a practical point of view is fully manifested only when their results, with the required degree of accuracy and reliability, can be presented in the form of analytical relationships or modeling algorithms suitable for obtaining the corresponding characteristics of the process of functioning of the systems under study.

Typically, a model is built on a hierarchical principle, when individual aspects of the functioning of an object are sequentially analyzed and when the focus of the researcher’s attention moves, the previously considered subsystems move into the external environment. The hierarchical structure of models can also reveal the sequence in which a real object is studied, namely the sequence of transition from the structural (topological) level to the functional (algorithmic) level and from the functional to the parametric.

The result of modeling largely depends on the adequacy of the initial conceptual (descriptive) model, on the obtained degree of similarity to the description of a real object, the number of implementations of the model and many other factors. In a number of cases, the complexity of an object does not allow not only to build a mathematical model of the object, but also to give a fairly close cybernetic description, and promising here is to isolate the part of the object that is most difficult to mathematically describe and include this real part of the physical object in the simulation model. Then the model is implemented, on the one hand, on the basis of computer technology, and on the other hand, there is a real part of the object. This significantly expands the capabilities and increases the reliability of the simulation results.

The simulation system is implemented on a computer and allows you to study the simulation model M, specified in the form of a certain set of individual block models and connections between them in their interaction in space and time during the implementation of any process. There are three main groups of blocks:

1.blocks characterizing the simulated process of functioning of the system S;

2.blocks displaying the external environment E and its impact on the process being implemented;

.blocks that play an auxiliary role, ensuring the interaction of the first two, as well as performing additional functions for obtaining and processing simulation results.

In addition, the simulation system is characterized by a set of variables with the help of which it is possible to control the process being studied, and a set of initial conditions when it is possible to change the conditions for conducting a machine experiment.

Thus, a simulation system is a means of conducting a machine experiment, and the experiment can be performed many times, planned in advance, and the conditions for its conduct can be determined. In this case, it is necessary to choose a method for assessing the adequacy of the results obtained and to automate both the processes of obtaining and the processes of processing results during a machine experiment.

With simulation modeling, as with any other method of analysis and synthesis of system S, the issue of its effectiveness is very important. The effectiveness of simulation modeling can be assessed by a number of criteria, including the accuracy and reliability of the modeling results, the time it takes to build and work with the M model, the cost of machine resources (time and memory), and the cost of developing and operating the model.

When characterizing the modeling problem as a whole, it is necessary to take into account that from setting the modeling problem to interpreting the results obtained, there is a large group of complex scientific and technical problems, the main ones of which include the following: identification of real objects, selection of the type of models, construction of models and their computer implementation, interaction of the researcher with the model during a machine experiment, checking the correctness of the results obtained during modeling, identifying the main patterns studied during the modeling process. Depending on the object being modeled and the type of model used, these problems may have different significance.

II Statistical modeling and forecasting

1 The essence of statistical modeling

Statistical modeling is a method of obtaining, using a computer, statistical data about the processes occurring in the simulated system. To obtain interesting estimates of the characteristics of the modeled system, taking into account the influences of the external environment, statistical data is processed and classified using methods of mathematical statistics.

Statistical modeling is a numerical method for solving mathematical problems, in which the required quantities are represented by the probabilistic characteristics of some random phenomenon, this phenomenon is modeled, after which the necessary characteristics are approximately determined by statistical processing of the “observations” of the model.

Statistical modeling is a young and promising scientific field that developed in the mid-twentieth century due to the growth of computing capabilities. The scientific direction under consideration has a lot of applications in different fields of knowledge (biology, chemistry, physics, economics, etc.), which makes its study especially relevant.

The essence of the statistical modeling method comes down to constructing for the process of functioning of the system under study a certain modeling algorithm that simulates the behavior and interaction of system elements, taking into account random input influences and influences of the external environment, and implementing this algorithm using software and hardware.

There are two areas of application of the method:

) for studying stochastic systems;

) for solving deterministic problems.

The main idea that is used to solve deterministic problems using the statistical modeling method is to replace the deterministic problem with an equivalent circuit of some stochastic system, the output characteristics of the latter coincide with the result of solving the deterministic problem. Naturally, with such a replacement, instead of an exact solution to the problem, an approximate solution is obtained and the error decreases with an increase in the number of tests (implementations of the modeling algorithm).

As a result of statistical modeling of the system, a series of partial values ​​of the desired quantities or functions is obtained, the statistical processing of which allows one to obtain information about the behavior of a real object or process at arbitrary moments in time. If the number of implementations is large enough, then the obtained system modeling results acquire statistical stability and can be accepted with sufficient accuracy as estimates of the required characteristics of the system functioning process.

The theoretical basis of the method of statistical modeling of computer systems is the limit theorems of probability theory.

Sets of random phenomena (events, quantities) are subject to certain patterns, which make it possible not only to predict their behavior, but also to quantify some of their average characteristics that exhibit a certain stability. Characteristic patterns are also observed in the distributions of random variables that are formed by adding a set of influences.

The fundamental importance of limit theorems is that they guarantee high quality statistical estimates with a very large number of tests (implementations). Quantitative estimates of system characteristics that are practically acceptable for statistical modeling can often be obtained with relatively small ones (using a computer). Statistical modeling of systems on a computer requires the generation of values ​​of random variables, which is implemented using random number sensors (generators).

When using statistical modeling, regardless of the nature of the research object (whether it will be deterministic or stochastic), it is necessary to first construct a stochastic system, the output characteristics of which allow us to evaluate the required ones.

Modeling is a multifunctional study used to determine or clarify the characteristics of existing or newly constructed objects. Its main scientific task is to reproduce a model based on its similarity to an existing object. The model must be similar to the original, but not be its complete analogue (this is the main condition), since in this case the modeling loses its meaning. The main difference between the model and the original is the ability to make flexible forecast changes that do not affect the initial data of the model.

It must be taken into account that modeling is always used together with other general scientific and special methods, based on an interdisciplinary approach, especially when it is used to study global problems that are multifaceted, i.e. covering essentially all human life activity. Modeling in such cases is a multi-module construction. It retains its essential characteristics when modeling more “narrow” problems in the social sphere: the demographic situation in the conditions of market relations (in certain specific regions); employment dynamics; the state of education, healthcare, the service sector, the housing market, etc. - since these problems, in essence, represent complex social components.

The purpose of modeling is to reproduce data assessing natural loads, the progress of an object’s operation, and also to explore its internal processes. The need for modeling arises when the study of the object itself is impossible, difficult, too expensive or takes too long - this specifically applies to social objects represented by individuals, social groups, and society as a whole.

Models, if we ignore the areas and spheres of their application, are of three types: cognitive, pragmatic and instrumental.

A cognitive model is a form of organization and presentation of knowledge, a means of connecting new and old knowledge. A cognitive model, as a rule, is adjusted to reality and is a theoretical model.

A pragmatic model is a means of organizing practical actions, a working representation of the goals of the system for its management. Reality in them is adjusted to some pragmatic model. These are usually applied models.

An instrumental model is a means of constructing, researching and/or using pragmatic and/or cognitive models.

Cognitive ones reflect existing ones, and pragmatic ones - although not existing ones, but desirable and, possibly, feasible relationships and connections.

According to the level, “depth” of modeling, models are:

· empirical - based on empirical facts, dependencies;

· theoretical - based on mathematical descriptions;

· mixed, semi-empirical - based on empirical dependencies and mathematical descriptions.

Simulation functions:

) deepening knowledge of existing systems and objects;

) determination of the main parameters, ways of their subsequent application;

)carrying out a comparative analysis of the original and the model, determining quality characteristics.

Modeling also performs important heuristic functions: it identifies negative trends, identifies positive ways to solve problems, and offers alternative options.

Modeling must meet certain requirements:

To be the simplest, most convenient, to provide information about the object, to contribute to the improvement of the object itself.

Contribute to the definition or simplification of the characteristics of an object, the rationalization of ways of constructing, managing or knowing it.

2 The essence of statistical forecasting

In the process of economic reform, the demand for predictive studies of socio-economic processes at various levels of management and decision-making is increasingly increasing. The correct choice of solution is directly dependent on the quality of its justification. Forecasting is one of the management functions, along with analysis, organization, planning, motivation, etc. Active consumers of forecast developments are millions of market agents, households, state and territorial authorities. In a democratic society, it is necessary to present alternative options for the development of society, the opportunities that exist for each participant in market relations.

To date, sufficient experience and a set of tools have been accumulated for both long-term and short-term forecasting. Forecasting is a scientifically based prediction of the most probable state, trends and features of the development of a managed object in the long-term period based on the identification and correct assessment of stable connections and dependencies between the past, present and future. A distinctive feature of forecasting is that it substantiates the emergence of such processes and forms of the material and spiritual life of society that are currently inaccessible to direct perception, as well as testing in practice.

Forecasting makes it possible to reveal stable trends, or, conversely, significant changes in socio-economic processes, assess their likelihood for the future planning period, identify possible alternative options, accumulate scientific and empirical material for an informed choice of a particular development concept or planning decision.

Thus, forecasting is a special scientific study of the prospects for the development of phenomena.

Forecasting is not about trying to predict the details of the future, although in some cases this is essential. In this case, the researcher proceeds from the dialectical determination of the phenomena of the future, from the understanding that necessity makes its way through overcoming chance, that a probabilistic approach is needed to the phenomena of the future, taking into account a wide range of possible options. Only with this approach can forecasting be effectively used to select the most likely or most desirable, optimal option when justifying a goal, plan, program, project, or decision in general.

Forecasts must precede plans, contain an assessment of the course of the consequences of the implementation (or non-fulfillment) of plans, and cover everything that cannot be planned or decided. They can cover, in principle, any period of time. A forecast and a plan differ in the way they handle information about the future. A probabilistic description of what is possible or desirable is a forecast.

An informed decision regarding measures to achieve the possible and desirable is a plan. The forecast and plan can be developed independently of each other. But for a plan to be effective and optimal, it must be preceded by a forecast, if possible continuous,

allowing to justify this and subsequent plans.

One of the important areas of forecasting social development is socio-economic forecasting - a scientific discipline whose object is the socio-economic system, and the subject is the knowledge of the possible states of functioning objects in the future, the study of patterns and methods for developing economic forecasts.

Socio-economic forecasting is based on the achievements of science in the field of knowledge of the patterns of social development, clarification of trends in socio-economic and technological progress.

Forecasting is closely related to statistics and is largely based on statistical data and methods for studying mass phenomena.

The main criterion for the typology of forecasts is functional, from the point of view of which forecasts are divided into two main types: search and target forecasts.

Normative forecast is the determination of ways and deadlines for achieving possible states of a phenomenon, taken as a goal. This forecast answers the question: what ways to achieve what you want?

A search forecast is built on a certain scale (field, spectrum) of possibilities, on which the degree of probability of the predicted phenomenon is then established. With normative forecasting, the same probability distribution occurs, but in the reverse order: from a given state to observed trends.

According to the scale of forecasting, there are: macroeconomic (national economy) and structural (intersectoral, intersectoral, interregional forecasts, forecasts for the development of individual complexes, sectors and regions, forecasts of economic entities, as well as individual industries and products. Note that macroeconomic objects are more stable and inertial in its development in comparison with objects of microeconomics.

3 Statistical modeling methods

Modeling is a logical and mathematical representation of the structure and process of functioning of the planned object with the aim of conducting an experiment using this model. The essence of modeling is to create an analogue of the objects under study, which reflects all their most important properties from the point of view of the purpose of the study and omits secondary, unimportant features.

New methods are widely used in planning, usually by large companies. They are based on the use of economic and mathematical models. In order to correctly apply these methods in planning, managers and planners must know the areas of their use and limitations at various stages of planning when solving specific problems.

Modeling methods include the following models:

Matrix models. These include:

a) static models of inter-industry balance. Designed for carrying out forecast macroeconomic calculations for a short-term period (year, quarter, month).

b) dynamic models of inter-industry balance. Designed for calculating economic development for the long term, reflecting the reproduction process in dynamics, and linking the forecast of production of products (services) with investments.

Optimal planning models. They are based on economic and mathematical models, which consist of an objective function and a system of restrictions.

The objective function describes the optimization goal and represents the dependence of the indicator used for optimization on independent variables.

At the macro level, the optimality criterion is the maximum gross national product. At the micro level - maximum profit, minimum costs, maximum output of products (services), etc. The system of restrictions reflects objective economic connections and dependencies and represents a system of equalities and inequalities.

Economic and statistical models. There are:

a) single-factor, allow you to take into account the impact of one factor on the level of the predicted indicator;

b) multifactorial, they allow you to simultaneously take into account the impact of several factors on the level of the predicted indicator. They are used to forecast demand for products, costs, prices, profits and other indicators.

c) econometric models, used to describe complex socio-economic processes (GNP, personal income, consumption of goods and services, etc.). 3 Simulation models. The essence is to create a model of a real economic situation and manipulate it with various parameters of controlled variables in order to justify the development of a forecasting or planning object.

They are used to distribute capital investments in conditions of possible risk and other cases.

The most famous models are Jay Forrester's "Industrial Dynamics", which covers the entire production and economic process, and the Monte Carlo model - used when modeling any process.

Decision-making models. Based on game theory. They are used in conditions of uncertainty or situations where the interests of the parties do not coincide. Each party chooses a strategy of action that, from their point of view, ensures the greatest gain or the least loss. Moreover, it is clear to each of the parties that the result depends not only on their own actions, but also on the actions of competitors.

Network planning models. It is based on the construction of a network diagram depicting a complex of interrelated works and the sequence of stages necessary to achieve a predetermined goal.

They are used to reduce the time required to complete complex projects and other work. An example of network planning models is the PERT-time, PERT-cost method.

When statistically modeling systems, one of the main issues is taking into account stochastic influences. The number of random numbers used to obtain a statistically stable estimate of the characteristics of the functioning process of the system S when implementing a modeling algorithm on a computer varies within fairly wide limits depending on the class of the modeling object, the type of characteristics being assessed, the required accuracy and reliability of the modeling results. The method of statistical modeling on a computer is characterized by the fact that a large number of operations, and, accordingly, a large proportion of computer time are spent on operations with random numbers. In addition, the results of statistical modeling significantly depend on the quality of the original (base) random number sequences. Therefore, the availability of simple and economical methods for generating sequences of random numbers of the required quality largely determines the possibility of practical use of machine modeling of systems.

2.4 Statistical forecasting methods

Some scientists estimate that there are more than 150 forecasting methods. There are much fewer basic methods; many of the “methods” rather refer to individual methods and procedures for forecasting, or are a set of individual techniques that differ from the basic methods in the number of private techniques and the sequence of their application.

The forecasting method is understood as a set of techniques and ways of thinking that allow, based on the analysis of retrospective data, exogenous (external) and endogenous (internal) connections of the forecast object, as well as their measurements within the framework of the phenomenon or process under consideration, to derive judgments of a certain reliability regarding the future development of the object. Based on the degree of formalization, economic forecasting methods can be divided into intuitive and formalized.

Intuitive methods are based on intuitive-logical thinking. They are used in cases where it is impossible to take into account the influence of many factors due to the significant complexity of the forecast object or the object is too simple and does not require labor-intensive calculations. It is advisable to use such methods in other cases in combination with formalized methods to increase the accuracy of forecasts.

Among intuitive methods, methods of expert assessments have become widespread. They are used both in our country and abroad to obtain forecast estimates of production development, scientific and technological progress, resource efficiency, etc.

Methods of historical analogies and model forecasting are also used. A kind of extrapolation takes place here. The forecasting technique consists of analyzing a highly developed system (country, region, industry) of the same approximate level, which is now available in a less developed similar system, and based on the history of the development of the process under study in the highly developed system, a forecast is constructed for the less developed system. Practice shows that such analogies can be used in determining the development paths of new industries and types of equipment (production of computers, televisions, etc.), the structure of production, consumption, etc. Naturally, the “sample” obtained in this way is only the starting point for forecasting. A final conclusion can be reached only by examining the internal conditions and patterns of development.

Formalized methods include extrapolation methods and modeling methods. They are based on mathematical theory.

Among extrapolation methods, the function selection method based on the least squares method (LSM) has become widespread. In modern conditions, increasing importance has been attached to modifications of the least squares method: the method of exponential smoothing with an adjustable trend and the method of adaptive smoothing.

Modeling methods involve the use of various kinds of economic and mathematical models in the process of forecasting and planning, which are a formalized description of the economic process (object) under study in the form of mathematical dependencies and relationships. The following models are distinguished: matrix, optimal planning, economic-statistical (trend, factor, econometric), simulation, decision-making. To implement economic and mathematical models, economic and mathematical methods are used.

In the practice of forecasting and planning, the method of economic (systemic) analysis, normative and balance methods are also widely used. To develop targeted complex programs, the program-target method (PTM) is used in combination with other methods. It should be noted that the presented list of methods and their groups is not exhaustive. Let's consider methods that have become widespread in world practice.

Expert assessment methods

The main idea of ​​forecasting based on expert assessments is to build a rational procedure for a person’s intuitive and logical thinking in combination with quantitative methods for assessing and processing the results obtained.

The essence of expert assessment methods is that the forecast is based on the opinion of a specialist or a team of specialists, based on professional, scientific and practical experience. There are individual and collective expert assessments.

There are formal and predictive extrapolation. The formal one is based on the assumption that past and present trends in the development of the forecast object will be preserved in the future; in forecasting, actual development is linked to hypotheses about the dynamics of the process under study, taking into account changes in the influence of various factors in the future. It should be noted that extrapolation methods must be applied at the initial stage of forecasting to identify trends in changes in indicators.

3. PRACTICAL PART

3.1 Problem statement

statistical modeling forecasting

Using the balance planning method and the Leontiev model, build a balance of production and distribution of enterprise products.

An industrial group of enterprises (holding) produces three types of products, with each of the three enterprises of the group specializing in the production of one type: the first enterprise specializes in the production of the first type of product; the second enterprise - products of the second type; the third enterprise - products of the third type. Part of the products produced is consumed by the holding's enterprises (for internal consumption), the rest is supplied outside its borders (to external consumers, is the final product). Specialists of the management company obtained economic estimates aij (i=1,2,3; j=1,2,3) of the elements of technological matrix A (consumption rates, direct material cost coefficients) and elements yi of the final product vector Y.

Required:

.Check the productivity of the technological matrix A=(aij) (matrix of direct material cost coefficients).

2.Build a balance (fill in the table) of production and distribution of products of the holding enterprises.

Enterprise (types of products) Direct cost coefficients aij Final product Y12310,20,3012020,30,10,225030,100,3180

3.2 Problem solution

1) Check the productivity of the technological matrix A=(aij) (matrix of direct material cost coefficients).

1. To solve this economic problem, the MS Excel spreadsheet environment will be chosen.

Appendix 1 (Fig. 1.1)

2. Find the difference between the identity matrix E and matrix A.

To do this, we will use the rule of subtracting matrices of the same dimension.

0.8-0.3-0.1E-A-0.30.9-0.2-0.100.7

1.3. Let's find the inverse matrix. Let's use the built-in functions of MS Excel (mathematical, inverse matrix)

Appendix 1 (Fig. 1.2)

1.4. To determine the Gross Product (matrix), you need to multiply the matrix by the Final Product (matrix). Let's again use the built-in functions of MS Excel (mathematical, matrix multiplication).

Appendix 1 (Fig. 1.3)

1.5. The matrix (matrix of direct material cost coefficients) is productive because there is a non-negative vector.

2) Build a balance (fill out the table) of production and distribution of products of the holding enterprises.

1. To distribute the products of the holding enterprises, it is necessary to find

Appendix 1 (Fig. 1.4)

2.2. Let's build an inter-industry balance of production.

Appendix 1 (Fig. 1.5)

Conditionally net production is the difference between the gross product and the sum of products consumed by each industry.

) The matrix (matrix of direct material cost coefficients) is productive because there is a non-negative vector.

Appendix 1 (Fig. 1.6)

CONCLUSION

Static models include most linear programming problems (maximizing output in a given assortment, the problem of diet, optimal assignments, cutting materials, and many others).

In the case of using productive functions, the economy is considered as a “black box”, the structure of which is unknown. It follows that in this model the economy acts as an integral unstructured unit, the input of which is resources, and the output, as a result of functioning, is gross output or gross domestic product. Resources are treated as inputs and gross output or gross domestic product as a function.

When creating a model of a process or object, you have to consider all components with varying degrees of detail. Excessive detail in this case does not contribute to a more accurate and adequate analysis of the economic phenomenon, but only makes the model more cumbersome and makes it difficult to obtain a solution. Consequently, the level of detail in the description of the economic phenomenon reflected in the model must be necessary and sufficient to adequately reflect reality and correspond to the stated goals of the modeling. Most often we have to move to larger components and units. For example, when modeling the work of an enterprise, it is advisable to consider workshops, and not production areas, as production units, and when modeling a workshop, sections, and not workplaces. Therefore, one of the principles that should be followed is to present the description of the model components with the same level of detail. On the other hand, all information that is of interest from the point of view of the purpose of the modeling should be presented with the maximum degree of detail - this is the principle of targeted information presentation. These two principles together determine the general essence of the necessary and sufficient degree of detail in the descriptions of economic objects in the model in accordance with the goals and objectives of the modeling.

In static models, a group of macroeconomic models can be distinguished. These include national-economic level models, which are designed to describe large sectors of the economy or the economy of the country as a whole.

Most economic and mathematical models are static. This point of view is so ingrained in the minds of most economists that the model is almost always considered static, and if this is not the case, then only then is it stated that the model is dynamic. In fact, a wide variety of problems of economic analysis and planning naturally lead to static models, which allow the problem to be formulated with a strictly fixed structure of the system being modeled. Since static models in a formalized form do not contain the time factor, they are always simpler than dynamic models of the same economic systems that take this factor into account with varying degrees of completeness. Therefore, for economic and mathematical modeling, a typical situation is when static models are first developed, and then they are complicated by the introduction of the time factor, i.e., they are transformed into dynamic ones. In particular, initially static models were the inter-industry balance, various models that could be reduced to the transport problem and the distribution problem of linear programming, to problems about flows in networks, etc. Subsequently, dynamic analogues and generalizations were developed for all these models. However, complication does not always turn out to be productive, even in cases where the dynamic aspect of the modeled system is not indifferent for the purpose of modeling.

Accordingly, when formulating a static economic-mathematical model, it is assumed that all dependencies relate to one point in time, and the modeled system is constant over time. In this case, possible (and sometimes even inevitable) changes are completely ignored, since their consideration is not required to achieve the modeling goal. In addition, it is assumed that all processes of interest occurring in the system do not require deployment in time in their description, since they can be characterized with a sufficient degree of accuracy by time-independent quantities, both known and unknown. Therefore, in the static model, time is not introduced explicitly. Static models characterize the simulated system at any fixed point in time. Such a moment can represent an entire time interval, usually as its end, middle or starting point, during which the system is assumed to remain unchanged.

A static economic system is understood as a system whose coordinates over the period of time being studied can be considered constant.

LIST OF REFERENCES USED

Basic

1. Akulich I.L. Mathematical programming in examples and problems. - M.: Higher School, 1986.

2. Vlasov M.P., Shimko P.D. Modeling of economic processes. - Rostov-on-Don, Phoenix - 2005 (electronic textbook)

3. Yavorsky V.V., Amirov A.Zh. economic informatics and information systems (laboratory workshop) - Astana, Foliant, 2008

4.Simonovich S.V. Informatics, St. Petersburg, 2003

5. Vorobiev N.N. Game theory for economists - cyberneticists. - M.: Nauka, 1985 (electronic textbook)

6.Alesinskaya T.V. Economic and mathematical methods and models. - Tagan Rog, 2002 (electronic textbook)

7.Gershgorn A.S. Mathematical programming and its application in economic calculations. -M. Economics, 1968

Additionally

1.Darbinyan M.M. Inventories in trade and their optimization. - M. Economics, 1978

2.Johnston D.J. Economic methods. - M.: Finance and Statistics, 1960.

3.Epishin Yu.G. Economic and mathematical methods and planning of consumer cooperation. - M.: Economics, 1975

4. Zhitnikov S.A., Birzhanova Z.N., Ashirbekova B.M. Economic and mathematical methods and models: Textbook. - Karaganda, KEU publishing house, 1998

5. Zamkov O.O., Tolstopyatenko A.V., Cheremnykh Yu.N. Mathematical methods in economics. - M.: DIS, 1997.

6.Ivanilov Yu.P., Lotov A.V. Mathematical methods in economics. - M.: Science, 1979

7. Kalinina V.N., Pankin A.V. Math statistics. M.: 1998

8.Kolemaev V.A. Mathematical Economics. M., 1998

9.Kremer N.Sh., Putko B.A., Trishin I.M., Fridman M.N. Operations research in economics. Textbook - M.: Banks and exchanges, UNITY, 1997

10. Spirin A.A., Fomin G.P. Economic and mathematical methods and models in trade. - M.: Economics, 1998

.#"justify">Appendix 1

Initial data

Determination of gross output (matrix)

Distribution of products of the holding enterprises

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