Simulation modeling of economic systems. Simulation modeling of economic processes

In modern literature one can find several points of view on what simulation modeling is. Some argue that these are mathematical models in the classical sense, others believe that these are models in which random processes are simulated, and others suggest that simulation models differ from ordinary mathematical ones in a more detailed description. However, everyone agrees that simulation is applied to processes in which humans may intervene from time to time. Methods for analyzing the development of situations based on varying the values ​​of various factors that determine these situations have become increasingly widespread.

The meaning of this variation is as follows. The activities of any business entity depend on many factors, the vast majority of which are interrelated; at the same time, some factors are amenable to certain regulation, and from here, by varying the set of key parameters or their values, it is possible to simulate various situations and, thanks to this, choose the most acceptable scenario for the development of events.

One of the difficulties in implementing this approach is the routineness of actions and the multiplicity of counting operations; this difficulty is eliminated by using a computer and an appropriate software within the framework of the so-called simulation modeling.

Simulation modeling - This is a formalized method (mathematics can be applied). The word "imitation" (from Lat. imatatio) means “imitation of someone or something, reproduction with possible accuracy.”

The essence of simulation modeling is as follows: a specific economic situation is simulated in a computer environment. After making several calculations, you can select a set of parameters and their values, which you then try to manage (for example, accounts receivable should not go beyond a given corridor, obtaining a certain amount of profit).

Simulation modeling of financial and economic activities is based on a combination of formalized (mathematical) methods and expert assessments specialists and managers of an economic entity, with the latter prevailing.

The simulation process is as follows: first, a mathematical model of the object under study (simulation model) is built, then this model is converted into a computer program. In the process of work, the indicators of interest to the researcher change: they are subject to analysis, in particular statistical processing.

A simulation model is used, on the one hand, in cases where the model (and therefore the system, process, phenomenon it reflects) is too complex to allow the use of conventional analytical solution methods. For many problems of management and economics, this situation is inevitable: for example, even such well-established methods as linear programming, in some cases, provide a solution that is too far from reality and it is impossible to draw reasonable conclusions from the results obtained. The choice itself between a simulation (numerical) or an analytical solution to a particular economic problem is not always an easy problem.

On the other hand, imitation is used when a real economic experiment is impossible or too complicated for one reason or another. Then it acts as a replacement for such an experiment. But even more valuable is its role as a preliminary stage, an “estimate”, which helps to make a decision about the need and possibility of conducting a real experiment. Using static simulation, it is possible to identify at what combinations of input factors the optimal result of the process being studied is achieved, and to establish the relative importance of certain factors. This is useful, for example, when studying various methods and means of economic incentives in production.

Simulation modeling is also used in forecasting, since it “reduces time” and, in particular, allows, in a matter of hours, to reproduce on a computer (in aggregated terms) the development of an enterprise or a branch of the national economy for months and even years in advance.

IN Lately widely used imitation of economic processes, in which various interests such as competition in the market collide. As the business game progresses, certain decisions are made, for example: “increase prices”, “increase or decrease production output”, etc., and calculations show which of the “competing” parties is doing better and which is doing worse. Simulation modeling of economic processes is essentially an experiment, but not in real, but in artificial conditions.

The criterion for the adequacy of a model is practice. When constructing a mathematical model of a complex system, difficulties may arise when the model contains many connections between elements, it has various nonlinear constraints, and a large number of parameters. Real systems are often influenced by various random factors that are difficult to take into account, so comparison of the model and the original in this case is only possible at the beginning. To overcome these difficulties, it is necessary to take into account the following rules when using simulation modeling:

• - clearly formulate the main questions on the behavior of a complex system, the answers to which we want to receive;
• - break down the system into simpler parts - blocks;
• - formulate laws and hypotheses regarding the behavior of the system and its parts;
• - depending on the questions posed, enter the system time, simulating the passage of time in a real system.

Course project

Subject: “Modeling of production and economic processes”

On the topic: “Simulation modeling of economic processes”

Introduction

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

1 Concept of modeling

1.2 Concept of a model

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

2.1 Improvement and development of economic systems

2 Components of a simulation model

III. Simulation Basics

3.1 Simulation model and its features

2 The essence of simulation modeling

IV. Practical part

1 Problem statement

2 Problem solution

Conclusion

List of used literature

Application

Introduction

Simulation modeling, linear programming and regression analysis have long occupied the top three places among all methods of operations research in economics in terms of range and frequency of use. In simulation modeling, the algorithm that implements the model reproduces the process of system functioning in time and space, and the elementary phenomena that make up the process are simulated while preserving its logical time structure.

Currently, modeling has become a fairly effective means of solving complex problems of automation of research, experiments, and design. But to master modeling as a working tool, its wide capabilities and further develop the modeling methodology is possible only with full mastery of the techniques and technology for practical solution of problems of modeling the processes of functioning of systems on a computer. This is the goal of this workshop, which focuses on the methods, principles and main stages of modeling within the framework of the general modeling methodology, and also examines the issues of modeling specific variants of systems and instills skills in using modeling technology in the practical implementation of models of system functioning. The problems of queuing systems on which simulation models of economic, information, technological, technical and other systems are based are considered. Methods for probabilistic modeling of discrete and random continuous variables are outlined, which make it possible to take into account random impacts on the system when modeling economic systems.

The demands that modern society places on a specialist in the field of economics are steadily growing. Currently, successful activity in almost all spheres of the economy is not possible without modeling the behavior and dynamics of development processes, studying the features of the development of economic objects, and considering their functioning in various conditions. Software and hardware should become the first assistants here. Instead of learning from your own mistakes or from the mistakes of other people, it is advisable to consolidate and test your knowledge of reality with the results obtained on computer models.

Simulation modeling is the most visual and is used in practice for computer modeling of options for resolving situations in order to obtain the most effective solutions to problems. Simulation modeling allows for the study of the analyzed or designed system according to the scheme of operational research, which contains interrelated stages:

· development of a conceptual model;

· development and software implementation of a simulation model;

· checking the correctness and reliability of the model and assessing the accuracy of the modeling results;

· planning and conducting experiments;

· making decisions.

This allows simulation to be used as universal approach for making decisions under conditions of uncertainty, taking into account factors that are difficult to formalize in models, and also apply basic principles systematic approach for solving practical problems.

The widespread implementation of this method in practice is hampered by the need to create software implementations of simulation models that recreate the dynamics of the functioning of the simulated system in simulated time.

Unlike traditional programming methods, developing a simulation model requires a restructuring of the principles of thinking. It is not without reason that the principles underlying simulation modeling gave impetus to the development of object programming. Therefore, the efforts of simulation software developers are aimed at simplifying software implementations of simulation models: specialized languages ​​and systems are created for these purposes.

Simulation software has evolved over several generations, from modeling languages ​​and model design automation tools to program generators, interactive and intelligent systems, distributed modeling systems. The main purpose of all these tools is to reduce the labor intensity of creating software implementations of simulation models and experimenting with models.

One of the first modeling languages ​​to facilitate the process of writing simulation programs was the GPSS language, created as a final product by Jeffrey Gordon at IBM in 1962. Currently there are translators for DOS operating systems - GPSS/PC, for OS/2 and DOS - GPSS/H and for Windows - GPSS World. Studying this language and creating models allows you to understand the principles of developing simulation programs and learn how to work with simulation models. (General Purpose Simulation System - a general purpose modeling system) is a modeling language that is used to build event-driven discrete simulation models and conduct experiments using a personal computer.

The GPSS system is a language and a translator. Like every language, it contains a vocabulary and grammar with the help of which models of systems of a certain type can be developed.

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

1.1 Concept of modeling

Modeling refers to the process of constructing, studying and applying models. It is closely related to such categories as abstraction, analogy, hypothesis, etc. The modeling process necessarily includes the construction of abstractions, inferences by analogy, and the construction of scientific hypotheses.

The main feature of modeling is that it is a method of indirect cognition using proxy objects. The model acts as a kind of cognition tool that the researcher puts between himself and the object, and with the help of which he studies the object of interest to him. Any socio-economic system is a complex system in which dozens and hundreds of economic, technical and social processes interact, constantly changing under the influence of external conditions, including scientific and technological progress. In such conditions, managing socio-economic and production systems turns into a complex task that requires special means and methods. Modeling is one of the main methods of cognition, is a form of reflection of reality and consists in finding out or reproducing certain properties of real objects, objects and phenomena with the help of other objects, processes, phenomena, or using an abstract description in the form of an image, plan, map , a set of equations, algorithms and programs.

In the most general sense, a model is a logical (verbal) or mathematical description of components and functions that reflect the essential properties of the object or process being modeled, usually considered as systems or elements of a system from a certain point of view. The model is used as a conventional image, designed to simplify the study of the object. In principle, not only mathematical (symbolic) but also material models are applicable in economics, but material models have only demonstrative value.

There are two points of view on the essence of modeling:

This is the study of objects of knowledge using models;

This is the construction and study of models of real-life objects and phenomena, as well as supposed (constructed) objects.

The possibilities of modeling, that is, transferring the results obtained during the construction and research of the model to the original, are based on the fact that the model in a certain sense displays (reproduces, models, describes, imitates) some features of the object that are of interest to the researcher. Modeling as a form of reflection of reality is widespread, and a fairly complete classification possible types modeling is extremely difficult, if only due to the polysemy of the concept “model”, which is widely used not only in science and technology, but also in art and in everyday life.

The word “model” comes from the Latin word “modulus”, meaning “measure”, “sample”. Its original meaning was associated with the art of building, and in almost all European languages ​​it was used to denote an image or prototype, or a thing similar in some respect to another thing.

Among socio-economic systems, it is advisable to highlight the production system (PS), which, unlike systems of other classes, contains as the most important element a consciously acting person performing management functions (decision making and control). In accordance with this, various divisions of enterprises, enterprises themselves, research and design organizations, associations, industries and, in some cases, the national economy as a whole can be considered as PS.

The nature of the similarity between the modeled object and the model differs:

Physical - the object and the model have the same or similar physical nature;

Structural - there is a similarity between the structure of the object and the structure of the model; functional - the object and the model perform similar functions under appropriate influence;

Dynamic - there is a correspondence between the sequentially changing states of the object and the model;

Probabilistic - there is a correspondence between processes of a probabilistic nature in the object and the model;

Geometric - there is a correspondence between the spatial characteristics of the object and the model.

Modeling is one of the most common ways to study processes and phenomena. Modeling is based on the principle of analogy and allows you to study an object under certain conditions and taking into account the inevitable one-sided point of view. An object that is difficult to study is studied not directly, but through consideration of another, similar to it and more accessible - a model. Based on the properties of the model, it is usually possible to judge the properties of the object being studied. But not about all properties, but only about those that are similar both in the model and in the object and at the same time are important for research.

Such properties are called essential. Is there a need for mathematical modeling of the economy? In order to verify this, it is enough to answer the question: is it possible to complete a technical project without having an action plan, i.e., drawings? The same situation occurs in the economy. Is it necessary to prove the need to use economic and mathematical models for making management decisions in the economic sphere?

Under these conditions, the economic-mathematical model turns out to be the main means of experimental research in economics, since it has the following properties:

Simulates a real economic process (or the behavior of an object);

Has a relatively low cost;

Can be reused;

Takes into account various operating conditions of the object.

The model can and should reflect the internal structure of an economic object from given (certain) points of view, and if it is unknown, then only its behavior, using the “Black Box” principle.

Fundamentally, any model can be formulated in three ways:

As a result of direct observation and study of the phenomena of reality (phenomenological method);

Isolation from a more general model (deductive method);

Generalizations of more particular models (inductive method, i.e. proof by induction).

Models, endless in their diversity, can be classified according to a variety of criteria. First of all, all models can be divided into physical and descriptive. We deal with both of them all the time. In particular, descriptive models include models in which the modeled object is described using words, drawings, mathematical dependencies, etc. Such models include literature, fine arts, and music.

Economic and mathematical models are widely used in managing business processes. There is no established definition of an economic-mathematical model in the literature. Let's take the following definition as a basis. Economic-mathematical model is a mathematical description of an economic process or object, carried out for the purpose of their study or management: mathematical notation economic problem being solved (therefore, the terms problem and model are often used as synonyms).

Models can also be classified according to other criteria:

Models that describe the momentary state of the economy are called static. Models that show the development of the modeled object are called dynamic.

Models that can be built not only in the form of formulas (analytical representation), but also in the form of numerical examples (numerical representation), in the form of tables (matrix representation), in the form of a special kind of graphs (network representation).

2 Concept of model

The region cannot be named at this time human activity, in which modeling methods would not be used to one degree or another. Meanwhile, there is no generally accepted definition of the concept of model. In our opinion, the following definition deserves preference: a model is an object of any nature that is created by a researcher in order to obtain new knowledge about the original object and reflects only the essential (from the developer’s point of view) properties of the original.

Analyzing the content of this definition, we can do the following conclusions:

) any model is subjective, it bears the stamp of the researcher’s individuality;

) any model is homomorphic, i.e. it does not reflect all, but only the essential properties of the original object;

) it is possible that there are many models of the same original object, differing in the purposes of the study and the degree of adequacy.

A model is considered adequate to the original object if it, with a sufficient degree of approximation at the level of understanding of the simulated process by the researcher, reflects the patterns of the functioning of a real system in the external environment.

Mathematical models can be divided into analytical, algorithmic (simulation) and combined. Analytical modeling is characterized by the fact that systems of algebraic, differential, integral or finite-difference equations are used to describe the processes of system functioning. 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;

c) qualitative, when, without having an explicit solution, one can find some properties of the solution (for example, assess the stability of the solution). In algorithmic (simulation) modeling, the process of system functioning over time is described, and the elementary phenomena that make up the process are simulated, preserving their logical structure and sequence of occurrence over time. Simulation models can also be deterministic and statistical.

The general goal of modeling in the decision-making process was formulated earlier - this is the determination (calculation) of the values ​​of the selected performance indicator for various strategies for conducting an operation (or options for implementing the designed system). When developing a specific model, the purpose of the modeling should be clarified taking into account the effectiveness criterion used. Thus, the purpose of modeling is determined both by the purpose of the operation being studied and by the planned method of using the research results.

For example, a problem situation that requires a decision is formulated as follows: find an option for building a computer network that would have the minimum cost while meeting the performance and reliability requirements. In this case, the goal of modeling is to find network parameters that provide the minimum PE value, which is represented by cost.

The task can be formulated differently: from several options for computer network configuration, choose the most reliable one. Here, one of the reliability indicators (mean time between failures, probability of failure-free operation, etc.) is selected as the PE, and the purpose of the modeling is a comparative assessment of network options according to this indicator.

The above examples allow us to recall that the choice of performance indicator itself does not yet determine the “architecture” of the future model, since at this stage its concept has not been formulated, or, as they say, the conceptual model of the system under study has not been defined.

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

2.1 Improvement and development of economic systems

Simulation modeling is the most powerful and universal method for studying and assessing the effectiveness of systems whose behavior depends on the influence of random factors. Such systems include an aircraft, a population of animals, and an enterprise operating in conditions of poorly regulated market relations.

Simulation modeling is based on a statistical experiment (Monte Carlo method), the implementation of which is practically impossible without the use of computer technology. Therefore, any simulation model is ultimately a more or less complex software product.

Of course, like any other program, a simulation model can be developed in any universal programming language, even in Assembly language. However, in this case the following problems arise on the developer's path:

It requires knowledge not only of the subject area to which the system under study belongs, but also of the programming language, and at a fairly high level;

The development of specific procedures for ensuring a statistical experiment (generation of random influences, planning of an experiment, processing of results) can take no less time and effort than developing the system model itself.

And finally, one more, perhaps the most important problem. In many practical problems, interest is not only (and not so much) in the quantitative assessment of the effectiveness of the system, but in its behavior in a given situation. For such observation, the researcher must have appropriate “observation windows” that could, if necessary, be closed, moved to another location, changed the scale and form of presentation of the observed characteristics, etc., without waiting for the end of the current model experiment. In this case, the simulation model acts as a source of answer to the question: “what will happen if...”.

Implementing such capabilities in a universal programming language is very difficult. Currently, there are quite a lot of software products that allow you to simulate processes. Such packages include: Pilgrim, GPSS, Simplex and a number of others.

At the same time, there is currently a product on the Russian computer technology market that allows one to very effectively solve these problems - the MATLAB package, which contains the visual modeling tool Simulink.

Simulink is a tool that allows you to quickly simulate a system and obtain indicators of the expected effect and compare them with the effort required to achieve them.

There are many different types of models: physical, analog, intuitive, etc. A special place among them is occupied by mathematical models, which, according to Academician A.A. Samarsky, “are the greatest achievement of the scientific and technological revolution of the 20th century.” Mathematical models are divided into two groups: analytical and algorithmic (sometimes called simulation).

Currently, it is impossible to name an area of ​​human activity in which modeling methods would not be used to one degree or another. Economic activity is no exception. However, in the field of simulation modeling of economic processes, some difficulties are still observed.

In our opinion, this circumstance is explained by the following reasons.

Economic processes occur largely spontaneously and uncontrollably. They do not respond well to attempts at strong-willed control on the part of political, government and economic leaders of individual industries and the country’s economy as a whole. For this reason, economic systems are difficult to study and formally describe.

Specialists in the field of economics, as a rule, have insufficient mathematical training in general and in mathematical modeling in particular. Most of them do not know how to formally describe (formalize) observed economic processes. This, in turn, does not allow us to establish whether this or that mathematical model is adequate for the economic system under consideration.

Specialists in the field of mathematical modeling, without having at their disposal a formalized description of the economic process, cannot create a mathematical model adequate to it.

Existing mathematical models, which are commonly called models of economic systems, can be divided into three groups.

The first group includes models that quite accurately reflect one aspect of a certain economic process occurring in a system of a relatively small scale. From a mathematical point of view, they represent very simple relationships between two or three variables. Usually these are algebraic equations of the 2nd or 3rd degree, in extreme cases a system of algebraic equations that requires the use of the iteration method (successive approximations) to solve. They find application in practice, but are not of interest from the point of view of specialists in the field of mathematical modeling.

The second group includes models that describe real processes occurring in small and medium-sized economic systems, subject to the influence of random and uncertain factors. The development of such models requires making assumptions to resolve uncertainties. For example, you need to specify distributions of random variables related to input variables. This artificial operation to a certain extent raises doubts about the reliability of the modeling results. However, there is no other way to create a mathematical model.

Among the models of this group, the most widely used models are those of the so-called queuing systems. There are two varieties of these models: analytical and algorithmic. Analytical models do not take into account the effect of random factors and therefore can only be used as first approximation models. Using algorithmic models, the process under study can be described with any degree of accuracy at the level of its understanding by the problem maker.

The third group includes models of large and very large (macroeconomic) systems: large commercial and industrial enterprises and associations, sectors of the national economy and the country’s economy as a whole. Creating a mathematical model of an economic system of this scale is a complex scientific problem, the solution of which can only be solved by a large research institution.

2.2 Simulation model components

Numerical modeling deals with three types of values: input data, calculated variable values, and parameter values. On an Excel sheet, arrays with these values ​​occupy separate areas.

Initial real data, samples or series of numbers, are obtained through direct field observation or in experiments. Within the framework of the modeling procedure, they remain unchanged (it is clear that, if necessary, the sets of values ​​can be supplemented or reduced) and play a dual role. Some of them (independent environmental variables, X) serve as the basis for calculating model variables; most often these are characteristics of natural factors (the passage of time, photoperiod, temperature, abundance of food, dose of toxicant, volumes of pollutants discharged, etc.). The other part of the data (dependent variables of the object, Y) is a quantitative characteristic of the state, reactions or behavior of the research object, which was obtained in certain conditions, under the influence of registered environmental factors. In a biological sense, the first group of meanings does not depend on the second; on the contrary, object variables depend on environment variables. Data is entered into an Excel sheet from the keyboard or from a file in the usual spreadsheet mode.

Model calculation data reproduce the theoretically conceivable state of the object, which is determined by the previous state, the level of observed environmental factors and is characterized by the key parameters of the process being studied. In the ordinary case, when calculating model values ​​(Y M i) for each time step (i), parameters (A), characteristics of the previous state (Y M i -1) and current levels of environmental factors (X i) are used:

Y M i = f(A, Y M i-1, X i, i),

where () is the accepted form of the relationship between parameters and environmental variables, the type of model, = 1, 2, ... T or i = 1, 2, ... n.

Calculations of system characteristics using model formulas for each time step (for each state) make it possible to generate an array of model explicit variables (Y M), which must exactly repeat the structure of the array of real dependent variables (Y), which is necessary for subsequent adjustment of model parameters. Formulas for calculating model variables are entered into the cells of the Excel sheet manually (see the section Useful techniques).

The model parameters (A) constitute the third group of values. All parameters can be represented as a set:

= (a 1 , a 2 ,…, a j ,…, a m ),

where j is the parameter number,

m - total number of parameters,

and placed in a separate block. It is clear that the number of parameters is determined by the structure of the adopted model formulas.

Occupying a separate position on the Excel sheet, they play the most significant role in modeling. The parameters are designed to characterize the very essence, the mechanism for the implementation of the observed phenomena. The parameters must have a biological (physical) meaning. For some tasks, it is necessary that parameters calculated for different data sets can be compared. This means that they must sometimes be accompanied by their own statistical errors.

The relationships between the components of the simulation system form a functional unity focused on achieving a common goal - assessing the parameters of the model (Fig. 2.6, Table 2.10). Several elements are simultaneously involved in the implementation of individual functions, indicated by arrows. In order not to clutter the picture, the graphical representation and randomization blocks are not reflected in the diagram. The simulation system is designed to support any changes in model designs that, if necessary, can be made by the researcher. Basic designs of simulation systems, as well as possible ways of their decomposition and integration are presented in the section Frames of simulation systems.

modeling simulation economic series

III. Simulation Basics

1 Simulation model and its features

Simulation modeling is a type of analog modeling implemented using a set of mathematical tools that specifically simulate computer programs and programming technologies that allow, through analogue processes, to conduct a targeted study of the structure and functions of a real complex process in computer memory in the “imitation” mode, and to optimize some of its parameters.

A simulation model is an economic and mathematical model, the study of which is carried out by experimental methods. The experiment consists of observing the results of calculations for various specified values ​​of the input exogenous variables. The simulation model is a dynamic model due to the fact that it contains such a parameter as time. A simulation model is also called a special software package that allows you to simulate the activities of any complex object. The emergence of simulation modeling was associated with the “new wave” in economics and topic modeling. Problems of economic science and practice in the field of management and economic education, on the one hand, and the growth of computer productivity, on the other, have caused a desire to expand the scope of “classical” economic and mathematical methods. There was some disappointment in the capabilities of normative, balance sheet, optimization and game-theoretic models, which at first deservedly attracted the attention of the fact that they bring an atmosphere of logical clarity and objectivity to many problems of economic management, and also lead to a “reasonable” (balanced, optimal, compromise) solution . It was not always possible to fully comprehend a priori goals and, even more so, to formalize the optimality criterion and (or) restrictions on admissible solutions. Therefore, many attempts to nevertheless apply such methods began to lead to unacceptable, for example, unrealizable (albeit optimal) solutions. Overcoming the difficulties that arose took the path of abandoning complete formalization (as is done in normative models) of procedures for making socio-economic decisions. Preference began to be given to a reasonable synthesis of the intellectual capabilities of an expert and the information power of a computer, which is usually implemented in dialogue systems. One trend in this direction is the transition to “semi-normative” multi-criteria man-machine models, the second is a shift in the center of gravity from prescriptive models focused on the “conditions-decision” scheme to descriptive models that answer the question “what will happen if... ."

Simulation modeling is usually resorted to in cases where the dependencies between the elements of the simulated systems are so complex and uncertain that they cannot be formally described in the language of modern mathematics, i.e., using analytical models. Thus, simulation researchers complex systems forced to use when purely analytical methods are either inapplicable or unacceptable (due to the complexity of the corresponding models).

In simulation modeling, the dynamic processes of the original system are replaced by processes simulated by a modeling algorithm in an abstract model, but maintaining the same ratios of durations, logical and time sequences as in the real system. Therefore, the simulation method could be called algorithmic or operational. By the way, such a name would be more successful, since imitation (translated from Latin as imitation) is the reproduction of something by artificial means, i.e. modeling. In this regard, the currently widely used name “simulation modeling” is tautological. In the process of simulating the functioning of the system under study, as in an experiment with the original itself, certain events and states are recorded, from which the necessary characteristics of the quality of functioning of the system under study are then calculated. For systems, for example, information and computing services, such dynamic characteristics can be defined as:

Processing device performance;

Length of queues for service;

Waiting time for service in queues;

The number of requests that left the system without service.

In simulation modeling, processes of any degree of complexity can be reproduced if there is a description of them, given in any form: formulas, tables, graphs, or even verbally. The main feature of simulation models is that the process under study is, as it were, “copied” on a computer, therefore simulation models, unlike analytical models, allow:

Take into account a huge number of factors in models without gross simplifications and assumptions (and therefore increase the adequacy of the model to the system under study);

It is enough to simply take into account the uncertainty factor in the model caused by the random nature of many model variables;

All this allows us to draw a natural conclusion that simulation models can be created for a wider class of objects and processes.

2 The essence of simulation modeling

The essence of simulation modeling is targeted experimentation with a simulation model by “playing” on it various options for the functioning of the system with their corresponding economic analysis. Let us immediately note that it is advisable to present the results of such experiments and the corresponding economic analysis in the form of tables, graphs, nomograms, etc., which greatly simplifies the decision-making process based on the modeling results.

Having listed above a number of advantages of simulation models and simulation, we also note their disadvantages, which must be remembered when using simulation in practice. This:

Lack of well-structured principles for constructing simulation models, which requires significant elaboration of each specific case of its construction;

Methodological difficulties in finding optimal solutions;

Increased requirements for the speed of computers on which simulation models are implemented;

Difficulties associated with collecting and preparing representative statistics;

The uniqueness of simulation models, which does not allow the use of ready-made software products;

The complexity of analyzing and understanding the results obtained as a result of a computational experiment;

Quite a large investment of time and money, especially when searching for optimal trajectories of behavior of the system under study.

The number and essence of the listed shortcomings is very impressive. However, given the great scientific interest in these methods and their extremely intensive development in last years, we can confidently assume that many of the above disadvantages of simulation modeling can be eliminated both conceptually and in application terms.

Simulation modeling of a controlled process or controlled object is a high-level information technology that provides two types of actions performed using a computer:

) work on creating or modifying a simulation model;

) operation of the simulation model and interpretation of the results.

Simulation modeling of economic processes is usually used in two cases:

To manage a complex business process, when a simulation model of a managed economic entity is used as a tool%in the contour of an adaptive management system created on the basis of information technology;

When conducting experiments with discrete-continuous models of complex economic objects to obtain and monitor their dynamics in emergency situations associated with risks, the full-scale modeling of which is undesirable or impossible.

The following typical problems can be identified that can be solved by means of simulation modeling when managing economic objects:

Modeling of logistics processes to determine time and cost parameters;

Managing the process of implementing an investment project on various stages its life cycle, taking into account possible risks and tactics for allocating funds;

Analysis of clearing processes in the work of a network of credit institutions (including application to mutual settlement processes in the Russian banking system);

Forecasting the financial results of an enterprise for a specific period of time (with analysis of the dynamics of account balances);

Business reengineering of an insolvent enterprise (changing the structure and resources of a bankrupt enterprise, after which, using a simulation model, one can make a forecast of the main financial results and give recommendations on the feasibility of one or another option for reconstruction, investment or lending to production activities);

A simulation system that provides the creation of models to solve the listed problems must have the following properties:

The ability to use simulation programs in conjunction with special economic and mathematical models and methods based on control theory;

Instrumental methods for conducting structural analysis of a complex economic process;

The ability to model material, monetary and information processes and flows within a single model, in general, model time;

The possibility of introducing a regime of constant clarification when receiving output data (main financial indicators, time and space characteristics, risk parameters, etc.) and conducting an extreme experiment.

Many economic systems are essentially queuing systems (QS), i.e. systems in which, on the one hand, there are requirements for the performance of any services, and on the other, these requirements are satisfied.

IV. Practical part

1 Problem statement

Investigate the dynamics of an economic indicator based on the analysis of a one-dimensional time series.

For nine consecutive weeks, demand Y(t) (million rubles) for credit resources of a financial company was recorded. The time series Y(t) of this indicator is given in the table.

Required:

Check for anomalous observations.

Construct a linear model Y(t) = a 0 + a 1 t, the parameters of which can be estimated by least squares (Y(t)) - calculated, simulated values ​​of the time series).

Assess the adequacy of the constructed models using the properties of independence of the residual component, randomness and compliance with the normal distribution law (when using the R/S criterion, take tabulated limits of 2.7-3.7).

Assess the accuracy of models using the average relative error of approximation.

Using the two constructed models, forecast demand for the next two weeks (calculate the confidence interval of the forecast at a confidence probability of p = 70%)

Present the actual values ​​of the indicator, modeling and forecasting results graphically.

4.2 Solving the problem

1). The presence of anomalous observations leads to distortion of the modeling results, so it is necessary to ensure the absence of anomalous data. To do this, we will use Irwin’s method and find the characteristic number () (Table 4.1).

; ,

The calculated values ​​are compared with the tabulated values ​​of the Irvine criterion, and if they are greater than the tabulated ones, then the corresponding value of the series level is considered anomalous.

Appendix 1 (Table 4.1)

All obtained values ​​were compared with the table values ​​and did not exceed them, that is, there were no anomalous observations.

) Construct a linear model, the parameters of which can be estimated by least squares methods (calculated, simulated values ​​of the time series).

To do this, we will use Data Analysis in Excel.

Appendix 1 ((Fig. 4.2).Fig. 4.1)

The result of the regression analysis is contained in the table

Appendix 1 (table 4.2 and 4.3.)

In the second column of the table. 4.3 contains the coefficients of the regression equation a 0, a 1, the third column contains the standard errors of the coefficients of the regression equation, and the fourth contains t - statistics used to test the significance of the coefficients of the regression equation.

The regression equation for the dependence (demand for credit resources) on (time) has the form .

Appendix 1 (Fig. 4.5)

3) Assess the adequacy of the constructed models.

1. Let’s check the independence (absence of autocorrelation) using the Durbin-Watson d test according to the formula:

Appendix 1 (Table 4.4)

Because the calculated value d falls in the range from 0 to d 1, i.e. in the interval from 0 to 1.08, then the property of independence is not satisfied, the levels of a number of residuals contain autocorrelation. Therefore, the model is inadequate according to this criterion.

2. We will check the randomness of the levels of a number of residues based on the criterion of turning points. P>

The number of turning points is 6.

Appendix 1 (Fig. 4.5)

The inequality is satisfied (6 > 2). Therefore, the randomness property is satisfied. The model is adequate according to this criterion.

3. Let us determine whether a number of residuals correspond to the normal distribution law using the RS criterion:

,

The maximum level of a number of residues,

The minimum level of a number of residues,

Standard deviation,

,

The calculated value falls within the interval (2.7-3.7), therefore, the property of normal distribution is satisfied. The model is adequate according to this criterion.

4. Checking whether the mathematical expectation of the levels of a number of residues is equal to zero.

In our case, therefore, the hypothesis of equality mathematical expectation values ​​of the residual series to zero are fulfilled.

Table 4.3 summarizes the analysis of a number of residues.

Appendix 1 (Table 4.6)

4) Assess the accuracy of the model based on the use of the average relative error of approximation.

To assess the accuracy of the resulting model, we will use the relative approximation error indicator, which is calculated by the formula:

, Where

Calculation of relative approximation error

Appendix 1 (Table 4.7)

If the error calculated by the formula does not exceed 15%, the accuracy of the model is considered acceptable.

5) Based on the constructed model, forecast demand for the next two weeks (calculate the confidence interval of the forecast at a confidence level of p = 70%).

Let's use the Excel function STUDISCOVER.

Appendix 1 (Table 4.8)

To build an interval forecast, we calculate the confidence interval. Let us accept the value of the significance level, therefore, the confidence probability is equal to 70%, and the Student’s test at equals 1.12.

We calculate the width of the confidence interval using the formula:

, Where

(we find from table 4.1)

We calculate the upper and lower limits of the forecast (Table 4.11).

Appendix 1 (Table 4.9)

6) Present the actual values ​​of the indicator, modeling and forecasting results graphically.

Let's transform the selection schedule, supplementing it with forecast data.

Appendix 1 (Table 4.10)

Conclusion

An economic model is defined as a system of interrelated economic phenomena, expressed in quantitative characteristics and presented in a system of equations, i.e. is a system of formalized mathematical description. For a targeted study of economic phenomena and processes and the formulation of economic conclusions - both theoretical and practical, it is advisable to use the method of mathematical modeling. Particular interest is shown in methods and means of simulation modeling, which is associated with the improvement of information technologies used in simulation modeling systems: the development of graphical shells for constructing models and interpreting the output results of modeling, the use of multimedia tools, Internet solutions, etc. In economic analysis, simulation modeling is the most universal tool in the field of financial, strategic planning, business planning, production management and design. Mathematical modeling of economic systems The most important property of mathematical modeling is its universality. This method allows, at the stages of design and development of an economic system, to form various options its model, conduct repeated experiments with the resulting model variants in order to determine (based on the given criteria for the functioning of the system) the parameters of the created system necessary to ensure its efficiency and reliability. In this case, there is no need to purchase or produce any equipment or hardware to perform the next calculation: you just need to change the numerical values ​​of the parameters, initial conditions and operating modes of the complex economic systems under study.

Methodologically, mathematical modeling includes three main types: analytical, simulation and combined (analytical-simulation) modeling. An analytical solution, if possible, provides a more complete and clear picture, allowing one to obtain the dependence of the modeling results on the totality of the initial data. In this situation, one should move to the use of simulation models. A simulation model, in principle, allows one to reproduce the entire process of functioning of an economic system while preserving the logical structure, connections between phenomena and the sequence of their occurrence over time. Simulation modeling allows you to take into account a large number of real details of the functioning of the simulated object and is indispensable in the final stages of creating a system, when all strategic issues have already been resolved. It can be noted that simulation is intended to solve problems of calculating system characteristics. The number of options to be evaluated should be relatively small, since the implementation of simulation modeling for each option for constructing an economic system requires significant computing resources. The fact is that a fundamental feature of simulation modeling is the fact that in order to obtain meaningful results it is necessary to use statistical methods. This approach requires repeated repetition of the simulated process with changing values ​​of random factors, followed by statistical averaging (processing) of the results of individual single calculations. The use of statistical methods, inevitable in simulation modeling, requires a lot of computer time and computing resources.

Another disadvantage of the simulation modeling method is the fact that to create sufficiently meaningful models of an economic system (and at those stages of creating an economic system when simulation modeling is used, very detailed and meaningful models are needed) significant conceptual and programming efforts are required. Combined modeling allows you to combine the advantages of analytical and simulation modeling. To increase the reliability of the results, a combined approach should be used, based on a combination of analytical and simulation modeling methods. In this case, analytical methods should be used at the stages of analyzing the properties and synthesizing the optimal system. Thus, from our point of view, a system of comprehensive training of students in the means and methods of both analytical and simulation modeling is necessary. Organization of practical classes Students study ways to solve optimization problems that can be reduced to linear programming problems. The choice of this modeling method is due to the simplicity and clarity of both the substantive formulation of the relevant problems and the methods for solving them. In the process of performing laboratory work, students solve the following typical problems: transport problem; the task of allocating enterprise resources; the problem of equipment placement, etc. 2) Studying the basics of simulation modeling of production and non-production queuing systems in the GPSS World (General Purpose System Simulation World) environment. Methodological and practical issues of creating and using simulation models in the analysis and design of complex economic systems and decision-making in commercial and marketing activities are considered. Methods for describing and formalizing simulated systems, stages and technology for constructing and using simulation models, and issues of organizing targeted experimental studies using simulation models are studied.

List of used literature

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. Vorobyov 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: Tutorial. - 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

Annex 1

Table 4.1

Table 4.2

Table 4.3

Withdrawal of balances

Table 4.6

Table 4.7

Table 4.9

Forecast table

Simulation modeling method and its features. Simulation model: representation of the structure and dynamics of the simulated system

The simulation method is an experimental method for studying a real system using its computer model, which combines the features of the experimental approach and the specific conditions for using computer technology.

Simulation modeling is a computer modeling method; in fact, it never existed without a computer, and only the development of information technology led to the establishment of this type of computer modeling. The above definition focuses on the experimental nature of simulation and the use of a simulation research method (experimentation is carried out with the model). Indeed, in simulation modeling, an important role is played not only by conducting, but also by planning the experiment on the model. However, this definition does not clarify what the simulation model itself is. Let's try to figure out what properties a simulation model has, what is the essence of simulation modeling.

In the process of simulation modeling (Fig. 1.2), the researcher deals with four main elements:

• real system;
• logical-mathematical model of the simulated object;
• simulation (machine) model;
• The computer on which the simulation is carried out is directed

computational experiment.

The researcher studies a real system, develops a logical-mathematical model of a real system. The simulation nature of the study presupposes the presence logical or logical-mathematical models, described process (system) being studied. To be machine-implementable, a complex system is built on the basis of a logical-mathematical model modeling algorithm, which describes the structure and logic of interaction of elements in the system.

Rice. 1.2.

There is a software implementation of the modeling algorithm simulation model. It is compiled using automated modeling tools. Simulation technology and modeling tools - languages ​​and modeling systems with the help of which simulation models are implemented - will be discussed in more detail in Chapter. 3. Next, a directed computational experiment is set up and carried out on a simulation model, as a result of which the information necessary for making decisions in order to influence the real system is collected and processed.

Above we defined a system as a set of interacting elements operating over time.

The composite nature of a complex system dictates the representation of its model in the form of a triple A, S, T>, where A - many elements (including the external environment); S- set of permissible connections between elements (model structure); T - multiple points in time considered.

A feature of simulation modeling is that the simulation model allows you to reproduce simulated objects while preserving their logical structure and behavioral properties, i.e. dynamics of element interactions.

In simulation modeling, the structure of the simulated system is directly displayed in the model, and the processes of its functioning are played out (simulated) on the constructed model. The construction of a simulation model consists of describing the structure and functioning processes of the modeled object or system.

There are two components in the description of the simulation model:

• static description of the system, which is essentially a description of its structure. When developing a simulation model, it is necessary to perform structural analysis modeled processes, determining the composition of model elements;
• dynamic description of the system, or a description of the dynamics of interactions of its elements. When compiling it, it actually requires the construction of a functional model that displays the simulated dynamic processes.

The idea of ​​the method from the point of view of its software implementation was as follows. What if some software components were assigned to the elements of the system, and the states of these elements were described using state variables. Elements, by definition, interact (or exchange information), which means that an algorithm for the functioning of individual elements and their interaction according to certain operational rules can be implemented - a modeling algorithm. In addition, elements exist in time, which means that an algorithm for changing state variables must be specified. Dynamics in simulation models is implemented using mechanism for advancing model time.

A distinctive feature of the simulation method is the ability to describe and reproduce the interaction between various elements of the system. Thus, to create a simulation model, you need to:

• 1) present a real system (process) as a set of interacting elements;
• 2) algorithmically describe the functioning of individual elements;
• 3) describe the process of interaction of various elements with each other and with the external environment.

The key point in simulation modeling is the identification and description of system states. The system is characterized by a set of state variables, each combination of which describes a specific state. Therefore, by changing the values ​​of these variables, it is possible to simulate the transition of the system from one state to another. Thus, simulation is the representation of the dynamic behavior of a system by moving it from one state to another according to well-defined operating rules. These state changes can occur either continuously or at discrete points in time. Simulation modeling is a dynamic reflection of changes in the state of a system over time.

So, we figured out that during simulation, the logical structure of a real system is displayed in the model, and the dynamics of interactions of subsystems in the simulated system are also simulated. This is an important, but not the only feature of the simulation model, which historically predetermined the not entirely successful, in our opinion, name of the method ( simulation modeling), which researchers more often call systems modeling.

The concept of model time. Model time promotion mechanism. Discrete and continuous simulation models

To describe the dynamics of the simulated processes in simulation, it is implemented mechanism for advancing model time. These mechanisms are built into the control programs of any modeling system.

If the behavior of one component of the system were simulated on a computer, then the execution of actions in the simulation model could be carried out sequentially, by recalculating the time coordinate. To ensure the simulation of parallel events of a real system, some global variable is introduced (providing synchronization of all events in the system) / 0, which is called model (or system) time.

There are two main ways to change t Q:

• 1) step-by-step (fixed intervals of model time changes are used);
• 2) event-by-event (variable intervals of change in model time are used, while the step size is measured by the interval until the next event).

When step by step method time advances with the minimum possible constant step length (principle A/). These algorithms are not very efficient in terms of using computer time for their implementation.

At event-based method(principle "special conditions") time coordinates change only when the state of the system changes. In event-based methods, the length of the time shift step is the maximum possible. Model time changes from the current moment to the nearest moment of the next event. The use of the event-by-event method is preferable if the frequency of occurrence of events is low, then a large step length will speed up the progress of model time. The event-by-event method is used when events occurring in the system are unevenly distributed on the time axis and appear at significant time intervals. In practice, the event-based method is most widespread.

The fixed step method is used if:

• the law of change over time is described by integrodifferential equations. A typical example: the solution of integra- differential equations numerical method. In such methods, the modeling step is equal to the integration step. When using them, the dynamics of the model is a discrete approximation of real continuous processes;
• events are distributed evenly and the step of changing the time coordinate can be selected;
• it is difficult to predict the occurrence of certain events;
• There are a lot of events and they appear in groups.

Thus, due to the sequential nature of information processing in a computer, parallel processes occurring in the model are transformed using the considered mechanism into sequential ones. This method of representation is called a quasi-parallel process.

The simplest classification into the main types of simulation models is associated with the use of these two methods of advancing model time. There are continuous, discrete and continuous-discrete simulation models.

IN continuous simulation models variables change continuously, the state of the simulated system changes as continuous function time, and, as a rule, this change is described by systems of differential equations. Accordingly, the advancement of model time depends on numerical methods for solving differential equations.

IN discrete simulation models variables change discretely in certain moments simulation time (occurrence of events). The dynamics of discrete models is the process of transition from the moment of the onset of the next event to the moment of the onset of the next event.

Since in real systems continuous and discrete processes are often impossible to separate, continuous-discrete models, which combine the mechanisms of time progression characteristic of these two processes.

Problems of strategic and tactical planning of a simulation experiment. Directed computational experiment on a simulation model

So we have determined that simulation methodology- This is a system analysis. It is the latter that gives the right to call the type of modeling under consideration system modeling.

At the beginning of this section, we gave a general concept of the simulation method and defined it as an experimental method for studying a real system using its simulation model. Note that the concept of a method is always broader than the concept of “simulation model”.

Let us consider the features of this experimental method (simulation research method). By the way, the words “ simulation", "experiment", "imitation" of one plan. The experimental nature of simulation also determined the origin of the name of the method. So, the goal of any research is to find out as much as possible about the system being studied, to collect and analyze the information necessary to make a decision. The essence of studying a real system using its simulation model is to obtain (collect) data on the functioning of the system as a result of conducting an experiment on a simulation model.

Simulation models are run-type models that have an input and an output. That is, if you feed certain parameter values ​​to the input of the simulation model, you can get a result that is valid only for these values. In practice, the researcher is faced with the following specific feature of simulation modeling. A simulation model produces results that are valid only for certain values ​​of the parameters, variables, and structural relationships embedded in the simulation program. Changing a parameter or relationship means that the simulation program must be run again. Therefore, to obtain the necessary information or results, it is necessary to run simulation models rather than solve them. The simulation model is not capable of generating its own solution in the same way as is the case in analytical models (see. calculation method research), but can serve as a means for analyzing the behavior of the system under conditions determined by the experimenter.

For clarification, consider the deterministic and stochastic cases.

Stochastic case. A simulation model is a convenient apparatus for studying stochastic systems. Stochastic systems are systems whose dynamics depend on random factors; the input and output variables of a stochastic model are usually described as random variables, functions, processes, sequences. Let's consider the main features of modeling processes taking into account the action of random factors (the well-known ideas of the method of statistical tests and the Monte Carlo method are implemented here). The simulation results obtained by reproducing a single implementation of processes, due to the action of random factors, will be implementations of random processes and will not be able to objectively characterize the object being studied. Therefore, the required values ​​when studying processes using the simulation method are usually determined as average values ​​based on data from a large number of process implementations (estimation problem). Therefore, an experiment on a model contains several implementations, runs, and involves estimation based on a set of data (samples). It is clear that (according to the law of large numbers) the greater the number of implementations, the more the resulting estimates become more and more statistically stable.

So, in the case of a stochastic system, it is necessary to collect and evaluate statistical data at the output of the simulation model, and to do this, carry out a series of runs and statistical processing of the simulation results.

Deterministic case. IN In this case, it is enough to carry out one run with a specific set of parameters.

Now let’s imagine that the goals of modeling are: studying the system under various conditions, evaluating alternatives, finding the dependence of the model’s output on a number of parameters, and, finally, finding the optimal option. In these cases, the researcher can gain insight into the functioning of the modeled system by changing the values ​​of the parameters at the input of the model, while performing numerous machine runs of the simulation model.

Thus, conducting experiments with a model on a computer involves conducting multiple machine runs in order to collect, accumulate and subsequently process data on the functioning of the system. Simulation modeling allows you to explore a model of a real system in order to study its behavior through repeated runs on a computer under various operating conditions of the real system.

The following problems arise here: how to collect this data, conduct a series of runs, how to organize a targeted experimental study. The output data obtained as a result of such experimentation can be very large. How to process them? Processing and studying them can turn into an independent problem, much more difficult tasks statistical evaluation.

In simulation important issue is not only conducting, but also planning a simulation experiment in accordance with the stated purpose of the study. Thus, a researcher using simulation modeling methods always faces the problem of organizing an experiment, i.e. choosing a method for collecting information that provides the required volume (to achieve the research goal) at the lowest cost (an extra number of runs means extra computer time). The main task is to reduce the time spent on operating the model, reduce the computer time for simulation, which reflects the expenditure of computer time resources on conducting a large number of simulation runs. This problem is called strategic planning simulation research. To solve it, methods of experiment planning, regression analysis, etc. are used, which will be discussed in detail in section 3.4.

Strategic planning is the development of an effective experimental plan, as a result of which either the relationship between the controlled variables is clarified, or a combination of values ​​of the controlled variables is found that minimizes or maximizes the response (output) of the simulation model.

Along with the concept of strategic, there is the concept tactical planning, which is associated with determining how to conduct simulation runs outlined in the experimental plan: how to conduct each run within the framework of the drawn up experimental plan. Here the problems of determining the duration of a run, assessing the accuracy of simulation results, etc. are solved.

We will call such experiments with a simulation model directed computational experiments.

A simulation experiment, the content of which is determined by a previously conducted analytical study (i.e., which is an integral part of a computational experiment) and the results of which are reliable and mathematically justified, is called directed computational experiment.

In ch. 3 we will consider in detail the practical issues of organizing and conducting directed computational experiments using a simulation model.

General technological scheme, capabilities and scope of simulation modeling

Summarizing our reasoning, we can present in the most general form the technological scheme of simulation modeling (Fig. 1.3). (The technology of simulation modeling will be discussed in more detail in Chapter 3.)

Rice. 1.3.

• 1 - real system; 2 - construction of a logical-mathematical model;
• 3 - development of a modeling algorithm; 4 - construction of a simulation (machine) model; 5 - planning and conducting simulation experiments; 6 - processing and analysis of results; 7 - conclusions about the behavior of a real system (decision making)

Let us consider the capabilities of the simulation modeling method, which have led to its widespread use in a variety of fields. Simulation modeling traditionally finds application in a wide range of economic research: modeling of production systems and logistics, sociology and political science; modeling of transport, information and telecommunication systems, and finally, global modeling of world processes.

The simulation method allows you to solve problems of exceptional complexity, provides the simulation of any complex and diverse processes, with big amount elements, individual functional dependencies in such models can be described by very cumbersome mathematical relationships. Therefore, simulation modeling is effectively used in problems of studying systems with a complex structure in order to solve specific problems.

The simulation model contains elements of continuous and discrete action, therefore it is used to study dynamic systems, when an analysis of bottlenecks is required, a study of the dynamics of functioning, when it is desirable to observe the progress of a process on a simulation model over a certain time

Simulation modeling is an effective tool for studying stochastic systems, when the system under study can be influenced by numerous random factors of a complex nature (mathematical models for this class of systems have limited capabilities). It is possible to conduct research under conditions of uncertainty, with incomplete and inaccurate data.

Simulation modeling is the most valuable, system-forming link in decision support systems, as it allows you to explore a large number of alternatives (decision options) and play out various scenarios for any input data. The main advantage of simulation modeling is that the researcher can always get an answer to the question “What will happen if?” to test new strategies and make decisions when studying possible situations. ...". The simulation model allows you to predict when we're talking about about the system being designed or development processes are studied, i.e. in cases where no real system exists.

The simulation model can provide various (including very high) levels of detail of the simulated processes. In this case, the model is created in stages, gradually, without significant changes, evolutionary.

The purpose of studying the discipline is to develop in students theoretical knowledge and practical skills in the application of simulation modeling methods in economics, management and business. In the process of studying the course, students become familiar with the means of simulation modeling of the functioning of economic systems, master simulation modeling methods, typical stages of modeling processes that form a “chain”: construction of a conceptual model and its formalization - algorithmization of the model and its computer implementation - simulation experiment and interpretation of simulation results ; master practical skills in implementing modeling algorithms to study the characteristics and behavior of complex economic systems.

To study the course “Simulation Modeling of Economic Processes,” a student must know the theory of systems and system analysis, economics, mathematics, probability theory, mathematical statistics, programming, and also have PC user skills.
The discipline is based on the previously studied disciplines “Economics”, “Mathematics”. Mathematical analysis", "Probability theory", "Statistics theory", "Mathematics. Linear algebra", "Mathematics. Discrete mathematics”, “Numerical methods”, “Computer science and programming”, “High-level methods of computer science and programming”, “Theory of economic information systems”, “Optimization methods”, “Systems theory and system analysis” and is used in the study of disciplines: “Design information systems”, “Technology for implementing corporate information systems”, “Business process reengineering”.

OBSESSION
Goal and objectives of course 8
Introduction 11
Section I. Theoretical basis simulation modeling 13
Chapter 1. Basic concepts of the theory of modeling economic systems and processes 13
§1. Fundamentals of decision-making regarding the creation, improvement, development of economic systems 13
§2. Basics of Simulation Modeling 20
2.1. Concept of model 20
2.2. Model classification 21
2.3. Sequence of development of mathematical models 24
2.3.1. Defining the purpose of modeling 25
2.3.2. Building a Conceptual Model 26
2.3.3. Development of a system model algorithm 29
2.3.4. Development of a system model program 29
2.3.5. Planning model experiments and conducting machine experiments with a system model 30
Chapter 2. Mathematical schemes for modeling economic systems 31
§1. Classification of simulated systems 31
§2. Mathematical schemes (models) 34
Chapter 3. Modeling random events and quantities 38
§1. Simulation of random events 41
1.1. Simulation of a simple event 41
1.2. Modeling full group incompatible events 47
§2. Modeling random variables 49
2.1. Modeling a discrete random variable 49
2.2. Modeling continuous random variables 50
2.2.1. Inverse function method 50
2.2.2. Modeling random variables with exponential distribution 50
2.2.3. Modeling random variables with uniform distribution 51
2.2.4. Simulation of random variables with normal distribution 52
2.2.5. Modeling random variables with truncated normal distribution 54
2.2.6. Modeling random variables with arbitrary distribution 56
2.2.7. Modeling random variables with given parameters using Matlab 58
Section II. Concept and capabilities of an object-oriented modeling system 63
Chapter 4. General information about MATLAB/SIMULINK. SIMULINK 63 block library
§1. Launch MATLAB, interface 64
§2. Editor/debugger - program editor\debugger 67
§3. Simple calculations in command mode 69
§4. Introduction to Simulink 70
§5. Working with Simulink 71
§6. Simulink 73 Library Section Browser
§7. Creation of Model 75
§8. Model 78 window
§9. Basic techniques for preparing and editing model 81
§10. SIMULINK 87 block library
10.1. Sources - signal sources 87
10.2. Sinks - signal receivers 88
10.2.1. Scope 88 Oscilloscope
10.2.2. Digital display Display 93
10.3. Continuous - analog blocks 95
10.3.1. Integrator 95 integrating unit
10.3.2. Transport Delay 98 fixed signal delay block
10.3.3. Controlled signal delay block Variable Transport Delay 99
10.4. Nonlinear - nonlinear blocks 100
10.4.1. Saturation 100 limit block
10.4.2. Switch block Switch 102
10.4.3. Manual Switch Unit 103
10.5. Math - blocks mathematical operations 103
10.5.1. Sum calculation block Sum 103
10.5.2. Gain and Matrix Gain 105 Amplifiers
10.5.3. Block for calculating the relational operation Relational Operator 107
10.6. Signal&Systems - signal conversion blocks and auxiliary blocks 109
10.6.1. Multiplexer (mixer) Mux 109
10.6.2. Demultiplexer (separator) Demux 110
10.7. Function & Tables - blocks of functions and tables 112
10.7.1. Fen 112 function setting block
10.7.2. MATLAB Fen 114 Function Specifier Block
10.8. Modeling stages 115
Chapter 5. Model time management 117
§1. Types of time representation in the model 117
§2. Changing time in constant steps 118
§3. Progression of time according to special states 121
§4. Simulation of parallel processes 122
§5. Model time management in matlab 128
§6. Setting the Simulated System Output Options output options 141
§ 7. Setting parameters for exchange with the work area 142
§8. Setting diagnostic parameters for model 143
Section III. Basic rules of modeling 145
Chapter 6. Classification of mathematical models of economic systems 145
§1. General economic models 145
§2. Enterprise management models 149
Chapter 7. Modeling of application servicing processes under failure conditions 153
Chapter 8. Planning model experiments 160
§1. Objectives of Experimental Design 160
§2. Strategic planning for a simulation experiment 162
§3. Tactical planning of experiment 166
§4. Matlab/Simulink capabilities for planning and implementing model experiments 169
4.1. Development of experimental plans 169
4.2. Conducting Simulation Experiments Using Script Files 172
Chapter 9. Examples of building simulation models 174
§1. Simulation model of cycles of growth and decline in the economy (crises) 174
1.1. Statement of the modeling problem 174
1.2. Building a Conceptual Model 174
1.3. Mathematical model 175
§2. Using simulation to find the optimal income tax rate 178
2.1. Statement of the modeling problem 178
2.2. Building a Conceptual Model 179
2.3. Mathematical model 180
2.4. Computer model in Simulnk 181 program
2.5. Input data for parameters, variables and indicators of the model 183
2.6. Mathematical scheme of the model and solution method 183
2.7. Experiment Controls 183
2.8. Simulation experiment control program 184
§3. “Spiderweb” model of the firm (equilibrium in a competitive market) 185
3.1. Statement of the modeling problem 185
3.2. Building the Model 188
Workshop 190
Practical lesson 1 190
Practical lesson 2 196
Practical lesson 3 201
Practical lesson 4 206
Practical lesson 5 207
Practical lesson 6 209
Tests (for correspondence department) 211
Topics of laboratory (semester) work 211
Final questions 212
Glossary 214
List of recommended literature 227

• Emelyanov A.A., Vlasova E.A., Duma R.V. Simulation modeling of economic processes. M.: Finance and Statistics, 2002.
• Aleksandrovsky N.M., Egorov S.V., Kuzin R.E. Adaptive systems for managing complex technological processes. M.: NRE, 1973.
• Buslenko N.P. Modeling of complex systems. M.: Nauka, 1978.
• GOST 24.702? 85. Efficiency of automated control systems. Basic provisions. ? M.: Standards Publishing House, 1985.
• Emelyanov A.A., Vlasova E.A., Duma R.V. Simulation modeling in economic information systems. Tutorial. - M.: MESI, 1996.
• Emelyanov A.A. Techniques for developing and analyzing managed programs. M.: Publishing house "AtomInform", 1984.
• Emelyanov A.A. Simulation systems for discrete and discrete-continuous processes (PILIGRIM). 10785338.00027-01 92 01-LU. Tver: Mobility, 1992.
• Lipaev V.V., Yashkov S.F. efficiency of methods for organizing the computing process of automated control systems. M.: Finance and Statistics, 1975.
• Nazin A.V., Poznyak A.S. Adaptive selection of options. M.: Nauka, 1986.
• Pritzker A. Introduction to simulation modeling and the SLAM language PM: Mir, 1987.
• Robert F.S. Discrete mathematical models with applications to social biological and environmental problems. M.: Nauka, 1986.
• Shannon R. Simulation modeling of systems: science and art. M.: Mir, 1978.
• Simulation modeling of random factors [Text]: method. instructions for practical classes course “Simulation modeling of economic processes” / Voronezh. state technol. academic; comp. A. S. Dubrovin, M. E. Semenov. Voronezh, 2005. 32 p.
• Afanasyev, M. Yu. Research of operations in economics: models, problems, solutions [Text]: textbook. allowance / M. Yu. Afanasyev, B. P. Suvorov. – M.: INFRA-M, 2003. – 444 p. (Series. Higher education).
• Varfolomeev, V.I. Algorithmic modeling of elements of economic systems [Text]: workshop: textbook. manual / V. I. Varfolomeev, S. V. Nazarov; Ed. S. V. Nazarova. – M.: Finance and Statistics, 2004. – 264 p.
• Emelyanov, A. A. Simulation modeling in economic information systems [Text] / A. A. Emelyanov, E. A. Vlasova, R. V. Duma; Ed. A. A. Emelyanova. – M.: Finance and Statistics, 2002.
• Maksimey, I.V. Simulation modeling on a computer [Text] / I.V. Maksimey. – M.: Radio and Communications, 1988. – 232 p.
• Naylor, T. Machine simulation experiments with models of economic systems [Text] / T. Naylor. – M.: Mir, 1975.
• Fomin, G. P. Systems and models of queuing in commercial activities[Text]: textbook. allowance / G. P. Fomin. – M.: Finance and Statistics, 2000.
• Buslenko, N. P. Modeling of complex systems [Text] / N. P. Buslenko. – M.: Nauka, 1978.
• Novikov, O. A. Applied issues of queuing theory [Text] / O. A. Novikov, S. I. Petukhov. – M.: Soviet radio, 1969. – 400 p.
• Riordan, J. Probabilistic queuing systems [Text] / J. Riordan. – M.: Communication, 1966. – 184 p.
• Sovetov, B. Ya. Modeling of systems [Text]: textbook for universities / B. Ya. Sovetov, S. A. Yakovlev. – M.: Higher School, 1998.
• Shannon, R. Simulation modeling of systems - art and science [Text] / R. Shannon. – M.: Mir, 1978.
• Hemdi A. Taha Chapter 18. Simulation // Introduction to Operations Research = Operations Research: An Introduction. - 7th ed. - M.: “Williams”, 2007.
• Strogalev V.P., Tolkacheva I.O. Simulation modeling. - MSTU im. Bauman, 2008.
• Lowe A., Kelton V. Simulation modeling. St. Petersburg: Publishing house: Peter, 2004. – 848 p.