Introduction.

1. Basic principles of modeling control systems.

1.1. Principles of a systematic approach in modeling control systems.

1.2. Approaches to the study of control systems.

1.3. Stages of model development.

2. General characteristics of the problem of modeling control systems.

2.1. Goals of modeling control systems.

3. Classification of types of system modeling.

Conclusion.

Bibliography.

1.1. INTRODUCTION

In this term paper on the topic “The use of modeling in the study of control systems”, I will try to reveal the basic methods and principles of modeling in the context of the study of control systems.

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 to make decisions in various fields of engineering. Existing and designed systems can be effectively investigated using mathematical models (analytical and simulation) implemented on modern computers, which in this case act as an experimenter's tool with a system model.

At present, it is impossible to name an area of ​​human activity in which, to one degree or another, modeling methods would not be used. This is especially true for the management of various systems, where the main ones are decision-making processes based on the information received. Let us dwell on the philosophical aspects of modeling, or rather the general theory of modeling.

Methodological basis of modeling. Everything that human activity is aimed at is called an object (lat. objection - an object). The development of a methodology is aimed at streamlining the receipt and processing of information about objects that exist outside of our consciousness and interact with each other and external environment.

AT scientific research Hypotheses play an important role, i.e., certain predictions based on a small amount of experimental data, observations, guesses. A quick and complete test of the put forward hypotheses can be carried out in the course of a specially designed experiment. When formulating and testing the correctness of hypotheses, analogy is of great importance as a method of judgment.

In general, modeling can be defined as a method of indirect cognition, in which the studied object-original is in some correspondence with another object-model, and the model is capable of replacing the original in one way or another at some stages of the cognitive process. The stages of cognition at which such a replacement takes place, as well as the forms of correspondence between the model and the original, can be different:

1) simulation as cognitive process, containing the processing of information coming from the external environment, about the phenomena occurring in it, as a result of which images corresponding to objects appear in the mind;

2) modeling, which consists in building a certain model system (second system), connected by certain similarity relations with the original system (first system), and in this case, the mapping of one system to another is a means of identifying dependencies between the two systems, reflected in similarity relations and not the result of a direct study of the incoming information.

1. BASIC CONCEPTS OF THE THEORY OF SIMULATION OF SYSTEMS

Modeling begins with the formation of the subject of research - a system of concepts that reflects the characteristics of the object that are essential for modeling. This task is quite complex, which is confirmed by different interpretations in the scientific and technical literature of such fundamental concepts as a system, model, modeling. Such ambiguity does not indicate the fallacy of some and the correctness of other terms, but reflects the dependence of the subject of research (modeling) both on the object under consideration and on the goals of the researcher. A distinctive feature of modeling complex systems is its versatility and variety of ways to use it; it becomes an integral part of the entire life cycle of the system. This is explained primarily by the manufacturability of models implemented on the basis of computer technology: a fairly high speed of obtaining simulation results and their relatively low cost.

1.1. Principles of the system approach in system modeling.

At present, in the analysis and synthesis of complex (large) systems, a systematic approach has been developed, which differs from the classical (or inductive) approach. The latter considers the system by moving from the particular to the general and synthesizes (constructs) the system by merging its components, developed separately. In contrast, the systematic approach involves a consistent transition from the general to the particular, when the consideration is based on the goal, and the object under study is distinguished from environment.

Simulation object. Specialists in the design and operation of complex systems deal with control systems various levels, which have a common property - the desire to achieve some goal. This feature will be taken into account in the following definitions of the system. System S is a purposeful set! interconnected elements of any nature. The external environment E is a set of elements of any nature existing outside the system that affect the system or are under its influence. "

Depending on the purpose of the study, different relationships between the object S itself and the environment E can be considered. Thus, depending on the level at which the observer is located, the object of study can be distinguished in different ways and various interactions of this object with the environment can take place.

With the development of science and technology, the object itself is continuously becoming more complex, and even now they are talking about the object of study as some kind of complex system that consists of various components interconnected with each other. Therefore, considering the system approach as the basis for building large systems and as the basis for creating a methodology for their analysis and synthesis, it is first of all necessary to define the very concept of the system approach.

A systematic approach is an element of the doctrine of the general laws of the development of nature and one of the expressions of the dialectical doctrine. You can give different definitions of the system approach, but the most correct one is the one that allows you to evaluate the cognitive essence of this approach with such a method of studying systems as modeling. Therefore, it is very important to single out the system S itself and the external environment E from an objectively existing reality and describe the system based on system-wide positions.

With a systematic approach to modeling systems, it is necessary first of all to clearly define the purpose of modeling. Since it is impossible to completely model a really functioning system (the original system, or the first system), a model (model system, or the second system) is created for the problem posed. Thus, in relation to modeling issues, the goal arises from the required modeling tasks, which allows you to approach the choice of criterion and evaluate which elements will be included in the created model M. Therefore, it is necessary to have a criterion for selecting individual elements in the created model.

1.2. Approaches to the study of systems.

Important for the system approach is the definition of the structure of the system - the totality of links between the elements of the system, reflecting their interaction. The structure of the system can be studied from the outside in terms of the composition of individual subsystems and the relationships between them, as well as from the inside, when individual properties are analyzed that allow the system to achieve a given goal, that is, when the functions of the system are studied. In accordance with this, a number of approaches to the study of the structure of a system with its properties have been outlined, which should primarily include structural and functional.

In the structural approach, the composition of the selected elements of the system S and the links between them are revealed. The totality of elements and links between them makes it possible to judge the structure of the system. The latter, depending on the purpose of the study, can be described in different levels consideration. The most general description of the structure is a topological description, which makes it possible to define the constituent parts of the system in the most general terms and is well formalized on the basis of graph theory.

A functional description is less general, when individual functions are considered, i.e., algorithms for the behavior of the system, and a functional approach is implemented that evaluates the functions that the system performs, and a function is understood as a property that leads to the achievement of a goal. Since the function displays the property, and the property displays the interaction of the system S with the external environment E, the properties can be expressed as either some characteristics of the elements S iV) and subsystems Si of the system, or the system S as a whole.

If there is a certain standard of comparison, it is possible to introduce quantitative and qualitative characteristics of systems. For a quantitative characteristic, numbers are entered that express the relationship between this characteristic and the standard. The qualitative characteristics of the system are found, for example, using the method of expert assessments.

The manifestation of system functions in time S(t), i.e., the functioning of the system, means the transition of the system from one state to another, i.e., movement in the space of states Z. When operating the system S, the quality of its functioning is very important, determined by the efficiency indicator and which is the value of the efficiency evaluation criterion. There are various approaches to the choice of performance evaluation criteria. The system S can be evaluated either by a set of particular criteria or by some general integral criterion.

It should be noted that the created model M from the point of view of the system approach is also a system, i.e. S "= S" (M), and can be considered in relation to the external environment E. The models that are the simplest in terms of representation are those that retain a direct analogy phenomena. Models are also used in which there is no direct analogy, but only the laws and general patterns of behavior of the elements of the system S are preserved. A correct understanding of the relationships both within the model M itself and its interaction with the external environment E in to a large extent determined by the level at which the observer is located.

A simple approach to studying the relationships between the individual parts of the model involves considering them as a reflection of the relationships between the individual subsystems of the object. This classical approach can be used to create fairly simple models. The process of synthesizing the model M based on the classical (inductive) approach is shown in Fig. 1.1, a. The real object to be modeled is divided into separate subsystems, i.e., the initial data D for modeling are selected and goals C are set, reflecting certain aspects of the modeling process. Based on a separate set of initial data D, the goal is to model a separate aspect of the functioning of the system; on the basis of this goal, some component K of the future model is formed. The set of components is combined into the model M.

Thus, the development of model M based on the classical approach means the summation of individual components into a single model, and each of the components solves its own problems. own tasks and isolated from other parts of the model. Therefore, the classical approach can be used to implement relatively simple models in which separation and mutually independent consideration of individual aspects of the functioning of a real object are possible. For a model of a complex object, such a disunity of the tasks to be solved is unacceptable, since it leads to significant resource costs when implementing the model based on specific software programs. technical means. Two distinctive aspects of the classical approach can be noted: there is a movement from the particular to the general, the created model (system) is formed by summing up its individual components and the emergence of a new systemic effect is not taken into account.

With the complication of modeling objects, it became necessary to observe them from a higher level. In this case, the observer (developer) considers this system S as some subsystem of some metasystem, i.e., a system of a higher rank, and is forced to move to the position of a new system approach, which will allow him to build not only the system under study that solves a set of problems, but also create a system that is an integral part of the metasystem.

The systems approach has been used in systems engineering due to the need to study large real systems, when the insufficiency, and sometimes the error, of making any particular decisions has affected. The emergence of a systematic approach was influenced by an increasing amount of initial data during development, the need to take into account complex stochastic relationships in the system and the effects of the external environment E. All this forced researchers to study a complex object not in isolation, but in interaction with the external environment, as well as in conjunction with other systems of some metasystems.

A systematic approach allows solving the problem of building a complex system, taking into account all factors and possibilities, proportional to their significance, at all stages of studying the system 5 "and building a model M". The systems approach means that each system S is an integrated whole even when it consists of separate disparate subsystems. Thus, the system approach is based on the consideration of the system as an integrated whole, and this consideration during development begins with the main thing - the formulation of the goal of functioning. Based on the initial data D, which are known from the analysis external system, those restrictions that are imposed on the system from above or on the basis of the possibilities of its implementation, and on the basis of the purpose of functioning, the initial requirements T to the model of the system S are formulated. Based on these requirements, approximately some subsystems P, elements E are formed and the most difficult stage of synthesis is carried out -< бор В составляющих системы, для чего используются специальные критерии выбора КВ.

When modeling, it is necessary to ensure the maximum efficiency of the system model, which is defined as a certain difference between some indicators of the results obtained as a result of the operation of the model and the costs that were invested in its development and creation.

1.3. Stages of model development.

On the basis of a systematic approach, a certain sequence of model development can also be proposed, when two main design stages are distinguished: macro-design and micro-design.

At the stage of macro-design, on the basis of data about the real system S and the environment E, a model of the environment is built, resources and constraints for building a system model are identified, a system model and criteria are selected to assess the adequacy of the model M of the real system S. Having built a model of the system and a model of the environment , on the basis of the criterion of the efficiency of the functioning of the system in the process of modeling, the optimal control strategy is chosen, which makes it possible to realize the capabilities of the model for reproducing certain aspects of the functioning of the real system S.

The micro-design stage largely depends on the particular type of model chosen. In the case of a simulation model, it is necessary to ensure the creation of information, mathematical, technical and software modeling systems. At this stage, it is possible to establish the main characteristics of the created model, estimate the time of working with it and the cost of resources to obtain a given quality of the correspondence of the model to the process of functioning of the system S.

Regardless of the type of model M used, when building it, it is necessary to be guided by a number of principles of a systematic approach: 1) proportionally sequential progress through the stages and directions of creating a model; 2) coordination of information, resource, reliability and other characteristics; 3) the correct ratio of individual levels of the hierarchy in the modeling system; 4) the integrity of individual isolated stages of model building.

Model M must meet the given purpose of its creation, so the individual parts must be arranged mutually, based on a single system task. The goal can be formulated qualitatively, then it will have more content and for a long time can reflect the objective capabilities of this modeling system. With a quantitative formulation of the goal, an objective function arises that accurately reflects the most significant factors influencing the achievement of the goal.

Building a model is one of the systemic tasks in which solutions are synthesized based on a huge number of initial data, based on the proposals of large teams of specialists. The use of a systematic approach in these conditions allows not only to build a model of a real object, but also, on the basis of this model, to select the required number of control information in a real system, to evaluate the indicators of its functioning and, thereby, on the basis of modeling, find the most effective construction option and an advantageous mode of functioning of the real system S.

2. GENERAL CHARACTERISTICS OF THE PROBLEM OF SYSTEM MODELING

With the development of system research, with the expansion of experimental methods for studying real phenomena, abstract methods are becoming increasingly important, new scientific disciplines appear, and elements of mental labor. Mathematical methods of analysis and synthesis are of great importance in creating real systems S; a number of discoveries are based on! purely theoretical research. However, it would be wrong to forget that the main criterion of any theory is practice, and even purely mathematical, abstract sciences are based in their basis on the foundation of practical knowledge.

Experimental studies of systems. Simultaneously with the development of theoretical methods of analysis and synthesis, the methods of experimental study of real objects are also being improved, and new research tools are emerging. However, the experiment was and remains one of the main and essential tools of knowledge. Similarity and modeling allow you to describe the real in a new way! process and simplify its experimental study. The very concept of modeling is also being improved. If earlier modeling! meant a real physical experiment or the construction of a model that imitates a real process, then at present new types of modeling have appeared, which are based on the formulation of not only physical, but also mathematical experiments.

Cognition of reality is a long and complex process. Determining the quality of functioning of a large system, choosing the optimal structure and algorithms! behavior, the construction of the system S in accordance with the set! before her goal - the main problem in the design of modern systems, so modeling can be considered as one of the methods used in the design and study of large systems.

Modeling is based on some analogy between real and thought experiment. Analogy is the basis for explaining the phenomenon under study, however, only practice, only experience, can serve as a criterion of truth. Although modern scientific hypotheses can be created purely theoretically, they are, in fact, based on broad practical knowledge. To explain the real; processes, hypotheses are put forward, to confirm which an experiment is set up or such theoretical reasoning is carried out that logically confirms their correctness. In a broad sense, an experiment can be understood as a certain procedure for organizing and observing some phenomena that are carried out under conditions close to natural, or imitate them. 3

A distinction is made between a passive experiment, when the researcher observes the ongoing process, and an active experiment, when the observer intervenes and organizes the process. AT recent times an active experiment is widespread, since it is on its basis) that it is possible to identify critical situations, obtain the most interesting patterns, provide the possibility of repeating the experiment at various points, etc.

At the heart of any kind of modeling is some model that has a correspondence based on some general quality that characterizes the real object. An objectively real object has a certain formal structure, therefore, any model is characterized by the presence of a certain structure corresponding to the formal structure of a real object, or the studied side of this object.

Modeling is based on information gaps, since the very creation of the M model is based on information about a real object. In the process of implementing the model, information about a given object is obtained, at the same time, during the experiment with the model, control information is introduced, and the processing of the results obtained plays an important role, i.e., information underlies the entire modeling process.

Characteristics of system models. Complex organizational and technical systems, which can be attributed to the class of large systems, act as an object of modeling. Moreover, in terms of its content, the created model M also becomes a system S(M) and can also be classified as a class of large systems, which are characterized by the following.

1. The purpose of functioning, which determines the degree of purposefulness of the behavior of the model M. In this case, the models can be divided into single-purpose, designed to solve one problem, and multi-purpose, allowing to resolve or consider a number of aspects of the functioning of a real object.

2. The complexity, which, given that the model M is a collection of individual elements and relationships between them, can be estimated by total number elements in the system and the relationships between them. According to the variety of elements, a number of hierarchy levels, separate functional subsystems in the M model, a number of inputs and outputs, etc., can be distinguished, i.e. the concept of complexity can be identified by a number of features.

3. Integrity, indicating that the created model M is one integral system S(M), includes a large number of components (elements) that are in a complex relationship with each other.

4. Uncertainty that manifests itself in the system: according to the state of the system, the possibility of achieving the goal, methods. solving problems, the reliability of the initial information, etc. The main characteristic of uncertainty is such a measure of information as entropy, which in some cases makes it possible to estimate the amount of control information necessary to achieve a given state of the system. When modeling, the main goal is to obtain the required correspondence of the model to a real object, and in this sense, the amount of control information in the model can also be estimated using entropy and find the limiting minimum amount that is necessary to obtain the required result with a given reliability. Thus, the concept of uncertainty, which characterizes a large system, is applicable to the model M and is one of its main features.

5. Behavioral stratum, which allows you to evaluate the effectiveness of the system achieving the goal. Depending on the presence of random influences, one can distinguish between deterministic and stochastic systems, in their behavior - continuous and discrete, etc. The behavioral stratum of considering the system ^ allows, in relation to the model M, to evaluate the effectiveness of the constructed model, as well as the accuracy and reliability of the results obtained. Obviously, the behavior of the model M does not necessarily coincide with the behavior of a real object, and often the simulation can be implemented on the basis of another material carrier.

6. Adaptability, which is a property of a highly organized system. Thanks to adaptability, it is possible to adapt to various external disturbing factors in a wide range of changes in the effects of the external environment. As applied to the model, the possibility of its adaptation in a wide range of disturbing influences, as well as the study of the behavior of the model in changing conditions close to real ones, is essential. It should be noted that the question of the stability of the model to various perturbing influences may turn out to be significant. Since the M model is a complex system, the issues related to its existence, i.e., issues of survivability, reliability, etc., are very important.

7. The organizational structure of the modeling system, which largely depends on the complexity of the model and the degree of perfection of modeling tools. One of the latest achievements in the field of modeling can be considered the possibility of using simulation models to conduct computer experiments. The optimal organizational structure of the complex of technical means, information, mathematical and software of the S "(M) modeling system, the optimal organization of the modeling process are needed, since special attention should be paid to the modeling time and the accuracy of the results obtained.

8. Controllability of the model, arising from the need to provide control on the part of experimenters in order to be able to consider the course of the process under various conditions simulating real ones. In this sense, the presence of many controlled parameters and model variables in the implemented simulation system makes it possible to conduct a wide experiment and obtain a wide range of results.

9. The possibility of developing a model that, based on the current level of science and technology, allows you to create powerful modeling systems S (M) for studying many aspects of the functioning of a real object. However, when creating a modeling system, it is impossible to be limited only to tasks today. It is necessary to provide for the possibility of developing the modeling system both horizontally, in the sense of expanding the range of functions studied, and vertically, in the sense of expanding the number of subsystems, i.e., the created modeling system should allow the use of new modern methods and tools. Naturally, an intelligent modeling system can only function in conjunction with a team of people, so ergonomic requirements are imposed on it.

2.1. Goals of modeling control systems.

One of the most important aspects of building simulation systems is the goal problem. Any model is built depending on the goal that the researcher sets for it, so one of the main problems in modeling is the problem of the intended purpose. The similarity of the process occurring in the model M to the real process is not a goal, but a condition for the correct functioning of the model, and therefore the goal should be to study some aspect of the functioning of the object.

To simplify the M model, goals are divided into sub-goals and create more effective types models depending on the received modeling subgoals. There are a number of examples of modeling goals in the field of complex systems. For example, it is very important for an enterprise to study the processes of operational management of production, operational scheduling, advanced planning and here also modeling techniques can be successfully used.

If the purpose of modeling is clear, then the following problem arises, namely, the problem of building a model M. Building a model is possible if information is available or hypotheses are put forward regarding the structure, algorithms and parameters of the object under study. Based on their study, the object is identified. Currently, various methods for estimating parameters are widely used: by the method of least squares, by the method of maximum likelihood, Bayesian, Markov estimates.

If the model M is built, then the next problem can be considered the problem of working with it, i.e., the implementation of the model, the main tasks of which are to minimize the time for obtaining the final results and ensure their reliability.

A well-constructed model M is characterized by the fact that it reveals only those regularities that the researcher needs and does not consider the properties of the system S that are not essential for this study. It should be noted that the original and the model must be simultaneously similar in some respects and different in others, which makes it possible to single out the most important properties under study. In this sense, the model acts as a kind of “substitute” for the original, which ensures the fixation and study of only some properties of a real object.

In some cases, identification is the most difficult; in others, it is the problem of constructing the formal structure of an object. Difficulties are also possible in the implementation of the model, especially in the case of simulation modeling of large systems. At the same time, the role of the researcher in the modeling process should be emphasized. The statement of the problem, the construction of a meaningful model of a real object is largely a creative process and is based on heuristics. And in this sense there are no formal ways of choosing optimal view models. Often there are no formal methods that allow to accurately describe the real process. Therefore, the choice of this or that analogy, the choice of this or that mathematical apparatus of modeling is completely based on the existing experience of the researcher, and the researcher's mistake can lead to erroneous results of modeling.

Computer technology, which is currently widely used either for calculations in analytical modeling or for the implementation of a simulation model of a system, can only help in terms of the efficiency of implementing a complex model, but do not allow you to confirm the correctness of a tone or another model. Only on the basis of the processed data, the experience of the researcher, it is possible to reliably assess the adequacy of the model in relation to the real process.

If a real physical experiment occupies a significant place in the course of modeling, then the reliability of the tools used is also very important, since failures and failures of software and hardware can lead to distorted values ​​of the output data that reflect the course of the process. And in this sense, when conducting physical experiments, special equipment is needed, specially developed mathematical and information support, which allow implementing the diagnostics of modeling tools in order to weed out those errors in the output information that are caused by malfunctions of the functioning equipment. In the course of a machine experiment, erroneous actions of a human operator may also occur. Under these conditions, there are serious tasks in the field of ergonomic support for the modeling process.

3. CLASSIFICATION OF TYPES OF SIMULATION OF SYSTEMS.

Modeling is based on the theory of similarity, which states that absolute similarity can only take place when one object is replaced by another exactly the same. When modeling, absolute similarity does not take place and they strive to ensure that the model reflects the studied side of the object's functioning well enough.

Classification signs. As one of the first features of the classification of types of modeling, one can choose the degree of completeness of the model and divide the models according to this feature into complete, incomplete and approximate. Full simulation is based on complete similarity, which manifests itself both in time and in space. Incomplete modeling is characterized by incomplete similarity of the model to the object under study. Approximate modeling is based on approximate similarity, in which some aspects of the functioning of a real object are not modeled at all.

Depending on the nature of the processes under study in the system S, all types of modeling can be divided into deterministic and stochastic, static and dynamic, discrete, continuous and discrete-continuous. Deterministic modeling displays deterministic processes, i.e. processes in which the absence of any random influences is assumed; stochastic modeling displays probabilistic processes and events. In this case, a number of implementations of a random process are analyzed and the average characteristics are estimated, i.e., a set of homogeneous implementations. 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 you to reflect continuous processes in systems, and discrete-continuous modeling is used for cases where you want to highlight the presence of both discrete and continuous processes.

Depending on the form of representation of the object (system J, one can distinguish mental and real simulation.

Mental modeling is often the only way modeling 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 of the microworld that are not amenable to physical experiment can be analyzed. Mental modeling can be implemented in the form of visual, symbolic and mathematical.

Analog modeling is based on the application of analogies of various levels. The highest level is a complete analogy, which takes place only for fairly simple objects. With the complication of the object, analogies of subsequent levels are used, when the analog model displays several or only one side of the object's functioning.

Prototyping occupies an essential place in mental visual modeling. A mental layout can be used in cases where the processes occurring in a real object are not amenable to physical modeling, or it can precede other types of modeling. The construction of mental models is also based on analogies, however, they are usually based on cause-and-effect relationships between phenomena and processes in an object. If you introduce a symbol of individual concepts, i.e. signs, as well as certain operations between these signs, then you can implement sign modeling and use signs to display a set of concepts - to make 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.

At the heart of language modeling is a certain 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. Thesaurus is a dictionary that is cleared of ambiguity, i.e. in it only a single concept can correspond to each word, 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 main properties of its relations using a certain system of signs or symbols.

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

By mathematical modeling we will understand the process of establishing correspondence to a given real object of some mathematical object, called a mathematical model, and the study of this model, which allows obtaining the characteristics of the real object under consideration. The type of mathematical model depends on both 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,

Fig 1. Classification of types of system modeling.

describes a real object only with some degree of approximation to reality. Mathematical modeling for studying the characteristics of the process of functioning of systems can be divided into analytical, simulation and combined.

For analytical modeling, it is characteristic that the processes of functioning of the elements of the system are written in the form of some functional relationships (algebraic, integro-differential, finite-difference, etc.) or logical conditions. An analytical model can be studied by the following methods: a) analytical, when they seek to obtain general view explicit dependencies for the desired characteristics; b) numerical, when, not being able to solve equations in a general form, they strive to obtain numerical results with specific initial data; c) qualitative, when, without having a solution in an explicit form, it is possible to find some properties of the solution (for example, to estimate the stability of the solution).

In some cases, studies of the system can also satisfy the conclusions that can be drawn using the qualitative method of analyzing a mathematical model. Such qualitative methods are widely used, for example, in the theory of automatic control to evaluate the effectiveness of various options for control systems.

Conclusion.

At the end of this term paper I want to draw some conclusions from the above material about modeling in the study of control systems. So let's define the epistemological nature of modeling.

Defining the epistemological role of modeling theory, i.e. its significance in the process of cognition, it is necessary, first of all, to abstract from the variety of models available in science and technology and highlight the common features that are inherent in models of objects of the real world that are different in nature. This common feature is the presence of some structure (static or dynamic, material or mental) that is similar to the structure of the given object. In the process of studying, the model acts as a relative independent quasi-object, which makes it possible to obtain some knowledge about the object itself during the study.

AT modern Russia management and its research is on the path of complication. By applying modeling techniques such as analogy, impressive results can be achieved in economic activity enterprises. An analogy is a judgment about some particular similarity of two objects, and such similarity can be significant and insignificant. It should be noted that the concepts of materiality and insignificance of the similarity or difference of objects are conditional and relative. The significance of similarity (difference) depends on the level of abstraction and is generally determined by ultimate goal ongoing research. A modern scientific hypothesis is created, as a rule, by analogy with scientific provisions tested in practice.

In conclusion, the above can be summed up that modeling is the main way in the system of research of control systems and is of extreme importance for a manager of any level.

Bibliography.

1. Ignatieva A. V., Maksimtsov M. M. RESEARCH OF CONTROL SYSTEMS, Moscow, 2000

2. Paterson J. Theory of Petri nets and system modeling. - M.: Mir, 1984.

3. Priiker A. Introduction to simulation modeling and the SLAMP language. - M.: Mir, 1987.

4. Sovetov B. Ya.. Yakovlev S. A. Modeling of systems. - M.: graduate School, 1985.

5. Sovetov B. Ya., Yakovlev S. A. Modeling systems (2nd ed.). - M.: Higher school, 1998.

6. Sovetov B. Ya.. Yakovlev S. A. Modeling of systems: course design. - M.: Higher school, 1988.

7. Short E.M. Study of control systems. - M.: "DeKA", 2000.

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Business Process Improvement (BPI) is a one-time initiative or project to better align the organization's strategy with customer expectations. BPI includes the selection, analysis, design and implementation of an improved process.

Enterprise Process Management (EPM) is the application of BPM principles, methods and processes in a particular organization. EPM: a) ensures that the portfolio and end-to-end process architecture aligns with the organization's strategy and resources, and b) provides a governance model for evaluating and managing BPM initiatives.

Continuous optimization is a long-term approach to improving the effectiveness and productivity of specific processes based on a continuously functioning feedback control system.

Business Process Management

What is Business Process Management (BPM)?

BPM is a management discipline that assumes that the best way to achieve the goals of an organization is the purposeful management of its business processes. BPM treats processes as assets. It accepts that the objectives of the organization can be achieved through the description, design, control of business processes and the pursuit of their continuous improvement.

To be able to effectively manage business processes (that is, to develop BPM as a capability), an organization must have processes, people, and technology in place:

1. Business processes that support business process management. For example, an organization should have processes that ensure:
   • description and design of business processes;
   • development and implementation of business processes;
   • monitoring and control of the execution of business processes;
   • continuous and continuous improvement of business processes, despite and in response to internal and external changes.
2. Defined roles (people) involved in business process management. These include (but are not limited to) the following:
   • process architect, who is responsible for describing and designing business processes;
   • process analyst who is responsible for building, implementing, monitoring and optimizing business processes;
   • process owner, who is responsible for executing the business process from start to finish, in accordance with defined performance targets, and ultimately for creating value for the customer.
3. Introduction of specialized information technologies business process management, providing the following functionality:
   • description of business processes in the context of corporate architecture;
   • designing business processes for the purpose of implementation;
   • execution of business processes in the context of operational activities;
   • monitoring of target indicators of efficiency of business processes;
   • analysis of business processes in order to identify and evaluate opportunities for improvement;
   • business process change management.

Buisness process is a set of actions that transform one or more inputs into a specific result (product or service) that has value for the consumer.

Figure "Business process"

The concept of the consumer in the interaction of functions within the organization

Value in the form of design specifications

Example: IT department pharmaceutical company provides services to business units. Each such service is provided through a business process within the IT department. The provider-consumer relationship is shown below. A business process creates value for a customer in the form of a product or service. The essence of BPM is to optimize how that value is created.

Visualization and understanding of the business process is facilitated by the graphical representation of actions in the form of rectangles connected to each other in a path diagram.

Among the artifacts that organizations often create and maintain in process work are the following.

• Business context: what intrinsic capabilities the process provides and what the business process contributes to the creation of a product or service for an external customer.
• Process context: providers and inputs, outputs and consumers, start and end events, regulations, resources used and performance targets.
• Business transactions that accompany the transfer of work between functions and roles within an organization and between the organization, providers, and customers.
• State changes that describe the transformation of a product as it passes through a process.
• Business events that occur outside and inside the process, as well as actions and forks in the process that are activated by these events.
• A decomposition showing the breakdown of a process into smaller and smaller pieces of work from the top level of the process as a whole to the bottom level of tasks.
• Expected performance indicators detailing the commitment to the customer to provide a product or service, and performance metrics established for the process and measured to ensure that commitments to the customer are being met.
• The structure of the organization and the picture of how the various functions and roles within the organization are put together to support the execution of the process.
• The functionality of information systems and how this functionality is involved in the execution of the process.

Buisness process is a set of actions that create a certain value (product or service) for the consumer. This definition contains both an internal aspect (set of activities) and an external aspect (customer value), so it is best to monitor process performance from both perspectives.
Performance indicators measured from the outside or from the point of view of the consumer are commonly called performance, they are designed to answer the question: “Are we doing what we need to do?” These indicators should confirm that we systematically meet the needs and expectations of the customer.

The secret to the usefulness of metrics at the Check stage is the correct architecture of the process description at the Planning stage. Process performance targets are determined by customer expectations. These top-level performance indicators are in turn decomposed into underlying performance targets that can be set at the functional and operational levels. In theory:

• if all operational targets are achieved, then functional indicators are met;
• if all functional indicators are achieved, then the process performance indicators of the highest level are met;
• if all indicators of process efficiency are achieved, then the consumer is satisfied.

Categories of business processes

Business processes can be divided into three categories:

• Core Processes- end-to-end and, as a rule, cross-functional processes that directly create value for the consumer. Core processes are also referred to as core processes because they represent the activities necessary for an organization to fulfill its mission. These processes constitute a value chain in which each step adds value to the previous one, as measured by the contribution to the creation or delivery of a product or service and ultimately to the creation of value for the customer.
• Helper Processes designed to support core processes, usually through the management of resources and/or infrastructure required by core processes. The difference between primary and secondary processes is that secondary processes do not directly create value for the customer. Examples of supporting processes are usually related to IT, finance, human resources. Although support processes are often closely related to functional areas (for example, the process of granting and revoking network access permissions), they can and often do cross functional boundaries.
• Management processes designed to measure, monitor and control business activities. They are designed to ensure that the main and auxiliary processes are designed and executed in accordance with the established operational, financial goals, regulatory and legal restrictions. Like supporting processes, management processes do not directly add value to the customer, but they are necessary to ensure that operations meet performance and performance targets.

BPM maturity model

Business Process Modeling

Process Modeling Goals

The purpose of the simulation- to develop such a representation of the process that will describe it accurately and sufficiently fully, based on the task. The depth of detail and content of the model is determined by what is expected of a modeling project: one project may need a simple diagram, while another may need a fully developed model.

Process Models are the means:

• organization process management;
• process efficiency analysis;
• descriptions of changes.

The process model can describe the desired state of the business and determine the requirements for resources that ensure the efficient execution of operations, such as people, information, equipment, systems, finance, energy.

Motives for process modeling:

Common process notations:

BPMN:

Path chart by Bruce Silver:

Block diagram:

UML:

IDEF:

Value stream map:

Basic principles of business process modeling

What does business process modeling mean in practice? Business process modeling in a company can be aimed at solving a large number of different tasks:

• Accurately define the outcome of a business process and evaluate its value to the business.
• Determine the set of activities that make up the business process. A clear definition of the set of tasks and activities to be performed is essential to a detailed understanding of the process.
• Determine the order in which actions should be performed. Actions within a single business process can be performed either sequentially or in parallel. It is obvious that parallel execution, if allowed, reduces the overall execution time of the process and, consequently, increases its efficiency.
• Separate areas of responsibility: determine and then track which employee or department of the company is responsible for the implementation of a particular action or process as a whole.
• Determine the resources consumed by the business process. By knowing exactly who is using what resources and for what operations, you can improve resource efficiency through planning and optimization.
• Understand the essence of the interactions between the employees and departments of the company involved in the process and evaluate, and then improve the effectiveness of communication between them.
• See the movement of documents during the process. Business processes produce and consume various documents (in paper or electronic form). It is important to understand where and where documents or information flows come from and determine whether their movement is optimal and whether all of them are really necessary.
• Identify potential bottlenecks and opportunities for process improvement, which will be used later to optimize it.
• It is more efficient to implement quality standards such as ISO 9000 and successfully achieve certification.
• Use business process models as a guide for new hires.
• Effectively automate business processes as a whole or their individual steps, including automation of interaction with the external environment - customers, suppliers, partners.
• Having understood the totality of the company's business processes, understand and describe the activities of the enterprise as a whole.

In its turn, the main task in modeling the company's business processes is a description of the processes existing in it in order to build their models "as is". To do this, it is necessary to collect all available information about the process, which, as a rule, is fully owned only by company employees directly involved in the process. Thus, we come to the need for a detailed survey (interview) of all employees involved in the business process. It should be emphasized that one should not be limited to information about the process provided by the head of the unit and managers. Usually, only a conversation with an employee who directly performs actions within the described business process gives an adequate idea of ​​how the process functions in reality.

The first question when building a model "as is" concerns the result of the considered business process. It happens that it is not easy to get a clear statement of the result of a business process, despite the importance of this concept for the efficiency of the company.

After determining the result, you should understand the sequence of actions that make up the process. The sequence of actions is modeled at different levels of abstraction. At the top level, only the most important steps in the process are shown (usually no more than ten). Then, each of the high-level steps (sub-processes) is decomposed. The depth of decomposition is determined by the complexity of the process and the required level of detail. In order to get a truly complete picture of the business process, it is necessary to decompose to atomic business functions - well-understood elementary actions (individual operations in software or performed by a person), which make no sense to decompose into components.

Based on the collected information, a model of the usual, or optimal, execution of the process is built and possible scenarios for its execution with failures are determined. Various failures (exceptions - exceptions) can disrupt the optimal course of the process, so you should specify how the exceptions will be "handled", that is, what actions are taken in case of an exception. The figure shows the main steps in building a business process model.

An important part of building a business process model is the study of aspects of its effectiveness. This includes resource usage, employee turnaround time, potential delays and downtime. It is necessary to develop a system of indicators, or metrics, to evaluate the effectiveness of the process. Partially, KPI (Key Performance Indicator) used in the company can be taken as metrics, however, additional indicators characterizing the process under consideration may also be required.

Modeling defines business goals, to which the simulated process contributes. It is necessary to distinguish between the concepts of a business goal and the result of a process. Each business process must have at least one result and be aimed at achieving at least one business goal. For example, the result of the process “Execute a connection order for a subscriber” can be defined as “Receive a connection confirmation from the client”, while the business goals that are pursued by performing this process may include “Ensure a minimum order lead time” and “Ensure a minimum percentage of claims ". To determine the goals, you should refer to the company's business strategy.

It is necessary to identify events that can interrupt the course of the process. In the event of an interruption, it may be necessary to correctly "roll back" (compensate) those process steps that have already been completed. To do this, you must define the logic of compensating actions for each interrupting event.

Finally, it is necessary to consider the available software tools that implement business process support. This is important because software may hide some features of the process behavior that are not fully known to the employees performing individual steps. The information collected at this stage will be useful in further automation of the process.

By collecting all of the above information, you can get a good idea of ​​the progress of the business process. At the modeling stage, the following results should be obtained:

• Process card, showing the relationship between different business processes and their interactions. On the process map, as a rule, each business process of the company is shown as a rectangle, the arrows show the links between them (for example, the dependence of one process on another, or the replacement of one process by another when a certain condition is met), and also presents various documents that are transferred from process to process or regulate their course (standards, instructions, etc.).
• Role Diagram A that shows the roles in the execution of the process and the relationships between them. The role diagram is not hierarchical. It represents relationships such as group participation, leadership, communication, replacing one role with another, etc.
• The "as is" model each considered business process, describing the process in detail and reflecting the course of the process, actions, roles, movement of documents, as well as points of possible optimization. This model includes:
  • process environment diagram, representing a business process as a single activity (that is, not revealing the course of the process), for which the process triggering event, required inputs, result, roles, performance indicators, interrupting events and compensating processes, regulating documents, related business processes can be shown. goals;
  • high-level process diagram, showing his major steps (usually no more than ten) and the roles associated with them;
  • detailed diagrams for each step of the high-level model(depending on the complexity of the process, several hierarchically organized diagrams may be used here) showing in detail the progress of the process, interrupting events, business rules, roles and documents;
  • exception handling diagram, showing what actions are performed in the event of a given exception and by whom, as well as where control is transferred after the exception is processed.

• the owner of the business process and one or two employees of the same division of the company who help him;
• quality management specialist;
• business analyst(s);
• representative of the IT department;
• external consultant (optional).

BPM-System Platform for creating and managing business processes

Bpm'online studio is a business process management system (BPMS) that allows you to automate various business tasks. Bpm'online studio- an intuitive tool for implementing a process approach in the work of various departments of the company and effectively manage changes throughout the enterprise.

Annotation: The concept of a model is given, the classification of models is given, the stages of mathematical modeling of control processes are described. The model of learning management is considered.

Basic concepts of modeling theory

A model in the general sense (generalized model) is a specific object created for the purpose of obtaining and (or) storing information (in the form of a mental image, description by sign means or material system), reflecting the properties, characteristics and connections of the original object of an arbitrary nature, essential for the task being solved by the subject. For theory decision making the most useful models are those that are expressed in words or formulas, algorithms and other mathematical means.

Word model example. Let us discuss the need to take into account the effect of loyalty in the management of an organization in modern conditions. Loyalty is an honest, conscientious attitude towards something or someone. Loyalty-based management was founded in 1908 by Harvard professor Joshua Royce. He is the author of the book "Philosophy of Loyalty", where the concept of "loyalty" is scientifically defined for the first time.

As part of the proposed verbal model business loyalty is considered from the point of view of three independent basic aspects: consumer loyalty, employee loyalty and investor loyalty. Each time, the word "loyalty" means something different:

• commitment (from the point of view of buyers),
• integrity (from the point of view of employees),
• mutual trust, respect and support (from the point of view of investors).

But despite the pronounced components, this system should only be considered as a whole, since it is impossible to create loyal customers without paying attention to employee loyalty, or to cultivate employee loyalty without due attention to investor loyalty. None of the parts can exist separately from the other two, but all three together allow the organization to reach unprecedented heights in development.

It must be clearly understood that loyalty-based management is primarily focused on people. First of all, it is people and their role in business that are considered here. It is more a model of motivation and behavior than marketing, financial or production development. Only secondarily, loyalty-based management generalizes people into more abstract categories and manages technical processes.

As practice shows, people are always more willing to work for an organization that has a purpose of service than for an organization that exists only to "make money". Therefore, people willingly work in the church or in public organizations.

Managers who wish to successfully use the loyalty effect management model should not consider profit as a primary goal, but as a necessary element for the well-being and survival of the three components of every business system: customers, employees and investors. Even at the beginning of the twentieth century. Henry Ford said that "an organization cannot work without profit, ... otherwise it will die. But to create an organization only for the sake of profit ... means to lead it to certain death, since it will not have an incentive to exist."

The basis of the loyalty model under consideration is not profit, but attracting additional customers, a process that consciously or unconsciously lies at the heart of most successful organizations. Creating a target number of buyers permeates all areas of a company's business. The forces that govern the relationship between customers, employees, and investors are called the forces of loyalty. The measure of success is whether customers come back to buy more, or whether they go somewhere else, ie. whether they are loyal.

How cause loyalty initiates several economic effects, which affect the entire business system in the following way:

1. Earnings and market share increase when the most promising buyers cover the entire spectrum of the company's activities, creating a good image about it. public opinion and keep shopping. Due to the large and high-quality offer, the company can afford to be more picky when choosing new customers and focus on more profitable and potentially loyal projects to attract them, further stimulating its long-term growth.
2. Long-term growth allows the firm to attract and retain the best employees. Consistently maintaining a target number of buyers increases employee loyalty, giving them a sense of pride and job satisfaction. Further, in the process of interaction, regular employees learn more about their regular customers, in particular, how to better serve them so that the volume of purchases grows. This increasing volume of sales spurs both customer loyalty and employee loyalty.
3. Loyal employees in long term learn to reduce costs and improve the quality of work (learning effect). The organization can use this extra productivity to expand the reward system, to buy the best equipment and learning. All this, in turn, will spur employee productivity, reward growth and, consequently, loyalty.
4. This productivity spiral provides a cost advantage that is very difficult to replicate for purely competitive organizations. Long-term cost advantages, coupled with a steady growth in the number of loyal customers, bring profits that are very attractive to investors. This, in turn, enhances the company's ability to attract and retain the "right" investors.
5. Loyal investors behave like partners. They stabilize the system, lower the cost of raising capital, and ensure that diverted cash flows are put back into the business as an investment. This strengthens the organization and increases its productive capacity.

Let's discuss once again the main ideas of the loyalty model. Everyone knows that customers are the assets of any organization, and in order to be successful, it must be managed as effectively as other assets. But to do this, you need to be able to segment buyers, predict their behavior, as well as the life cycle of their cash flows.

Most failures are based on the common business language of the organization - Accounting, which currently limits the possibilities of forming loyalty. Accountants fail to draw the line between revenue from new customers and revenue from regular, loyal customers. This is because they don't know, or rather they don't care, that serving a new customer is more expensive than serving a regular customer. Worse, in most organizations, accountants consider investments in customer acquisition to be short-term. And this is instead of taking them to a special account of the buyer and depreciating during the entire time of the relationship with him.

So how do you build a portfolio of loyal customers? There are two options. The first is an increase in the list of buyers. The organization is constantly adding new customers to the top of the list, but its old customers are also constantly being purged from the bottom of the list. It turns out the effect of a leaky basket. The bigger the hole, the harder it is to fill and keep full. The second one lies in the effect of profit from each buyer. In most organizations, each customer's profit grows as long as he remains a customer. In other words, it is unprofitable for the organization to lose regular customers, even replacing them with new ones. It turns out a situation where "for one beaten they give two unbeaten."

When selecting buyers, you need to remember that there are three main types of loyal buyers. This helps determine if the organization can make a customer loyal:

1. Some buyers are inherently predictable and loyal, no matter how the organization works with them. They are simply loyal by nature. They prefer more stable and lasting relationships.
2. Some buyers are more profitable than others. They spend more money than others, pay for purchases without delay and require less attention from service personnel.
3. Some buyers find the organization's products or services (because of their features) more attractive than those of competitors. There is no such organization whose products would be liked by everyone without exception. Strengths its products or services will simply be better suited to certain customers, more fully satisfying their desires and capabilities.

Without a doubt, each organization is unique, but still, to one degree or another, its profit indicators will fit into the general model of economic effects derived from the persistence or loyalty of customers. Among them it is worth noting the following:

• acquisition costs (advertising directed to new customers, commissions on sales to new customers, sales overhead, etc.),
• basic profit (the price paid by newly appeared buyers exceeds the cost of the organization to create a product),
• revenue growth (as a rule, if the buyer is satisfied with the parameters of the product, he is inclined to increase the volume of purchases over time),
• savings costs (close familiarity with the organization's products reduces the dependence of buyers on its employees for information and advice),
• reviews (customers satisfied with the level of service recommend the organization to their friends and acquaintances),
• additional price ( regular customers those who have been with an organization long enough to explore all of its products and services get disproportionately more from continuing the relationship and do not need additional discounts or promotions).

To assess the true long-term loyalty potential of a customer or group of customers, it is necessary to know their propensity to exhibit consistency. So some buyers will defect to a competitor for a 2% discount, while others will remain at a 20% price difference. The amount of effort it takes to lure different types of customers is called the loyalty ratio. In some organizations, the history of development or the behavior of buyers in individual segments is used to evaluate loyalty coefficients. In others, especially those whose future is loosely connected to the past, they try to find out by data analysis how big the discount should be in order for buyers to switch to their organization. But despite all the measurement challenges, using a loyalty metric allows organizations to identify customer retention and implement sound practices proven in one department throughout the organization.

The development of systems for measuring, analyzing and managing loyalty cash flows can lead an organization to make investments that will further ensure the growth of the number of customers and the organization as a whole.

So, the loyalty model is substantiated in detail at the verbal level. This justification mentioned mathematical and computer support. However, they are not required to make initial decisions.

Mathematical models in decision making. With a more thorough analysis of the situation, verbal models, as a rule, are not enough. It is necessary to use rather complex mathematical models. Thus, when making decisions in management production systems are used:

• models technological processes(primarily models of control and management);
• product quality assurance models (in particular, reliability assessment and control models);
• queuing models;
• inventory management models (logistics models);
• simulation and econometric models of the enterprise as a whole, etc.

In preparation and decision making often used simulation models and systems. The simulation model allows you to answer the question: "What will happen if ..." The simulation system is a set of models that simulate the course of the process under study, combined with a special system of auxiliary programs and an information base that allows you to quite simply and quickly implement variant calculations.

Basic terms of mathematical modeling. Before starting to consider specific mathematical models of management processes, it is necessary to recall the definitions of basic terms, such as:

• system components- parts of the system that can be isolated from it and considered separately;
• independent variables- they can change, but these are external values ​​that do not depend on the processes taking place in the system;
• dependent variables- the values ​​of these variables are the result (function) of the impact on the system of independent external variables;
• controlled (control) variables- those whose values ​​can be changed by the researcher;
• endogenous variables- their values ​​are determined during the activity of the system components (i.e. "inside" the system);
• exogenous variables- are determined either by the researcher or from the outside, i.e. in any case act on the system from the outside.

When building any management process model, it is desirable to adhere to the following action plan:

1. Formulate the goals of studying the system;
2. Select those factors, components and variables that are the most significant for this task;
3. Take into account in one way or another extraneous factors not included in the model;
4. Evaluate the results, check the model, evaluate the completeness of the model.

Models can be divided into the following types:

1. Functional models - express direct relationships between endogenous and exogenous variables.
2. Models expressed using systems of equations with respect to endogenous quantities. They express balance ratios between various economic indicators (for example, a model of input-output balance).
3. Optimization type models. The main part of the model is a system of equations with respect to endogenous variables. But the goal is to find the optimal solution for some economic indicator(for example, to find such values ​​of tax rates to ensure the maximum inflow of funds to the budget for a given period of time).
4. Simulation models are a very accurate representation of an economic phenomenon. In this case, mathematical equations may contain complex, non-linear, stochastic dependencies.

On the other hand, models can be divided into controlled and predictive. Managed models answer the question: "What happens if...?"; "How to achieve the desired?", and contain three groups of variables: 1) variables characterizing the current state of the object; 2) control actions - variables that affect the change in this state and are amenable to purposeful choice; 3) initial data and external influences, i.e. externally set parameters and initial parameters.

In predictive models, control is not explicitly identified. They answer the questions: "What will happen if everything remains the same?"

Further, models can be divided according to the method of measuring time into continuous and discrete. In any case, if time is present in the model, then the model is called dynamic. Most often, discrete time is used in models, because information is received discretely: reports, balance sheets and other documents are compiled periodically. But from a formal point of view continuous model may be easier to learn. Note that in physical science there is a continuing discussion about whether the real physical time is continuous or discrete.

Usually, fairly large socio-economic models include material, financial and social sections. Material section - balances of products, production capacities, labor, natural resources. This is a section that describes the fundamental processes, this is a level that is usually poorly controlled, especially fast, because it is very inertial.

The financial section contains cash flow balances, rules for the formation and use of funds, pricing rules, etc. At this level, many controlled variables can be identified. They can be regulators. The social section contains information about people's behavior. This section introduces the models decision making there are many uncertainties, since it is difficult to correctly take into account such factors as labor productivity, consumption patterns, motivation, etc.

When constructing models that use discrete time, econometric methods are often used. Among them, regression equations and their systems are popular. Various systems regression equations constructed for solving practically important problems are considered in. Lags are often used (analysis of an economic phenomenon using variant calculations) - this is mathematical model. The simulation system is a set of models simulating the course of the process under study, combined with a special system of auxiliary programs and an information base, which make it possible to quite simply and quickly implement variant calculations. Thus, simulation is understood as a numerical method for conducting computer experiments with mathematical models that describe the behavior of complex systems over long periods of time, while the simulation experiment consists of the following six stages:

1. problem statement,
2. building a mathematical model,
3. compiling a computer program,
4. model suitability assessment,
5. experiment planning,
6. processing of experimental results.

Simulation ( simulation modeling) is widely used in various fields, including economics.

Economic and mathematical methods of management can be divided into several groups:

• - optimization methods,
• methods that take into account uncertainty, primarily probabilistic-statistical,
• methods for constructing and analyzing simulation models,
• methods of analysis of conflict situations (game theory).

In all these groups, static and dynamic settings can be distinguished. If there is a time factor, differential equations and difference methods are used.

Game theory (more appropriately called conflict theory, or conflict theory) originated as a theory rational behavior two players with opposite interests. It is most simple when each of them seeks to minimize their average loss, i.e. maximize your average payoff. From this it is clear that game theory tends to oversimplify real behavior in conflict situations. Participants in the conflict may assess their risk according to other criteria. In the case of several players, coalitions are possible. Of great importance is the stability of equilibrium points and coalitions.

In economics, 150 years ago, the theory of duopoly (competition of two firms) by O. Cournot was developed on the basis of considerations that we now attribute to game theory. A new impetus was given by the classic monograph by J. von Neumann and O. Morgenstein, published shortly after the Second World War. Economics textbooks usually deal with the "prisoner's dilemma" and the Nash equilibrium point (he was awarded the Nobel Prize in Economics in 1994).

The life cycle of an information system is divided into four stages:

Clarification;

Construction;

Transfer to operation.

The boundaries of each stage are defined by certain points in time at which it is necessary to make certain critical decisions and, therefore, achieve certain key goals.

Initial stage: modeling, requirements management

At the initial stage, the scope of the system is established and the boundary conditions are determined. To do this, it is necessary to identify all external objects with which the developed system should interact, and to determine the nature of this interaction at a high level. At the initial stage, all the functional capabilities of the system are identified and a description of the most significant of them is made.

Business applications include:

Development success criteria;

risk assessment;

Estimating the resources needed to complete the development;

Calendar plan indicating the deadlines for completion of the main stages.

Within the framework of this stage, research and analysis of the activity of the automated object is carried out; Of course, only those processes that correspond to the goals and objectives of this object are of importance. The result is an object model that is usually described in terms of business processes and business functions. In parallel with this, the shortcomings of existing information systems are identified (remember the principle of continuity) and the needs are formulated for improving the facility management system and / or automating its individual functions. Requirements must be economically justified. The result of the implementation of the described stages of the stage is the execution of a feasibility study (FS) and terms of reference(TOR) for the development of IP. Usually, a feasibility study is drawn up as part of the TOR. In addition, the TOR necessarily reflects the requirements for IP and restrictions on design resources (primarily, deadlines). IS requirements are defined as a set of functions implemented by the system, as well as a description of the information provided to it.

2. Refinement stage: analysis and design.

At the refinement stage, an analysis of the application area is carried out, and the architectural basis of the information system is developed.

When making any decisions regarding the architecture of the system, it is necessary to take into account the system being developed as a whole. This means that it is necessary to describe most of the functionality of the system and take into account the relationships between its individual components.

At the end of the clarification stage, an analysis of architectural solutions and ways to eliminate the main risk factors in the project is carried out.

In accordance with the received requirements, designers develop functional architecture IS, which reflects the structure of its functions, and system architecture IS, which is a composition of supporting subsystems. The construction of a system architecture is carried out on the basis of a description of the functional architecture of the IS and, in fact, consists in compiling information processing technologies with the participation of all supporting IS subsystems (first of all, information, technical, and software). The output of the design stage is usually:

1) conceptual, logical and physical data models of IS;

2) specifications of IS modules;

3) specification of IS user interfaces;

4) a set of selected design decisions that determine the IS architecture - including the selected software platform, the number of links in the architecture (one-tier, two-tier [client-server or file-server], three-tier), etc. The final document that completes the design stage - technical project(TP).

3. Design stage: coding and testing

At the design stage, a finished product is developed, ready for transfer to the user.

At the end of this stage, the performance of the developed software is determined.

At this stage, complex debugging of the IS is carried out, checking for compliance of the system modules with their specifications (the presence of all necessary functions, the absence of unnecessary functions), checking the reliability of operation (recoverability after software and hardware failures, time between failures, etc.), personnel training . Complex Information Systems usually require experimental implementation: for example, first, IS is installed in one department of the organization, then the rest of the departments are gradually connected to automation. The implementation stage ends with the signing acceptance test report- which establishes the compliance of the implemented IS with the requirements of the customer.

4. Commissioning stage: installation and maintenance.

At the stage of commissioning, the developed software is transferred to users. When operating the developed system in real conditions, various kinds of problems often arise that require additional work to make adjustments to the developed product. This is usually associated with the detection of errors and flaws.

At the end of the handover phase, it must be determined whether the development objectives have been achieved or not.

At this stage, the process of regular operation of the IS is provided, which, among other things, includes the collection of complaints (claims) and statistics on the functioning of the IS, the correction of errors and shortcomings, and the registration of requirements for the modernization of the IS.

The urgency of the problem. For the successful implementation of management activities, it is necessary to have a clear idea of ​​​​the structure of the organization, the interaction of its constituent parts and the organization's relations with the external environment.

Organizations currently in existence are different huge variety both in terms of activities, and in terms of ownership, scale, and other parameters. However, each organization is unique in its own way. However, the same principles, methods and methods apply to the management of all organizations. To adapt them to the characteristics of a particular enterprise, to clearly define the place of management structures in the overall structure of the enterprise, as well as their interaction with each other and with other departments, modeling is widely used. Therefore, the study of modeling in management activities is topical issue.

The degree of knowledge of the problem. Modeling problems management processes the works of foreign scientists A. Demodoran, M.Kh. Mescon, J. Neumann, L. Plunkett, G. Hale, O. Morgentain, P. Scott, M. Eddowes, R. Stansfield, C.G. Corley, S. Walley, and J. R. Baum.

Of the domestic specialists involved in the study of modeling in management, the works of K.A. Bagrinovsky, E.V. Berezhnoy, V.I. Berezhny, V.G. Boltyansky, A.S. Bolshakova, V.P. Busygin, G.K. Zhdanova, Ya.G. Neuimina, A.I. Orlova, G.P. Fomina and others.

The purpose of the course work is the study of simulation in management. To achieve our goal, we need to solve the following tasks:

1. study the literature on this issue;

2. determine the essence of the concept of the modeling process and the classification of models;

3. analyze the model of the organization as an object of management;

4. consider the features of modeling management processes:

The verbal model

· mathematical modeling;

practical management model.

The structure of the course work consists of an introduction, two chapters, five paragraphs, a conclusion, a list of references.

Chapter 1. The essence of modeling in management activities

1.1. The concept of the modeling process. Model classification

Modeling is the creation of a model, i.e., an image of an object that replaces it, in order to obtain information about this object by conducting experiments with its model.

A model in the general sense (generalized model) is a specific object created for the purpose of obtaining and (or) storing information (in the form of a mental image, description by sign means or a material system), reflecting the properties, characteristics and connections of the original object of an arbitrary nature, essential for the task , solved by the subject.

Object models are simpler systems, with a clear; structure, precisely defined relationships between the constituent parts, allowing a more detailed analysis of the properties of real objects and their behavior in different situations. Thus, modeling is a tool for analyzing complex systems and objects.

A series of mandatory requirements. First, the model must be adequate to the object, i.e., correspond to it as fully as possible in terms of the properties chosen for study.

Secondly, the model must be complete. This means that it should make it possible, with the help of appropriate methods and methods of studying the model, to investigate the object itself, i.e., to obtain some statements regarding its properties, operating principles, and behavior under given conditions.

The set of applied models can be classified according to the following criteria:

· method of modeling;

the nature of the system being modeled;

scale of modeling.

According to the modeling method, the following types of models are distinguished:

· analytical, when the behavior of the object of modeling is described in the form of functional dependencies and logical conditions;

· simulation, in which real processes are described by a set of algorithms implemented on a computer.

According to the nature of the modeled system, the models are divided into:

· to deterministic, in which all elements of the modeling object are constantly clearly defined;

· to stochastic, when the models include random controls.

Depending on the time factor, models are divided into static and dynamic. Static models (diagrams, graphs, data flow diagrams) allow one to describe the structure of the system being modeled, but do not provide information about its current state, which changes over time. Dynamic models make it possible to describe the development of processes occurring in the system over time. Unlike static models, dynamic models allow you to update the values ​​of variables, the models themselves, dynamically calculate various process parameters and the results of impacts on the system.

Models can be divided into the following types:

1) Functional models - express direct relationships between endogenous and exogenous variables.

2) Models expressed using systems of equations with respect to endogenous quantities. They express balance ratios between various economic indicators (for example, a model of input-output balance).

3) Optimization type models. The main part of the model is a system of equations with respect to endogenous variables. But the goal is to find the optimal solution for some economic indicator (for example, to find such values ​​of tax rates to ensure the maximum inflow of funds to the budget for a given period of time).

4) Simulation models - a very accurate reflection of the economic phenomenon. The simulation model allows you to answer the question: "What will happen if ...". The simulation system is a set of models simulating the course of the process under study, combined with a special system of auxiliary programs and an information base, which make it possible to quite simply and quickly implement variant calculations.

In this case, mathematical equations may contain complex, non-linear, stochastic dependencies.

On the other hand, models can be divided into controlled and predictive. Managed models answer the question: "What will happen if ...?"; “How to achieve what you want?” and contain three groups of variables: 1) variables that characterize the current state of the object; 2) control actions - variables that affect the change in this state and are amenable to purposeful choice; 3) initial data and external influences, i.e. externally set parameters and initial parameters.

In predictive models, control is not explicitly identified. They answer the questions: “What will happen if everything remains the same?”.

Further, models can be divided according to the method of measuring time into continuous and discrete. In any case, if time is present in the model, then the model is called dynamic. Most often, discrete time is used in models, because information is received discretely: reports, balance sheets and other documents are compiled periodically. But from a formal point of view, the continuous model may be easier to study. Note that in physical science there is a continuing discussion about whether the real physical time is continuous or discrete.

Usually, fairly large socio-economic models include material, financial and social sections. Material section - balances of products, production capacities, labor, natural resources. This is a section that describes the fundamental processes, this is a level that is usually poorly controlled, especially fast, because it is very inertial.

The financial section contains cash flow balances, rules for the formation and use of funds, pricing rules, etc. At this level, many controlled variables can be identified. They can be regulators. The social section contains information about people's behavior. This section introduces many uncertainties into decision-making models, since it is difficult to correctly take into account such factors as labor productivity, consumption patterns, motivation, etc.

When constructing models that use discrete time, econometric methods are often used. Among them, regression equations and their systems are popular. Lags are often used (delays in the reaction). For systems that are nonlinear in parameters, the application of the least squares method encounters difficulties.

Currently popular approaches to business reengineering processes are based on the active use of mathematical and information models.

When building any management process model, it is desirable to adhere to the following action plan:

1) Formulate the goals of studying the system;

2) Select those factors, components and variables that are the most significant for this task;

3) Take into account in one way or another extraneous factors not included in the model;