When studying the decision-making process, it is necessary to take into account two nuances. Firstly, making decisions is generally not as difficult as it seems, but it’s precisely correct solution really difficult. Secondly, decision-making is a psychological process, but, as you know, human behavior is not always amenable to logic - sometimes it is controlled by feelings. For this reason, decisions can be either spontaneous and illogical, or logical and deliberate.

Below we will talk about the rational approach to decision-making in detail, but you need to understand that a person is often influenced by all sorts of psychological factors such as personal values, experiences, or attitudes. So we start by looking at the impact of psychological and behavioral factors on decision making. Thus, the following discussion will focus on decisions of an intuitive, judgmental and rational nature.

Intuitive Solutions

Intuitive decisions can be described as a choice made on the basis of feelings about its correctness. The person making the decision does not analyze all the pros and cons, and often does not even assess the situation in detail. He just chooses. Interestingly, intuitive judgments are common. Moreover, many people depend on their intuition, tend to trust it in every possible way, tk. it helps to find the right solutions and effective ways out of difficult situations.

Despite this, when it comes to serious decisions, where there are many options to choose from, a person comes face to face with such a phenomenon as chance. And if you look at the issue of choice from a position, the chances of making the right decision are very low. Hence the conclusion: you need to listen to intuition and even follow it, but right choice is possible only when all the pluses and minuses of the situation are carefully analyzed.

Judgment Based Decisions

Decisions made on the basis of judgments may seem intuitive at first glance. The reason for this is the non-obviousness of logic. But in reality, such decisions are the product of knowledge and accumulated experience. People use knowledge of what happened in similar cases in the past to find alternative elections in the present and predicting their results in the future. Taking common sense as a basis, a person makes a decision that was successful earlier. Judgment is the basis of the decision, and this is useful, because many life situations are often repeated. So what worked then can still work now.

Considering that a decision based on judgment is made in the mind of a person, it will always be distinguished by speed and a low “price”. However, common sense in its purest form is a very rare phenomenon. everyone has their own needs, tasks, beliefs, etc. So some judgments for making decisions are not enough in unique and difficult situations where problems only seem obvious.

If the situation is new and the person has no experience yet, he cannot justify his choice logically. Judgment here can be bad, because. There are a lot of factors that need to be taken into account, and the mind is not able to process them all at once due to its limited capabilities. Because judgment is based on experience, focusing too much on the latter can bias decisions toward the side familiar to the person through past actions. In such a situation, it is very easy not to notice good alternatives. But more importantly, a person who relies too much on judgment and experience may consciously or unconsciously avoid the new. And this, in turn, can cause big problems in the future, because the relevance of almost any information decreases over time.

Adapting to a new and even more complex is never too easy, because there is always the possibility of making the wrong decision. But in many situations, a person may well improve his chances of making the right choice - if only he tries to make a decision rationally.

Rational Decisions

Rational decisions differ in that they do not depend on past experience, but are justified through a process of objective analysis. It consists of several stages:

• Problem Diagnosis
• Identification of alternatives
• Evaluation of alternatives
• Final Choice
• Solution Implementation

We will analyze each of the stages so that it is clearer what and how to do.

Problem Diagnosis

We discussed this topic in detail in the last lesson, so here we will only give the most general information. Diagnosing a problem is the first step in solving any problem. But there are two ways to go in the diagnostic process.

In the first problem is the situation when it was not possible to achieve goals. What man expected to happen does not happen. In the second case, the problem is an opportunity. A person realizes it when he understands that something can be done to improve specific situation.

It is difficult to define the problem completely, because it is influenced by several factors. As experience shows, the successful definition of a problem is already 50% of its solution. Therefore, it is customary to pay a lot of attention and a lot of time to diagnosing problem situations in the business sphere. This process, in a sense, can be called independent, because. It is itself subdivided into a number of its stages:

• Diagnosis (identifying and accepting that there is a problem)
• Understanding (need to understand the essence of the problem)
• Identification of causes (analysis of external and internal information)
• Data filtering (discarding everything that is not relevant to get relevant information)

With regard to relevant information, it should be noted that this is information that relates to the current problem, the people involved in it, the goals of its resolution and the period during which they need to be achieved. With these data, you can proceed to the second stage of making a rational decision.

Formulation of criteria and restrictions

When diagnosing a problem in order to make a decision, a person must understand what exactly he can do with it, i.e. how to solve. Decisions are often unrealistic as resources for implementation may be limited, especially if we are talking about one person. Also, the problem may be due to external causes, which cannot be influenced.

At this stage, it is necessary to impartially determine the constraints in which alternatives will be sought. This allows you to save a lot of time and find a feasible solution. Limitations always depend on the specific situation and the persons involved.

In addition to boundaries, it is important to establish criteria for evaluating alternatives. These are the so-called recommendations for evaluating the decision being made. They include everything that can help cut off unrealistic options and stay within the above boundaries.

Definition of alternatives

At the third stage, it is necessary to draw up and formulate a set of alternatives that can solve the problem. It is recommended to record all options for action that can positively affect the result. But given that people rarely have the knowledge and resources to evaluate all alternatives, the most serious options should be identified.

Alternatives are considered until one is found that satisfies all needs. To do this, consider a wide range of options. Difficult problems need to be analyzed as deeply as possible in order to be able to develop several solutions at once.

Evaluation of alternatives

Before choosing final version solution to the problem, it is necessary to evaluate the whole variety of options, considering the pros and cons of each and predicting possible consequences. Almost always all options are associated with negative aspects, but at the same time, in most situations, a compromise can be found.

In order to compare solutions, it is necessary to have standards for evaluating effectiveness (which we discussed earlier). You need to focus on both quantitative and qualitative parameters. Sometimes, of course, it is not possible to fully compare the options, but in any case, the decision must take on a specific form, and it is better that it also reflects the purpose for which the decision is made.

When scoring alternatives, it is effective to use a scoring system to understand which choice is better. It is also desirable to take into account and predict the development of events. The more points and the higher the probability of implementation of some option, the more it indicates the correctness of the choice.

Final Choice

If all the previous stages have been successfully completed, it will be quite simple to make a choice - it remains only to decide on the most suitable option. But if many factors matter, and if the data and analysis are purely subjective, it may be that none of the options will work. If this happens, experience and judgment are required. They will make it possible to form a more objective picture of the current situation and advance in its resolution.

It is also important to say that a person's behavior when making a decision should not be maximizing, but satisfying. Those. it is required to choose the most obvious and acceptable solution, even if it is not the best one, than to look for an ephemeral ideal option, which may not exist at all.

Solution Implementation

It’s not enough just to decide on a course of action. It is much more important to implement a solution in order to solve a problem or gain a benefit. The most successful decisions are those that are approved by all the parties involved in resolving the issue. If there are several parties and there are disagreements, you should not waste time convincing people of your position and insisting on its correctness. It is much better to try to find a compromise that satisfies everyone and everyone.

As a result of all the above actions, you need to get feedback. To do this, you should measure and evaluate the consequences of your choice or compare the results with the predicted ones. Under feedback you need to understand the flow of information about what happened before the decision was made and what happened after.

On this subject of acceptance rational decisions may be considered closed. However, the question of decision-making methods is still open, because we did not talk about approaches to this process. They should not be correlated with the classification already considered, because. they view the phenomenon in a different way.

Decision-making approaches

There are four pairs of decision-making approaches in total:

• Centralized and decentralized
• Group and individual
• Participation and non-participation
• Democratic and deliberative

Let's see what their features are.

Centralized and decentralized approaches

The centralized approach is based on the fact that the maximum number of decisions is made by some higher authority, for example, the board of directors in the company. And in decentralized decision-making responsibility extends to all levels, including the lowest. The amount and nature of decentralization in each specific case are determined separately.

Group and individual approaches

In a group decision-making approach, several parties are involved in working together on a problem. Individual approach allows only single choice. The first option is more expedient, because. collective decision is easier to implement. But the second option is more preferable if there is a time constraint or the other party involved cannot take part in the decision physically.

Participation and non-participation approaches

In a participatory approach, you need to get the opinion of all parties on the decision being made. If the choice is based on opinions stakeholders increases the likelihood of success. This approach should not be confused with the group approach, because in it the decision is made collectively, and in the participatory approach there is only a survey - the final decision is made by the responsible person. When it comes to the non-participatory approach, only one person collects information and analyzes alternatives, and then makes a choice.

Democratic and deliberative approaches

The democratic approach involves making decisions in the direction of the majority. It is not very effective for organizations because often divides people into two camps - "winners" and "losers", which can lead to conflict situations and failures in management and operation. The deliberative approach involves all parties in decision-making, which allows finding a compromise that suits everyone.

The deliberative approach usually serves as a form of group approach, but the focus is on getting the points of view of as many stakeholders as possible (through meetings, interviews, meetings, etc.) and then making a choice.

Interestingly, in the practice of applying the group approach, the following was noticed:

• Groupthink is activated, in which the majority exerts social pressure on the minority, as a result of which individuals agree to what is beneficial to the mass, even if their interests are not taken into account in any way.
• The group approach serves as a ground for the clash of personal opinions of the participants to a much greater extent than all other approaches.

At the same time, it should be taken into account that the use of a group approach has a number of serious advantages:

• The group solves problems more effectively by having a broader view of the problem and its causes.
• The group has a much wider perspective, and therefore is able to find the best solution
• Group enthusiasm (especially encouraged) is much stronger than individual
• The group is less prone to and distrustful of new solutions

Based on all of the above, we can conclude that if the problem being solved concerns several parties, it is most effective to make decisions collectively and taking into account the opinions of everyone. If the problem concerns one person, he can make decisions himself, but at the same time he is free to use any other approaches and means of finding solutions.

Everything that we have managed to talk about is more advisory in nature than it is a system. However, this information is universal - it will help you make effective decisions in any simple and complex situations. But you should always look at the characteristics of problem situations, the interests of the parties involved and other factors that affect decision making. It is these factors that will be discussed next.

Factors influencing decision making

In fact, the volume of the topic of factors influencing the decision-making process is very large, so we will cover only the most important, in our opinion, subtleties that most directly affect the choice and its effectiveness.

First of all, these are personal factors. These include , states and processes. Next come the situational factors: external and internal. External environment are economic and political conditions, legal regulations, socio-cultural factors and technologies, natural and geographical factors. The business sphere here is also complemented by consumers, suppliers, competitors, infrastructure - all this matters. The internal environment is the goals and structure of the organization, corporate culture, organizational processes and available resources. Speaking about the decision-making environment, it is equally important to mention risks, certainty and uncertainty, time and changes in the environment itself.

There are also uncertain factors (they differ in the source of uncertainty (environmental uncertainty or personal uncertainty), nature (random or non-random)), informational and behavioral factors, as well as negative consequences and interconnectedness of decisions.

As you can see for yourself, the topic of factors influencing decision-making is not only very interesting, but also broad. To better understand it, as well as how people make decisions in general, one can (highly recommended for those who want to become an expert in this field) pay attention to the theory of decision making. She is able to answer many questions.

Decision Theory: Fundamentals

Decision theory is a special area of ​​research, operating in mathematical, statistical, economic, psychological and managerial terms, to study the patterns of people's choice of ways to make decisions and solve problems and ways to achieve their goals.

There is a normative theory describing the rational choice process and a descriptive theory describing its practical aspects. From a rational position, decision making consists of several stages:

• Problem Analysis
• Problem identification and task definition
• Collection of information
• Definition of alternatives
• Determination of criteria for evaluating alternatives
• Definition of indicators to monitor the implementation of decisions
• Evaluation of alternatives
• Choice the best alternative
• Create an action plan
• Implementation of the action plan
• Monitoring the implementation of the action plan
• Evaluation of results

You can go through these stages, depending on the specifics of the situation, in parallel, simultaneously or with a return to the passed stages. The passage of all stages must be rationally justified. Decision theory also says that you need to be able to statistically predict the development of events. But for this it is necessary to have a sample of future data. The impossibility of this indicates the need to use statistics from past experience.

The core of decision-making theory is a separate area - decision-making under uncertainty, i.e. in situations where the outcome of a choice is unknown. Uncertainty can be stochastic (when there is data on the distribution of probability over a group of outcomes), behavioral (when there is data on the impact on the outcome of the behavior of the persons involved), natural (when there is data from probable outcomes and there is no information about the relationship between decisions and outcomes) and a priori ( when there is no data even about possible outcomes).

What we call the expected value today was once called the expected value. Its essence is that, given different options behaviors, each of which can lead to several possible outcomes, rational approach must identify all possible outcomes, establish their value and probability, and indicate, based on their totality, the total expected value. It cuts negative impact on the decision of the effect of uncertainty.

Subsequently, the theory of subjective probability appeared, significantly expanding the theory of expected value, and promoting the theory of real human behavioral decision making under risks (we also recommend reading Kahneman and Tversky's prospect theory).

As for the difference between risk and uncertainty, situations with an unknown outcome are described either by risk or by uncertainty. Choosing under risk means that the probable outcomes are known, but some of them are more favorable, and some are less. And choice under uncertainty is based on an unknown set of outcomes. Experienced business people always strive to follow the rule , i.e. bring uncertainty to risk. This can be achieved through the collection additional information about the problem and its application.

According to decision theory, erroneous decisions are divided into errors of the first and second row. This is due to the fact that the results of wrong choices are fundamentally different in terms of the fact that an unrealized favorable outcome affects the problem much less than a realized unfavorable one. But the division into errors of the first and second order is possible only when all risks are taken into account and analyzed.

If we touch on the theory of probability, which is most directly related to the theory of decision making, we can say that it is rather problematic to replace the use of probability with alternatives. Some experts argue that probability is only one of many alternatives. Others say that the rejection of the theory of probability may give rise to theoretical difficulties, and so on.

It is easy to see that decision theory is fraught with a huge number of useful information, the study of which will allow you to delve deeper into behavioral psychology. In general, it determines the norms of behavior for the person making the decision. It sets up signs to follow in order to avoid contradictions with its own preferences, judgments and principles.

But theory does not dictate human behavior at all. It only helps him, provides him with a methodology that allows him to make decisions that include elements of subjectivism. Interestingly, as the complexity of problems grows, the ability of a person to informally process information based on their own judgments weakens. This is where decision theory comes into its own, offering advantages over any other analytical approach to problem solving. It includes many subjective aspects of problems, which is especially important when making decisions on an individual basis.

We repeat that we do not insist on mastering the theory of decision making. To a greater extent, this is necessary for specialists, for example, managers, psychologists, sociologists and professionals from other fields of science. However, the study of this theory, even for the sake of interest, can raise the effectiveness of your decisions by a qualitatively new level. However, you probably noticed that the process of making rational decisions, which we described in the first block, is based on the foundations of decision theory. Therefore, one way or another, you will encounter it constantly.

So, we have already managed to study two important issues - we talked about problems, their types and methods of working with them and figured out how people make decisions, at the same time getting acquainted with the theory of decision making. But solutions, as one should assume, can be more or less effective. Our task is to learn how to find and develop effective solutions, and there are many practical methods.

In the third lesson, we will talk about methods for finding new ideas and solutions: brainstorming, creative collaboration techniques, the 635 method, the conference of ideas, the Discussion-66 method, synectics and synectic conference, the Delphi method, idea engineering and others. You will have at your disposal a fairly solid arsenal of techniques to increase personal effectiveness in life, training and work.

Do you want to test your knowledge?

If you want to test your theoretical knowledge on the topic of the course and understand how it suits you, you can take our test. Only 1 option can be correct for each question. After you select one of the options, the system automatically moves on to the next question.

2.4. Decision theory

2.4.2. Basic concepts of decision theory

Decision-making in the process of managing complex socio-economic systems is associated with the need to perceive and process a large amount of heterogeneous information. Limited opportunities human perception and processing of information lead to non-optimality of decisions made. Strengthening the intellectual capabilities of a person is achieved through the use of scientific approach, which presupposes the presence of decision theory (DMT); a set of practical recommendations arising from the theory and the experience of its application; integrated use all means to make a decision: logical thinking and human intuition mathematical methods and computer technology.

The mental activity of a person in the process of making management decisions can be strengthened through the rational application of formal (logical, mathematical) methods and technical means. Various kinds of calculations, search and preliminary processing of information, reduction in the number of alternative solutions when assessing their preferences in many indicators can be effectively carried out using formal methods and technical means. correct complex application all means significantly increases the efficiency of the decision-making process. TPR gives practical advice on the rational integration of all means at various stages and in certain procedures of the decision-making process.

The TPR prescribes the norms of behavior for the decision maker, which he must follow in order not to conflict with his own judgments and preferences. As the complexity of the task increases, the ability of a person to informally process all information in accordance with his own judgments and preferences decreases. The importance of TPR for the development and adoption of effective SD is especially growing in modern conditions development of society and economic relations, which are characterized by an increase in the amount of information that the decision maker must take into account and process, as well as an increase in the degree of uncertainty of the current state and development trends environment organizations.

Decision theory(TPR) is a scientific discipline that studies and develops concepts, principles, axioms, models and methods for the development and adoption of SD in order to improve the decision-making process.

Decision problem is aimed at determining the best (optimal) course of action to achieve the goals. Under purpose refers to the ideal representation of a desired state or outcome of an activity. If the actual state does not correspond to the desired one, then problem. The development of a plan of targeted (aimed at achieving the goal) actions to eliminate the problem is essence of the decision problem. The problem is always associated with certain conditions in which the organization or its element exists, and which are generally called situation. The combination of problems and situations problem situation. Identification and description of the problem situation provides the initial information for setting the PR problem.

The subject of every decision is decision maker (LPR). The concept of decision maker is collective. It can be one person individual decision maker or a group of persons working out a collective decision, - group decision maker. To assist decision makers in collecting and analyzing information and making decisions, experts - problem solvers. The concept of an expert in TPR is interpreted in a broad sense and includes employees of the administrative apparatus who prepare the decision, scientists and practitioners.

In the decision-making process, alternative (mutually exclusive) solutions and their preference is evaluated. Alternative – one of the possible mutually exclusive solutions. Alternative set – a set of several mutually exclusive possibilities, methods of action. Method of action – a set of actions leading to possible different outcomes(consequences).

Preference – this is an integral assessment of the quality of solutions based on objective analysis (knowledge, experience, calculations and experiments) and subjective understanding utility(value, degree of expediency), effectiveness of decisions. To make a choice best solution individual decision maker determines selection criterion, i.e. the standard by which to evaluate alternatives choice . Choice – selecting an element from a set. Group decision makers make choices based on principle of harmonization.

The end result of the decision task is solution, which is a command to act. From a substantive point of view, a solution can be a course of action, a work plan, a project option, etc. The solution is called admissible, if it satisfies the restrictions: resource, legal, moral and ethical. A feasible solution is called optimal (best) if it provides an extremum (maximum or minimum) of the selection criterion for an individual decision maker or satisfies the matching principle for a group decision maker.

A generalized characteristic of a solution is its efficiency. This characteristic includes the effect of the decision, which determines the degree of achievement of goals, referred to the costs of achieving them. The decision, the more effective, the greater the degree of achievement of goals and the lower the cost of their implementation.

Decision making takes place in time, so the concept is introduced decision-making process. This process consists of a sequence of steps and procedures and is aimed at eliminating the problem situation.

The TPR is based on the assumption that the choice of alternatives should determined by two factors:

1) representations of the decision maker, about probabilities various possible outcomes (consequences) that may occur when choosing one or another solution option;

2) preferences given to different possible outcomes.

Subjective probabilities

The decision maker can assign to each possible event, outcome X the number Р(X) from the interval , which will be referred to as subjective probability . Subjective Probability reflects degree of certainty The decision maker is that event B will occur, and it is based on readiness given decision maker to act in accordance with this confidence. The decision maker can form his subjective probabilities for possible events based on numerous considerations. This includes knowledge about physical phenomena, empirical data, results of modeling the relationship of various factors and expert judgments.

Subjective probability based on physical phenomena. In some situations, it can be assumed that all possible outcomes of some experiment (random event) have an equal chance of appearing as a result of the experiment. This means that if there are K possible outcomes, then the subjective probability of each of them is 1/K. Based on this assumption, one usually assigns a 1/2 chance of getting a coat of arms on a regular coin and a 1/6 chance of getting a six on a die. The probabilities that can be tested by exhaustive experiments are often called objective probabilities. Most people agree with these probabilities. If some decision maker accepts them as a guide to action, then objective probabilities, by definition, are also subjective probabilities.

Subjective probability based on available data. If there is data on the possibility of the occurrence of events that are of interest to the decision maker, then they can be used to form judgments about the probabilities of events. Let beX1,…, Xk- a complete set of mutually exclusive events. If in each of the K trials one of the following events was observed: orX1, orX2, …, orXk, moreover, the eventxm observedkmtimes, then the probabilityxmis taken equal to the frequency of the event, i.e. TOm/TO. For example, if among the last 10,000 property fire insurance contracts in 100 cases it was necessary to pay insurance compensation, then subjectively it can be assumed that the probability of property loss in a fire is 0.01.

Subjective probability based on simulation results. The probabilities of stochastic events are often impossible to obtain based on statistical data due to their absence or lack. The theory of operations research recommends in this case to build an analytical or simulation model phenomenon, which can be used to obtain estimates of the probability of a stochastic event. In analytical models, methods of probability theory are used to estimate the probability of a stochastic event, and when simulation modeling – method of statistical tests (Monte Carlo method). The essence of the method Monte Carlo consists in using a sample of random numbers (generated computer program) to obtain the required estimates.

Utility rating

The TPR assumes that there is a single measure of effectiveness, against which it is necessary to evaluate the preferences of the decision maker. Measure - normalized numerical set function. We need to evaluate the usefulnessevery possible outcome... large numbers possible outcomes it is necessary to evaluate the utility function . There are special procedures for identifying the utility function of the decision maker, but they are complemented by the art of the researcher, his ability to establish contact with the decision maker. To assess the utility function, the researcher must prove the importance of such assessments to the DM, enlist his support and make the assessment procedure convenient.

Figure 2.13 shows graphs of eight typical preference functions. On each graph, the objectively measured parameter y is plotted along the horizontal axis. Such a parameter can be, for example, a gain for y > 0 or a loss for y< 0, выраженные в денежной оценке. По вертикальной оси на всех графиках дано значение функции предпочтения f (у), характеризующей subjective understanding The decision maker of the value (utility) of the values ​​of an objectively measured parameter. For f(y)>0 utility takes place, and for f(y)<0 – неполезность оценки значений объективного параметра у.

The preference function shown in Figure 2.13a characterizes the “objective” decision maker, who believes that utility is proportional to the value of the parameter f(y) = y. It should be noted that the “objective” decision maker is an abstraction, since real decision makers do not have such a preference function, and it is used to better understand the essence of other preference functions.

The preference function in Fig. 2.13.6 describes the psychology of thinking of a "gambling" decision maker; with an increase in the value of the objective gain, it ascribes to it a much greater value, i.e. exaggerates the benefits. With negative values ​​of the parameter (loss), this decision maker diminishes the unutility.

On fig. 2.13, in the preference function of the "cautious" decision maker is presented. This decision maker pays special attention to the prevention of large losses and underestimates the usefulness of gaining.

Figure 2.13d shows a graph of the preference function that describes the behavior of a decision maker who tends to exaggerate utility for large gains and unutility for large losses.

Figure 2.13e shows the decision maker's preference function, whose attitude is cautious both to big wins and big losses.

In Fig. 2.13, e the preference function describes the “normal” decision maker. With small gains and losses, this decision maker behaves as an objective one; with slightly larger absolute values ​​of the parameter, moderate gambling and caution are manifested, and with very large values ​​of the parameter, caution towards winning and indifference to loss are manifested.

In Fig. 2.13, g a discontinuous preference function is given. From a psychological point of view, this function characterizes a “winning” decision maker, which, in addition to objectively taking into account gains and losses, also adds a constant “premium”: positive for winning and negative for losing.

In Fig. 2.13, h a preference function is given, which considers only a gain no less than a certain value (point a on the graph) to be useful, and then its utility is constant.

The considered typical preference functions characterize the features of the psychology of thinking of the decision maker. These features must be taken into account when placing personnel, establishing relationships with people in the process of joint activities and forecasting possible decisions of managers in various problem situations.

For example, if a person has a "cautious" preference function, then it is inappropriate to use it in an area of ​​activity that requires risk. A person with a “gambling” preference function is suitable for such an activity, since with risk you can get a much greater reward than with a cautious action.

Fig.2.13. Types of Preference Functions

2.4.4. Classification of decision-making tasks

Several classifications of decision-making problems based on various feature systems have been proposed in the scientific literature. The most common and essential classification features found in most works are:

Ø the degree of certainty of information;

Ø use of the experiment to obtain information;

Ø number of decision makers;

Ø Significance and duration of decisions.

The certainty of information is characterized by the completeness and reliability of the data necessary for decision-making. By sign information certainty Decision-making tasks are classified into three groups:

1) tasks under conditions of certainty (deterministic tasks);

2) tasks under conditions of probabilistic certainty;

3) tasks under conditions of uncertainty.

Decision making under certainty is carried out in the presence of complete and reliable information about the problem situation, goals, limitations and consequences of decisions. Another definition deterministic tasks- problems of choosing the best solution in situations where each option leads to a single result.

For this class of problems, there is no need to extend the definition of the problem situation by hypothetical situations. Goals and constraints are formally defined as objective functions and inequalities (equalities). The preference function in the case of one goal coincides with the objective function, and in the case of multiple goals with some functional dependence of the objective functions. The selection criterion is determined by the minimum or maximum of the objective function. The presence of the above information makes it possible to construct a formal mathematical model of the decision-making problem and algorithmically find the optimal solution.

At present, standard problems have been formulated, mainly of a production and economic nature, for which algorithms for making optimal decisions based on mathematical programming methods have been developed. Such tasks include, for example, tasks of resource allocation, assignment of work, inventory management, transportation tasks, etc. Human role in solving problems of this class is reduced to reducing the real situation to a typical mathematical programming problem and asserting the resulting formally optimal solution.

Probabilistic tasks ( decision making under conditions of probabilistic certainty ) – in situations where, as a result of each action, different results can be obtained, the probabilities of achieving which are known or can be estimated. Decision-making under conditions of probabilistic certainty is based on the theory of statistical decisions. In this theory, the incompleteness and unreliability of information in real problems are taken into account by considering random events and processes. The description of the patterns of behavior of random objects is carried out with the help of probabilistic characteristics. The probabilistic characteristics themselves are already non-random, so it is possible to perform operations with them to find the optimal solution in the same way as with deterministic characteristics. Incompleteness and unreliability of information are reflected in probabilistic characteristics. The general criterion for finding the optimal solution in the theory of statistical decisions is the average risk, therefore, in the literature, problems of this class are often called decision-making problems under risk.

Human role in solving problems by methods of the theory of statistical decisions is to formulate the problem, i.e. reduction of a real problem to a typical mathematical problem, approval of the resulting optimal solution, and also (in the absence of statistical data) in determining the subjective probabilities of events. Subjective probabilities are a person's opinion about the reliability of random events. Obtaining the optimal solution in problems of this class is carried out formally without human participation.

Mathematical models considered in decision-making problems under conditions of certainty and probabilistic certainty describe the simplest situations that are typical for the functioning of technical and economic systems. Therefore, problems of this class are widely used for the synthesis of control in automatic systems and are of limited use for managerial decisions in the socio-economic field.

Decision-Making Problems Under Uncertainty directly related to management decisions. They arise in situations where the probabilities of implementing the options of actions from among those considered are unknown (partial uncertainty) or the set of possible options for actions is generally unknown.

These tasks are characterized by great incompleteness and unreliability of information, the diversity and complexity of the influence of social, economic, political and technical factors. These circumstances do not allow, at least at present, to build adequate mathematical models for solving problems to determine the optimal solution. That's why main role in search of an optimal or acceptable solution, a person performs. Formal methods and technical means are used by a person in the process of forming decisions as auxiliary tools.

The problem of decision-making under conditions of uncertainty is more general and includes, as a special case, decision-making under conditions of certainty and probabilistic certainty. The adoption of managerial decisions in organizational systems corresponds to the conditions of uncertainty.

By sign using experiment to getinformation Decision-making tasks are classified into two groups:

1) decision-making tasks according to a priori data;

2) decision-making tasks according to a posteriori data.

Decision-making on a priori data is characteristic of conditions of certainty and partly of conditions of probabilistic certainty, since the concept of "prior data" means that only known information is used. Under conditions of uncertainty, a priori information is very small, so it is necessary to obtain new information by conducting a set of activities called an experiment. The experimental results provide a posteriori information.

Two control strategies are used to control the conduct of the experiment.

In one of them, a series of experiments is planned and carried out, providing the necessary information, on the basis of which a decision is made.

In the other, the experiments are carried out sequentially, and after each experiment, it is necessary to make a procedural decision on the continuation or termination of the experiments.

If the experiment is associated with random factors, then a consistent strategy for managing the experiment is more rational, since it allows, with a fixed degree of certainty of information, to reduce the series of experiments on average. Planning and managing an experiment are essential for optimizing the technology of problem solving under conditions of uncertainty.

By sign number of decision makers, tasks are divided into individual and group (collective). Individual decisions are made by one person, and groupoyou- a collective body.

By sign number of targets Distinguish between single-purpose and multi-purpose decision-making tasks. Real management decisions, as a rule, are multi-purpose. In these tasks, the problem of coordinating conflicting goals arises when choosing solutions. If the goals are described formally, in the form of objective functions, then single-purpose tasks are called single-criteria, and multi-purpose - multicriteria decision-making tasks.

By sign the content of the decision-making task classified according to the field of activity. There are economic, political, ideological, technical, military and other types of tasks.

By sign actions Distinguish between long-term, medium-term and short-term solutions. long-term decisions are aimed at achieving general long-term goals. Such decisions, for example, include long-term national programs in the economic, scientific, technical, social and other fields of activity. TO medium term decisions include, for example, plans for the economic and social development of organizations or the national economy within 3-5 years. Short term solutions are aimed at eliminating current problems.

The classification of decision-making problems according to the listed features leads to various combinations of problem types. For example, some specific task can be classified as a decision-making task under uncertainty, according to a priori data, as a group and multi-purpose one. Other combinations are also possible. The type of decision-making problem determines the choice of method and technology for developing solutions.

2.4.4. Concepts and principles of TPR

Concept (from lat. conceptio - understanding) is a generalized system of views on the object or phenomenon under consideration, an idea of ​​how to approach the perception and study of this object (for example, the concept of the universe, the concept of evolutionary development).

Principle (from lat. principle - the fundamental idea) is what an active subject must necessarily be guided by in his theoretical (cognitive, methodological, research, didactic, etc.) or practical activities.

The relationship of concepts and principles that the TPR methodology operates with is conveniently displayed by a certain hierarchical structure that shows their relationship horizontally and vertically (Table 2.2).

Structure of concepts and principles of TPR

System concept reflects ideas about the unity of the world, about the universal connection and mutual conditioning of the processes and phenomena of the material world. According to this concept, when making a decision, one should constantly remember and understand that we never do one thing. In other words, striving to achieve the goal, we put active resources into action: ideas, people, machines, money, raw materials and materials; consciously or involuntarily create and break ties between a wide variety of objects (material and ideal, natural and artificial); we change concepts and ideas and as a result we generate (sometimes unwittingly) not only the desired beneficial effect, but also a lot of unexpected side effects. Methodologically purpose principle directly follows from the concept of the system, it is therefore the first principle that the decision maker should be guided by when developing a solution. This has been known for a long time. For example, the ancient Greeks said that for a ship that does not know where to sail, there is no favorable wind, and the famous theorist of the scientific organization of labor F.N. Taylor at the beginning of the 20th century. directly indicated how the process of managing an economic enterprise should be organized: “Understand well what you want! And then - just make sure it's done in the best and cheapest way."

essence concepts of rational decisions (from lat. ratio - reason) consists in the fact that the decisive argument in making a decision, i.e. with a conscious choice of the best option among others, a logically consistent, complete and, best of all, quantitatively confirmed system of evidence serves. As a logical consequence of understanding reasonableness, it is concluded that one should never accept, but one should never reject a solution option if it is the only one in the choice. It is imperative to look for other options, to develop other alternatives for solving the problem, in order to choose the most preferable solution to the problem based on their rational comparison. Such a rational idea, which should guide the development of decisions, is called the principle of multiple alternatives.

essence concept of "best solution" can be formulated as follows: choose the alternative that is better than any of the considered ones. We note right away that the well-known concept of optimality in mathematics and operations research is nothing more than a formal expression of the concept of the best solution, namely, for the case when a single scalar indicator is used as a preference criterion.

Of course, in order to compare alternatives according to the rule "better-worse", "more preferred - less preferred", you need to use a measurement, i.e. a rational consequence of the concept of the best solution is measuring principle. It corresponds to another important postulate of management, which says: "Measured - it's done!". In the process of measurements, a person penetrates deeper into the essence of things, better understands the connections between objects, more precisely, he can imagine how these objects or connections can be influenced in order to change them or their properties in the desired direction.

2.4.7. Features of management decisions

1. Multipurpose nature. In most complex tasks, you have to strive to achieve various goals. These goals are almost always contradictory, i.e. progress towards achieving some goal is usually accompanied by worsening results for others. Thus, the decision maker inevitably faces the need to choose between conflicting goals.

2. The impact of the time factor.All important consequences of solving a problem do not appear immediately, and it is impossible to indicate a specific moment in time when one or another consequence can be observed. For example, in the production of a new product, it is sometimes necessary to risk significant amounts over many years.

3. Non-formalizable concepts.Unknown elements of the task: situations, goals, constraints, decisions, preferences - are primarily of a meaningful nature and are only partially determined by quantitative characteristics. Concepts such as prestige, morale, brand recognition, consumer perception, etc. are some examples of very important non-formalizable concepts that greatly complicate the task.

4. informal procedures. The definition of unknown elements of the problem and, ultimately, finding the best solution cannot be formalized, since there are no methods and algorithms that allow, for example, to formulate goals, criteria, and solutions.

5. Uncertainty(the impossibility of an unambiguous description of the object in all its characteristics). As a rule, at the moment of making a decision, the future consequences of each of the alternatives of actions are not known exactly. The number of unknown elements of the problem is significantly greater than the number of known ones.

6. Subjective measurements. The elements of the task are described by characteristics, some of which can be measured objectively, while for the other part only subjective measurement is possible (for example, priorities of goals, preferences of criteria and solutions, etc.).

7. Expert Participation. Experts play a supporting role, carrying out informational and analytical work to reduce the uncertainty of information. They are responsible for their recommendations.

8. Possibilities for obtaining information. Obtaining the information needed to make decisions can be time consuming and costly, and it may not be entirely reliable.

9. The Importance of Intuition. In many cases, it is necessary to solve the problem of decision making under conditions of uncertainty due to an incomplete description of the problem situation and the impossibility of a sufficiently accurate assessment of other elements of the decision, the expected consequences of the decision made. In these cases, along with logical thinking, the decision maker's intuition is important.

10.Dynamic aspects of the decision-making process. After a certain solution has been worked out (an alternative has been chosen), it may turn out that the task has not been exhausted to the end and it will be necessary to make another decision in a few years. Today's decision may "slam the door" on some possible actions and "open it wide" on others. It is important to recognize in advance such dynamic aspects of the problem.

11. Impact of Decisions on Groups. A given alternative may affect a large number of different groups, such as the owners of the organization, workers, customers, suppliers, the local community, and so on.

12.Collective decision making. Often the responsibility for choosing an alternative lies not with an individual, but with a whole group. In fact, for a certain set of tasks, it is impossible to clearly delineate the functions and responsibilities of the decision maker for a certain range of issues.

13.Comparison of alternatives. Measurement of the quality of decisions is carried out on the basis of the formation of alternative options and their comparative assessment.

14.Lack of a single optimal solution. Under conditions of uncertainty, there may not be a single optimal solution. For decision makers with different preferences, the solutions will be different.

15.Human factor. Decisions made may directly affect the interests of decision makers and system analysts. Therefore, their interests, motives of behavior influence the choice of solution.

16.Uncertainty Reduction in the decision-making problem, it is carried out in successive stages: structuring, characterization (formation of a set of characteristics), optimization.

The description of the preferences of the decision maker in the form of a preference function reflects not only the objective, rational characteristics of the decision, but also the psychology of thinking of the decision maker, his understanding of the usefulness of decisions. Since the preference function is used to select a decision, the decision made will always contain an element of subjectivity..

Experts in the decision-making process clarify the problem situation, generate hypothetical situations, form goals and constraints, offer solutions and evaluate their consequences based on their preferences. Involving experts in the formation and selection of decisions is the use of collective knowledge and experience, allowing deeper development of decisions and, therefore, reducing the likelihood of making suboptimal decisions.

The basis for measuring the quality of decisions in terms of the degree of achievement of the set goals is a comparative assessment of the preference of decisions. Comparative evaluation of solutions is the only way to measure preference in the absence of established standards, such as, for example, standards for measuring length, mass, temperature, etc. The absence of solutions does not give grounds to raise the question of choosing the best solution. Decision preference is measured by experts and decision makers. Expert assessments should be displayed in numbers using qualitative and quantitative scales. The presentation of the results of the examination in numerical form allows for formal processing on a computer in order to obtain new information that is not explicitly contained in the judgments of experts. To evaluate decisions, it is necessary to formulate a system of indicators that characterize the quality of these decisions and clearly determine the degree of achievement of the formulated goals and the cost of resources.

In conditions of incomplete information, as well as the peculiarities of the psychology of thinking, the decision maker may not have a single optimal solution. The unreliability of information enhances the influence of subjective factors on decision making.

A characteristic feature of decision-making is the presence of a consistent process of reducing the uncertainty of information. Structuring is the selection of the main elements of the task and the establishment of relationships between them. Characterization – determination of a system of characteristics (parameters, indicators, functions) that quantitatively describe the structure of the task. Determining the probabilities of situations, priorities of goals, preferences of decisions is an example of characterization in a decision-making problem. Carrying out the characterization leads to a more complete and accurate description of the problem being solved in comparison with the structuring phase and provides initial data for the last phase - optimization, in which all available information is converted into the final form - the solution. The practical use of the sequence of phases of uncertainty reduction in the decision-making problem increases the efficiency of the decision maker's mental activity.

Simple decision-making methods are those that do not require the use of advanced mathematical tools. However, in many cases their use is sufficient.

3.1.1. Operational decision-making techniques

When discussing the problems of strategic management, a number of operational decision-making techniques were considered - analysis of "gaps", analysis of chances and risks (strengths and weaknesses), portfolio analysis, checklist method, scoring method, etc. Such methods are good to use with a quick comparison of options, for example, at a meeting of senior managers.

Consider, as an example, the portfolio matrix of the Boston Consulting Group. According to this method of preparing managerial decisions, the goods manufactured by the company are distributed according to the cells of Table 1. However, it is clear that such a distribution can only serve as a starting point for further analysis.

Table 1.

Boston Consulting Group Portfolio Matrix

Indeed, it is necessary to rely on data on the profit and profitability of certain goods. It is clear, for example, that the high growth in demand for the "Question Mark" can be ensured by a dumping price below cost.

It is necessary to assess the dynamics of changing brands of goods, to understand how long Cash Cows can stay on the market, how high Stars can fly.

Dogs deserve special consideration. Perhaps they are being replaced by other goods. But something else is also possible - their buyers represent a separate market, only due to the shortcomings of the preliminary analysis attached to the general market. Then the problem statement changes. Company management should not compare "Dogs" with other products. He has to decide a very different question - whether to serve the relatively small market of buyers of "Dogs" or give it to competitors.

It is absolutely undeniable that informed decisions cannot be made based only on the analysis of the portfolio matrix of the Boston Consulting Group. However, this is also true for any other method of preparing a solution. Only a comprehensive analysis using many methods can give the management of the organization the necessary arguments for making an informed decision. But even in this case, the responsibility lies with the "decision makers" - the managers.

There are a lot of operational decision-making techniques, or, in other terminology, simple decision-making methods. One of them is to put the situation in writing. This simple recommendation is often very helpful. The fact is that when compiling a description, it is necessary to clarify many facts and estimates that usually cannot be compared during reflection. Further, the written description suggests various alternatives of action, as well as estimates of the consequences of these alternatives. The presentation of the situation in writing largely removes the emotional component when making a decision, and also provides initial data and options for analytical analysis.

0) Is the solution being considered compatible with my moral principles?

1) What will I gain with this solution?

and money;

c) fame;

d) confidence;

e) pleasure, etc.

2) What will I lose with this decision?

and money;

b) time, etc. (see question 1);

3) What new opportunities will I have?

4) What new challenges will I face?

5) What responsibilities will I have?

6) What new situation will arise for me?

7) What side effects should I expect?

a) positive

b) negative.

8) Will I harm society or other people?

9) Will I benefit society or other people?

10) Will new problems arise as a result of my solution?

11) Will new solutions be required? Etc.

It is possible to single out the stages of situation analysis, preparation and decision-making, analysis of consequences:

1) Understand the situation.

2) Determine if there is a problem to be solved.

3) Generate possible solutions.

4) Describe the consequences of the decisions.

5) Choose a solution.

6) Summarize the accumulated experience of decision-making.

It is advisable to clarify the content of each of the listed stages. For example, to clarify the situation, it is advisable to answer five questions:

1) WHO should or must (or wants) to make the decision?

2) WHERE (in what place, in what environment, in what environment, under what circumstances) will the decision be made?

3) WHEN (by what date, or how often, with what frequency) should a decision be made?

4) HOW (how, in what form, by what document) should the decision be expressed?

5) WHAT determines the decision? Why is it needed? What is its purpose? What is the intention behind it? What is it for? Why should it be accepted?

After the situation is considered, it is necessary to consider options for solutions. Consider an example.

Example 1 The telephone on the desk of the chief's secretary rings. The caller asks a question about the company, but one that neither the secretary nor her boss can answer. How should the secretary react? And what should be expected from the caller?

Reaction of the secretary number 1. She explains to the caller that she cannot provide the required information and connects the caller with the right person.

Caller response #1. He will be grateful to the secretary for being promptly put in touch with a person who can inform him competently and adequately.

Secretary reaction #2. She asks the caller to wait at the phone and runs through the entire building to get the information he needs.

Caller response #2. He will be annoyed because he will be forced to wait senselessly for a long time by the phone, in order to eventually find out that the information he was given here is not enough.

Side effect. For a long time, the phone of the company's management will be busy.

Secretary reaction #3. She addresses the caller to the boss, who, of course, will not be able to help him either.

Caller response #3. He will be annoyed because he will be forced to make telephone conversations with two employees of the firm and not get the information he needs.

side effect - the same as in the previous case.

Secretary reaction #4. She returns the caller to the company's switchboard, as she cannot be useful to him.

Caller response #4. He will be annoyed this time as well, as he has only wasted time.

Obviously, only the first solution can be considered correct. Note, however, that for its implementation, the secretary must have at his disposal the appropriate technical means to transfer a telephone call to the number of the desired employee.

In the considered example, it is not difficult to compare the solution options directly. However, in most decision-making tasks, it is advisable to single out a list of factors, based on the values ​​of which it is advisable to compare solutions.

Example 2 Petya Ivanov graduated from Moscow State Technical University. N.E. Bauman and chooses a place of work. He has four options.

A. To enroll in graduate school at Moscow State Technical University. N.E. Bauman. The scholarship is negligible, but there are opportunities for part-time work. In 5 years, you can become an assistant professor at a world-famous university, work part-time as a teacher, consultant, employee of firms.

B. Become an engineer at a large enterprise that was previously part of the military-industrial complex, but now has a permanent package of orders, including foreign ones.

C. Join a small business that fulfills specific orders and get paid for each order completed.

D. Become a computer scientist in a branch of a foreign expert-import firm.

How to compare these options? Consider natural factors.

Salary. At the moment - growing from A to D.

Growth prospects (including pay). The largest in A, present in B, practically absent in C and D.

Workplace sustainability. Largest in A, significant in B, small in C and D.

bosses. Familiar and respected in A, solid and gloomy in B, frivolous but active in C, strict and incomprehensible in D.

Collective. Familiar and acceptable in A, understandable and benevolent in B, competitive (struggle for orders and thus for income) in C, saturated with squealing in D.

Criminality. Absent in A and B, constant (albeit relatively small) in C, possible in D (moreover, on a large scale).

Mode. Quite free in A, hard (entrance and exit by releases at a given time) in B, “striped” in C (actually free, but if the authorities orders ...), prison type in D (doors through which you can pass through are fixed, for drinking tea at the workplace - a fine of 10% of the monthly salary, etc.)

Travel time to work. C is closest, then D, A, and B.

We will limit ourselves to these eight factors. To make a decision, it is advisable to make a table in which the rows correspond to the factors, the columns correspond to possible solutions, and in the cells of the table there are estimates of the factors for the corresponding variants of the table. Let, for definiteness, the numbers 1, 2, 3, ..., 9, 10 be used as possible estimates, and the worst value is 1, and the best is 10. Let Petya Ivanov's opinion be expressed in Table 1.

Table 1.

Evaluation of facts when choosing a job.

		MSTU im. N.E.	Large enterprise	Small business	Foreign company
	Salary
	Growth prospects
	Sustainability
	superiors
	team
	Crime
	Travel time
	Sum of points

Direct analysis of the data in Table 1 does not allow Petya Ivanov to draw an unambiguous conclusion. According to some indicators, one option is better, according to others, the other. We need to balance the factors somehow. The easiest way is to assign weights to them, and then add the weights for each of the options (this approach has disadvantages, which are discussed in chapter 3.4). And what weight to take? The easiest way is to take all factors with the same weights - unit. Simply put, add up the scores assigned to the factors. The results are shown in the last line. By the sum of points in the first place - MSTU. N.E. Bauman, on the second - a large enterprise, on the third - a small enterprise, on the last - a branch of a foreign company.

Similarly, a feasibility study is carried out in some real situations. For example, Table 2 gives a comparative description of the competitiveness factors of the main manufacturers of glass wool products. In addition to a direct comparison of manufacturers, such a table makes it possible to prepare decisions on measures to increase competitiveness, as well as indicate possible limits for promotion. So, according to the data of Table 2 JSC Mostermosteklo is at the level of one of its main competitors in terms of competitiveness and loses to the second one by 4 points. However, by improving the ease of installation by 1 point (and reaching the worst of its competitors in this factor), moving to a more attractive discount system (while scoring 2 points), and also increasing promotions by 2 points (and reaching the level of the worst of its competitors in this factor), it will increase the score by 5 and become the best.

Table 2.

Comparative characteristics of the main manufacturers of glass wool products by competitiveness factors

	Factors of competitiveness	OAO Mostermo-Steklo	Main competitors
	Quality
	Brand prestige
	Laminating**
	Ease of mounting
	Availability of certificates
	Selling
	Price discounts
	Promotion of goods in the markets
	Total points

Note. TEP* - technical and economic planning

Lamination** - additional coating

In practice, it is sometimes necessary to introduce factor weights. So, when developing the organizational and economic support for the implementation of the project for installing gas cleaning equipment at OJSC Magnitogorsk Iron and Steel Works, four projects were compared (Table 3).

Table 3

Project scoring

	Given quality indicators
	MTBF
	Assigned service life before decommissioning
	Assigned service life before overhaul
	Average recovery time
	Set shelf life
	Energy costs for cleaning 1000 m 3 of gas
	Cleaning degree
	Total cost of the project
	Period of execution
Integral final indicator of project quality

Projects were evaluated by the “integral final project quality indicator”, equal to the sum (for all factors) of the products of the factor value and the weight of this factor. For tables 1 and 2, all weights were single; for table 3, the weights are given in the right column. (The values ​​of the weights are usually determined with the help of experts.) In accordance with the "integral final indicator of the quality of the project", the best is the project "Russia-2", then the project "Sweden" follows, then the project "Russia-1", and the project " Ukraine". In accordance with the approach under consideration, it is necessary to recommend that the Russia-2 project be accepted for execution.

3.1.2. An example of preparing a solution based on

macroeconomic data

Decisions are prepared, adopted and implemented to cope with the problems at hand. This is preceded by the discovery of the problem and the analysis of the situation. At all stages specific economic data and econometric methods of their analysis are used.

Let us consider an example of the chain “detection of a problem” - “analysis of the situation” - “preparation of a solution” using the example of macroeconomic data related to Russia for 1989-2001. The choice of the object of consideration is explained by the fact that each of the readers has extensive preliminary information about it.

The results of the decade of "reforms". Table 1 shows data on the output of various types of industrial and agricultural products in Russia in 1989 and 2001. These data are taken from the official publications of the State Statistics Committee of the Russian Federation and from its website www.gks.ru.

Table 1.

Comparison of Russia's economic indicators for 1989 and 2001

	Product type	measurements			which year corresponds production in 2001
	INDUSTRY
	Steel pipes
	Metal cutting machines
	Forging and pressing machines
	Trucks
	Tractors
	Combine harvesters
	radio receivers
	TVs
	soda ash
	Chemical fibers and threads
	Export of timber
	lumber
		Million tiles
	Building brick
	Fabrics of all kinds
	Woolen fabrics
	AGRICULTURE
	Whole milk products
	animal oil
	LIVESTOCK
	Cattle	Million goals
		Million goals
	Sheep and goats	Million goals

The last column of Table 1 provides information about the level of which year in the past the production of 2001 corresponds to. It can be seen that in terms of production, the rollback was several tens, and sometimes hundreds of years. At the same time, it can hardly be considered justified to reduce the volume of production of these types of products. Questions may arise only for certain types. For example, do consumers need radios now (line 10), or is a reduction in their production by more than 20 times justified?

From the data in Table 1 follows the hypothesis of trouble in the development of the national economy of Russia. However, this table shows only selected types of products, i.e. just a few examples. It is necessary to move on to the data characterizing the situation as a whole (Table 2).

Table 2.

Dynamics of the main economic indicators of Russia

(according to official data of the State Statistics Committee and the Central Bank of the Russian Federation)

	Gross domestic product		Volume of industrial output		Capital investments
	previous year	% by 1990	% to the previous year	% by 1990	% to the previous year	% by 1990

In Table 2 for 1999-2001. instead of data on GDP, data on the IBO are given - an index of changes in the output of five basic sectors (industry, agriculture, construction, transport, retail trade).

From Table 2 it is clear that the hypothesis of trouble in the development of the national economy of Russia is correct. Indeed, between 1990 and 2001, the volume of industrial output decreased by 41%, despite the rise that began in 1999. Table 2 also shows a catastrophic drop in investment. Fixed assets age, but are not replaced by new ones. An increase in the number of accidents is to be expected. It is known that in the housing and communal services over the past 10 years the number of accidents has increased by 5 times.

From the above facts it follows that the course of "reforms" in Russia, carried out since the early 1990s, has led to a reduction in production volumes in general and certain types of goods in particular, to a "rollback" of the national economy back decades (according to our assessment, to the level of the beginning 1960s). If we consider that the purpose of the "reforms" was to increase the efficiency of the national economy, then it must be admitted that the direction of the "reforms" was chosen incorrectly. What should be done, based on economic theory?

Nobel laureates - for state regulation of the economy. Economic theory is unlucky in our country. For the most part, Russian experts at first faithfully commented on the decisions of political leaders, and then just as zealously repeated the basics of Western introductory courses on economics. Although for several years the Department of Economics of the Russian Academy of Sciences has tirelessly explained the fallacy of the "reform" course, neither the government nor society pays attention to this criticism. This is natural - the reputation is undermined.

For the last three hundred years, people in Russia have treated with reverence the march coming from the West. And the propagandists of the current "reforms" tirelessly swear allegiance to the advanced Western economic theories, namely, the monetarism of M. Friedman and D. Sachs. One might get the impression that the majority of Western economists support the "reform course" in Russia.

However, this is not at all the case. In fact, monetarism does not enjoy support among serious experts, and the actions of the Russian "reformers" contradict the generally accepted foundations of economic theory. And we do not know about it because the information curtain is lowered before us.

What do Western economists really think? It turns out that during the 1996 presidential election, five Nobel Prize winners in economics addressed the future president of Russia with a joint statement. These were Kenneth Arrow, Wassily Leontiev, Lawrence Klein, James Tobin, Robert Solow. They were joined by a number of other American scientists, as well as full members of the Russian Academy of Sciences L. Abalkin, O. Bogomolov, V. Makarov, S. Shatalin, Yu. Yaremenko.

The appeal of the US and Russian economic elites was almost completely ignored by the domestic media. Only the newspaper of the PANINTER concern told about him. And even then, after one of the authors of the appeal, Professor of the University of California Michael Intrilligator, came to Moscow and spoke at our scientific seminar. Later, publications appeared in scientific journals.

The main idea of ​​the appeal is that the Russian government should play a more important role in the economy. We must look up to the governments of the United States, Sweden, Germany and other countries whose main concern is state regulation of the economy. It is necessary to develop the public sector of the economy.

In Russia, the critics of the planned economy have clearly gone too far - market America is advising us to strengthen the role of the state! And they explain to negligent students: "The government must understand that competition is the basis of a market economy, and by no means property relations."

The use of expressions that do not have a clear, generally accepted meaning, such as "reforms" or "market economy", leads to erroneous decisions. Nobel laureates in economics remind: the main thing is competition, i.e. competition, competition. They know from experience that the main figure in the enterprise is the manager (i.e. manager, director), and not the owner. Firms must compete to make the best products for consumers and provide the best services. If there is no competition, there is no market economy. And there is the plundering of property of privatized enterprises. There is inflation by private monopolies.

The second thought of the appeal is the need for "strong state action" to prevent further criminalization of the economy. Alas, a sad record: the "Russian mafia" is one of the most powerful in the world. The only pity is that the criminal world and a normal market economy are incompatible. Private armies protect not the capitalists, but the feudal lords. Americans say: stop the mafia - or slide into the Middle Ages.

Why are sane Americans interested in the fate of Russia? Not only from general scientific or humane considerations. They do not need - moreover, dangerous - chaos in Russia.

During the 1990s, the main macroeconomic indicators of Russia (output, real wages, etc.) decreased, according to our data, by 4 times (according to the official data of the State Statistics Committee of the Russian Federation, which undoubtedly embellishes the real picture, by 2 times). In terms of industrial development, the country was thrown back in the 1950s. The economic growth that began in 1999 made it possible to move, as already noted, to the level of the early 1960s. However, in a number of significant positions, the situation continues to deteriorate, in particular, fixed assets are catastrophically aging (Table 2). If the trend of degradation of the national economy is not reversed, the collapse of power structures and the armed struggle of various groups such as the events of 1609-1613 are ahead. and 1917-1922.

However, on the battlefields of future turmoil, there are missiles with nuclear warheads and chemical weapons depots. They will be used. And not only in the internal struggle between Tyumen and Perm. But also in acts of retaliation against the countries of the West, guilty, in the opinion of one of the future leaders of the armed detachments, in the catastrophe of Russia. Imagine an ultimatum from the commander of a missile regiment of the former Russia to the US government - either a ship with food, fuel and a billion dollars arrives at the mouth of the Pechora by May 14, 2004, or the missiles of the regiment are sent to New York and San Francisco under their own power, taking nuclear warheads.

Such a scenario of development of events cannot be considered improbable. Therefore, the emergence of unrest in Russia is a deadly - in the truest sense of the word - danger to the inhabitants of Paris, Berlin, London, Rome, Washington and other centers of Western civilization. Perhaps, for their own safety, the Americans will soon be saving us from the incompetence of our own government.

Therefore, the third thesis of the Nobel laureates is as follows: it is necessary to quickly find a way out of the crisis, and this can be done only on the basis of active state regulation of economic relations. We must act as actively as US President F. Roosevelt worked in the 1930s, leading the country out of the "Great Depression." His administration was not afraid to actually nationalize the banks and organize public works. And the corresponding economic theory was already then - the works of the most famous economist of the twentieth century. Englishman John Keynes.

The economy for our country is a sore point. Just as a bad tooth keeps us from thinking about anything else, so a sick economy occupies our thoughts. But in fact, the economy should be a servant of society. If society believes that older people should be paid pensions that ensure a decent living, then it is the duty of the economy to achieve this. If society believes that children should go to school for free, then the government, through state regulation of the economy, should do everything necessary. Some two hundred years ago there were no pensions or free schools. So what, back to feudalism for the dogma of liberal economics?

The fourth thesis of the Nobel laureates is the need for a new "social contract" (a social contract, as Russov said in the 18th century) between government and society. The country's leadership must provide us with a "social safety net" - pensions, free schools and hospitals, and so on.

And it is completely contrary to the norms of a market economy, non-compliance with contracts and obligations of the state and firms, above all - the delay in the payment of salaries and pensions. In a traditional market state, the court instantly speaks its word, firms go under the hammer, and officials, entrepreneurs and managers go to jail.

And the fifth thesis is: "The Russian government must understand that the secret of a market economy lies not in private property, but rather in competition and competition again." We need not just an owner, but an effective owner who would increase the property of the company, and not squander it.

In order to move to a market economy, it would be necessary first of all to create, in the words of Professor M. Intrilligator, "institutions of a market economy." We are talking about a powerful legal system - laws and courts. About banks, reliable and engaged in investments. About a simple and steadily implemented tax code. On the accounting and auditing system, i.e. control over the activities of firms. On insurance, including ecological. And about many other things.

Clearly, these "institutions of a market economy" are underdeveloped in Russia, and state officials are in no hurry to create them. The slogans of the "reforms" that began in the 1990s were: stabilization, liberalization, privatization. What is the bottom line?

There is no stabilization - fixed assets are catastrophically aging; there is a degradation of production structures. Total output of goods and services (according to official data, gross domestic product has been growing since 1999). However, the methods of calculation are questionable. For example, according to the methodology of the State Statistics Committee of the Russian Federation, banking services account for 13 percent of the gross domestic product. What services do banks provide? He gave a loan of a billion rubles - so write this billion into the gross domestic product, it is as important for the State Statistics Committee as baking 140,000 loaves of bread. With all due respect to the hard work of bank clerks, experts and security guards, the labor costs are incommensurable.

Liberalization tore the economy into a tailspin of inflation, ruined a lot of small entrepreneurs, but did not and could not lead to equilibrium prices, at which demand is equal to supply. At the cost of the collapse of economic life and the deprivation of workers of their livelihood, by the beginning of 1996 the government had stopped inflation at a level of about 10,000. In other words, by 10,000 rubles. then it was possible to buy as much as for 1 ruble. in 1990. By 2002, prices increased another 5 times. But the denomination of the ruble was carried out (1 new ruble corresponds to 1000 old ones). So in 2002, for 50 rubles. you can buy as many consumer goods as for 1 rub. in 1990. Each citizen, taking the value of his salary, pension, stipend and dividing by 50, can get its size in 1990 prices. Now compare it with your own or similar income in 1990. You will immediately see that you were given "reforms" . Roughly speaking, the income of an ordinary citizen was halved, since production fell by half. Of the remaining half, about 50% is redistributed in favor of the owners who appeared during the “reforms”. As a result, an ordinary citizen gets a quarter of what he had in 1990.

Privatization for the majority ended in complete embarrassment (as, indeed, in the UK). As it turned out, those who sold the voucher for a case of vodka acted most intelligently. Units have enriched. But the privatized enterprises in their mass by no means began to work more efficiently than the state ones. In 1997, out of a hundred and fifty Moscow textile firms, one PANINTER concern was "afloat", and even that was created from scratch in 1989, and not privatized.

So, everything was done wrong according to economic theory. One gets the impression that our country is by no means heading towards a market economy. Rather, she moves away from it. Towards feudalism? Perhaps, we were closest to a normal market economy in 1990? Or in 1927, under the New Economic Policy, when state trusts and syndicates competed with each other?

The leading economists of the world - Nobel laureates are independent, they do not work for the International Monetary Fund and the World Bank. Their set of advice is the opposite of what the current leadership of Russia blindly follows. Economic "reforms" in Russia are carried out without relying on modern economic science. Both domestic and American leading economists are convinced of the need for a radical change in the "course of reforms".

Unfortunately, there is almost no hope that the voice of Nobel laureates will be heard by the current rulers. However, those who work for the future of Russia need to know their opinion.

But it is unwise to follow him blindly. Do we need a classical market economy? The fact is that Western economic theories are developed on the basis of someone else's experience, which differs from ours. They do not work in Russian conditions, because the Russian mentality is fundamentally different from the Western one. In particular, this is manifested in the relationship between employees and employers, in the preservation of economic activity in the conditions of a destroyed money circulation, and so on. Is it possible to imagine Americans working for several months without a paycheck? If they don't receive the envelope with their weekly pay on Friday, they won't work on Monday. And how the working people of France or Korea are fighting for their rights!

Obviously, an appropriate theory is needed to develop and implement a program for overcoming the crisis. It, alas, does not exist at present, since both the domestic pseudo-Marxist-anti-Stalinist political economy, frozen in the dogmas of the 30-50s, and various Western concepts (Soviet specialists in mathematical economics spent a lot of effort on their analysis), on which in the early 1990s 1990s, they had high hopes, do not correspond to modern Russian conditions. This issue has been covered in detail in the literature.

Therefore, it is necessary to develop a theory of state regulation of market production relations in modern Russian conditions (a fundamentally new theory!). As well as systems of economic and mathematical models and related software.

Dynamics of the role of states in national economies. At present (2003), the Russian leadership and, in general, the mass media supporting its policy (mass media) are promoting the need to reduce the participation of the state in the economy. As a result, various “reforms” are underway, privatization of state enterprises, structures and functions is being carried out, taxes are being reduced, etc. Nobel laureates in economics say the opposite - the role of the state should increase. Let's look at what happened in different countries over the past century. As an indicator, let's take the amount of government spending, expressed as a percentage of the gross domestic product (GDP). With a sufficient degree of accuracy, it can be called the share of the state budget in the gross domestic product (neglecting the difference between the revenue and expenditure parts of the state budget). This indicator measures the role of the state in the economy. In accordance with the well-known decomposition of J. Keynes for GDP, the possible values ​​for it are from 0 to 100%. The larger the indicator under consideration, the more significant the role of the state in the national economy. Table 3 shows the data of the International Monetary Fund for 11 most economically developed foreign countries.

Table 3

Government spending (expenditure part of the budget)

as a percentage of GDP

	Netherlands
	Germany
	Norway
	Great Britain
	Australia
	Average for 11 countries

Notes e. *For 1870 - the average for 7 countries.

The data in Table 3 are very eloquent. In all eleven countries in the twentieth century. there is a significant increase in the role of the state in the economy. By the end of the century, it ranges from 1/3 (USA) to 1/2 or more (58.5% - Sweden, 54.3% - France, 49.4% - Belgium, 49.1% - Italy, etc.). d.). At the same time, from 1870 to 1913, the indicator increased slightly on average - by 1.7%, and decreased in individual countries.

For Russia, the indicator under consideration behaved quite differently. In 1913, Russia occupied one of the middle places among those considered. Then the indicator increased significantly and reached 74% in the post-war years. In 1960 this was more than twice the average for 11 countries. By the end of the twentieth century. a number of countries (Sweden, France) approached the level of state control over the economy, which was in the USSR. But in Russia there was a rollback to the level of 1913. At present, the role of the Russian state in the national economy is three times less than the American one, and five times less than the French one.

In terms of control theory, we can say this. In the post-war USSR, excessively tight state control over the economy was observed (it was ahead of other countries by half a century). In order to return to the "mainstream" it was recognized to reduce the role of the state in the economy. It would be natural to go somewhere between France and Germany, ie. reduce the share of government spending from 74% of GDP to about 50% of GDP. However, there was a very large overshoot, and Russia found itself far below all the countries under consideration in terms of the indicator under consideration. If before the deviation was +15.5% from the nearest country (Sweden), now it is (-21.8%) compared to the USA, i.e. the influence of the state on the economy in Russia is 3 times less than the similar influence in the United States.

What to strive for? The advantages of the Soviet project (1917-1991) and the shortcomings of its implementation are analyzed quite well. For example, many believe that the use of "gross" indicators in assessing the activities of an enterprise and planning "from what has been achieved" held back the pace of economic development of the USSR and the introduction of scientific and technological progress.

But the main thing is the future. What to strive for? The projected future is little discussed. And if there is no clear goal, then there are no means to achieve it. Behind the veil of general words, the constructions of the planned society are unclear. And the meaning of the words is not always clear. For example, the main idea of ​​the so-called "market socialism", as it turns out, is to provide state-owned enterprises with a certain independence in economic activities.. Hardly anyone will object to this.

First, as shown above, the participation of the state in the economy should increase by 3-5 times. The initial steps are quite clear. The state must take the economy as a whole under control. First of all, the state should take control and management of enterprises involved in the production of oil, gas and other natural resources. Foreign economic activity is also the business of the state, as well as the management of natural monopolies (transport, communications, electric power industry). Large enterprises, primarily of the military-industrial complex, should belong to the state. It may be advisable to nationalize the banks. As a careful analysis shows, private ownership of land has no place in Russia.

Planning and control is the core of a scientific approach to managing organizations. It is well known, both theoretically and practically, that centralized planned management with clearly defined goals is more effective than any form of "market". Not without reason, in a situation of war, any state switches to such a control system.

The second problem is the provision of natural fundamental human rights. Rights to food, housing, work, protection from crime, medical care. For information, education, pension and social security, etc. In particular, to ensure the right to objective information, a state presence in the media is necessary, as well as a system of protection against the "subjectivism" of the media.

The third problem is how to organize the economic system. The main thing is the distribution of powers between different levels of the management hierarchy. What is within the competence of national governments, what should be decided at the level of an industry or region, what - at the level of an enterprise, division or individual employee? What decisions can be made by the director of the plant alone, and which are not? Who should give permission - the work team or a higher organization?

In the USSR, there were two main forms of organizations - state and collective (collective farms, artels, etc.). An intermediate form is leased enterprises, in which fixed assets owned by the state, under certain conditions, are provided for the use of the labor collective. In addition, a fairly large share of the national income was created as a result of individual activities, primarily on household plots.

How to build an economy in the future Russia? What should be the ratio of state and "kolkhoz" enterprises? In particular, what is the role of both in trade and banking? How to use competition between enterprises to improve the quality of work and accelerate scientific and technological progress and at the same time provide social protection to the "losers" in the competitive struggle?

How to ensure the possibility of implementing the initiatives of employees and labor collectives? We need an appropriate legal framework. Apparently, the possibility of creating your own small business should be provided to any citizen of Russia.

The optimal construction of the organizational and economic mechanism of management in the future Russia deserves a detailed discussion, but not within the framework of this textbook.

How many rich people are in Russia? Informed decision making is hindered by common myths. One of them is analyzed above - the myth about the need to further reduce the role of the state in the Russian economy. Let's take another example as an example: "The policy pursued and pursued by the state authorities has made 10-15% of the population rich and very rich."

In fact, the share of the rich is at least 100 times less. Their number is measured as fractions of a percentage of the total population.

According to official data from the Ministry of Taxes and Duties, only about 35,000 people throughout Russia submitted tax returns for 2000 worth at least a million rubles (this was the last year when all citizens with medium and high incomes were required to submit tax returns). What is a million rubles a year? This is, at the rate of the Central Bank of that time, about 33 thousand dollars - slightly higher than the average salary in the United States, the annual income of a nurse or teacher. An American university professor or a police officer gets a lot more.

So a million rubles a year is objectively not such a big income. Although, of course, not small. Advertisements are posted in the Moscow metro - the driver earns 10 thousand rubles a month, i.e. 120 thousand per year. Probably a rich person is one whose income is at least 10 times that of a skilled worker. So, wealth begins with an annual income of one million rubles. This means that in 2000 there were 35,000 law-abiding rich people in Russia; approximately 0.05% of all economically active citizens. (Offenders who have not submitted tax returns cannot be included in their number. Otherwise, the entire Russian economy will have to be recognized as criminal.)

Add family members and those whose income is only slightly below a million. We get that the layer of "rich and very rich" 150-200 thousand people. This is about 0.15% of the total population, and by no means 10% (14 million) or 15 percent (21 million).

This assessment is supported by many circumstantial evidence. For example, in 2001 about 500 Mercedes cars were imported into Russia. But wealth is associated with a luxurious foreign car ...

Although the percentage of "rich and very rich" is very small, nevertheless, there are hundreds of thousands of them, and this is enough to create your own subculture, chain of stores, casinos, etc. Before the Great October Socialist Revolution, there were about 50 thousand families of landowners, and the total number of rich people was about the same as now. The mass media create a greatly exaggerated idea of ​​the size of this layer. Then, specialists in the analysis of consumer preferences (marketers), conducting surveys, look for and do not find “rich and very rich” ... It was our work in a marketing firm that forced us to understand the issue at hand.

Why was the myth of a significant number of rich people created? Firstly, in order to establish in the mass consciousness the idea of ​​the success of the "reforms". Secondly, to inspire the idea of ​​a dozen or two million of those who have become "rich and very rich" thanks to "reforms". As a result, the idea arises of the need for a social contract between the poor and the rich - the interests of 10-15% of the population cannot be completely neglected. The considered myth, of course, contributes to the preservation of the stability of modern society. However, it interferes with solving specific tasks of decision-making, economic and public administration, and marketing.

Solve problems in turn. It is natural to want to break up a complex decision problem into several parts in order to take advantage of the opportunity to solve them one by one.

Example 1 The simplest option is a dichotomous scheme for visual representation of possible solutions. For example, you need to solve the problem: “How to celebrate the new year?” The first step is to choose one of two possible solutions:

1) stay at home;

2) leave.

In each of the two cases, it becomes necessary to make second-level decisions. So, in the first case:

1.1) invite guests:

1.2) do not invite guests.

In the second case:

2.1) go to relatives or friends;

2.2) go to public places (go on a trip, go to a club or restaurant, etc.).

After two steps, we got four possible solutions. Each of them, generally speaking, implies a further division. So, for example, the option "invite guests" leads to further discussion of their list. In this case, different options can be compared. For example, what do you prefer - gastronomic pleasures over TV in a well-known company or a heated discussion of topical problems or customs of distant countries with interesting people whom you have not met for a long time?

The “stay at home and not invite guests” option also has its own options. You can spend New Year's Eve in the family circle, and one of the tasks to be solved is which television program to watch. And you can speech to sleep shortly after midnight, for example, in case of illness or after a long hard work.

The option “to go to relatives or friends” also requires further decisions. Is the trip connected primarily with the maintenance of family relations or with the desire to have fun? What kind of food do you prefer - physical or spiritual (gastronomic pleasures or an interesting conversation)?

The remaining fourth option, “go to public places,” offers even more choices. You can stay in your city, go to another city (for example, from Moscow to Smolensk), go to nature (to a ski base, to a resort), cross the border. And here there are a lot of opportunities - all countries, all continents, you can ride an elephant in Thailand, swim in the Atlantic Ocean or wander around Paris.

So, the ordinary task of making a decision “How to celebrate the new year?” when worked out, it turns into a choice from an unimaginable number of options. However, there is no need to go to the list of specific options (leaving on December 28 on such and such a train there), since the decision is obviously made sequentially, and the decision to “stay at home” makes it unnecessary to consider all tourist routes.

What does decomposition of solutions give us? Example 1 demonstrates how several decisions taken one after another can cope with a variety of options. When making decisions, the entire arsenal of decision theory can be used, such concepts as goals, criteria, resources, risks, etc. (see Chapter 1.1), but quite often decisions are made on an intuitive level, without introducing these concepts into the discussion.

Decision tree. Quite often it is convenient to represent options graphically. Usually, possible solutions are presented in the form of one of the types of graphs - a tree (Fig. 1). Strictly speaking, this is an inverted tree. The root is the original task - "How to celebrate the New Year?" Two branches go from it - to the options "Stay at home" and "Leave". From these options, which in turn are decision problems (“What to do when you stay at home?” and “Where to go?”), Branches lead to warrants of decision problems of the following order.

Fig.1. A decision tree is a dichotomous diagram for visualizing possible solutions.

Example 2 Let us give the beginning (root) of the "Project Decision Tree" used in practical work.

The task of the enterprise is to produce high-quality fiberglass products, because. the need for heaters is growing and the market is expanding. You must choose from two options:

1) work on existing equipment;

2) to reconstruct the workshop.

When choosing the first option, it should be borne in mind that the capacity of the equipment is not so large as to meet the increased demand (physical wear of the line), and the quality of the products does not meet international requirements (obsolescence of the line). Therefore, it should be expected that even under the conditions of the expected increased demand, the materials produced on the existing equipment will not be in demand (sales will fall), and accordingly, the production capacity will not grow.

When choosing the second solution option after the reconstruction, the productivity increases by 2 times compared to the existing technological line, the quality of the products manufactured by the enterprise will meet international requirements, it will be able to compete with the main manufacturers of glass wool. The main technical and economic indicators will increase. However, there is a certain risk of the project, since large capital investments are required (most of which are from borrowed sources).

Further construction of the decision tree is quite obvious here. From the “Run on existing equipment” option, lines will go to solutions related to simplifying the range of products, finding a market niche that is ready to accept lower quality products, etc. This is a line for survival in the conditions of lagging behind scientific and technological progress, up to the liquidation of the enterprise. In some circumstances, the liquidation of the enterprise is the best way out.

Two types of lines will go from the “Reconstruct the workshop” option - first “technological” and then “financial”. First, you need to choose a specific reconstruction option and prepare a business plan for the corresponding investment project. Then it is necessary to provide financial income for the implementation of this investment project, ensuring minimal risk for the enterprise. Here the problem is the choice of creditors and borrowers, the conclusion of contracts with them on acceptable terms.

In addition to sequential decision making, decision task decomposition is used to "separate problems into parts". At the same time, the result of decomposition is not the choice of one of a large number of options, as in sequential decision making, but the representation of the problem to be solved in the form of a set of smaller problems, in the limit - such problems, the methods for solving which are known.

Example 3 Consider the problem of combating traffic noise. It is advisable to distinguish the following types of events:

1) activities related to the noise source;

2) activities at the place of manifestation of noise;

3) measures to prevent noise propagation;

4) activities related to the entire vehicle system;

5) activities related to the reconstruction of the transport system and the development of methods for its technical and economic assessment.

Unlike example 1, here we are not talking about choosing one of the solution options. On the contrary, in order to effectively combat traffic noise, it is necessary to use all branches, all five types of measures.

The source of the noise is a car. Therefore, three directions of influence on the situation immediately stand out:

1.1) the design of the motor vehicle (including the adjustment of its components);

1.2) fuel;

1.3) road.

Direct noise protection can be individual - helmets, headphones, ear plugs - ear plugs (from "take care of your ears"). Or maybe collective (soundproof window frames, soundproof walls). Therefore, activities at the place of manifestation of noise are naturally divided into two classes:

2.1) personal noise protection;

2.2) noise suppression in buildings.

You can reduce the noise "on the road." There are various well-known ways to do this:

3.1) construction of soundproof walls and screens that reflect sound waves in safe directions;

3.2) creation of soundproof strips from trees and shrubs;

3.3.) anti-noise location of buildings on the ground (both in distance from the noise source and in the orientation of buildings relative to it and to each other.

Noise reduction is also possible through various measures related to the entire vehicle system. We are talking about the rational organization of traffic within the existing transport system. This rational organization is carried out by the regional authorities by administrative and partially organizational and economic methods. Examples of such activities are:

4.2) restriction of traffic at certain hours or on certain streets;

4.3) traffic planning - in terms of time, speed, routes.

Finally, it is necessary to discuss activities aimed at the future. They are associated with the reconstruction of transport systems and the development of methods for its technical and economic assessment. What should be the transport of the future? It is clear that it should include measures aimed at reducing the noise load. The technical and economic assessment of transport systems of the future should be determined taking into account the noise load. Let's express it as

5.1) noise suppression in designed and reconstructed transport systems.

Thus, one original problem gave rise to 12 new ones. You should not choose one of them, but solve all 12. However, each of the 12 is more specific than the original one. It is easier to solve (after further decomposition) than the original one.

Decomposition of decision-making tasks "from branches to root". So far, we have analyzed situations where the decision-making problem was divided into components (in order to clarify the formulation and choose one of the specific formulations, or to divide one large problem into a number of smaller ones). Let us now consider the opposite process, when the specific needs of the organization's business processes generate a single set of decision-making tasks.

Example 4. Consider the process of decomposition of decision-making tasks “from branches to the root” using the example of the formation of tasks for the controlling service of an organization. For many organizations, the following issues are relevant.

1) The lack of operational information about production processes requires the introduction of a production accounting system at the enterprise.

2) The high level of overhead costs in the total amount of costs makes it necessary to identify the places of occurrence of "unnecessary" costs.

3) An unnecessarily large amount of work in progress entails the need to develop an order management system.

4) There is no effective mechanism for monitoring the activities of the procurement service. There is only occasional control by the management of the organization. This necessitates the development of an organizational and economic mechanism that makes it possible to control the level of prices for purchased materials.

5) Overhead costs are planned at the enterprise upon the fact of the previous period. This requires the implementation of a budgeting process.

6) The system of indicators used is insufficient for enterprise management. Therefore, it is necessary to develop a system of indicators of the financial, economic, industrial and social activities of the enterprise.

7) The management of the enterprise does not have a systematic understanding of the activities of the enterprise. To make informed decisions on enterprise management, it is necessary to create an analytical support service for making such decisions.

To solve the seven listed urgent problems of decision-making in enterprise management, there is a need for a special integrating service - the controlling service. It is quite obvious that all the "branches" in the decomposition task under consideration are directed to one "root", and this "root" describes the decision-making tasks supported by the controlling service.

Until now, in the process of decomposition, all tasks of the same level were considered equivalent, weight coefficients were not introduced. However, sometimes it turns out to be useful to consider various options with certain coefficients.

Example 5 It is necessary to develop a procedure for making decisions related to the evaluation of the effectiveness of the developed medical device (magnetic separator). To calculate the generalized quality indicator and the technical level of such devices, it is natural to decompose into three decision-making tasks about three groups of indicators:

1) the main indicators of the appointment;

2) economic conditions of consumption;

3) terms of service.

Let be X– assessment for the first group of indicators, Y- on the second Z- on the third. The first estimate is taken into account with a weighting factor of 0.6, the second - 0.2, the third - also 0.2 (the sum of the three weighting factors is 1). Thus, the generalized indicator of the quality and technical level of the medical device is estimated as

W = 0,6X + 0,2Y + 0,2Z.

At the next stage of decomposition, single indicators of quality and technical level are singled out in each of the three groups. So, for the block of "main indicators of purpose" allocate:

1.1) degree of purification X(1),

1.2) cleaning time X(2),

1.3) mass of substrate X(3),

1.4) the likelihood of damage to healthy cells X(4).

They are also assigned weights of 0.44, 0.09, 0.18, 0.29, respectively (the sum of the weights is 1). Therefore, the score on the main assignment indicators is calculated as

X = 0,44 X(1) + 0,09 X(2) + 0,18 X(3) + 0,29 X(4).

For the block "economic conditions of consumption" there are two single indicators:

2.1) separation methods At(1)

2.2) patent purity At(2).

They are also assigned weights of 0.74 and 0.26, respectively (the sum of the weights is 1). Therefore, the estimate for the economic conditions of consumption is calculated as

At = 0,74At(1) + 0,26At(2).

For the block "conditions of service" there are three single indicators:

3.1) working mode Z(1),

3.2.) ergonomics Z(2),

3.3) reliability Z(3).

They are also assigned weights of 0.55, 0.14 and 0.31, respectively (the sum of the weights is 1). Therefore, the score for the "conditions of service" block is calculated as

Z = 0,55Z(1) + 0,14Z(2) + 0,31Z(3).

Thus, a decomposition algorithm is described in the problem of making a decision regarding the evaluation of the effectiveness of a medical device. To calculate the generalized indicator of quality and technical level, it is necessary to obtain estimates of nine single indicators. This is usually done with the involvement of experts who compare the device being developed with domestic and foreign analogues. The use of such indicators is demonstrated in subsection 3.1.1 using the examples of total scores and weighted total scores. However, only here it is shown how systems of factors can be reasonably built on the basis of the idea of ​​decomposition.

Expert judgments are usually used to find the weighting factors (see chapter 3.4). At the same time, for each group of indicators, as well as when assigning weights to groups at the top level of decomposition, their own expert procedures can be applied and their experts can be polled. This important advantage of the procedure under consideration is ensured by the fact that the sum of the weighting coefficients is equal to 1 each time.

The fact is that from the above relations it follows that to calculate the generalized indicator of quality and technical level, one can use directly the estimates of single indicators:

W = 0,6X + 0,2Y + 0,2Z = 0,6 (0,44 X(1) + 0,09 X(2) + 0,18 X(3) + 0,29 X(4)) +

0,2 (0,74At(1) + 0,26At(2)) + 0,2 (0,55Z(1) + 0,14Z(2) + 0,31Z(3)) =

0,264X(1) + 0,054X(2) + 0,108 X(3) + 0,174X(4) +

0,148At(1) + 0,052At(2) + 0,11Z(1) + 0,028Z(2) + 0,062(3).

The sum of the final nine weight coefficients, of course, is equal to 1, since this is how the decomposition scheme is constructed.

At first glance, it may seem rational to evaluate these nine coefficients directly (with the help of experts). Chapter 3.4 criticizes this proposal. It is also clear from the above that the step-by-step decomposition method makes it possible to compare weight coefficients more accurately (separately within groups, separately groups among themselves) than can be done when combining all single indicators together.

The above methods of averaging the values ​​of single indicators are actually the use of weighted arithmetic averages for the values ​​of single indicators. It is advisable to pay attention to the possibility of using other types of averages. And also on the approaches and results of the measurement theory, which allow choosing the most adequate types of average values ​​in accordance with the measurement scales used (see Chapter 2.1).

In the theory and practice of decision-making, a large number of different methods for preparing and making decisions, both relatively simple and based on sophisticated mathematical techniques, have been accumulated. In the following chapters, we will consider in detail the decision-making methods based on optimization, probabilistic-statistical and expert methods, and in the next part we will get acquainted with the modeling method and various types of models used in the theory and practice of decision-making.

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test questions

1. Conduct a primary formalization of the description of the situation during a hypothetical transition to a new job.

2. How would you rate the points if you were Petya Ivanov when making a decision about choosing a job?

3. Evaluate the dynamics of the development of the domestic industry over the past 15 years.

4. What forecasts and decisions follow from the dynamics of capital investments in fixed assets in recent years?

5. Decompose the decision problem for a hypothetical transition to a new job.

6. Why is the decomposition method very useful in solving many decision-making problems?

Topics of reports and abstracts

1. The role of the portfolio matrix of the Boston Consulting Group in making managerial decisions.

2. Enter the weights of the factors (based on your individual expert assessment) and, based on the data in Table 1 of subsection 3.1.1, solve Petya Ivanov's problem of ordering by the attractiveness of possible jobs.

3. Possible erroneous managerial decisions based on common prejudices.

4. Changes in the role of the state in the economy over the past 200 years and the consequences of these changes for managerial decision-making.

5. Classification of formulations of decomposition problems in the theory and practice of decision making.

6. Use of weight coefficients in decision making problems.

7. The problem of aggregating the values ​​of single indicators in decision making.

Professor M. Schemer from the University of Berkeley (USA, California) is a world-famous economist. In 1975, we published a translation of his book "Mathematical Methods of Optimization and Economic Theory".

Previous

Gulina O.M.

"Applied Methods of Decision Making"

Volume - 72 pages.

Circulation 50 copies.

Appointment - for students of the specialties of CT, ACS, Information systems, areas of ICT, as well as the specialty Management of the organization of all forms of education.

The methodology and problems of decision theory, the main types of uncertainties and general approaches and methods of decision making in these situations are considered. Examples of practical situations are given with detailed explanations and solutions. For self-control of students, the lecture course is supplemented with control questions on topics.

Introduction

The decision theory course is included in the training programs for specialists in the field of computer science, engineering and technology, as well as in the training programs for managers, emphasizing the important role of the ability to make optimal management decisions. This course consists of a whole class of disciplines focused on the use of information in decision-making (DM) in a variety of situations.

Decision-making processes underlie any purposeful activity:

without making decisions it is impossible to do in everyday life:

We choose a university, work, home, vacation spot, planning family budget etc.

without making decisions development of production, firms, Research institutes, branches of economy,…

it is also impossible to do without political decisions– the distribution of state budget funds, the method of implementing the education reform, land reform, the methods of implementing tax policy, ...

The problem of choice is one of the central ones in economics. The buyer decides what to buy and at what price. The producer decides what to invest in, what goods to produce. The choice, as a rule, is carried out on the basis of the analysis of some indicator of efficiency. Appropriate calculation models are actively used in deterministic choice. However, the choice often has to be made under conditions of uncertainty of various nature. And for a comprehensive analysis, you need:

In each specific case, understand the internal nature of the existing uncertainty and its sources;

Understand how this uncertainty is taken into account by the chosen mathematical model;

Understand the essence of the method by which a solution is found for a given model in the presence of proper initial data, since the choice of method depends on the awareness of the decision maker (DM).

The choice must be justified, i.e. made on the basis of solving a certain optimization problem. The formulation of such a problem, depending on the situation, leads to various mathematical models.

Decision-making in the conditions of conflict and confrontation of the parties, decision-making in a team, strategic planning and forecasting, building plans to achieve the goal.. .

To learn how to make the right, optimal decisions, it is necessary to consider the general principles of their development and methods that allow you to make decisions that are optimal in a certain sense. First of all, this applies to decisions, the consequences of which can be quite significant. Hence, there is a need to develop methods that simplify the decision-making process (DPR) and give decisions greater reliability.

Decision theory studies the general schemes used by people when choosing the right solution from a variety of alternative possibilities.

In this regard, when starting to study a specific control problem, it is necessary first of all to find out

What types of uncertainty will have to be faced, and how this may affect the choice of the optimal solution;

Is it possible to adequately take into account the non-deterministic nature of the situation under study within the framework of the adopted model?

The participation of people in decision-making requires justification of the position in the implementation of the choice. Subjectivism in decision making problems is associated with the choice of model, analysis of situations, assignment of preferences, etc.

One of the main problems that arise when analyzing a situation and making a decision is the formalized presentation of information, i.e. development of a mathematical model of the situation under consideration. Depending on what kind of information is available, different formal procedures are used. For example, if information is present in the form of expert judgments, then heuristic methods are used. If conflict situations are considered, then game theory models are used.

The book includes material from a course of lectures on the theory of decision making, read by the author at the Obninsk State Technical University of Atomic Energy.

Chapter 1 presents the main provisions and terminology of decision theory. Any activity is associated with risk. Decision-making under risk, search for additional information, elements of the theory of statistical decisions are described in Chapter 2. Almost any PR problem is multicriteria. Chapter 3 discusses both the setting of multicriteria tasks and ways to overcome the uncertainty of goals for various initial data and the degree of awareness of the decision maker.

At the end of each topic is a list of key concepts that define the content of the topic, as well as self-test questions.

It remains to add that, since decision-making processes underlie any purposeful activity, knowledge of the elements of decision theory will be useful to any educated person.

Decision making needs to be learned .

1 The main provisions of the theory of decision making

1.1 Features of decision-making problems

Decision-making (PR) is far from always taking place in conditions of complete certainty. This is more the exception than the rule.

Uncertainty associated with the random influence of external factors, with the indeterminacy of the proper properties of a system or situation, with the incompleteness of the constructed mathematical model.

Decisions have to be made in conditions of different information. Therefore, it is necessary to strive to use all available information and, after weighing all possible options, try to find the best among them. The elimination of uncertainty in PR requires the use of appropriate methods and procedures.

“Only decisions and plans are ideal, but people and circumstances are always real. Therefore, any managerial decision carries the possibility of not only success, but also failure.”

The central role in PR is played by the concept risk.

And in commerce, and in politics, and in economic activity, and in technical tasks, risk is often inevitable and must be taken into account. The concept of risk is very diverse and depends on the situation in which it is considered. As required by the scientific approach, in each case it can be given a specific, but certainly quantitative definition. And the challenge is to minimize that risk.

Methods for finding optimal solutions are considered in sections of classical mathematics related to the study of extrema of functions or functionals. In practice, decisions need to be evaluated from various points of view, taking into account physical (dimensions, weight, ...), economic (cost, profit, ...), technical and other aspects. This requires building decision optimization models at the same time according to several criteria- a multicriteria problem arises.

Decisions often need to be made conflict. Then game decision-making methods are used.

Thus, the task is to formalize the decision-making process (DPR) and study the mathematical methods of decision-making under various types of uncertainty.

Elements of a decision problem

Goals

Target indicators can be qualitative or quantitative depending on the conditions, including the time period for which the forecast is made:

Quality goals are called landmarks

quantitative - target functions.

The goal is described in terms of the desired result. For example, the goals are: “Choosing an educational institution”, “Placing an order for the production of products”, “Recruiting personnel for an enterprise”, etc.

The goal can be refined using subgoals or objective functions. For example, the goal “Recruitment for an enterprise” can be disclosed in the form of such target functions as “qualification in the specialty as high as possible”, “knowledge of foreign languages ​​as much as possible”, “good knowledge of information technology”, “additional qualifications are welcome” etc.

Strategies

The formulated goals require the development of appropriate ways to achieve them. And strategies designed for one purpose may not be applicable to another.

Alternatives

Each strategy has several options for its implementation, or alternative solutions.

The alternatives are decisions, behavior strategies,options for action they are an integral part of the PR task.

To set a task, you must have at least two alternatives.

Alternatives are dependent and independent. Independent are those alternatives, any actions with which (removal from consideration, selection as the only best one) do not affect the quality of other alternatives.

At dependent alternatives, evaluations of some of them affect the quality of others. There are various types of dependency alternatives. The simplest and most obvious is the direct group dependence: if it is decided to consider at least one alternative from the group, then the whole group must be considered. So, when planning the modernization of production, it is necessary to consider all options.

The successful solution of a problem is largely due to how accurately the possible alternatives are formulated. There is always the danger that one or more potentially better alternatives will be missed. As a rule, efforts expended in carefully identifying possible alternatives are not in vain.

Alternatives can be defined in advance, they can also be built in the process of solving the problem. An example is the problem of choosing a city development project: after considering the proposed alternatives and noting their strengths and weaknesses, it is possible to design a new alternative, free from these shortcomings, and take it as a basis.

From the many options for solving the problem, one should exclude those that cannot be implemented for any reason, including within the time frame allotted for solving. The remaining alternatives form initial set of alternatives(IMA)  ={ x} .

Choice of this or that alternative хЄ  leads to the goal, but quantitative indicators of goal achievement however, will be different.

IMA formation methods

Depending on the degree of formalization of technologies, the following classes of methods are distinguished:

Empirical (causal)

Logical-heuristic

Abstract-logical (mathematical)

Reflective.

empirical methods are based on the use of common features inherent in certain practical methods for solving specific problems. These are methods for solving specific problems, accumulated in a set of rules, how to act in a particular case. For example, machine technology CBR (Case-Based Reasoning - “reasoning method based on past experience”): the analyzed decision-making situation is compared in the computer memory with all similar situations known from the past; from the database, the machine selects several situations similar to the analyzed one and presents them to the decision maker.

Logical-heuristic methods generating a set of alternatives involves dividing the problem under consideration into separate tasks, subtasks, operations, etc. to such elementary actions for which heuristic solutions and specific technologies for their execution are already known. In terms of frequency of application, these methods are leading. An example of such methods is the decision tree method.

Consider the method "decision tree". It is used to represent possible actions and to find a sequence of correct decisions leading to the maximum expected utility. This is a special type of graph, where there are two types of nodes: a square, where a person makes a decision, and a circle, where everything is decided by chance. An example of such a graph is shown in Fig.1. Here the decision maker must choose one of the actions -D 1 or D 2 . The intervention of chance consists in the fact that, due to circumstances beyond the control of the decision maker, with probability P 1 he will receive the result C 1, and with probability P 2 - the result C 2 if he chooses the first solution; when choosing D 2 as a solution, he will receive C 3 or C 4 with the corresponding probabilities.

Rice. 1. An example of a decision tree

The total utility of each action is calculated as expected:

U 1 \u003d U (D 1) \u003d C 1 P 1 + C 2 P 2; U (D 2) \u003d C 3 P 3 + C 4 P 4, - and choose as the best alternative with the maximum expected utility.

Such a graph is built from left to right for the entire sequence of making multi-step decisions, and then analyzed from right to left, calculating the utility of each alternative and deleting disadvantageous decisions.

TO abstract-logical methods include those that allow you to abstract from the essence of specific actions or methods of work and focus only on their sequence. The tasks where such methods are applied include methods for the formation of plans for the execution of interrelated work (network planning and management methods, scheduling methods).

reflexive methods are used in tasks with behavioral uncertainty (economic, social, political conflicts). The method is based on the consistent hypotheses about the possible goals of another subject of the operation and the formation of responses. After that, both lists are analyzed, the alternatives of both sides are corrected and specified.

Therefore, the task is to quantify the achievement of the goal - objective function- was optimal (for example, profit - maximum, costs - minimal under certain restrictions: resources, time, labor, etc.).

Unfortunately, there are no universal recipes to make this choice unmistakable. Therefore, the decision maker must rely on experience, common sense and continuous analysis of situations.

In this course, we will explore PPR models and their properties.

The company "Cottage" wants to expand its influence in the market. However, success in achieving the goal is also determined by the presence of competitors and their behavior. The task is to develop an optimal behavior strategy.

Example 2

The investor solves the problem of investing in a modern project. The result will depend on how well the proposed product will be accepted in the market. The task is to assess the effectiveness of the project and decide on the investment of funds.

Example 3

The Golden Key firm, which specializes in the production of sweets, faces a dilemma: should we increase the production resources of an existing plant or build a new enterprise of the same profile? According to the president, the decision depends on what share of the sales markets will belong to the company in the next ten years.

In all these examples and in many other situations, the following is common: there is a decision maker (company manager, investor, president); set of options, or alternatives  (set of strategies, dilemmas of the investor and the “Golden Key”). It is necessary to select some subset of them  0 , better - one option.

How to select  0 ? How to compare alternatives?

Any option has its own quality, which is characterized by various indicators and determines the usefulness of the considered option in terms of achieving the goal. In the aggregate, the preferences of the decision maker in this respect can be determined by some principle of optimality (OP) - “what is good”.

For example, the decision to invest in a project is reasonable if the net present value corresponding to its implementation is positive. For the president of the Golden Key, the result characterizing each of the considered alternatives can be considered the annual income of the enterprise (the more it is, the better) or profit.

Then the decision-making problem is a combination of two components (, OP) – the initial set of alternatives and the assigned optimality principle, its solution 0 .

If the options are not defined, then there is nothing to choose from, if there is no principle of comparison, then it is impossible to compare the options and find a solution.

FEDERAL FISHING AGENCY

FEDERAL STATE EDUCATIONAL INSTITUTION OF HIGHER PROFESSIONAL EDUCATION "MURMANSK STATE TECHNICAL UNIVERSITY"

INSTITUTE OF DISTANCE LEARNING

Yaretenko N.I.

Mathematics (Operations Research)

Lecture course

for the direction of training (specialty)

230105.65 "Applied Informatics (Software VT and AS)",

080801.65 "Applied Informatics (in Economics)", 080507.65 "Organization Management", 080105.65 "Finance and Credit", 080109.65 "Accounting, Analysis and Audit".

(With the use of elements of distance learning)

to. Sciences, Associate Professor

Department of Information Systems and

Applied Mathematics MSTU.

Lecture course

reviewed

and approved by the Department of IP and PM

"__" _______ 2010

Reviewers:

V.V. Kovalchuk,

Doctor of Technical Sciences, Professor, Head of Department

IS and PM MSTU.

N. N. Morozov department

Physicists MSTU.

Lecture. Fundamentals of decision theory

1.1. General provisions………………………………………………………….6

1.2. Basic concepts of system analysis…………………………………..8

1.3. Basic concepts of operations research…………………………….12

1.4. Setting tasks for making optimal decisions……………………13

1.5. Methodology and decision-making methods……………………………………………15

Control questions………………………………………………...17

2. Lecture. Economic - mathematical modeling

2.1.Basic concepts.............................................. ...............................eighteen

2.2.Classification of models............................................................... ......................19

2.3. Classification of economic tasks to be solved ..............................................21

Test questions................................................ ....................22

Lecture. Linear programming

3.1.General statement of the problem............................................... ...................23

3.2. Duality in linear programming problems……………25

3.3. Duality theorems............................................................... ...................26

3.4. Solving linear programming problems with geometric

method................................................. ...............................................28

3.5. Simplex method for solving linear programming problems...35

Test questions................................................ .................39

Lecture. Transport task

4.1. Statement of the problem............................................... ...................................41

4.2.Algorithm for solving transport problems………………………….………42

4.3 Least element method .................................................................. .................43

4.5.Method of potentials.................................................... ...............................44

4.6. Examples of solving transport problems .............................................. ....45

Test questions................................................ .................55

5. Lecture. Integer programming

5.1. Statement of the problem of integer programming .........................................57

5.2. Graphical method for solving problems of integer programming .............................................................. ...............................................58

5.3.An example of solving the problem of integer programming…………..59

5.4.Traveling salesman problem……………………………………………………..61

5.5.An example of solving the traveling salesman problem……………………………………62

Test questions................................................ ...... .....64

Lecture. Dynamic programming

6.1. Formulation of the problem................................................ ...............................65

6.2. Bellman's principle of optimality .............................................. .......66

6.3. The task of distributing funds for 1 year…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

6.4. The task of distributing funds for 2 years .............................. ……….72

Test questions................................................ ........72

7. Lecture. Manufacturing control

7.1. The task of replacing equipment ………………………………………………………………………………………73

7.2 Stock management. Warehouse task ……………………………….79

Test questions................................................ ..........81

Lecture. Game theory

8.1.Basic concepts…………………………………………………………..82

8.2. Antagonistic games …………………………………………………..83

8.3. Games with "nature" .............................................. ................................................85

Control questions………………………………………….93

Lecture. Mass service systems

9.1.Formulation of the task and characteristics of the QS………………………..94

9.2.QS with failures……………………………………………………………..96

9.3.QS with unlimited waiting.................................................................. .....96

9.4. QS with waiting and with a limited queue length……………….97

9.5. Examples of problem solving ............................................................... ....................98

Control questions……………………………………….…..101

Lecture. Network planning

10.1. Basic concepts of the network planning method .............................. 101

10.2. Calculation of network diagrams ............................................................... .................105

Control questions………………………………………...…………………109

Lecture. Nonlinear programming

11.1. Basic concepts……………………………………………………..109

11.2. Unconditional extreme …………………………………..………….109

11.3. Conditional extremum …………………………………………………111

Test questions................................................ ................112

The list of tasks for solving when mastering the material…………………. 112

Literature............................................................................... 128

Questions for self-examination………………………………….………… .129

Appendix: Greek alphabet……………………………….…131

INTRODUCTION

Course "Mathematics. Operations Research occupies a key position in the educational programs of students of most industrial and economic specialties. In the process of mastering it, students should develop an understanding of the principles, mathematical models formulated within the framework of these problem models and the corresponding methods for finding their solution. All these questions form the foundation that any qualified specialist needs in modern conditions to solve problems of managing various organizational systems.

The beginning of the development of operations research as a science is associated with the forties of the twentieth century. The very name of the discipline is associated with the application of mathematical methods to manage military operations.

One of the first studies is the work of L. V. Kantorovich, Mathematical methods of organization and planning of production, published in 1939, and in foreign literature - the work of J. Danzing, published in 1947, devoted to solving extremal linear problems. In 1975, L. V. Kantorovich won the Nobel Prize for his work on the optimal use of resources in the economy.

The 1950s and subsequent years were marked by a wide application in practice of the obtained fundamental theoretical research and the rethinking of the potential possibilities of the theory of operations research associated with this. An important contribution to the development of the new science was also made by such prominent scientists as J. Fon. Neumann, D. Gale, K. Arrow, R. Bellman, R. Gomory, E. S. Wentzel, M. K. Gavurin and other scientists.

The course of lectures was developed on the basis of work programs for the direction of training (specialty) 230105.65 "Applied Informatics (BT and AS Software)", 080801.65 "Applied Informatics (in Economics)", 080507.65 "Organization Management", 080105.65 "Finance and Credit", 080109.65 "Accounting, analysis and audit".

When presenting the content of the topics of lectures, their most important elements are indicated with consideration of theoretical issues and examples of practical problems, as well as questions for self-control. In the final part, numerous options for tasks on each topic are given, which will allow students to better learn the material when studying the discipline on their own in the process of preparing for the exam or test.

The lists of basic and additional literature indicate modern educational and periodicals, including problems with applied solutions.

Lecture. Fundamentals of the theory of decision making.

1.1. General provisions

1.2. Basic concepts of system analysis

1.3. Basic Concepts of Operations Research

1.4. Statement of problems of making optimal decisions

1.5. Methodology and methods of decision making.

General provisions

Man is endowed with consciousness, being free and doomed to make decisions, trying to do everything in the best way.

Theory of optimal decision makingin the most general sense, it is a set of mathematical and numerical methods aimed at finding the best options from a variety of alternatives and avoiding their complete enumeration.

Since the dimension of practical problems, as a rule, is quite large, and calculations in accordance with optimization algorithms require a significant investment of time, therefore, methods for making optimal decisions are mainly focused on their implementation using a computer.

The practical need of society for the scientific basis of decision-making arose with the development of science and technology.

In the 18th century, the beginning of the science "Decision Theory" should be considered the work of Joseph Louis Lagrange, the meaning of which was as follows:

how much earth a digger should take on a shovel so that his shift productivity is the greatest.

It turned out that the statement "take more, throw more" is not true.

The rapid growth of technical progress, especially during and after the Second World War, posed more and more new tasks, for the solution of which new scientific methods were involved and developed.

The scientific and technical prerequisites for the formation of the "Decision Theory" are:

· rise in price of "the price of an error". The more complex, expensive, larger-scale the planned event, the less "strong-willed" decisions are allowed in it, and the more important scientific methods become, which make it possible to assess in advance the consequences of each decision, exclude unacceptable options in advance and recommend the most successful ones;

· Accelerating the scientific and technological revolution of engineering and technology. The life cycle of a technical product was reduced so much that the "experience" did not have time to accumulate and the use of a more developed mathematical apparatus in design was required;

development of computers. The dimension and complexity of real engineering problems did not allow the use of analytical methods.

This science, on the one hand, has become a certain branch of other more general sciences (systems theory, systems analysis, cybernetics, etc.), and on the other hand, has become a synthesis of certain fundamental more specific sciences (operations research, optimization, etc.). ), while creating their own methodology.

The economy is closely connected with sets of objects that are commonly called complex systems. They are characterized by numerous and diverse types of connections between separately existing elements of the system and the presence of a function of purpose in the system, which its constituent parts do not have.

At first glance, each complex system has a unique organization. However, a more detailed study can highlight what is common in the system of computer commands, in the processes of designing a machine, an aircraft, and a spacecraft.

In the scientific and technical literature, there are a number of terms related to the study of complex systems.

The most general term is "systems theory". Its main parts are:

system analysis, which is understood as the study of the problem of decision making in a complex system,

· Cybernetics, which is considered as the science of information management and transformation.

Cybernetics studies separate and strictly formalized processes, and

system analysis- a set of processes and procedures.

Very close to the term "systems analysis" is the concept of "operations research", which traditionally denotes a mathematical discipline covering the study of mathematical models for the selection of quantities that optimize a given mathematical construction (criterion).

Systems analysis can be reduced to solving a number of problems in operations research, but has properties that are not covered by this discipline.

However, in foreign literature, the term "operations research" is not purely mathematical and approaches the term "system analysis."

Systems analysis, based on operations research, includes:

setting a problem for making a decision;

description of the set of alternatives;

research of multicriteria tasks;

methods for solving optimization problems;

processing of expert assessments;

work with macromodels of the system.

Basic concepts of system analysis

System Analysis- a science dealing with the problem of decision making in the conditions of analyzing a large amount of information of various nature.

goal system analysis (to a specific problem) - increasing the degree of validity of the decision made from the set of options among which the choice is made, while indicating the methods for discarding obviously unfavorable ones.

IN system analysis distinguish

· methodology;

· hardware implementation;

practical applications.

Methodology includes definitions concepts used and principles of a systematic approach.

Similar information.