Formation of the initial set of alternatives. Introductory provisions. At the stage of generating ideas, criticism is completely prohibited, since each idea is useful just because it stimulates others. Classification of decision-making tasks

Appearance

Vmax≤ 100 km / h

Defects in paintwork

Condition of decorative elements

Chips and rust spots with a diameter of ≥ 2 cm

Scratches ≥ 3 cm long

Aging of elements

Missing two elements

The service life of plastic elements is more than 10 years

Rust on nickel plated parts

Fig. 3.4. A variant of the decomposition of the "actual state"

Table 3.2. List of elementary solutions for subgoals

As you can see from the table. 3.2, for most of the sub-goals, the decision maker has found several elementary solutions, which significantly expands his capabilities in accordance with the principles of multiple alternatives and freedom of decision-making. Certain combinations of some elementary solutions define the descriptions of individual alternatives. For example, a combination of elementary solutions ("B1-1, B2-5") meaningfully means the following way of solving the problem: "Replace the body in a complete set, which includes the missing elements, and purchase a new gasoline engine." This alternative belongs to the class of composite solutions, since the solution B1-1 - "Replace the body in a complete set, including missing elements" - simultaneously eliminates all subproblems that reveal B1 (appearance), and B2-5 (purchase a new gasoline engine) is a way reaching the terminal subgoal determined by characteristic B2 (dynamic characteristics of the engine).

An example of an alternative to elementary solutions is any combination of solutions for the final characteristics Dl, D2, D3, El, E2. Decisions to improve the dynamic characteristics of the engine were obtained by the decision maker by branching the solution methods and constructing a decision tree, which is presented on fig.3.5.

The decision tree contains both compatible solutions and incompatible ones. For example, it makes no sense to boost an existing engine and purchase a new one (alternatives "B2-4, B2-5", "B2-4, B2-6"), but the forced engine can be adjusted to obtain maximum power (alternatives "B2-1" B2 -4 "," B2-2, B2-4 ").

Dynamic characteristics of the engine:

Vmax≤ 100 km / h

Adjust the engine

modify the engine

Get a more powerful engine

1. Adjust at the service center

3. Modify the engine to use high octane fuel

5. Purchase a gasoline engine

2. Adjust by yourself

4. Boost the engine

6. Purchase a diesel engine

Fig. 3.5. Decision tree

Using the given example, it is enough to simply see and understand the advantages and disadvantages of the method. Its undoubted advantage is its clarity and logical validity. The disadvantage of this method is its cumbersomeness, especially with deep decomposition and a large number of subgoals, and low flexibility in relation to the search for unconventional options.

The method of morphological tables essentially represents a slightly different form of implementing the idea of \u200b\u200ba tree of goals (decisions). The morphological method itself was developed in 1942 by the Swiss astronomer F. Zwicky for the analysis of systems of great complexity.

The main advantage of the morphological tables method is that it allows you to easily check the set for completeness, and in some cases, it is relatively easy to generate unconventional (previously unknown) solutions.

The reflexive method is used when the leading type of uncertainty is behavioral. The method is based on consistent hypotheses about the possible goals of another subject of the operation and the formation of responses on the assumption that he will not change his line of behavior under any circumstances.

The solution to the problem is always accompanied by the preparation of the initial set of alternatives (IMA) ft d, ftd e ftB - to achieve the set goal and the choice of the best one according to a certain algorithm and criterion. Here? 2B is the area of \u200b\u200bpossible alternatives, which belongs to the area of \u200b\u200ball conceivable alternatives, i.e. ftB e fty. With this formulation of the problem, we can assume that the decision-making problem is being solved (dv, OP), where OP is the optimality principle.
The process of solving the problem (ftB, OP) is organized according to the following scheme. For the general case, the formation of IMA begins with the compilation of a universal set of all conceivable alternatives? Y. If we use? Y when solving the problem, then it turns out to be not always solvable, therefore, the first procedure will be to determine a certain range of possible alternatives QB by the condition? B \u003d Cx (Pu), where Cx is a choice function that establishes the membership of alternatives to the set of possible ones.
The availability of special information in the form of technical, technological, economic and organizational constraints makes it possible to single out from Δjj a set of feasible alternatives Dd by solving the choice problem \u003d Con (ftB), where Con is the choice function that establishes the admissibility of alternatives, and OP is the optimality principle, expressing the condition of admissibility of alternatives. The resulting set? A is the IMA of a solution to a specific problem.
Let us explain the stated procedures in the following simple example. When appointing to a position, first a list of candidates is prepared, then a person from this list is appointed. If the list of candidates includes all specialists, then we are dealing with all imaginable al-
11 - 7571
tendencies expressed in many. The admissibility condition is determined by specific restrictions, such as the duties stipulated by the position, and the specialization of the employee's work, education, wage and etc.
In the general case, the process of forming an IMA is described by a scheme that includes two stages: generating possible alternatives and checking them for admissibility. In specific algorithms, the steps can be combined, since in some cases they are carried out using the same procedure.
A characteristic feature of solving the problem of choice is the participation of a decision maker (DM) and an expert. The decision maker is a competent specialist who has a goal that serves as a motive for setting a problem. An expert is a person who owns information about the problem under consideration and gives the assessments necessary for the formation of an IMA.
The IMA formation algorithm depends on the specifics of the alternatives that can be presented:
an indivisible object, such as a product;
information object - strategy, plan, budget, and schedule;
cargo delivery routes;
systems endowed with hierarchical structures;
mathematical objects.
Consider algorithms based on informal and formal procedures known to managers.

This problem was already mentioned in the previous lecture. Considering its exceptional importance, let us consider it in more detail.

The degree of experience of the decision maker is largely characterized by the ability to correctly predict the situation and find the best way solving the problem.

At the same time, correctly determining the mechanism of the situation means quickly establishing the leading factors, and the decision maker's ability to generate new, non-standard solutions is generally identified in the minds of people with art. In this regard, it is clear that the task of forming the initial set of alternatives does not lend itself to complete formalization. The solution to this problem is a creative process in which the main role, of course, belongs to the decision maker. The emergence of this problem as a theoretical object of research is a direct consequence of the use of the systemic principle of multiple alternatives in TPR.

Before solving the problem of forming the initial set of alternatives, it is necessary to determine the system requirements that this set must meet. First, the set of alternatives should be as complete as possible. This will provide the decision maker with the necessary freedom of choice in the future and minimize the opportunity to miss the "best" decision. However, this first fundamental requirement is in contradiction with the second, arising from the principle of correspondence of the decision to the time, place and capabilities of the decision maker. Most often, in practice, such compliance is understood as a requirement to work out a solution as soon as possible. Consequently, secondly, the initial set of alternatives should be foreseeable, narrow enough so that the decision maker has enough time to assess the consequences and preferability of alternatives under the existing resource constraints. The problem of satisfying these two contradictory requirements is solved systemically, based on the principle of decomposition.

Following the systemic principle of decomposition, they first form a set of alternatives, all of whose elements potentially, by their appearance, by the possibilities hidden in them, ensure the achievement of the target result in the current situation. The set of applicants for a way to solve the problem obtained in this way will be called the set of target alternatives.

Then, from the set of target alternatives, those options are selected that are logically consistent and can be implemented within the time allowed for the operation. In addition, the selected alternatives must be satisfied with the necessary active resources and meet the general system of preferences of the decision maker.

These options selected from the target alternatives will be called physically realizable target alternatives. The rest of the options, potentially leading to the goal, but physically unrealizable, are discarded.

The options obtained as a result of such manipulations are supplemented with methods of action that give the alternatives the necessary flexibility and stability in relation to the changing or currently unknown components of the conditions of the operation.

As a result, the original set of alternatives is obtained.

Technologically, the method of forming the initial set of alternatives involves the implementation of a number of special purposeful modifications of the main factors of the situation mechanism. They consist in the simultaneous or sequential impact on the controlled (subject to the will of the decision maker) part of the quality characteristics of the active resources used, the characteristics of the conditions and methods of action.

It is this idea that underlies most of the known methods and algorithms for the formation of the initial set of alternatives.

Historically, the first to emerge were empirical methods that require minimal formalization. The simplest of this class is the causal diagram method. A typical modern representative of empirical methods is the CBR method (Case-Based Reasoning - "method of reasoning based on past experience").

The next class is formed by logical-heuristic procedures, where formalization is carried out at the level of management of logical relationships. Decision tree methods and morphological tables method are examples of such methods implementation.

Typical representatives of the class of methods for forming alternatives, in which the highest degree of formalization of all stages of generation has been achieved, are the methods of network and scheduling.

A special class is formed by methods of forming alternatives in conditions when a decision is developed by a "group decision-maker", when there is a complete or partial coincidence of interests of the participants in the decision-making process, however, due to the unequal interpretation of the goals of actions, the peculiarities of the individual perception of the problem situation and for other reasons, the sovereign opinions of the participants the decision-making process needs to be agreed upon in the overall decision. Other representatives of the methods of this class are methods for generating alternatives in conditions of conflict and counteraction of sovereign subjects involved in the decision-maker's operation either of their own free will or against their will. Such situations are characteristic of economic, social, political and military conflicts. In all such situations, as a rule, reflexive methods are used to form alternatives. Such methods are characterized by an average level of formalization using simple mathematical models.

In terms of frequency of application in practice, perhaps, the first place is occupied by logical-heuristic methods. They acquired this position because of their inherent visibility, simplicity and versatility of the approach, and the convenience of computerizing their algorithms. The essence of these methods boils down to the fact that, first, based on the logical analysis of the goal of the operation, a tree of goals and objectives is built. Then each subgoal or task is also detailed, and this operation continues until the decision maker becomes clear which of the known means (or in what way) to solve each particular task.

More on the topic The task of forming the initial set of alternatives:

1. D. Formation of the initial set of alternatives, formalization of preferences and choice.

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Thus, we can assume that the reliability, reliability and completeness of information are its qualities that give the decision maker full confidence in the success of the solution development process, leave the decision maker no doubts that what he was told is "true", and it is essential reduces the uncertainty of choosing the best solution,

When analyzing the table. 4.1 it is important to keep in mind the following. Some cells of the table contain a special character *. This means that the level of quality of information that one can provide

or another method, turns out to be no higher than the initial level of qualities ^ of the considered source of information itself.

Planning the collection processit is convenient to carry out using the causal diagram presented in Fig. 4.3.

Fig. 4.3. Causal diagram

The diagram simulates how the result follows from the main factors of the "situation mechanism", which are the "reasons", i.e. "Consequence".

The causal diagram is constructed as follows. Draw a horizontal arrow on a sheet of paper in the middle and put "Consequence" (the name of the result, the question under study) at its tip. The arrows of the four pointers denoting the main factors are reduced to the arrow line. The pointer is a rectangle from which the arrow goes to the line of the central arrow, leading, in turn, to the corollary. This construction graphically simulates the presence of some contribution of the factor under consideration to the effect. Moreover, the very designation of the index field on a sheet of paper constantly pushes the researcher to the idea that it is necessary to enter some information in this field, to write something in. This means that the pointers on the diagram play the role of a special psychological stimulus, forcing the researcher to search ("to complete exhaustion") and find the factors of the considered category. After all the pointers are indicated on the chart sheet, you should fill in the appropriate fields in any order (just not to forget, not to miss something significant).

We emphasize once again that the order of filling in the fields does not matter, it is arbitrary. The main thing is to form as much as possible full list the main "reasons" that gave rise to the "effect". For this purpose, in the fields of the index for the factor "Quality" we enter the significant, in our opinion, for the considered

pG on the outcome, result or issue of the characteristics of the level of professionalism of the performers and quality of funds, materials and

bORUD ° vanIa-F acto R "Conditions" is disclosed through the characteristics of the penalty of favorable conditions of the situation (circumstances of time, place, possible influences of other subjects, etc.), and the factor

Ways "we describe through categories that characterize the perfect

the method of action, such as the methods used, the sequence of performing certain labor or creative techniques. As a result, it is possible to quickly form a list of representative ("significant") factors, which, in the opinion of the decision maker. should be taken into account.

The work on the formation of the list of factors must be carried out in conditions of complete liberation of imagination. This means that at the stage of list synthesis, no criticism is allowed, no doubt about whether or not to include the applicant in the list of factors. In other words, at the stage of filling in the index fields, the main goal is to RECORD as many factors as possible on paper. Precisely to write down, as it frees the researcher's brain for creative work, frees you from having to remember the generated information. This step of working with a causal diagram can be call the stage of generating reasons(stage of synthesis of reasons).

After the fantasy has dried up and the generation of causes is completed, you can proceed to the stage of analyzing the contributions of factors. At the beginning, the analysis is carried out verbally, in qualitative scales, and at the final stage - in more perfect quantitative-qualitative and quantitative ones. Such a rational procedure for the use of rating scales makes it possible to obtain a final answer to the main questions of interest to decision makers at the stage of planning the information collection process much faster. At the same time, it is very simple to establish not only the required nominations and the quality of important information (that is, what information is needed about, with what accuracy, reliability, completeness), but also by what time and from which source this information should be obtained.

4.3. The problem of forming the initial set of alternatives

If you ask a person who is well versed in problems of the Office, what determines the degree of experience of a manager, then most often you can get the following answer: the ability to predict the situation and "Quickly find the best way to solve the problem. What is" able to predict the situation ", we have already discussed in the previous paragraph

graph. But what is the "best way to solve a problem"? How can we formulate the ways to achieve the sang operation?

System requirements for many alternatives.The ability of the decision maker to generate new, non-standard solutions is identified in the minds of many with art. Apparently, this is explained by the fact that the task of forming the initial set of alternatives does not lend itself to complete formalization. Since the solution of such a problem is a creative process, in the results of which, first of all, the decision maker is interested. the main role in this process, of course, belongs to him. However, before we propose a scientific approach to solving this very difficult task, we will define the system requirements that many alternatives must meet.

First, many alternatives should be possible wider.This will provide in the future the necessary freedom of choice of decisions of decision makers and will minimize the possibility of missing the "best" decision. But this first, fundamental requirement is in conflict with the natural restrictions on time, place and opportunities in which one usually has to work. Decision maker.It is impossible to come up with a solution for an infinitely long time. Otherwise, there will be no time left for its implementation. Therefore, most often in practice, the decision maker is required to work out a solution as soon as possible. This immediately implies the second requirement for the original set of alternatives. This multitude should be visible,narrow enoughso that Decision makerthere is more time left to assess the preference of alternatives, and the performers have more time to implement the found best solution in practice. In order to reasonably satisfy these contradictory requirements, art is required, and in order not to make gross mistakes, science should be involved. So, in accordance with the systemic principle of decomposition, science first recommends the formation of a set of alternatives, all of whose elements potentially, in their appearance, the possibilities hidden in them, ensure the achievement of the goal.

The method of forming the initial set of alternatives. INin cases of deterministic, stochastic or naturally indeterminate "situation mechanisms", the method of forming the initial set of alternatives involves the performance of fairly simple actions. To one degree or another, they all boil down to a series of targeted modifications of controlled factors that determine the effectiveness of the operation (see Fig. 4.1). At the same time, the decision maker is exploring the possibility of simultaneous action on the "controlled" component of these factors, since it is this method of control that most often leads to the emergence of positive emergent properties in future alternatives. If the decision maker intends to influence, for example, on

the quality of active resources, then in this case all methods of forming alternatives are referred to the category of the so-called engineeringsynthesis.If the object of the decision maker's efforts will be the factors 03 classes "Conditions" and "Methods", then we will keep in mind the methods operational synthesisoptions for solutions.

The set of options for solving the problem obtained in the course of engineering or operational synthesis will be called the set "Targetalternatives ".After obtaining “target alternatives” from their set, one should select those options that are logically consistent and can be implemented within the time frame allowed for the operation. At the same time, the alternatives left must be necessarily satisfied with both active resources and meet the general system of preferences of the decision maker. The selected options (from among the target ones) will be called "Physically realizable."Thus, we discard the rest of the options, potentially leading to the goal, but physically unrealizable.

The resulting subset of "physically realizable" alternatives is supplemented with options that give the methods the necessary flexibility and stability in relation to possible changes in future conditions of the operation. As a result of the work done, exactly what we will call "The original set of alternatives."

As for the technological methods for the implementation of the presented general methodology for the formation of the initial set of alternatives, then everything here depends on which of the theoretical classes of problems TPRwe face in a specific situation. For obvious reasons, the greatest "technological tricks" have to be applied in situations with behavioral uncertainty.

Methods for the formation of many alternatives.Conventionally, all methods of forming a set of alternatives can be divided into the following classes, differing in the degree of formalization of the technologies used:

empirical (causal);

logical-heuristic;

abstract logical (mathematical); ..

reflective.

Historically, the first empirical methods.At first, people noticed some common features inherent in certain practical methods of solving specific problems. Then this experience was creatively generalized and turned into a set of rules for how to act in this or that case. Similar methods are used nowadays. For example, the machine technologyCBR (Case-Based Reasoning - “method of reasoning based on past experience *.). Its essence is that the analyzed decision-making situation is compared

"Management decisions -, _

in computer memory with all similar situations known from the past. The machine selects several situations similar to the analyzed one from the database and presents them to the decision maker.

The choice of a specific decision by the head (manager) is based on comparing the observed situation with the situation from the database and adjusting the decisions known for these situations in relation to the peculiarities of the case under consideration.

Logical-heuristic methodsgenerating a set of alternatives imply a gradual breakdown of the problem or task under consideration into separate subtasks, questions, suboperations, etc. to such elementary actions for which heuristic solutions and specific technologies for their execution are already known. In terms of the frequency of application in practice, perhaps, it is the logical-heuristic methods that take the first place. Typical logical-heuristic methods are the decision tree method and the morphological table method. They acquired this position because of their inherent visibility, simplicity and versatility of the approach, and the convenience of computerizing their algorithms.

Decision tree method. Let's consider the technology of the "decision tree" method. For a holistic and unified understanding of it, we will use three basic concepts: "important circumstance", "measurable characteristic", "final" element. We will consider as an "important circumstance" any factor that the decision maker considers necessary to take into account in the process of working on the problem. Important circumstances, properties of objects or tasks that can not only be described verbally, but also measured, we will call "measurable characteristics." An important circumstance, which ends any branch of the tree, we will call "final". By analogy, we will use the concepts “final subgoal”, “final measurable characteristic”.

As already noted, first, based on the logical analysis of the goal of the operation, the decision maker builds a “tree of goals”. This is the first step. In this case, the “tree of goals” should be built either on the basis of a detailed description of the “desired” state (goal), or decomposition of the “actual” state (which does not satisfy the decision maker in it, which must be eliminated). In fact, they are one and the same, because the decision maker must understand "what he wants." However, in terms of the form of logical activity, these are different approaches (like synthesis and analysis).

If the “goal tree” is based on the analysis of the “desired” state, it is more convenient to display the branching procedure graphically. The result of constructing the "goal tree" is not unambiguous. This is due to the fact that each decision maker decides for himself when to finish branching goals. At the second stage, in the constructed "tree of goals", each of the final partial tasks is assigned a known

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The main purpose of the decision maker and the final product of it management activities is the development of solutions. Of course, his other management functions, such as the organization of interaction, comprehensive support of the operation, control, assistance, assessment of the actual effectiveness of the operation, fixation, generalization and dissemination of the experience gained during the operation.

Acceptance structure diagram management decisions is presented in Figure 1.7.

The basis for making all decisions at all stages of the decision-making process, of course, is the preferences of the decision maker.

Undoubtedly, the formalization of preferences should become a reasonable start of the decision-making process.

After the preferences of the decision maker are formalized and the necessary information about the preferences is obtained, they proceed to the next important decision-making step - to the construction of the choice (utility) function.

The choice function in decision theory is of fundamental importance. It is precisely at its construction that the solution of the problems of forming the initial set of alternatives, the analysis of the conditions of the operation, the identification and measurement of the preferences of the decision maker are ultimately oriented.

According to the formal definition adopted in the TPM, the selection function is a mapping of the form

where is some set (initial for the considered decision-making step), from which the choice is made; - a subset with certain (known or given) properties, and

In the step-by-step receipt of information from the decision maker about his preferences in the course of measurements, a selection function is first built based on the results of measurement and evaluation in the most reliable, but also less accurate nominal scale based on qualitative judgments about preferences. As a result, from the original set A of alternatives, the first representation of the desired subset of alternatives is obtained, which contains the best alternative.

If the decision maker, having carried out an informal analysis of the subset, has not yet been able to decide on the choice, then the construction of the choice function should be continued. To do this, the decision maker must clarify the measured preferences by applying a more perfect, for example, ordinal or point scale, to measure them.

As a result of the refinement of the form of the choice function, in the general case, another subset of alternatives will be obtained, moreover. Now the decision maker should focus on the analysis of this last set, since, again, the best alternative is contained in it. Then, if necessary, the decision maker's preferences can be refined again by measuring them in any of the proportional scales, and so on until the decision maker confidently stops choosing the best alternative.

It should be borne in mind that specific species the choice function that implements the mapping (1.3) depends on the mechanism of the situation.

This circumstance is noted in the diagram in Fig.1.7. options for constructing a choice function with their detailing according to the type of uncertainty conditions: in conditions of stochastic uncertainty, in conditions of behavioral uncertainty and in conditions of natural uncertainty.

The target difference in the use of scalar and vector criteria determined the need to display in Fig. 1.7, in the general case, two variants of the form of initial data and procedures for constructing a selection function - according to a scalar or vector criterion.

Receiving the information

The decision-making process requires the fullest possible amount of information both about the control system itself and about the environment of its functioning ( environment). Without information of this kind, it is impossible to analyze the conditions for making decisions, identify the mechanism of the situation and form the initial set of alternatives. The decision maker should carry out a meaningful analysis of information about the conditions of the operation, obtain reliable ideas about the mechanism of the situation. Only after gaining this information, the decision maker will be able to systems approach not only verbally describe the main (leading) factors that contribute to and hinder the formation of a successful outcome of the operation, but also formally assess the degree of their influence on the effectiveness of the outcome.

To do this, you need to understand exactly what information, what quality and by what time frame is needed. The result of this intermediate decision (content, required accuracy and reliability of information, promptness of its receipt) will help the decision maker consciously choose one of the available sources of information and make a decision. The classification scheme for possible sources and methods of obtaining information is shown in Figure 1.8.

From the analysis of the circuit in Fig. 1.8. it follows that, in principle, there are only three sources of information:

· Empirical data;

Knowledge, personal experience and the intuition of the decision maker;

· Expert advice (expertise).

It is clear that practically most often people get information from own experience and knowledge, and their own intuition helps them fill in the gaps in positive knowledge.

In addition, there are two more fundamental possibilities: to look for the necessary information in one of the "objective sources" where the historical experience of mankind is recorded (empirical data), or to turn to the "subjective source" - to the knowledge, skills and abilities of recognized specialists in their field (experts) ...

The TPR believes that an expert is a person who personally works in the field of activity under consideration, is a recognized expert on the problem being solved, and can and has the opportunity to express a judgment on it in a form accessible to decision makers.

Experts carry out informational and analytical work based on their personal ideas about the problem being solved. In the general case, the views of experts may not coincide with the opinion of the decision maker. This difference of opinion plays both negative and positive role... On the one hand, if the opinions do not coincide, the decision-making process is delayed, but, on the other hand, the decision maker can critically interpret an alternative point of view or correct his own preferences.

To increase personal confidence in what the specialist has given him correct advice, The decision maker can turn to not one, but several experts. Accordingly, distinguish between individual (one expert) and group expertise. If the question is strictly confidential, time is limited, or it is not possible to ask several specialists for an answer to a question of interest, then an individual examination is the best way to obtain information. But if the listed restrictions are not significant, then, undoubtedly, a group examination is, on the whole, a more reliable and accurate way of obtaining information.

At the same time, in the course of a group examination, it is possible that the subjective judgments of individual specialists do not coincide. In this regard, it is required to undertake special techniques for processing expert information in order to increase the reliability of the results.

TPR has developed a special complex of organizational, technical and mathematical procedures that give harmony and logical conditioning to the entire process of obtaining, processing and analyzing group expert information. This set of procedures, which includes an examination (that is, the survey of experts itself) only as one of the stages of obtaining information, in the TPR was called the method of expert assessment.

Historically accumulating knowledge, having learned writing, people began to record their objective experience. The whole useful information began to be recorded in one form or another on special media. Initially, these media were imperfect (for example, manuscripts, books) and inaccessible, but gradually they acquired a more perfect form, and with the development of printing they turned into libraries, data banks (BND), databases (BZD) and knowledge bases (BZZ) ... The process of finding publicly available information has become more convenient, efficient and even creative. But at the same time, some information and some sources of information became inaccessible to the general public. Therefore, in the case when the decision maker due to different reasons cannot find the information he needs in publicly available sources, it has to be actively extracted. To obtain inaccessible information, the decision maker can organize and conduct a full-scale or model experiment, he can resort to the help of intelligence or use some kind of special means.

Intelligence or special equipment is costly; the same applies to an experiment, especially if the experiment is large-scale and is carried out under the conditions of an ambiguous mechanism of the situation. Therefore, in order to save money, it is advisable to carry out strictly scientific planning of the experiment, to quantitatively establish its parameters that are optimal in relation to the effectiveness of future decisions and actions of the decision maker.

Significant theoretical advances have been made in planning experiments on mathematical models using computers. The apparatus of the mathematical planning theory is mainly focused on the study of random mechanisms of the situation. At the same time, it is often useful in other situations as well.

Consider the formulation of the experiment planning problem.

If the goal of the study is to maximize the useful effect of the experiment with constraints on costs, and the useful effect itself is correlated in the mind of the decision maker with the provision of an extremum (for example, maximum) of the output result, then the problem of establishing the optimal parameters of the experiment will be reduced to the desire to maximize the output result under constraints on costs. For example, if it is necessary to increase the yield of some useful substance in the process of chemical production, and the yield depends on such important parameters as temperature, pressure, etc., then the formulation of the problem of planning an experiment for the release of a chemical product may look like this: find the optimal combination the listed controlled variables of the chemical production process, which ensure the maximum output of the finished product of the required quality, provided that the costs of the experiment are not higher than the finances allocated for it.

Approximately according to the same scheme, the formulation of the problem of obtaining information is also formulated in the case when the effect is identified with the accuracy of predicting the output result, that is, with the magnitude of the error in reproducing the mechanism of the situation, as well as the formulation of the problem in which the goal of the decision maker is to strive to minimize the cost of modeling while ensuring the levels of claims of the decision maker for the expected effect.

The problem of forming the initial set of alternatives

This problem was already mentioned in the previous lecture. Considering its exceptional importance, let us consider it in more detail.

The degree of experience of the decision maker is largely characterized by the ability to correctly predict the situation and find the best way to solve the problem. At the same time, correctly determining the mechanism of the situation means quickly establishing the leading factors, and the decision maker's ability to generate new, non-standard solutions is generally identified in the minds of people with art. In this regard, it is clear that the task of forming the initial set of alternatives does not lend itself to complete formalization. The solution to this problem is a creative process in which the main role, of course, belongs to the decision maker. The emergence of this problem as a theoretical object of research is a direct consequence of the use of the systemic principle of multiple alternatives in TPR.

Before solving the problem of forming the initial set of alternatives, it is necessary to determine the system requirements that this set must meet. First, the set of alternatives should be as complete as possible. This will provide the decision maker with the necessary freedom of choice in the future and minimize the opportunity to miss the "best" decision. However, this first fundamental requirement is in contradiction with the second, arising from the principle of correspondence of the decision to the time, place and capabilities of the decision maker. Most often, in practice, such compliance is understood as a requirement to work out a solution as soon as possible. Consequently, secondly, the initial set of alternatives should be foreseeable, narrow enough so that the decision maker has enough time to assess the consequences and preferability of alternatives under the existing resource constraints. The problem of satisfying these two contradictory requirements is solved systemically, based on the principle of decomposition.

Following the systemic principle of decomposition, they first form a set of alternatives, all of whose elements potentially, by their appearance, by the possibilities hidden in them, ensure the achievement of the target result in the current situation. The set of applicants for a way to solve the problem obtained in this way will be called the set of target alternatives.

Then, from the set of target alternatives, those options are selected that are logically consistent and can be implemented within the time allowed for the operation. In addition, the selected alternatives must be satisfied with the necessary active resources and must meet the general system of preferences of the decision maker.

These options selected from the target alternatives will be called physically realizable target alternatives. The rest of the options, potentially leading to the goal, but physically unrealizable, are discarded.

The options obtained as a result of such manipulations are supplemented with methods of action that give the alternatives the necessary flexibility and stability in relation to the changing or currently unknown components of the conditions of the operation. As a result, the original set of alternatives is obtained.

Technologically, the method of forming the initial set of alternatives involves the implementation of a number of special purposeful modifications of the main factors of the situation mechanism. They consist in the simultaneous or sequential impact on the controlled (subject to the will of the decision maker) part of the quality characteristics of the active resources used, the characteristics of the conditions and methods of action.

It is this idea that underlies most of the known methods and algorithms for the formation of the initial set of alternatives.

Historically, the first to emerge were empirical methods that require minimal formalization. The simplest of this class is the causal diagram method. A typical modern representative of empirical methods is the CBR method (Case-Based Reasoning - "method of reasoning based on past experience").

The next class is formed by logical-heuristic procedures, where formalization is carried out at the level of management of logical relationships. Decision tree methods and morphological tables method are examples of such methods implementation.

Typical representatives of the class of methods for forming alternatives, in which the highest degree of formalization of all stages of generation has been achieved, are the methods of network and scheduling.

A special class is formed by methods of forming alternatives in conditions when a decision is developed by a "group decision-maker", when there is a complete or partial coincidence of interests of the participants in the decision-making process, however, due to the unequal interpretation of the goals of actions, the peculiarities of the individual perception of the problem situation and for other reasons, the sovereign opinions of the participants the decision-making process needs to be agreed upon in the overall decision. Other representatives of the methods of this class are methods for generating alternatives in conditions of conflict and counteraction of sovereign subjects involved in the decision-maker's operation either of their own free will or against their will. Such situations are characteristic of economic, social, political and military conflicts. In all such situations, as a rule, reflexive methods are used to form alternatives. Such methods are characterized by an average level of formalization using simple mathematical models.

In terms of frequency of application in practice, perhaps, the first place is occupied by logical-heuristic methods. They acquired this position because of their inherent visibility, simplicity and versatility of the approach, and the convenience of computerizing their algorithms. The essence of these methods boils down to the fact that, first, based on the logical analysis of the goal of the operation, a tree of goals and objectives is built. Then each subgoal or task is also detailed, and this operation continues until the decision maker becomes clear which of the known means (or in what way) to solve each particular task.

Assessment of alternatives

As already noted, an informed choice should be made on the basis of a comparison of the results of evaluating alternatives. Therefore, the problem of evaluating alternatives has main goal obtaining for each alternative the values \u200b\u200bof the results characterizing the intensity of the essential properties of the outcomes of the operation planned to be carried out under the given conditions. Let us formulate the problem of evaluating alternatives as the problem of obtaining results for each alternative as follows.

Set A of the decision maker's alternatives characterizing the order of using available resources to achieve the goal of the operation; many S factors that define the conditions for the operation to achieve the goal, and their quantitative and qualitative characteristics; type of situation mechanism.

Required

Estimate the value of the result Y (a, s) for each of the alternatives of the set A under the conditions of S.

Depending on the type of the mechanism of the situation, the result Y (a, s) of applying the alternative, and under the conditions of s, will be understood in different ways.

If the mechanism is deterministic, then the result Y (a) (in the general case, vector) depends on the alternative uniquely, the conditions are fixed and only determine the form of the mapping A -\u003e Y.

For the stochastic mechanism of the situation, in the general case, each alternative is associated with the probability distribution of the vector result, the conditions are fixed and determine the form of the probability distribution. For other types of the situation mechanism, we will look for the set of possible values \u200b\u200bof the vector result Y (a, s).

Information on the values \u200b\u200b(estimates) of the result Y (a, s) for any of the listed types of situation mechanisms can be obtained in various ways, however, mathematical modeling should be considered the main means of obtaining new information for solving large-scale problems.

It is advisable to organize modeling as a process of building models with a gradually increasing "image scale". At the same time, at the initial stage of the modeling process, models of the greatest degree of generalization of factors are used, taking into account only the most noticeable patterns - the so-called conceptual models (this is the "smallest scale" of research). Then the object of research is specified and the model is supplemented by introducing a greater number of factors into it and measuring their characteristics in scales of an intermediate degree of perfection ("average scale"). Finally, when the researcher is so determined in the object of research that he has isolated a specific element from reality and decided which regularities to reproduce in all details, a detailed modeling (the "largest scale" of the study) is carried out using the most perfect quantitative scales.

The experience of decision-making based on modeling shows that in any case, the results obtained in the course of modeling will contribute to a deeper understanding of the essence of the operation and improvement of existing methods of managing it.

An important independent element of the model development process is the verification of its operability.

Among such checks, many researchers usually call consistency checks first of all. common sense (the simulation results agree with ordinary concepts), asymptotic stability (the limiting minimum or maximum values \u200b\u200bof the input parameters lead to correct conclusions, confirmed by asymptotic estimates), sensitivity to important parameters (the model reacts to small changes in the input parameters), compliance with experimental data (the results of the experiment should reproduce well on the model), efficiency (the ability to obtain the results required in terms of quality within the allotted deadline).

After establishing the adequacy of the model, they proceed to obtaining and processing the simulation results necessary for making a decision. Data processing is carried out in order to make it visible and bring it to a form that is convenient for making a decision. The method of data processing is chosen depending on the type of scale (qualitative or quantitative) and the nature of the factor corresponding to these data (random, "natural", etc.).

The results of experimental data processing must be presented to the decision maker in a concise and expressive form, with the required degree of detail.