Decision-making methods under risk conditions are also developed and justified within the framework of the so-called theory statistical decisions. The theory of statistical decisions is the theory of making statistical observations, processing these observations and using them. As you know, the task of economic research is to understand the nature of the economic object, to reveal the mechanism of the relationship between its most important variables. Such an understanding allows the development and implementation of the necessary measures for the management of this object, or economic policy. This requires methods adequate to the task, taking into account the nature and specifics of economic data that serve as the basis for qualitative and quantitative statements about the studied economic object or phenomenon.
Any economic data are quantitative characteristics of any economic objects. They are formed under the influence of many factors, not all of which are available. external control. Uncontrollable factors can take on random values from a set of values and thereby cause the randomness of the data they determine. The stochastic nature of economic data necessitates the use of special statistical methods adequate to them for their analysis and processing.
Quantifying entrepreneurial risk regardless of content specific task is possible, as a rule, with the help of methods of mathematical statistics. The main tools of this estimation method are variance, standard deviation, coefficient of variation.
Applications make extensive use of generic constructs based on measures of variability or likelihood of risky states. So, financial risks, caused by fluctuations of the result around the expected value, for example, efficiency, is estimated using the variance or the expected absolute deviation from the mean. In money management problems, a common measure of the degree of risk is the probability of a loss or shortfall in income compared to the predicted option.
To assess the magnitude of the risk (degree of risk), we will focus on the following criteria:
- 1) average expected value;
- 2) fluctuation (variability) of a possible result.
For a statistical sample
where Xj - expected value for each case of observation (/" = 1, 2, ...), n, - number of cases of observation (frequency) of the value n:, x=E - average expected value, st - variance,
V - coefficient of variation, we have:
Consider the problem of risk assessment for business contracts. LLC "Interproduct" decides to conclude a contract for the supply of food from one of the three bases. Having collected data on the timing of payment for goods by these bases (Table 6.7), it is necessary, after assessing the risk, to choose the base that pays for the goods in the shortest possible time when concluding a contract for the supply of products.
Table 6.7
|
Payment terms in days |
Number of cases of observation P |
hp |
(x-x) |
(x-x ) 2 |
(x-x) 2 p |
|
For the first base, based on the formulas (6.4.1):
For second base
For third base
The coefficient of variation for the first base is the smallest, which indicates the expediency of concluding a contract for the supply of products with this base.
The considered examples show that the risk has a mathematically expressed probability of a loss, which is based on statistical data and can be calculated with a fairly high degree of accuracy. When choosing the most acceptable solution, the rule of optimal result probability was used, which consists in the fact that from possible solutions the one at which the probability of the result is acceptable for the entrepreneur is chosen.
In practice, the application of the rule of optimal outcome probability is usually combined with the rule of optimal outcome variability.
As you know, the fluctuation of indicators is expressed by their variance, standard deviation and coefficient of variation. The essence of the rule of optimal volatility of the result is that of the possible solutions, one is chosen at which the probabilities of winning and losing for the same risky investment of capital have a small gap, i.e. the smallest value of the variance, the standard deviation of the variation. In the problems under consideration, the choice of optimal solutions was made using these two rules.
Give the concept of statistical decisions for one diagnostic parameter and for making a decision in the presence of a zone of uncertainty. Explain the decision making process in different situations. What is the connection between decision boundaries and the probabilities of errors of the first and second kind The methods under consideration are statistical ....
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Lecture 7
Topic. STATISTICAL SOLUTION METHODS
Target. Give the concept of statistical decisions for one diagnostic parameter and for making a decision in the presence of a zone of uncertainty.
Educational. Explain the decision making process in different situations.
Developing. Develop logical thinking and natural - scientific worldview.
Educational . Raise interest in scientific achievements and discoveries in the telecommunications industry.
Interdisciplinary connections:
Providing: computer science, mathematics, computer engineering and MT, programming systems.
Provided: Internship
Methodological support and equipment:
Methodical development to occupation.
Academic plan.
Safety briefing.
Technical means learning: personal computer.
Providing jobs:
Workbooks
Lecture progress.
Organizing time.
Analysis and verification homework
Answer the questions:
- What makes it possible to determine Bayes formula?
- What are the basics of the Bayes method?Give a formula. Give a definition of the exact meaning of all the quantities included in this formula.
- What does it mean thatimplementation of some set of features K* is determining?
- Explain the principle of formationdiagnostic matrix.
- What does decision decision rule?
- Define the method of sequential analysis.
- What is the relationship between decision boundaries and the probabilities of errors of the first and second kind?
Lecture plan
The considered methods are statistical. In statistical decision methods, the decision rule is chosen on the basis of some optimality conditions, for example, from the condition of minimum risk. Originating in mathematical statistics as methods for testing statistical hypotheses (the work of Neumann and Pearson), the methods under consideration have found wide application in radar (detection of signals against the background of interference), radio engineering, general communication theory, and other areas. Statistical decision methods are successfully used in problems of technical diagnostics.
STATISTICAL SOLUTIONS FOR A SINGLE DIAGNOSTIC PARAMETER
If the state of the system is characterized by one parameter, then the system has a one-dimensional feature space. The division is made into two classes (differential diagnosis or dichotomy(bifurcation, consecutive division into two parts that are not connected with each other.) ).
Fig.1 Statistical distributions of the probability density of the diagnostic parameter x for serviceable D 1 and defective D 2 states
It is significant that the areas of serviceable D 1 and defective D 2 states intersect and therefore it is fundamentally impossible to choose the value x 0 , at which there was no would be wrong decisions.The problem is to choose x 0 was in some sense optimal, for example, gave the least number of erroneous solutions.
False alarm and missing target (defect).These previously encountered terms are clearly related to radar technology, but they are easily interpreted in diagnostic problems.
It's called a false alarmthe case when a decision is made about the presence of a defect, but in reality the system is in good condition (instead of D 1 is taken D 2 ).
Missing target (defect)making a decision about a healthy state, while the system contains a defect (instead of D 2 is taken D 1 ).
In control theory, these errors are calledsupplier risk and customer risk. It is obvious that these two kinds of errors may have different consequences or different aims.
The probability of a false alarm is equal to the probability of the product of two events: the presence of a good state and the value x > x 0 .
Medium risk. The probability of making an erroneous decision is the sum of the probabilities of a false alarm and the defect skipping (expectation) of the risk.
Of course, the cost of an error has a conditional value, but it should take into account the expected consequences of false alarms and missing a defect. In reliability problems, the cost of skipping a defect is usually much higher than the cost of a false alarm.
Method minimum risk . The probability of making an erroneous decision is defined as minimizing the extremum point of the average risk of erroneous decisions at the maximum likelihood i.e. the calculation of the minimum risk of the occurrence of the event is carried out at availability of information about the most similar events.
rice. 2. Extremum points of the average risk of erroneous decisions
Rice. 3. Extremum points for two-hump distributions
The ratio of the probability densities of the distribution of x under two states is called the likelihood ratio.
Recall that the diagnosis D1 is in good condition, D2 defective state of the object; FROM 21 cost of a false alarm, С 12 target skip price (first index accepted state, second actual); FROM 11 < 0, С 22 < 0 цены правильных решений (условные выигрыши). В большинстве practical tasks conditional winnings (incentives) for correct decisions are not introduced.
It often turns out to be convenient to consider not the likelihood ratio, but the logarithm of this ratio. This does not change the result, since the logarithmic function increases monotonically with its argument. The calculation for normal and some other distributions using the logarithm of the likelihood ratio turns out to be somewhat simpler. The risk minimum condition can be obtained from other considerations, which will turn out to be important in what follows.
Method of the minimum number of erroneous decisions.
Probability of an erroneous decision for a decision rule
In reliability problems, the considered method often gives "careless decisions", since the consequences of erroneous decisions differ significantly from each other. Typically, the cost of missing a defect is significantly higher than the cost of a false alarm. If the indicated costs are approximately the same (for defects with limited consequences, for some control tasks, etc.), then the application of the method is fully justified.
The minimax method is intendedfor a situation where there is no preliminary statistical information about the probability of diagnoses D1 and D2 . The “worst case” is considered, i.e. the least favorable values of P 1 and R 2 leading to the highest value (maximum) of risk.
It can be shown for unimodal distributions that the risk value becomes minimax (i.e., the minimum among the maximum values caused by the "unfavorable" value Pi ). Note that for R 1 = 0 and R 1 = 1 there is no risk of making an erroneous decision, since the situation has no uncertainty. At R 1 = 0 (all products are faulty) follows x 0 → -oo and all objects are indeed recognized as faulty; at R 1 = 1 and P 2 = 0 x 0 → +oo and in accordance with the existing situation, all objects are classified as serviceable.
For intermediate values 0< Pi < 1 риск возрастает и при P 1=P 1* becomes the maximum. The value of x is chosen by the method under consideration 0 in such a way that at the least favorable values Pi the losses associated with erroneous decisions would be minimal.
rice . 4. Determination of the boundary value of the diagnostic parameter using the minimax method
NeumannPearson method. As already mentioned, estimates of the cost of errors are often unknown and their reliable determination is associated with great difficulties. However, it is clear that in all with l y teas, it is desirable, at a certain (permissible) level of one of the errors, to minimize the value of the other. Here the center of the problem is transferred to a reasonable choice of an acceptable level errors from past experience or intuition.
According to the NeumannPearson method, the probability of missing a target is minimized for a given acceptable level of false alarm probability.Thus, the probability of a false alarm
where А is the given admissible false alarm probability level; R 1 probability of good condition.
Note that usually this is condition is referred to the conditional false alarm probability (multiplier P 1 missing). In the problems of technical diagnostics, the values of P 1 and R 2 in most cases are known from statistical data.
Table 1 Example - Calculation results using statistical decision methods
|
No. p / p |
Method |
limit value |
False alarm probability |
Probability of skipping a defect |
Medium risk |
|
|
Minimum risk method |
7,46 |
0,0984 |
0,0065 |
0,229 |
||
|
Minimum Error Method |
9,79 |
0,0074 |
0,0229 |
0,467 |
||
|
minimax method |
Basic option |
5,71 |
0,3235 |
0,0018 |
0,360 |
|
|
Option 2 |
7,80 |
0,0727 |
0,0081 |
0,234 |
||
|
NeumannPearson method |
7,44 |
0,1000 |
0,0064 |
0,230 |
||
|
Maximum likelihood method |
8,14 |
0,0524 |
0,0098 |
0,249 |
||
The comparison shows that the method of the minimum number of errors gives an unacceptable solution, since the error costs are significantly different. The boundary value by this method leads to a significant probability of missing a defect. The minimax method in the main variant requires a very large decommissioning of the devices under study (approximately 32%), since it proceeds from the least favorable case (the probability of a malfunction P 2 = 0.39). The application of the method can be justified if there are no even indirect estimates of the probability of a faulty state. In this example, satisfactory results are obtained by the method of minimal risk.
- STATISTICAL SOLUTIONS WITH A ZONE OF UNCERTAINTY AND OTHER GENERALIZATIONS
Decision rule in the presence of a zone of uncertainty.
In some cases, when high recognition reliability is required (high cost of target miss errors and false alarms), it is advisable to introduce an uncertainty zone (recognition rejection zone). The decision rule will be as follows
at denial of recognition.
Of course, failure to recognize is an undesirable event. It indicates that the available information is not enough to make a decision and additional information is needed.
rice. 5. Statistical solutions in the presence of a zone of uncertainty
Definition of average risk. The value of the average risk in the presence of a zone of refusal of recognition can be expressed by the following equality
where C o price of failure to recognize.
Note that with > 0, otherwise the task loses its meaning (the "reward" for refusing recognition). Exactly the same with 11 < 0, С 22 < 0, так как right decisions shouldn't be penalized.
Minimum risk method in the presence of an area of uncertainty. Let us define the boundaries of the decision-making area based on the minimum average risk.
If good decisions are not encouraged (C 11 = 0, C 22 = 0) and not pay for refusing recognition (С 0 = 0), then the area of uncertainty will occupy the entire area of parameter change.
The presence of a zone of uncertainty makes it possible to ensure the specified levels of errors by refusing to recognize in "doubtful" cases
Statistical solutions for several states.The above cases were considered when statistical decisions were made d to distinguish between two states (dichotomy). In principle, this procedure makes it possible to carry out the division into n states, each time combining the results for the state D1 and D2. Here under D 1 any states corresponding to the condition “not D2 ". However, in some cases it is of interest to consider the issue in a direct formulation statistical solutions for classification n states.
Above, we considered cases when the state of the system (product) was characterized by one parameter x and the corresponding (one-dimensional) distribution. The state of the system is characterized by diagnostic parameters x 1 x 2 , ..., x n or vector x:
x \u003d (x 1 x 2,..., x n).
M minimum risk method.
The methods of minimal risk and its special cases (the method of the minimum number of erroneous decisions, the method of maximum likelihood) are most simply generalized to multidimensional systems. In cases where the method of statistical decision requires the determination of the boundaries of the decision-making area, the computational side of the problem becomes much more complicated (the NeumannPearson and minimax methods).
Homework: § abstract.
Fixing the material:
Answer the questions:
- What is called a false alarm?
- What does missing a target (defect) imply?
- Give an explanationsupplier risk and customer risk.
- Give the formula for the method of the minimum number of erroneous decisions. Define a careless decision.
- What is the purpose of the minimax method?
- NeumannPearson method. Explain its principle.
- What is the purpose of the zone of uncertainty?
Literature:
Amrenov S. A. "Methods for monitoring and diagnosing systems and communication networks" LECTURE SUMMARY -: Astana, Kazakh State Agrotechnical University, 2005
I.G. Baklanov Testing and diagnostics of communication systems. - M.: Eco-Trends, 2001.
Birger I. A. Technical diagnostics. M .: "Engineering", 1978. 240, p.
Aripov M.N., Dzhuraev R.Kh., Jabbarov Sh.Yu."TECHNICAL DIAGNOSIS OF DIGITAL SYSTEMS" - Tashkent, TEIS, 2005
Platonov Yu. M., Utkin Yu. G.Diagnostics, repair and prevention of personal computers. -M.: Hotline- Telecom, 2003.-312 p: ill.
M.E. Bushueva, V.V. BelyakovDiagnostics of complex technical systems Proceedings of the 1st meeting of the NATO project SfP-973799 Semiconductors . Nizhny Novgorod, 2001
Malyshenko Yu.V. TECHNICAL DIAGNOSIS part I lecture notes
Platonov Yu. M., Utkin Yu. G.Diagnosis of freezing and computer malfunctions / Series "Technomir". Rostov-on-Don: "Phoenix", 2001. 320 p.
PAGE \* MERGEFORMAT 2
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MANAGEMENT DECISION-MAKING METHODS
Areas of training
080200.62 "Management"
is the same for all forms of education
Qualification (degree) of the graduate
Bachelor
Chelyabinsk
Management decision-making methods: Working program of the academic discipline (module) / Yu.V. Subpovetnaya. - Chelyabinsk: PEI VPO "South Ural Institute of Management and Economics", 2014. - 78 p.
Management decision-making methods: The work program of the discipline (module) in the direction 080200.62 "Management" is the same for all forms of education. The program was drawn up in accordance with the requirements of the Federal State Educational Standard of the Higher Professional Education, taking into account the recommendations and ProOPOP VO in the direction and profile of training.
The program was approved at a meeting of the Educational and Methodological Council dated August 18, 2014, protocol No. 1.
The program was approved at the meeting of the Academic Council on August 18, 2014, protocol No. 1.
Reviewer: Lysenko Yu.V. - Doctor of Economics, Professor, Head. Department of "Economics and Management at the Enterprise" of the Chelyabinsk Institute (branch) FGBOU VPO "PREU named after G.V. Plekhanov"
Krasnoyartseva E.G. - Director of the PEI "Center for Business Education of the South Ural CCI"
© Publishing house of PEI VPO "South Ural Institute of Management and Economics", 2014
I Introduction……………………………………………………………………………...4
II Thematic planning…………………………………………………….....8
IV Evaluation tools for current monitoring of progress, intermediate certification based on the results of mastering the discipline and educational and methodological support for independent work of students…………..……………………………………….38
V Educational-methodical and Information Support disciplines .......76
VI Logistics of discipline ………………………...78
I INTRODUCTION
The work program of the discipline (module) "Methods of making managerial decisions" is designed to implement the Federal State Standard of the Higher vocational education in the direction 080200.62 "Management" and is the same for all forms of education.
1 The purpose and objectives of the discipline
The purpose of studying this discipline is:
Formation of theoretical knowledge about mathematical, statistical and quantitative methods for the development, adoption and implementation of management decisions;
Deepening the knowledge used for the study and analysis of economic objects, the development of theoretically substantiated economic and managerial decisions;
Deepening knowledge in the field of theory and methods for finding the best solutions, both under conditions of certainty and under conditions of uncertainty and risk;
Formation of practical skills for the effective application of methods and procedures for selection and decision-making for implementation economic analysis searching for the best solution to the problem.
2 Entrance requirements and the place of the discipline in the structure of the undergraduate BEP
The discipline "Methods of making managerial decisions" refers to the basic part of the mathematical and natural science cycle (B2.B3).
The discipline is based on the knowledge, skills and competencies of the student obtained in the study of the following academic disciplines: "Mathematics", "Innovation Management".
The knowledge and skills obtained in the process of studying the discipline "Methods of making managerial decisions" can be used in studying the disciplines of the basic part of the professional cycle: " Marketing research”, “Methods and models in economics”.
3 Requirements for the results of mastering the discipline "Methods of making managerial decisions"
The process of studying the discipline is aimed at the formation of the following competencies presented in the table.
Table - The structure of competencies formed as a result of studying the discipline
| Competency code | Name of competence | Characteristics of competence |
| OK-15 | own methods of quantitative analysis and modeling, theoretical and experimental research; | know/understand: be able to: own: |
| OK-16 | understanding the role and importance of information and information technologies in development modern society and economic knowledge; | As a result, the student must: know/understand: - basic concepts and tools of algebra and geometry, mathematical analysis, probability theory, mathematical and socio-economic statistics; - basic mathematical models of decision making; be able to: - solve typical mathematical problems used in making managerial decisions; - use the mathematical language and mathematical symbols in the construction of organizational and managerial models; - process empirical and experimental data; own: mathematical, statistical and quantitative methods for solving typical organizational and managerial problems. |
| OK-17 | own the basic methods, ways and means of obtaining, storing, processing information, skills in working with a computer as a means of managing information; | As a result, the student must: know/understand: - basic concepts and tools of algebra and geometry, mathematical analysis, probability theory, mathematical and socio-economic statistics; - basic mathematical models of decision making; be able to: - solve typical mathematical problems used in making managerial decisions; - use the mathematical language and mathematical symbols in the construction of organizational and managerial models; - process empirical and experimental data; own: mathematical, statistical and quantitative methods for solving typical organizational and managerial problems. |
| OK-18 | the ability to work with information in global computer networks and corporate information systems. | As a result, the student must: know/understand: - basic concepts and tools of algebra and geometry, mathematical analysis, probability theory, mathematical and socio-economic statistics; - basic mathematical models of decision making; be able to: - solve typical mathematical problems used in making managerial decisions; - use the mathematical language and mathematical symbols in the construction of organizational and managerial models; - process empirical and experimental data; own: mathematical, statistical and quantitative methods for solving typical organizational and managerial problems. |
As a result of studying the discipline, the student must:
know/understand:
Basic concepts and tools of algebra and geometry, mathematical analysis, probability theory, mathematical and socio-economic statistics;
Basic mathematical models of decision making;
be able to:
Solve typical mathematical problems used in making managerial decisions;
Use the mathematical language and mathematical symbols in the construction of organizational and managerial models;
Process empirical and experimental data;
own:
Mathematical, statistical and quantitative methods for solving typical organizational and managerial problems.
II THEMATIC PLANNING
SET 2011
DIRECTION: "Management"
STUDY TERM: 4 years
Full-time form of education
| Lectures, hour. | Practical lessons, hour. | Laboratory classes, hour. | Seminar | Course work, hour. | Total, hour. | ||
| Topic 4.4 Expert assessments | |||||||
| Topic 5.2 PR Game Models | |||||||
| Topic 5.3 Positional games | |||||||
| Exam | |||||||
| TOTAL |
Laboratory workshop
| No. p / p | Labor intensity (hour) | ||
| Topic 1.3 Target orientation of management decisions | Laboratory work No. 1. Search for optimal solutions. Application of optimization in PR support systems | ||
| Topic 2.2 Main types of decision theory models | |||
| Topic 3.3 Features of measuring preferences | |||
| Topic 4.2 Method of paired comparisons | |||
| Topic 4.4 Expert judgment | |||
| Topic 5.2 PR Game Models | |||
| Topic 5.4 Optimality in the form of equilibrium | |||
| Topic 6.3 Statistical games with a single experiment |
2011 set
DIRECTION: "Management"
FORM OF TRAINING: part-time
1 Volume of discipline and types of educational work
2 Sections and topics of discipline and types of classes
| Name of sections and topics of discipline | Lectures, hour. | Practical lessons, hour. | Laboratory classes, hour. | Seminar | Independent work, hour. | Coursework, hour. | Total, hour. |
| Section 1 Management as a process of making managerial decisions | |||||||
| Topic 1.1 Functions and properties of management decisions | |||||||
| Topic 1.2 Management decision-making process | |||||||
| Topic 1.3 Target orientation of management decisions | |||||||
| Section 2 Models and modeling in decision theory | |||||||
| Topic 2.1 Modeling and analysis of action alternatives | |||||||
| Topic 2.2 Main types of decision theory models | |||||||
| Section 3 Decision making in a multi-criteria environment | |||||||
| Topic 3.1 Non-criteria and criteria methods | |||||||
| Topic 3.2 Multicriteria models | |||||||
| Topic 3.3 Features of measuring preferences | |||||||
| Section 4 Ordering alternatives based on experts' preferences | |||||||
| Topic 4.1 Measurements, comparisons and consistency | |||||||
| Topic 4.2 Method of paired comparisons | |||||||
| Topic 4.3 Principles of group choice | |||||||
| Topic 4.4 Expert judgment | |||||||
| Section 5 Decision Making under Uncertainty and Conflict | |||||||
| Topic 5.1 Mathematical model of the PR problem under conditions of uncertainty and conflict | |||||||
| Topic 5.2 PR Game Models | |||||||
| Topic 5.3 Positional games | |||||||
| Topic 5.4 Optimality in the form of equilibrium | |||||||
| Section 6 Decision making at risk | |||||||
| Topic 6.1 Theory of statistical decisions | |||||||
| Topic 6.2 Finding optimal solutions under risk and uncertainty | |||||||
| Topic 6.3 Statistical games with a single experiment | |||||||
| Section 7 Decision making in fuzzy conditions | |||||||
| Topic 7.1 Compositional models of PR | |||||||
| Topic 7.2 Classification models of PR | |||||||
| Exam | |||||||
| TOTAL |
Laboratory workshop
| No. p / p | No. of the module (section) of the discipline | Name of laboratory work | Labor intensity (hour) |
| Topic 2.2 Main types of decision theory models | Laboratory work No. 2. Decision making based on economic and mathematical models, queuing theory models, inventory management models, models linear programming | ||
| Topic 4.2 Method of paired comparisons | Laboratory work No. 4. The method of paired comparisons. Ordering Alternatives Based on Pairwise Comparisons and Accounting for Expert Preferences | ||
| Topic 5.2 PR Game Models | Laboratory work No. 6. Building a game matrix. Reduction of an antagonistic game to a linear programming problem and finding its solution | ||
| Topic 6.3 Statistical games with a single experiment | Laboratory work No. 8. Choosing strategies in a game with an experiment. Using Posterior Probabilities |
DIRECTION: "Management"
STUDY TERM: 4 years
Full-time form of education
1 Volume of discipline and types of educational work
2 Sections and topics of discipline and types of classes
| Name of sections and topics of discipline | Lectures, hour. | Practical lessons, hour. | Laboratory classes, hour. | Seminar | Independent work, hour. | Coursework, hour. | Total, hour. |
| Section 1 Management as a process of making managerial decisions | |||||||
| Topic 1.1 Functions and properties of management decisions | |||||||
| Topic 1.2 Management decision-making process | |||||||
| Topic 1.3 Target orientation of management decisions | |||||||
| Section 2 Models and modeling in decision theory | |||||||
| Topic 2.1 Modeling and analysis of action alternatives | |||||||
| Topic 2.2 Main types of decision theory models | |||||||
| Section 3 Decision making in a multi-criteria environment | |||||||
| Topic 3.1 Non-criteria and criteria methods | |||||||
| Topic 3.2 Multicriteria models | |||||||
| Topic 3.3 Features of measuring preferences | |||||||
| Section 4 Ordering alternatives based on experts' preferences | |||||||
| Topic 4.1 Measurements, comparisons and consistency | |||||||
| Topic 4.2 Method of paired comparisons | |||||||
| Topic 4.3 Principles of group choice | |||||||
| Topic 4.4 Expert judgment | |||||||
| Section 5 Decision Making under Uncertainty and Conflict | |||||||
| Topic 5.1 Mathematical model of the PR problem under conditions of uncertainty and conflict | |||||||
| Topic 5.2 PR Game Models | |||||||
| Topic 5.3 Positional games | |||||||
| Topic 5.4 Optimality in the form of equilibrium | |||||||
| Section 6 Decision making at risk | |||||||
| Topic 6.1 Theory of statistical decisions | |||||||
| Topic 6.2 Finding optimal solutions under risk and uncertainty | |||||||
| Topic 6.3 Statistical games with a single experiment | |||||||
| Section 7 Decision making in fuzzy conditions | |||||||
| Topic 7.1 Compositional models of PR | |||||||
| Topic 7.2 Classification models of PR | |||||||
| Exam | |||||||
| TOTAL |
Laboratory workshop
| No. p / p | No. of the module (section) of the discipline | Name of laboratory work | Labor intensity (hour) |
| Topic 1.3 Target orientation of management decisions | Laboratory work No. 1. Search for optimal solutions. Application of optimization in PR support systems | ||
| Topic 2.2 Main types of decision theory models | Laboratory work No. 2. Decision making based on economic and mathematical models, queuing theory models, inventory management models, linear programming models | ||
| Topic 3.3 Features of measuring preferences | Laboratory work No. 3. Pareto-optimality. Building a trade-off scheme | ||
| Topic 4.2 Method of paired comparisons | Laboratory work No. 4. The method of paired comparisons. Ordering Alternatives Based on Pairwise Comparisons and Accounting for Expert Preferences | ||
| Topic 4.4 Expert judgment | Laboratory work No. 5. Processing of expert assessments. Expert Consistency Estimates | ||
| Topic 5.2 PR Game Models | Laboratory work No. 6. Building a game matrix. Reduction of an antagonistic game to a linear programming problem and finding its solution | ||
| Topic 5.4 Optimality in the form of equilibrium | Laboratory work No. 7. Bimatrix games. Applying the Balance Principle | ||
| Topic 6.3 Statistical games with a single experiment | Laboratory work No. 8. Choosing strategies in a game with an experiment. Using Posterior Probabilities |
DIRECTION: "Management"
STUDY TERM: 4 years
FORM OF TRAINING: part-time
1 Volume of discipline and types of educational work
2 Sections and topics of discipline and types of classes
| Name of sections and topics of discipline | Lectures, hour. | Practical lessons, hour. | Laboratory classes, hour. | Seminar | Independent work, hour. | Coursework, hour. | Total, hour. |
| Section 1 Management as a process of making managerial decisions | |||||||
| Topic 1.1 Functions and properties of management decisions | |||||||
| Topic 1.2 Management decision-making process | |||||||
| Topic 1.3 Target orientation of management decisions | |||||||
| Section 2 Models and modeling in decision theory | |||||||
| Topic 2.1 Modeling and analysis of action alternatives | |||||||
| Topic 2.2 Main types of decision theory models | |||||||
| Section 3 Decision making in a multi-criteria environment | |||||||
| Topic 3.1 Non-criteria and criteria methods | |||||||
| Topic 3.2 Multicriteria models | |||||||
| Topic 3.3 Features of measuring preferences | |||||||
| Section 4 Ordering alternatives based on experts' preferences | |||||||
| Topic 4.1 Measurements, comparisons and consistency | |||||||
| Topic 4.2 Method of paired comparisons | |||||||
| Topic 4.3 Principles of group choice | |||||||
| Topic 4.4 Expert judgment | |||||||
| Section 5 Decision Making under Uncertainty and Conflict | |||||||
| Topic 5.1 Mathematical model of the PR problem under conditions of uncertainty and conflict | |||||||
| Topic 5.2 PR Game Models | |||||||
| Topic 5.3 Positional games | |||||||
| Topic 5.4 Optimality in the form of equilibrium | |||||||
| Section 6 Decision making at risk | |||||||
| Topic 6.1 Theory of statistical decisions | |||||||
| Topic 6.2 Finding optimal solutions under risk and uncertainty | |||||||
| Topic 6.3 Statistical games with a single experiment | |||||||
| Section 7 Decision making in fuzzy conditions | |||||||
| Topic 7.1 Compositional models of PR | |||||||
| Topic 7.2 Classification models of PR | |||||||
| Exam | |||||||
| TOTAL |
Laboratory workshop
| No. p / p | No. of the module (section) of the discipline | Name of laboratory work | Labor intensity (hour) |
| Topic 2.2 Main types of decision theory models | Laboratory work No. 2. Decision making based on economic and mathematical models, queuing theory models, inventory management models, linear programming models | ||
| Topic 4.2 Method of paired comparisons | Laboratory work No. 4. The method of paired comparisons. Ordering Alternatives Based on Pairwise Comparisons and Accounting for Expert Preferences | ||
| Topic 5.2 PR Game Models | Laboratory work No. 6. Building a game matrix. Reduction of an antagonistic game to a linear programming problem and finding its solution | ||
| Topic 6.3 Statistical games with a single experiment | Laboratory work No. 8. Choosing strategies in a game with an experiment. Using Posterior Probabilities |
DIRECTION: "Management"
STUDY TERM: 3.3 years
FORM OF TRAINING: part-time
1 Volume of discipline and types of educational work
2 Sections and topics of discipline and types of classes
How are approaches, ideas and results of probability theory and mathematical statistics used in decision making?
The base is a probabilistic model of a real phenomenon or process, i.e. a mathematical model in which objective relationships are expressed in terms of probability theory. Probabilities are used primarily to describe the uncertainties that need to be taken into account when making decisions. This refers to both undesirable opportunities (risks) and attractive ones (“lucky chance”). Sometimes randomness is deliberately introduced into the situation, for example, when drawing lots, random selection of units for control, conducting lotteries or consumer surveys.
Probability theory allows one to calculate other probabilities that are of interest to the researcher. For example, by the probability of a coat of arms falling out, you can calculate the probability that at least 3 coats of arms will fall out in 10 coin tosses. Such a calculation is based on a probabilistic model, according to which coin tosses are described by a scheme of independent trials, in addition, the coat of arms and the lattice are equally likely, and therefore the probability of each of these events is equal to ½. More complex is the model, which considers checking the quality of a unit of output instead of a coin toss. The corresponding probabilistic model is based on the assumption that the quality control of various units of production is described by a scheme of independent tests. In contrast to the coin toss model, a new parameter must be introduced - the probability p that a unit of production is defective. The model will be fully described if it is assumed that all units of production have the same probability of being defective. If the last assumption is false, then the number of model parameters increases. For example, we can assume that each unit of production has its own probability of being defective.
Let us discuss a quality control model with a common defect probability p for all units of production. In order to “get to the number” when analyzing the model, it is necessary to replace p with some specific value. To do this, it is necessary to go beyond the framework of a probabilistic model and turn to the data obtained during quality control.
Mathematical statistics solves the inverse problem with respect to probability theory. Its purpose is to draw conclusions about the probabilities underlying the probabilistic model based on the results of observations (measurements, analyses, tests, experiments). For example, based on the frequency of occurrence of defective products during control, conclusions can be drawn about the probability of defectiveness (see Bernoulli's theorem above).
On the basis of Chebyshev's inequality, conclusions were drawn about the correspondence of the frequency of occurrence of defective products to the hypothesis that the probability of defectiveness takes a certain value.
Thus, the application of mathematical statistics is based on a probabilistic model of a phenomenon or process. Two parallel series of concepts are used - those related to theory (a probabilistic model) and those related to practice (a sample of observational results). For example, the theoretical probability corresponds to the frequency found from the sample. The mathematical expectation (theoretical series) corresponds to the sample arithmetic mean (practical series). As a rule, sample characteristics are estimates of theoretical ones. At the same time, the quantities related to the theoretical series “are in the minds of researchers”, refer to the world of ideas (according to the ancient Greek philosopher Plato), and are not available for direct measurement. Researchers have only selective data, with the help of which they try to establish the properties of a theoretical probabilistic model that are of interest to them.
Why do we need a probabilistic model? The fact is that only with its help it is possible to transfer the properties established by the results of the analysis of a particular sample to other samples, as well as to the entire so-called general population. The term "population" is used to refer to a large but finite population of units being studied. For example, about the totality of all residents of Russia or the totality of all consumers of instant coffee in Moscow. The purpose of marketing or sociological surveys is to transfer statements received from a sample of hundreds or thousands of people to general populations of several million people. In quality control, a batch of products acts as a general population.
To transfer inferences from a sample to a larger population, some assumptions are needed about the relationship of sample characteristics with the characteristics of this larger population. These assumptions are based on an appropriate probabilistic model.
Of course, it is possible to process sample data without using one or another probabilistic model. For example, you can calculate the sample arithmetic mean, calculate the frequency of fulfillment of certain conditions, etc. However, the results of the calculations will apply only to a specific sample; transferring the conclusions obtained with their help to any other set is incorrect. This activity is sometimes referred to as "data analysis". Compared to probabilistic-statistical methods, data analysis has limited cognitive value.
So, the use of probabilistic models based on estimation and testing of hypotheses with the help of sample characteristics is the essence of probabilistic-statistical decision-making methods.
Let us emphasize that the logic of using sample characteristics for making decisions based on theoretical models involves the simultaneous use of two parallel series of concepts, one of which corresponds to probabilistic models, and the second to sample data. Unfortunately, in a number literary sources, usually outdated or written in a prescription spirit, no distinction is made between selective and theoretical characteristics, which leads readers to bewilderment and errors in the practical use of statistical methods.