Expert decision-making methods. Interactive Methods

The textbook discusses the methods of making managerial decisions in various problematic situations that arise in economic systems. Basic concepts, classification of problems and adequate methods for their resolution, methods of their structuring and description are given. Considerable attention is paid to automated support for decision-making procedures and tasks in fuzzy conditions. A feature of the publication is the method of solving typical tasks with substantiation of methods for choosing a rational solution.
The textbook was prepared in accordance with the program of the course "Management Decisions", which is included in the specialty "Management of Organizations and Public municipalities". Designed for students of economic specialties of all forms of education, it can be useful for everyone interested in the problems of effective decision-making in management, business and production. Recommended by the Council of the Educational and Methodological Association of Russian Universities for Education in the Field of Management as a textbook in the specialty "Organization Management".

Common problems making managerial decisions.
Scientific foundations of the theory of decision making as a section of the general theory of systems and system analysis were established during the Second World War. Its founders are J. von Neumann and O. Morgenstern, who in 1944 published materials on a new direction - game theory. Later, foreign experts R. Ackoff, F. Emery, St. Optner, R. Lewis, X. Rife, St. Beer, J. Forrester and others, as well as domestic ones - A. G. Vendelin, D. M. Gvishiani, O. I. Larichev, I. M. Syroezhin and others made a significant contribution to the development and enrichment of this theory.

Any management activity, including in the field of economics, management and marketing, is closely related to the adoption of appropriate decisions on various management situations.

Therefore, in the general case, a decision is understood as a set of managerial influences (actions on the part of the decision maker (DM)) on the object (system, complex, etc.) of management, which makes it possible to bring this object to the desired state or achieve the goal set for it.

The decision-making process (DP) is one of the stages management activities, on which the most preferred solution is selected from the feasible set of solutions, or the set of solutions is ordered by their importance.

Table of contents
Introduction
Section 1. General problems of making managerial decisions
Chapter 1. Problems of decision-making in the management of economic systems
1.1. General problems of managerial decision-making
1.2. Modeling of management processes
1.3. Information Representation Model in Management of Economic Systems
1.4. Model of information in the decision-making process
1.5. Management efficiency in modern conditions
1.6. Decision making in unique problem situations
Chapter 2. Basic concepts and categories of decision theory
2.1. Basic Definitions and Statement of the Decision-Making Problem
2.2. Classification of decision-making problems
2.3. Classification of management decisions
Chapter 3 Decision Technology
3.1. Formation and evaluation of decisions
3.2. Preparing to choose a solution
3.3. Technological process decision making
3.4. Modeling decision-making procedures
Chapter 4. Description and analysis of the problem situation
4.1. Methods for describing a problem situation
4.2. Problem Situation Analysis Procedures
4.3. The task of measuring the characteristics of a problem situation
4.4. Methods for subjective measurements of characteristics
4.5. Selection Criteria: Methods for Forming an Integral Criterion
Section 2. Decision-making methods in structured problem situations
Chapter 5 Decision Making in Structured Situations
5.1. Methods for solving problems like /. Search for the optimal solution
5.2. Analytical solution of the linear optimization problem (simplex method)
5.3. Automated solution of the linear optimization problem (Excel)
5.4. Methods for solving problems of type JA. Guaranteed result principle
5.5. Principle of Optimism (Maximax)
5.6. Hurwitz principle
5.7. Savage's principle (minimax regret)
Chapter 6
6.1. Decision making in problems of type G
6.2. Selection Procedure in Structured Problems Type GA
Chapter 7
7.1. Example 1
7.2. Example 2
7.3. Computer solution of the selection problem
Section 3. Methods for solving complex problem situations
Chapter 8
8.1. Statement and types of multicriteria tasks
8.2. Methods for solving multicriteria problems with unstructured criteria
8.3. Methods for analytical construction of distance metrics
Chapter 9
9.1. Justification of the method of choosing an investment decision
9.2. Selecting the best project using the lexicographic method
9.3. Project Selection Based on the Shifted Ideal Method
9.4. Equipment selection task
Chapter 10
10.1. Target tree method (hierarchy analysis method)
10.2. Solving problems using the hierarchy analysis method
Chapter 11
11.1. Application of methods of optimism, pessimism, Hurwitz, Savage
11.2. Application of the “shifted ideal” method
11.3. Applying the Hierarchy Analysis Method
Chapter 12
12.1. Example 1 Solution
12.2. Example 2 solution
Section 4. Methods for making decisions in unstructured situations
Chapter 13
13.1. Problems of Choice under Risk and Uncertainty
13.2. Classification of uncertainties in control problems
13.3. Decision making under conditions of probabilistic certainty (risk)
13.4. Methods for analyzing the consequences of events and decision trees
13.5. Selection Methods Under Full or Partial Uncertainty
Section 5. Expert (group) methods of choice in complex decision-making problems
Chapter 14
14.1. Statement and formalization of group decision-making problems (problems of type G)
14.2. Classification of group choice problems
14.3. Methodology for conducting the group selection procedure
Chapter 15
15.1. Methods for making decisions by a group of experts
15.2. Types of group approval of expert decisions
Chapter 16
16.1. Methods of group coordination when making a decision
16.2. Model of group estimation of objects of choice
16.3. Models for matching expert assessments
Chapter 17
17.1. Assessment of the degree of expert competence
17.2. An example of solving a GA type problem
Section 6. Automation of decision-making procedures
Chapter 18
18.1. Requirements and purpose of decision support systems
18.2. Functions of decision support systems
18.3. Decision Support Systems Application Technology
Chapter 19
19.1. Features, characteristics and implementation of expert systems
19.2. Work with typical management situations (module of standard situations of ES)
19.3. The logical structure of the information fund and the algorithm for the functioning of the WSN module
19.4. The structure of the model support system.

Page 1

ANALYSIS OF MEDICAL INFORMATION SYSTEMS FOR MEDICAL AND PREVENTIVE INSTITUTIONS OF SANATORIUM TYPE.

Informatization of the activities of health care institutions has long been an urgent need. Processing arrays of financial, medical and statistical information, which is constantly increasing, has become possible only with the use of modern information and computer technologies. Not only the volume of information has grown, but the requirements for the speed of its processing have also increased. Every year, higher-level organizations increase the requirements for the transfer of so-called “electronic reports” (that is, reports in in electronic format). The role of electronic data interchange between healthcare subjects using e-mail and the Internet is steadily growing.

At present, each medical institution (HCI) is covered by informatization to some extent. For the most part, these are local, not interconnected, automation systems for various areas of activity of healthcare facilities. In practice, the informatization of regional health care covers only the financial and economic services of health facilities: accounting, planning and economic department, insurance medicine. To improve quality and availability medical care in health care facilities, it is necessary to carry out complex automation of all types of activities in the institution.

Today, the medical information systems (MIS) market offers enough different solutions in a wide price range and with various functionalities. In the course of the study, we examined 30 medical information systems. Of these, 12 are products of a Ukrainian manufacturer, 18 are Russian. Most of the systems, namely 13, are specialized for sanatoriums.

The purpose of our study was to compare medical information systems for sanatorium-type medical and preventive institutions according to generally accepted criteria and determine the optimal one, using the theory of solving multi-criteria tasks.

The choice of the optimal system was carried out from the point of view of the buyer according to the data available in the open network. This problem was solved by the "shifted ideal" method. This method, described in , is designed to solve tasks for choosing the optimal object, in the case a large number objects and comparison criteria.

During the study, a comparison was made of 19 medical information systems, which were found in open sources the most detailed information. Comparison of systems was carried out according to generally accepted criteria for comparison. Namely:

the completeness of the functionality of the system;

The cost of the program (for one workplace);

· the need for investment in the acquisition of a database management system (DBMS);

the cost of a DBMS;

· adaptation to the legislation of Ukraine.

The "shifted ideal" method operates with the characteristics of objects, which are expressed in numbers, so the qualitative criteria for comparing systems were converted into numbers (Table 1).

Table 1. Conversion of comparison criteria into digital form.

The method is designed to select one or a subset of the most preferred objects. The characteristic features of the method are:

the presence of a procedure for the formation of an "ideal" object ( AT + ), which serves as a kind of goal to strive for. Such an “ideal”, as a rule, is not achievable and does not really exist, but it is useful to have it for the decision maker to understand his goals;

at each iteration, objects that do not claim to be the most preferred are excluded, i.e. the "best" objects are not singled out, but the "worst" ones are excluded.

In general, the algorithm of the method is as follows ( rice 2.2 ): Dominated objects are excluded first, since among them there cannot be the most preferred one.

An “ideal” object is formed AT +(1) from the most preferred criteria values and “anti-ideal” from the least preferred values. The distances from the objects from the original set to the “anti-ideal” are determined, on the basis of which the “worst” objects are selected. Among such objects, as a rule, there are objects that have one most preferred value (objects AT 1 and AT 6 on the rice 2.2 ).

After excluding the “worst” objects, we again proceed to the stage of the “ideal” formation, and it changes (in the figure, this AT +(2) ) approaching real objects.

The procedure ends when a small number of objects remain, which are considered the most preferable.

It should be noted that when comparing real-life objects with the “ideal”, the decision maker becomes dissatisfied, caused by the inaccessibility of the formed “ideal”. This dissatisfaction is called conflict before decision.

After choosing the most preferred object, the decision maker becomes dissatisfied, caused by the fact that this particular object was chosen, and not another. This dissatisfaction is called conflict after resolution.

At the first iterations of the method, the conflict prevails over the solution. At subsequent iterations, the “ideal” approaches real objects, and the conflict before the decision decreases. However, the conflict after the decision can increase. This indicates insufficient knowledge of the decision maker of the problem being solved.

Let us consider in detail the algorithm of the method, the block diagram of which is shown in fig.2.3.

Let the original set of objects include P objects. All criteria k j (j=l,…, m) measured on a scale of intervals or ratios.

At the first stage, an “ideal” object is formed
, where – the maximum preference value of the criterion among all objects, i.e.
if the object's preference increases with increasing k j , or
if the object's preference increases as the criterion decreases. If the “ideal” belongs to a set of objects, then it will be the most preferable. But since the MCZ is usually solved on the set of efficient objects, the “ideal” object will not belong to the original set.

At the same stage, the “worst” object is formed
of the least preferred values.

At the second stage, the transition from physical units of measurement of criteria to relative units is carried out in accordance with the expression:

In relative units, all criteria will change in the interval , while the less , topics closer object according to the criterion k j to the "anti-ideal".

The first two stages are performed automatically without the participation of the decision maker. At the third stage, the decision maker, based on his judgments about the importance of the criteria, sets the weights of the criteria W j (j = 1,...,m).

In case of difficulty, the decision maker can use information approach to determine the importance of the criteria. At the next, fourth, stage, the distances of objects to the “anti-ideal” are calculated. The following expression is used as a metric:

(2.2)

Using in ( 2.2 )various R, you can get different metrics. Yes, at p= 1, we obtain an additive operator, and when
(2.2 ) goes into
.The greater the value , the further the object is from the “anti-ideal” and closer to the “ideal”.

With It should be noted that other metrics can be used as a metric for comparing an object with an “ideal” one. aggregation operators.

At the next, fifth, stage, setting different values R, the decision maker defines different metrics for comparison with the “ideal” one. At every R, i.e. for each metric, all objects are ordered in order of proximity to the “ideal” value . decision maker in dialogue, changing p,explores the influence of various metrics on the ordering of objects.

Further, at the sixth stage, the decision maker makes a decision to exclude objects that do not claim to be the most preferable. Obviously, these are the objects that, with different metrics (different R) are at the end of the ordered rows. Indeed, if, regardless of the chosen metric, the object is far from the “ideal”, then there is every reason to exclude it.

After the objects are excluded, the next iteration begins with the formation of an “ideal” object already on the remaining subset of objects.

The procedure ends when, after the next exception, a small number of objects remain, which will be the most preferable.

It should be noted that at each iteration it is advisable to analyze the spread of criteria. The fact is that among the excluded objects, as a rule, there are objects that include the maximum and minimum values of the criteria. Thus, at each iteration, the area of change of the criteria decreases and, therefore, their scatter changes significantly. Then using informational approach, we can single out non-informative criteria and, in order to simplify the task, exclude such criteria.

In conclusion, we note that this method is most efficient for large problem dimensions.

- 275.50 Kb

Ministry of Education and Science of the Russian Federation

FGOU HPE "Mordovia State University named after N.P. Ogaryov"

Faculty of Mathematics

Department of Applied Mathematics

REPORT

4th year students of the Faculty of Mathematics

(specialty "Applied Mathematics and Informatics")

Korovina A.V.

on the passage of industrial practice during the period

from 09/01/11 to 05/15/12

Expert Decision Methods

The report was compiled by Korovina A.V.

404 group, d / o

The report was accepted by Dr. Safonkin V.I.

Saransk

2012

1.	Introduction………………………………………………………………………......				3
2.	Solution of multi-criteria tasks…………………………………….......				4
	2.1.		Statement of multicriteria tasks ……………………………..........		4
	2.2.		Methods for solving multicriteria problems ……………………………		5
3.	Expert decision-making methods…………………………………......				14
	3.1.		Stages of an expert assessment of a problem situation …………..
	3.2.		Statement of the problem for group decision makers ………………………………. .....
	3.3.		Types of group approval ……………………………………………
		3.3.1.		dictator principle………………………………………………………
		3.3.2.		voting principle………………………………………………… …...
		3.3.3.		off-system selection principles………………………………………...
	3.4.		Formation of decisions in groups ………………………………… …......
	3.5.		Processing the results of expert assessments ………………………………
		3.5.1.		methods of statistical processing of expert assessments…………….
4.		Conclusion…………………………………………………… ………………...
5.		List of used literature……………………………………......

1. Introduction

In the practice of managing economic systems, there are often such problem situations for which information is partially or completely unknown or difficult to access to describe the problem situation or which cannot be formalized with sufficient accuracy. In this case, such problems are usually solved with the help of an involved group of experts who analyze and evaluate the existing problem situation and generate a certain set of alternatives for solving it. The essence of the decision-making method with the involvement of experts is to obtain expert assessments individually for each expert and formulate a generalized opinion about the best object (solution) for the entire group as a whole.

The technology for solving decision-making problems by a group of experts is similar to the technology of individual choice and contains the same generalized procedures and operations: awareness and identification of the problem, its analysis; information preparation of decisions; search and decision making; implementation of decisions, etc.

Let's consider separate procedures of group choice, which characterize the peculiarities of expert methods.

2. Solving multicriteria problems

2.1. Statement of multicriteria tasks

Decision-making tasks are called multicriteria, the number of criteria for achieving the goal for which is more than two:

K Ì (K 1 , K 2 , ..., K m ),

and the tasks themselves are characterized by several alternatives:

Y = (A l , A 2 , ..., A n )

Table 1.1.

Description matrix of a multicriteria task

Objects (alternatives)	Criteria
Objects (alternatives)	K1	K2	…	Km
A 1			…
A 2			…
…	…	…	…	…
A n			…

Such tasks are usually described by the matrix given in Table. 1.1.

Mathematical interpretation of the multiobjective problem is that the objects are displayed as a point in the criteria space (K 1 ,K 2 ,...,K m ). Problems for which the criteria values change discretely are called discrete decision-making problems. An example of displaying a discrete problem for three objects in a two-dimensional space of criteria (k 1 , k 2 ) is shown in fig. 1.1.

Rice. 1.1.

Graphical interpretation of a multicriteria problem

(3 objects, 2 criteria)

If the values of the criteria change continuously, then the problem belongs to the problem of vector optimization. In this case, the graphical interpretation of such a problem is presented as a certain area in the space of criteria.

Depending on the required solution, multicriteria problems can be divided into the following classes:

selection tasks (selection of the most preferred object);
evaluation tasks (assessment of an object according to an integral criterion);
problems of determining Pareto-optimal solutions.

To solve problems belonging to different classes, appropriate solution methods are required. Let us consider a number of practical methods for solving multicriteria problems.

1.2. Methods for solving multicriteria problems

In accordance with approaches to solving multicriteria problems, there are three main groups of methods: lexicographic, interactive, axiomatic.

Solution methods related to first group, are based on the assumption of the dominance of the criteria. The problem is solved in several cycles, on each of which two stages are performed: criteria ranking; object selection by yourself important criterion.

Co. second group mainly include methods and algorithms for choosing the most preferred object (solution), which are mainly interactive procedures that depend on the specifics of the problem being solved.

Methods third group(axiomatic) use provisions developed in utility theory. Here it is necessary to define and set the properties of the implicit preference function, i.e., to set the preference structure that the decision maker operates when choosing and evaluating an object. Based on the identified properties, some analytical function (utility function) is selected that describes the structure of the decision maker's preferences. At the same time, the decision maker should be well versed in the content of the task. This method is the most time-consuming in comparison with the previous ones, but it allows to obtain more reasonable estimates of objects.

Let's take a closer look at some of these methods.

Lexicographic methods. When solving problems by this method, the criteria (k 1 , k 2 , ..., k m ) are ranked according to the degree of importance so that index 1 (rank) is assigned to the most important criterion. Further, the procedure for selecting objects is carried out according to this criterion. The remaining criteria (k 2 , k 3 , ..., k m ) are subject to the type constraints known from the structure of the problem: a 2 ≤ k 2 ≤ b 2 ; a 3 ≤ k 3 ≤ b 3 ; …; a m ≤ k m ≤ b m

If any criterion does not meet the specified restrictions, it is excluded from consideration. Consequently, a set of valid objects (alternatives) is formed, for example: when choosing a refrigerator, you can set the following criteria as criteria:

k 1 - total volume (m 3);

k 2 - volume freezer(m 3);

k 3 - power (kW);

k 4 - price (rubles), etc.

If according to the criterion k 1 , it is not possible to uniquely select an object a iÎ And, then a choice is made according to the next most important criterion - k 2, etc.

Condition dominance meaningfully means the following: if you order objects according to the k 1 criterion, then this order will not change when taking into account the criteria k 2 , k 3 , etc., i.e. k 1 is so important that it dominates in importance among all the others.

In the group of interactive methods, the most common principles of choice are preferred object(method of “shifted ideal”). This method includes a large group of algorithms that implement the solution of such problems. The common features that unite this method include the presence of an “ideal object” and the presence of screening procedures.

When forming an “ideal object”, it is quite possible that its image may not belong to the real set of objects (A l , A 2 , ..., A n ) or even not exist at all. In this case, objects from the set (A l ,A 2 ,...,A n ) are compared with the model of the formed ideal object, and a screening procedure occurs. When building a model of an “ideal object”, it is important to use the knowledge and experience of a user specialist (DM), since he more accurately understands the properties and parameters taken from the best real objects and constituting the content of an “ideal object”.

The sifting procedure is characterized by the exclusion from the initial set of objects (A l , A 2 , ..., A n ) of subsets that do not contain the desired most preferred object.

In general, the procedure for finding the most preferred object consists of a number of stages.

Formation of the “ideal object”.
Analysis of a set of objects to establish a correspondence
"ideal object".
Interactive exclusion of those objects from the initial set (A l ,A 2 ,...,A n ), which are recognized as obviously not the best in the analysis.
Go to step 1 for a reduced set of objects.

Consider an example of solving a decision-making problem using the shifted ideal method.

Example 1

Description of the problem situation S 0

Description of the problem.

Determine the most promising CNC machine to launch in a series.

Time for PR: T = 1 week.
Resources for PR: information about the characteristics of machines.
Criteria (K):

K 1 - average operation time (s);

K 2 - reliability of time between failures (thousand hours);

K 3 - the cost of the machine (thousand rubles).

Lots of restrictions (B).

The upper and lower limit limits for the change of criterion values are known.

Lots of alternative options.

Table 1.2

Variant Matrix

Description of work

2.1.
Statement of multicriteria tasks……………………………..........
4

2.2.
Methods for solving multicriteria problems……………………………
5
3.
Expert Methods decision making…………………………………......
14

3.1.
Stages of an expert assessment of a problem situation…………..

3.2.
Statement of the problem for group decision makers………………………………......

3.3.
Types of group approval……………………………………………

3.3.1.
principle of the dictator…………………………………………………………

3.3.3.
off-system principles of choice………………………………………...

3.4.
Formation of decisions in groups……………………………………......

3.5.
Processing the results of expert assessments………………………………

3.5.1.
methods of statistical processing of expert assessments…………….

4.
Conclusion……………………………………………………………………...

5.
List of used literature……………………………………......

Send your good work in the knowledge base is simple. Use the form below

Students, graduate students, young scientists who use the knowledge base in their studies and work will be very grateful to you.

Hosted at http://www.allbest.ru/

Application of methods of multicriteria analysis of business processes

Introduction

multicriteria decision business

At the core modern theory business process optimization lies the choice best alternative organizing business processes by conducting a qualitative or quantitative analysis of alternatives. Such an analysis is often multi-criteria, since several criteria must be evaluated simultaneously, which may be contradictory, such as cost, quality, costs, risk, efficiency, etc. In everyday life, such a choice based on several criteria is usually made intuitively, and its consequences may be quite acceptable to the decision maker (DM). However, when setting business tasks, intuition cannot be the only decision-making tool, since such tasks are much larger, and in a highly competitive environment, organizations need to obtain the most objective assessment of alternatives. Obtaining such an assessment requires a thorough study of all selection criteria, determining the dependencies between them and setting priorities.

Relevance This study is due to the fact that in the analysis of business processes, problems very often take a multi-criteria form. For example, when choosing a supplier, the analysis of the procurement business process requires the evaluation of parameters such as product quality, cost, after-sales service, financial stability, etc. Analysis of the investment management business process includes an assessment of risk, expected return, investment volume, and the attractiveness of the region where investment activities are carried out. The analysis of the recruitment business process that takes place in most organizations involves an assessment of parameters such as the candidate's experience, education, age, requested salary, etc. Furthermore, modern tendencies development of management theory are to consider various aspects of the enterprise, both financial and non-financial. Defining and examining a range of indicators from multiple perspectives often leads to problems that take on a multi-criteria form. For example, such a popular management tool as a balanced scorecard, developed by R. Kaplan and D. Norton, implies equal consideration by companies of at least four perspectives: finance, customers, internal business processes, training and development. In each of these perspectives, the authors recommend identifying at least five key performance indicators (KPIs). This approach makes it possible to form effective strategy companies, however, when monitoring the implementation of this strategy, as the authors themselves emphasize, it can often be difficult to evaluate numerous indicators. One of the practical examples given in the book shows how to analyze the effectiveness of a project in a company, 16 key indicators of this project were identified, which were evaluated by the company's clients. However, obtaining a conclusion about the success of the project according to these estimates became a multi-criteria task for the company's management, for the solution of which methods based on ranking and linear convolution of criteria were applied. R. Kaplan and D. Norton also gave an example of a task that the company's management could not cope with due to its multicriteria. The task was to optimize the delivery business process, and in order to increase the value of the “delivery on time” indicator, the company significantly increased the delivery time interval, as a result of which the client was dissatisfied, and the business process underwent “false optimization”. This error could have been avoided by applying multiobjective optimization methods.

Today, decision-making theory contains many approaches and methods for making decisions in a multi-criteria environment that a decision maker can use to solve various multi-criteria problems. At the same time, however, the problem of choosing the method most suitable for solving a particular problem remains extremely relevant. Due to the fact that the methods of multicriteria optimization have a number of differences both in the results obtained (the number of solutions found, the presentation of solutions, etc.) and in their application (the amount of necessary information about the preferences of the decision maker, methods of collecting information, etc.) , not all methods can be applied to solve a specific problem. In general, tasks can be combined into groups according to their belonging to a specific subject area. Due to the incorrect choice of the solution method, four serious problems can arise: firstly, the results of applying an inappropriate method will be unsatisfactory for the decision maker or even incorrect. Second, because of the poor results obtained, useful methods can be unfairly condemned, such as the ELECTRE method in Cohon and Marks (1977). Thirdly, the use of an inappropriate method entails a loss of time, effort and money spent during the decision-making process. Finally, as a result of errors in application, potential users may refuse to apply any MMRM to practical problems at all.

aim of this study is the development of a classification of methods for multi-criteria decision-making on the object of application in the framework of the analysis of business processes.

To achieve this goal, it is necessary to solve the following tasks:

1. Conduct an analysis of sources that reflect different approaches to decision-making in a multi-criteria environment in order to study the existing methods of multi-criteria analysis.

2. Conduct an analysis of software aimed at solving multicriteria problems.

3. Conduct an analysis of sources that reflect examples of the practical application of methods of multi-criteria analysis of business processes.

4. Identify methods of multi-criteria analysis applicable to the area of business processes.

5. Develop a classification of methods according to the object of application in the field of business processes.

7. Solve a practical multi-criteria problem that arises in the business process "Determination of the sales strategy" of the company "VARS Expo" LLC.

object of this study are business processes that require decision-making in a multi-criteria environment.

Subject research is the application of methods of multi-criteria analysis to optimize business processes that require decision-making in a multi-criteria environment.

Methodological basis of this work were scientific publications of leading domestic and foreign scientists, as well as articles reflecting current standards in the field of application of multicriteria methods for analyzing business processes. To solve the tasks set, the methods of the theory of decision making in the condition of multicriteria were used.

Theoretical significance research is to develop a classification of methods for multi-criteria analysis of business processes by the object of application.

Practical significance research consists in the possibility of using the developed classification in the analysis of business processes in order to select the method most suitable for solving a specific problem of multicriteria optimization.

Structurework includes the following sections: introduction, literature review and software analysis, main part, conclusion, bibliography. The main part of the study consists of three chapters, two of which reflect the theoretical part of the study, and one - practical. The first chapter is devoted to the choice of methods of multicriteria analysis for consideration and their description. The second chapter compares the methods of multicriteria analysis with the characteristics of the problem, the decision maker and the solution obtained. On the basis of the obtained comparison, a classification of methods by the object of application was developed as part of the analysis of business processes based on a reference 13-process model and recommendations were given for the application of methods. The third chapter reflects an example of the practical application of methods to solving a multicriteria problem that arises in the business process "Determining the sales strategy" of the company VARS Expo LLC. In conclusion, the results obtained in the course of the study are summarized.

1. Software analysis

The complexity of solving multicriteria tasks is determined, among other things, by a large amount of information that must be taken into account and processed when making a decision. A person is often not able to cope with this task without resorting to the help of modern computer technology. In this regard, to support decision-making in a multi-criteria environment, many software products or decision support systems (DSS) have been created, the operation of which is based on MCDA (multiple-criteria decision analysis) methods. The main functions performed by these software products are the ranking of decisions by preference and selection best solution. However, in addition to finding a solution and processing a large amount of information (which is necessary for the successful use of multi-criteria analysis methods in practice), such software also usually provides the user with the opportunity to analyze the results obtained. Of particular value is the graphical user interface, which provides the ability to visualize both the process and the results, to make the decision-making process the most obvious and transparent.

Due to the fact that this work is aimed at studying and classifying multi-criteria analysis methods that are well applicable in practice, analysis and comparison of existing software developed for decision support seems necessary and important. It is reasonable to start the analysis with the definition of criteria for comparison and evaluation.

Different software products may provide the user with different options both during the decision-making process itself and during the analysis of the results. Of course, the organization of the decision-making process is characterized, first of all, by multicriteria analysis methods supported by the product. It is on the supported methods that the procedure for finding solutions depends, and hence the applicability of the product to various situations. In addition, since this work is aimed at applying multi-criteria methods directly to business processes, it is extremely important to level of professionalcompetencies(special knowledge and skills) necessary for the successful use of the product. Many programs are designed for use by professionals in the field of multi-criteria analysis, and without experience and knowledge in this area, the user will not be able to effectively use such products. However, one of the main goals of the classification of methods developed in this paper is to help non-specialists in the field of multi-criteria analysis (for example, decision-makers) in the choice of appropriate methods. Therefore, product comparisons will also be made on the basis of the required specialist knowledge and skills. The third criterion for comparison is group decision support. Usually, decision maker in multi-criteria analysis is understood as an individual, but in business decisions rarely depend on one person. Most often, a certain group is responsible for decisions (board of directors, joint-stock company, problem commission, etc.), the preferences of each member of which must be taken into account when making a decision. The next criterion reflecting the practicality of using the product is accessibility via the Internet. And finally, an important factor for a user who does not have serious experience with such programs is the ability to import and / orexport data or results in Excel. Separately, it is worth considering the process of analyzing the results obtained, namely text and graphic methods of information visualization supported products.

Today there is a huge variety of programs and software systems for multicriteria analysis. The purpose of the software review in this work is to identify similarities and differences between available products in order to develop recommendations for their use. Therefore, it seems reasonable to pay attention to software products that have different purposes and support different methods, while being actively used or known both among experts in multi-criteria analysis and among specialists in other areas responsible for making decisions (which, of course, is an indicator of the practical product performance). Twelve such products were selected for analysis by comparing software reviews and comparative articles in international scientific publications (French and Xu, 2005; McGinley. P, 2014; Vassilev et al., 2005; Weistroffer et al., 2005), and also taking into account the ratings and reviews published on web pages dedicated to multi-criteria analysis software (Capterra, EWG-MCDA, Wikipedia). The selection was also based on the availability of a trial or demo version of the product. The results of the comparative analysis are reflected in tables containing parameters grouped by two main functions of the software: organization of the decision-making process itself (see Table 1) and analysis of the results (see Table 2).

Table 1. Comparison of software by characteristics of the decision-making process

Software name	Supported MCDA Methods	Required professional competence	Support for group decisions	Accessibility via the Internet	Ability to import / export to Excel
	PAPRIKA, AHP, MAUT

	AHP, Pareto Frontier Approximation
Criterium Decision Plus	AHP, SMART, MAUT, Swing
	PROMETHEE, UTILITY
	MAUT, Decision tree, AHP, Sequence method. concessions
	decision tree


Logical Decisions	AHP, MAUT, Swing

As can be seen from the tables, almost all the considered products provide excellent opportunities for analyzing the results, but have significant differences in the organization of the decision-making process. Programs support a different set of methods, but more than half of them have AHP or AHP (Analytic hierarchy process / Hierarchy analysis method) among the supported methods, which is quite expected, since the method is well applicable in practice in various industries and, moreover, does not require special training. It compares favorably with other methods in that it combines the mathematical approach and psychological aspects, and also allows you to compare dissimilar parameters, which is an extremely significant advantage when practical application. In products that support this method, there are two approaches to pairwise comparison of alternatives. Within the framework of the first approach, a matrix of assessments of some criteria relative to others is compiled, and within the framework of the second, all possible combinations of criteria are listed, and for each of them, the decision maker must evaluate how much one criterion is superior in importance to the other. As a result of the obtained estimates, the criteria are ranked by importance.

In addition, you can see that most programs that support AHP also support MAUT (Multi Attribute Utility Theory / Multicriteria Utility Theory). At the same time, in methodological studies, such methods are usually clearly separated. This fact suggests that, despite the fact that such software is based on the theory of decision making in a multicriteria environment, the product can go against the theory, combining a wide variety of methods from different schools for successful application in practice. This can also be confirmed by the simultaneous support of the MAUT and Swing methods by four products.

Slightly less popular is the method of successive concessions, which implies the use of certain intervals that reflect the permissible deviation of the parameter values from the priority ones. Most likely, this is due to the difficulty of objectively determining such intervals in practice. Also, some of the programs considered are based on a decision tree, which is characterized by a specific construction algorithm that is easy to understand, but does not always ensure the optimality of the entire tree. Finally, the Pareto frontier approximation method is also found in the programs discussed and is very effective in providing visualization, for example, on a bubble chart, as embodied in the Clafer Multi-Objective Optimizer.

When analyzing the remaining comparison parameters, it should be noted that most software products are intended for use by specialists in the field of multicriteria analysis, since the level of necessary professional competence to work with them is very high. However, products such as 1000Minds, Clafer MOO, D-Sight, Decision Lens and MakeItRational can be used for decision making even in the absence of special knowledge. It should be borne in mind that group decisions are supported only in three of the considered products - 1000Minds, D -Sight and MakeItRational. The first one provides only online voting, the second one assigns a weight to the opinion of each member of the group, and the last one calculates the average value for the group by taking into account all individual opinions. Most products are web-based (except Criterium DecisionPlus, Hiview3, Logical Decisions and M-MACBETH) and just under half provide the ability to import and export data and results to Excel.

Table 2. Comparison of software by results analysis characteristics

Software name	Visual Graphs	Total values	Sensitivity analysis	2D maps	Written report


Clafer Multi-Object. Optimizer
Criterium Decision Plus





Logical Decisions

Table 5 reflects the fact that all the considered software products provide the possibility of graphical visualization of the results. Approaches present in at least a few products include visualization of alternatives through spider-cys, tornado, thermometer, pie and bubble charts. In software products based on the concession method, the results are presented as acceptable ranges of values and may contain dominance relationships and a graphical representation of the area of optimal solutions. Most programs support the traditional method of sensitivity analysis, some of them also use statistical approaches for analysis, which consists in making various changes to the parametric model and observing the subsequent change in the results. This allows you to get a probabilistic ordering of alternatives or the percentage of cases where one alternative dominates over another. In the concession method, the use of intervals in itself can already be considered a type of sensitivity analysis. Some kind of two-dimensional maps is present in most software products. Criteria correspond to axes, alternatives correspond to points with corresponding coordinates on the graph. Some programs provide the ability to generate a written report reflecting the main results and explaining them to the user.

2 . Multi-criteria decision-making methods

2.1 Choice of methods to consider

The scientific discipline of decision-making under multi-criteria conditions is relatively young: the first works within this discipline appeared in the 1970s, and references to the application of MMRM to solving practical problems were made in the 1980s (Wallenius et al., ). Despite this, on this moment more than seventy different methods have already been developed for solving multicriteria problems (Aregai Tecle, ). A detailed consideration of all existing methods does not seem necessary and possible within the framework of this work, so the set of considered methods is limited. The criteria used to select methods include:

1. The popularity of the method(measured based on how often the method was mentioned in scientific literature between 1970 and 2016)

2. Applicability of the method to practical problems(measured based on the analysis of the literature on the application of MMRM to tasks in various business areas)

3. Originality of the method(methods based on techniques found in other more popular methods are not considered)

1. Hierarchy analysis method (AHP)

2. Nonlinear programming (NLP)

3. Compromise Programming (CP)

4. Cooperative Game Theory (CGT)

5. Displaced ideal method (DISID)

6. ELECTRE method (ELEC)

7. Sensitivity Assessment and Analysis Method (ESAP)

8. Target programming (CPU/GP)

9. Multicriteria utility theory (MAUT)

10. Multi-criteria Q-Analysis (MCQA)

11. Probabilistic method of compromise development (PROTR)

12. Zayonz-Wallenius method (Z-W)

13. STEM method

14. SWT method

15. PROMETHEE method (PRM)

The popularity and applicability of these methods to various problems in a wide range of areas is clearly presented in the table (see Appendix 1), where each method is compared with scientific publications that describe its application, and specific tasks, which were set in these works.

2.2 Brief description of methods

Hierarchy Analysis Method (AHP)

The hierarchy analysis method is a mathematical decision-making tool that takes into account psychological aspects. The method was developed by T. Saati. It allows you to streamline the available alternatives that need to be evaluated according to a variety of quantitative and qualitative criteria. Ordering occurs based on information about the preferences of the decision maker, which is expressed numerically and allows you to get the values of the total value of alternatives for all parameters. The alternative with the highest total value is the best. The method is widely used in practice. To use it, follow these steps:

1) Decompose the problem by compiling its hierarchical model, which should include the alternatives themselves, the parameters for their evaluation and the ultimate goal of finding a solution

2) Compare in pairs all the elements of the hierarchy, determining their priority based on the preferences of the decision maker

3) Synthesize the value of alternatives using linear convolution

4) Assess the consistency of judgments

5) Make a decision based on the results

MAI advantages:

Simplicity of pairwise comparisons, familiarity of the procedure for decision makers

Lack of direct evaluation of alternatives

Support for both quantitative and qualitative parameters

Checking the Consistency of Judgments

Wide applicability in practice

Disadvantages of MAI:

A limited number of alternatives and parameters for their evaluation (working with large number m difficult for the decision maker)

The possibility of distortion of preferences due to the same type of numerical representation

Unreasonable choice of additive or multiplicative criteria convolution

2.3 Nonlinear Programming (NLP)

Nonlinear programming is a special case of mathematical programming and implies a non-linear form of the objective function or constraint. The problem solved by this method can be formulated as a problem of finding the optimal value of a certain objective function under the conditions, where are parameters, are constraints, n is the number of parameters, s is the number of constraints.

The objective function can be concave or convex. In the first case, the decision maker will face the problem of maximization, in the second - the problem of minimization. If the constraint is given by a convex function, then the problem is considered convex and, most often, is solved using general methods of convex optimization. If the problem is non-convex, then special formulations of linear programming problems or branch and bound methods are used, which allow solving the problem by linear or convex approximations. Such approximations form a lower bound on the total value within a section. In the course of the following sections, one day a real solution will be found whose value is similar to the best lower bound found for any of the approximate solutions. Such a solution will be optimal, but not necessarily the only one. It is possible to stop such an algorithm at any time with confidence that the optimal solution is located within the acceptable deviation from the found best solution; such solutions are called e-optimal.

In non-linear programming, independent sections can be distinguished, such as convex, quadratic, integer, stochastic, dynamic programming, etc.

2.4 Compromise Programming (CP)

The idea of the compromise programming method is similar to that of the goal programming method. The technique of the method is based on determining the distance from the "ideal" point. To find the best solution, it is necessary to minimize the "distance" from the ideal solution. The point (solution) that is closest to the ideal point in all respects is a compromise solution. A set of solutions can also be a compromise.

The procedure for finding the best solution includes the following steps:

1) Determine the parameters for evaluating alternatives and the weights of these parameters.

2) Compile an alternatives evaluation matrix by recording information about the alternatives for each of the evaluation parameters.

3) Determine the direction of optimization for each of the criteria (maximizing or minimizing values is preferable).

4) Normalize the matrix in such a way that it takes the form of a payoff matrix (or payoff matrix).

5) Find the best and worst value of alternatives for each of the criteria.

6) Find the generalized value of each alternative for all evaluation parameters, using the weights of the criteria and the difference between the value of the alternative for each criterion and the best value for this criterion.

7) The alternative, the value of which is closest to the ideal, is the best solution.

Advantages of the compromise programming method:

Usefulness in solving problems on the solution space in which the decision maker tends to trust his intuition and experience

2.5 Theory of cooperative games (CGT)

A cooperative game is a game that involves the combined efforts of players. The theory of cooperative games explores the conflicts that arise between players when making a joint decision. Since there are usually several criteria for making such a decision and they are often contradictory, the theory is used as one of the decision-making methods in a multi-criteria environment. The theory studies what results of the association of players can be achievable and under what conditions.

The main tasks arising in the study of cooperative games:

1) Definition of a function that characterizes the preferences of the players

2) Finding the optimal solution regarding the division of the total gain of the parties

3) Checking the dynamic stability of the solution

The found solution can be unique if the division of the total gain can be done in only one way, characterized by maximum utility for both parties. If there are several such separation methods, then the optimal solution can be multivalued. The case of a single optimal solution is typical for the N-kernel and the Shapley vector, a multi-valued solution - for the C-kernel and the K-kernel.

2.6 Shifted ideal method (DISID)

This method was developed to determine the best solutions in the set of feasible solutions and is characterized by the following features:

The procedure for forming an "ideal" solution that sets the direction of optimization. Usually such a solution is unattainable, but it reflects the goals of the decision maker well.

Eliminate solutions that are least preferred at each iteration. Thus, the best solution is found by gradually eliminating the worst solutions at each step of the procedure.

When applying the method, the following steps can be distinguished:

1) Exclusion of dominated solutions.

2) Formation of the "ideal" solution and determination of the "worst" solution.

3) Determining the distance between the points of possible solutions and the point of the "worst" solution

4) Repeating the cycle of 1-3 stages until the admissible small number of the most optimal solutions remains.

At the same time, the comparison of alternatives with the formed “ideal” solution often causes dissatisfaction in the decision maker with existing alternatives, which is called a conflict before a decision. A post-decision conflict is a dissatisfaction that occurs after the exclusion of some alternatives from consideration. At the initial iterations, there is a strong conflict before the solution, which gradually decreases due to the approximation of the existing solutions to the "ideal" one, the conflict after the solution, on the contrary, increases, which indicates that the decision maker has not studied the problem sufficiently.

2.7 ELECTRE method

The selection procedure in the ELECTRE method consists of 6 steps:

1) Determining the minimum and maximum values of alternatives for each of the criteria

2) Determining the criteria weights

3) Construction of a graph for each of the criteria, in which the vertices are some objects of the solution set, and the arcs reflect the degree of dominance of one object over another

4) Compilation of a matrix of values of the so-called indices of agreement and disagreement based on the importance of criteria and the preference for decisions

5) Establishing a superiority value for each pair of objects if the value of the agreement index of one of the solutions exceeds a certain threshold value, and the disagreement index value does not reach this value

6) Construction of a general graph of superiority, taking into account the established restrictions

2.8 Sensitivity Assessment and Analysis Method (ESAP)

The sensitivity assessment and analysis method was originally developed as a planning technique in the field of environment to evaluate management alternatives water resources. ESAP is based on the determination of criteria weights to obtain a correct assessment of alternatives. An assessment of the availability and attractiveness of an alternative is determined by combining information about the impact on natural and cultural resources and information about the importance (determined by criteria weights) and preferred values of these resources. Information should be collected by interviewing several individuals or a group of individuals to determine the sensitivity of their estimates to differences in judgments about the importance and preferred values of resources, as well as to uncertainty in the consequences of choosing one or another alternative. Now this method is used not only in environmental planning, but also in other areas.

2.9 Target Programming (CPU/GP)

The target programming method is used to solve MCO problems and is based on the ranking of criteria according to their importance for decision makers. The main task of finding solutions includes several successive subtasks for optimizing each of the criteria. At the same time, such optimization is carried out according to the objective function, and the improvement of the value by one criterion cannot be achieved at the expense of the deterioration of the value by a more important criterion. Thus, the final result will be the discovery of the best solution to the problem. Usually the method of target programming is applied to the solution of linear problems. At the same time, its difference from the linear programming method lies in the formalization of many goals not as objective functions, but as constraints. Therefore, when using the method, the desired values of the objective functions and those variable deviations from these values that reflect the degree of achievement of the main goal of the search for a solution should be determined.

2.10 Multicriteria Utility Theory (MAUT)

Multicriteria utility theory is one of the most popular axiomatically justified methods. This theory was developed by R. Keaney, G. Rife, P. Fishburne. The theory is based on axioms that describe the preferences of decision makers and are presented graphically as a utility function. The most widely applicable axiomatic of utility in a multiobjective environment includes the axioms:

Complete comparability

transitivity

Solubility

Independence by preference

Independence by utility

Archimedes

Despite the obvious laboriousness of the method, it is important to note that it can be justified by the mathematical justification of the solutions found. In addition, the method is applicable when evaluating any number of alternatives, and the dialogue procedures with decision makers in the multicriteria utility theory are very well developed.

The main steps of the method include:

1) Development of a list of criteria

2) Building a utility function for each of the criteria

3) Checking the conditions that determine the form common function utility

4) Building a relationship between the assessments of options for each of the criteria and the overall attractiveness of the option for decision makers

5) Evaluation of all available options and selection of the best option

2.11 Multicriteria Q- BUTanalysis (MCQA)

This method of multi-criteria analysis is used to form an effective dialogue procedure between the conflicting parties. MCQA-I, MCQA-II and MCQA-III make it possible to rank the criteria for evaluating alternatives in terms of importance, and the alternatives themselves in terms of attractiveness for decision makers. Q-analysis was developed by Ronald Atkin (1974, 1977) as an approach to the study of the structural characteristics of social systems in which two sets of indicators, features or characteristics are related to each other. Subsequently, Q analysis has been applied in various fields such as chess theory (Atkin and Witten, 1975), flexible manufacturing systems (Robinson and Duckstein, 1986), competitive sports (Gould and Gatrell, 1980), and urban planning (Beaumont, 1984). Q analysis is a recognized useful tool in ecological studies, for example in the assessment of riverine ecosystems (Casti et al., 1979) and in the study of predator-prey relationships (Casti, 1979). Q analysis has also been used in clinical psychology (Macgill and Springer, 1984), geology (Griffiths, 1983), transportation systems research (Johnson, 1976), water distribution (Duckstein, 1983), and a number of other contexts (Casti, 1979) . Q analysis has proven to be especially useful in solving problems associated with complex systems, for example, modeling medical images. This approach requires a rigorous definition of datasets and their relationships, and calls for exploration of the implications of their interconnection within a system. After establishing approximately exact sets of data and examining their relationships, Q analysis involves fairly simple calculations that do not need additional information about the system. The Q analysis method provides an algebraic topographic infrastructure for data reduction, helping to simplify macroscopic system design concepts. To this end, it is possible to define and interpret indicators such as the degree of connectivity, decentralization and complexity. The Q analysis approach also provides ordering of information. Q analysis can also be associated with the analysis of the behavioral dynamics generated from the structural matrix (called the backcloth); this type of study (called traffic) draws on the discipline commonly referred to as polyhedral dynamics (Casti et al., 1979; Johnson, 1981).

2.12 Probabilistic method of compromise development (PROTR)

This method of multicriteria optimization is mainly used to solve nonlinear problems based on the preferences of the decision maker. The method involves the construction of individual utility functions to find the best solution to the problem.

The solution search procedure consists of 12 consecutive stages:

1) Development of a vector of objective functions

2) Development of vectors of the best and worst criteria values

3) Formulation of the substitution function

4) Obtaining a starting solution by maximizing this function and developing a goal vector based on it

5) Definition of a multicriteria utility function

6) Formulation of a new substitution function

7) Generation of an alternative solution by maximizing a new substitution function and development of a goal vector based on it

8) Development of a vector linking the target values of the vectors with the probability of their achievement

9) Making a decision by the decision maker on whether all the values of the criteria are satisfactory. If yes, then the resulting vector is a solution to the problem, if not, then step 10 is performed

10) Selection of the vector in which the relationship of the target value with the probability of its achievement is the most unsatisfactory, and the definition of a new probability

11) Creation of a new set of valid values

12) Formulation of a new substitution function and repetition of the cycle from the 6th to the 12th stage required amount once.

2.13 Zajonc-Wallenius method (Z-W)

The Zajonc-Wallenius method is based on the procedure for narrowing the set of values of the weight vectors.

The steps of this procedure can be described as follows:

1) Development of weight vectors

2) Calculation of the value of the global criterion (as a rule, the value corresponds to one of the vertices of the polygon that forms the set of valid values)

3) Calculation of the values of weights of criteria in adjacent vertices, under which this vertex can be the optimal solution

4) Calculation of the value of the vector of estimates in these vertices for each of the criteria

5) Pairwise comparison of vectors of decision maker criteria

6) Formation of restrictions on the values of criteria weights based on the judgments of the decision maker

7) Determining the center point in the range of acceptable weights

8) Repeat cycle 2-8

When comparing, the decision maker can express the following judgments:

An adjacent criteria vector is more preferred;

The initial criteria vector is more preferable;

There is no clear preference.

Thus, the search is systematic, which makes the results the most objective.

2.14 STEM Method

The STEM method is an iterative solution search procedure in which the best solution is reached after several iterations. Each cycle includes a computational stage and a decision-making stage, that is, it involves the interaction between the analyst and the decision maker.

The method is based on minimizing the Chebyshev distance from an ideal point on the solution space. The parameters that specify the distance formula and the measurable space can be changed using the method of normalizing weight coefficients based on the preferences of the decision maker expressed at the previous stage of the search for solutions. The search procedure allows the decision maker to select good decisions and determine the relative importance of the criteria. At each iteration, the decision maker can improve the values of alternatives according to some criteria, yielding to others. At the same time, the decision maker must indicate the maximum acceptable amount of the concession for each criterion. To carry out the next iteration, having received a decision, the decision maker must express his preferences regarding those criteria for which he would like to improve the value, and those for which the value is already satisfactory for him.

2.15 SWT Method

The SWT method is a multi-criteria optimization method that allows finding all the necessary Pareto-optimal solutions according to the problem optimization vector. When using the method, it must be taken into account that in modeling, defining, evaluating, comparing often conflicting criteria, the role of a system analyst should not be confused with the role of a decision maker. While the analyst is responsible for generating Pareto-optimal solutions and the corresponding values of the alternatives, he is not at liberty to determine acceptable and preferred concessions according to various conflicting criteria. The decision maker is responsible for expressing preference judgments based on the computational analysis performed by the analyst. Moreover, when any set of criteria values has already been obtained, it is much easier to obtain from the decision maker an estimate of the relative value of the concession (increase or decrease in value) between two criteria than an estimate of their absolute average values.

2.16 PROMETHEE method (PRM)

PROMETHEE is a well-designed decision support system that allows you to evaluate and select an alternative from a set based on criteria that reflect the pros and cons of alternatives, and also allows you to rank these alternatives according to their attractiveness for decision makers.

PROMETHEE does not require strict judgments about the actual structure of decision makers' preferences. When evaluating alternatives, the key task is to obtain information about whether some alternative is at least as attractive as another. Based on the so-called preference relations, which are determined in the first step, the ranking of alternatives is carried out.

Consider the main steps:

1) Defining a preference function

The starting point is the formation of a rating matrix that reflects the attractiveness of alternatives for each of the criteria. Based on the information contained in the scoring matrix, the alternatives are compared in pairs with respect to each of the criteria. The results are expressed by preference functions that are calculated for each pair of options and can range from 0 to 1. While 0 indicates no difference between the options, 1 means a large difference.

2) Evaluation of the degree of preference for options

The total value matrix is compiled on the basis of the values obtained by multiplying the values of the alternatives for each criterion by the weight of the corresponding criterion. In this matrix, the sum of all values in a row reflects the degree of dominance (attractiveness) of the alternative. The sum of all values in a column indicates how much the alternative is suppressed by others. A linear ranking can be obtained by subtracting the subdominant value from the dominant one.

The decision maker is required to set the criteria weights and choose a preference function. PROMETHEE does not imply a special way to determine these weights, but assumes that the decision maker is able to set the weights correctly, at least when the number of criteria is not too large. The definition of weighting factors is always subjective. Therefore, sensitivity analysis, which reflects how much the chosen weights affect the result, becomes an important part of the decision-making process.

Various tools and modules have been developed within the PROMETHEE method. The following 3 tools can be especially useful for analyzing an assessment problem:

PROMETHEE I for partial evaluation of alternatives,

PROMETHEE II for full ranking,

GAIA for visualizing solutions.

3. Development of a classification of methods

The problem of choosing the most appropriate multi-criteria method to apply to a particular situation is itself a multi-criteria problem, since there are several selection criteria and they are inherently contradictory (AI-Shemmeri et al., ). Therefore, the listed methods should be evaluated according to the relevant criteria in order to be able to compare them. To determine these criteria, it is necessary to consider the aspects that cause differences in the application of methods. It is customary to single out the following aspects or groups of criteria (Mollaghasemi and Pet-Edwards, ):

1) Task characteristics

2) Characteristics of the decision maker

3) Characteristics of the resulting solution

The most suitable method for application in a particular situation is the one whose technique best matches the characteristics of the problem being solved and the decision maker, and the results obtained can be correctly interpreted and useful to the decision maker.

So, the fifteen methods accepted for consideration should be evaluated according to some criteria describing the three selected aspects. Each aspect (group of criteria) in this work is devoted to the corresponding section, which provides a description of the criteria and a table of comparison of methods according to these criteria. The evaluation of methods is based on the comparison of MMRM in the works of Aregai Tecle and Ozernoy V.M. , as well as a review of the application of methods for solving practical problems in the works of Bardossy , Khalili , Brans and others.

3.1 Assessment of the conformity of methods to the characteristics of the problem being solved

First of all, it is necessary to determine the correspondence of the applied method to the characteristics of the problem under consideration. Multicriteria tasks can be described by several pairs of mutually exclusive characteristics. For example, if the problem is a mathematical programming problem, then the solution can be obtained by systematically searching for possible alternatives in the admissible set of decisions, while decision analysis problems usually assume the existence of a finite and relatively small number of alternatives, the evaluation of which leads to an efficient solution. Another pair of mutually exclusive characteristics, reflecting the availability of quantitative and qualitative information necessary for solving the MCO problem, can also be of great importance when choosing the appropriate MMRM. If the problem includes qualitative criteria, then mathematical programming techniques cannot be used to solve it. The dynamic nature of the task also greatly limits the set of applicable methods, since there are only a few MMRMs that support this type of task (Szidarovszky and Duckstein, , ). The scale of the problem, measured by the number of criteria and alternatives, imposes strict conceptual and computational restrictions on the set of available methods. And finally, the structural relationships between the parameters of the problem, describing its linearity or non-linearity, should also be taken into account when comparing methods, since many MMRMs are designed exclusively for solving linear programming problems.

Thus, the assessment of the applicability of the MMRM in accordance with the characteristics of the problem being solved should be carried out by answering positively or negatively to six questions about the following possibilities of the MMRM:

1) Solving problems containing qualitative criteria

2) Choice among a finite number of alternatives

3) Solving non-linear problems

4) Solving large-scale problems (with a large number of criteria and alternatives)

5) Solving problems with an infinite number of alternatives

6) Solution of dynamic problems

In the table of comparison of MMRM by applicability in accordance with the characteristics of the problem being solved (see Table 3), positive and negative answers to the above questions are presented in binary form, that is, by the numbers 1 and 0, respectively. For clarity, cells with a positive answer are highlighted in color. The evaluation is based on the experience of applying MMRM by authors of many scientific papers and experts in the field of MCO, such as Aregai Tecle , Gershon and Duckstein , Brans , Brink et al. (1986), Khalili et al.

Table 3. Correspondence table of methods to the characteristics of the problem

Qualitative Information Processing	Nonlinear problem	big challenge	Dynamic task	An infinite number of alternatives	Finite number of alternatives

3.2 Assessment of the conformity of methods to the characteristics of decision makers

Of course, the compliance of the applied method with the capabilities of the decision maker is also necessary for consideration. The degree of involvement of the decision maker in the interactive decision-making process and the amount of time in which the decision maker can be available for interaction are extremely important characteristics that can severely limit the set of suitable MMRMs. In addition, it is important to take into account the ability of the decision maker to indicate their preferences before starting the process of finding the best solution. If preferences cannot be expressed, then posterior methods, for which the necessary information about preferences must be obtained before starting to search for solutions, cannot be considered as suitable for solving this problem.

The degree of understanding of the decision maker of the principles of functioning of the MMRM can also limit their use. Methods that require special knowledge in the field of MCO may be less attractive to decision makers than intuitive methods, mainly due to the complexity of interpreting the results obtained. For example, to apply the SWO method, a serious professional training in the field of CIE, while the ELECTRE method, on the contrary, does not require practically any special knowledge, but is used only with discrete values.

Moreover, the characteristics relating directly to the analyst (specialist in the field of MCO) responsible for solving the task should also be taken into account. For example, it is necessary to determine whether the analyst has special knowledge in the use of decision support software products.

The results of the comparison of MMRM in terms of applicability in accordance with the characteristics of the decision maker are presented in Table 4 (see Table 4). Evaluation was made on a scale from 1 to 10. For clarity, the cells containing the highest values for each of the criteria are highlighted in color.

Table 4. Correspondence table of methods to characteristics of decision makers

Required level of knowledge of the decision maker in the field of MCO	The degree of interaction with decision makers	Available DM time	The required amount of information about the preferences of decision makers	Necessary level of competence of a specialist in the field of MCO





master's work, added 04/26/2011 Classification of analysis methods by groups. Collection and storage of information necessary for decision-making. Preparation of the results of operational and intellectual analysis for their effective perception by consumers and the adoption of adequate decisions on its basis. control work, added 02/15/2010 Analysis of similar developments in the field of building "selection assistance systems". The essence of the multicriteria approach. User interface development technology. Program development planning using various methods. Building a network graph. thesis, added 01/26/2013 Classification of information systems for managing the activities of an enterprise. Market analysis and characteristics of Business Intelligence class systems. Classification of decision-making methods used in DSS. Choosing a business intelligence platform, comparison criteria. thesis, added 09/27/2016 Characteristics of methods for solving systems of linear algebraic equations, the main types of numerical methods and the use of the Delphi 5.0 software product as the most effective. The essence of the methods of Gauss, Gauss-Jordan and Jacobi, features of the Seidel method. term paper, added 06/25/2010 Principles of computer steganography. Classification of methods of hiding information. The popularity of the least significant bit replacement method. Essence of palette extension and block hiding methods. Applying methods to GIF images. Implementation of algorithms. term paper, added 02/17/2013 Brief description of the control object, review and analysis of existing analogues that implement its functions. Development of the software system architecture, testing and evaluation of the effectiveness of the application. Deployment and use of the software product. term paper, added 02/05/2015 Man-machine complexes specially designed for decision making. The decision-making process and its stages. Methods for finding new solutions: decision tree, morphological tables, conferences of ideas. The principle of mathematical evaluation of trends. term paper, added 07/30/2009 An overview of the SQL Server DBMS architecture. Describe and analyze areas where business intelligence tools are used, such as multivariate data analysis and data mining. Review language tools, methods and experimental application of the obtained information. thesis, added 07/09/2014 The structure of the system of multi-criteria management of the safety of a technogenic object. Consideration of interrelations of security subsystems. Expert decision-making methods based on comparisons of multicriteria alternatives. The essence of the analytical hierarchy approach.

home > Civil Engineering