A classification of decision problems

Lecture

In his personal and production-economic activity, a person encounters the situation of decision-making. The diversity of situations, goals, and conditions within which decision-making problems arise makes it difficult to carry out a clear classification of DMPs themselves.

Nevertheless, among the multitude of parameters describing the specifics of decision-making problems, one can name those whose values determine the aggregated classes of DMPs and are taken into account in the conditions and prerequisites for applying the decision-making methods corresponding to them.

Note!

The specifics of decision-making problems are reflected in the values of a number of parameters describing these problems, and determine the classifications of DMPs and of the decision-making methods corresponding to these problems.

The features of decision-making problems are reflected in the conditions and prerequisites for applying the corresponding solution methods, so the classifications of DMPs and of their solution methods are closely related to one another.

Classification of decision-making methods is necessary for determining general and specific approaches to their development, use and evaluation, which makes it possible to improve the quality of the decisions made. The number of parameters determining the classification of decision-making methods can be very large and diverse.

However, among the parameters (attributes) most often used for classifying decision-making methods, and thereby DMPs, the following may be included .

• The domain of the decision-making problems being solved and of method application.

The classification parameter under consideration is related to the nature of the problems being solved: economic, organizational, technological, technical, environmental, etc.

• The target-oriented nature of decision-making problems. By this parameter, DMPs and their solution methods can be represented as current (operational), tactical, or strategic.
• The variant of hierarchical ordering of decision-making options. By hierarchical level, DMPs and their solution methods are distinguished at the level of the whole system, at the level of subsystems, and at the level of individual system elements. Most often, system-wide decisions are investigated and constructed, which are then brought down to the elementary level, although the reverse variant is also possible.
• The functional content of the algorithms and procedures for finding solutions. Decision-making problems and methods can be classified in relation to general management functions: problems and solution methods related to the accounting-and-planning function of management, the organizational function, forecasting, etc.
• The structure of the problem situations being analyzed. These can be decision-making problems and methods oriented toward structured, semi-structured and unstructured problem situations.
• Accounting for the quality and certainty of the initial information. Here one can distinguish large classes of decision-making problems and methods: problems and methods for decision-making under conditions of certainty — with deterministic characteristics; problems and methods for decision-making under conditions of uncertainty, including conditions of probabilistic uncertainty, conditions of risk, and conditions of complete uncertainty; problems and methods for decision-making in conflict situations, when in the process of managing economic systems situations arise in which the interests of several competing parties pursuing opposite goals collide . The assessment of the certainty (reliability) or stochasticity of information is very important, since when choosing a method for solving a problem with stochastic information it is important to identify the premises about the distribution laws of the criteria values and (or) the parameters of these laws. Note also that the initial information itself can be represented by data of a numerical, non-numerical, or mixed character . Among the solution methods using non-numerical data one can include, in particular, methods united under the name of «non-metric scaling methods», methods based on the theory of binary relations, as well as many methods using expert assessments .
• Scales of values of the selected criteria. Here we are talking not only about the fact that they can be either numerical or non-numerical, but also about the methods used for measuring these criteria for the purposes of their evaluation. This classification feature is significant especially for multi-criteria problems, since different scales of values of these criteria may be used for measuring different partial criteria.
• The number of criteria for evaluating the decision being made. By this parameter one can distinguish single-criterion and multi-criteria decision-making problems and methods. Owing to the complexity of developing solutions for both of these classes of decision-making problems and methods, depending on the degree of certainty (reliability) of the information available and used for decision-making, decision-making problems and methods are subdivided into classes of single-criterion and multi-criteria problems, determined by the complete certainty of the information used, its probabilistic uncertainty, conditions of risk, and complete uncertainty of the information used . In turn, multi-criteria methods at the level of algorithmic implementation can include a whole list of other methods, for example, the leading-criterion method, the linear convolution method, the maximin convolution method, the lexicographic optimization method, the Nelder—Mead method, the adaptive method, the Saaty method, the constraint method, and others . The multi-criteria nature of a DMP places additional obligations on the DM related to refining the decision-making method. Before making a decision on the final choice of method for solving a multi-criteria problem, the DM must carry out:
— the selection of partial criteria to be included in consideration, at least at the initial stage, for the purpose of determining the decision-making method;
— the selection of numerical or non-numerical scales of values for the chosen partial criteria, as well as of the methods used for measuring these criteria for the purposes of their evaluation;
— the evaluation of information, since when choosing a method for solving a problem with stochastic information it is important to identify the premises about the distribution laws of the values of the partial criteria and (or) the parameters of these laws;

— analysis of the structure and strength of the interrelations of the partial criteria;
— the selection of partial criteria linked by mutual compensation, when a decision that is of low effectiveness with respect to one of the partial criteria is offset by a decision that is highly effective with respect to another partial criterion.
• Method of ranking decision-making criteria. When using multi-criteria DM methods, lexicographic ranking of criteria, ranking of criteria by pairwise comparison, or ranking based on identifying non-dominated criteria (the Pareto set) may be used .
• Causal conditions for the actualization of the task and of the decision-making methods. By causes of occurrence, DM methods are divided into:
- — situational, related to the nature of the circumstances that arise; by order (directive) of higher authorities;
- — program-based, related to the inclusion of the given management object in a specific structure of program-target relations and measures;
- — initiative-based, related to the manifestation of initiative by the system, for example in the sphere of production of goods, services, intermediary activity;
- — episodic and periodic, arising from the periodicity of reproduction processes in the system (for example, the seasonality of agricultural production, timber rafting on rivers, geological work) and the like.
• Organizational structuring. Depending on the organization of decision development, the following categories of users are distinguished: single-person, collegial, collective. The choice of the decision-making task and the way of organizing the development of the decision-making method often depends on the competence of the manager, the qualification level of the team, the specifics of the tasks being solved, the resources used, etc.
• Initial methods of decision development . These include situational methods and quantitative DM methods.
— Situational methods, related to the nature of the circumstances that arise. A distinctive feature of situational DM methods is that they are applied to formalize a certain type of human activity oriented toward establishing the best course of action in the applied situation under consideration. It is assumed that the decision maker is a rational person and that their decisions are the result of an ordered thought process. In making a choice, the rational person maximizes some utility function. The most commonly used situational methods include the AHP situation-analysis method; the multi-attribute utility method MAUT; the ZAPROS method; the RIPSA methods; the ELECTRE methods, and others.
— Quantitative decision-making methods. These are based on a scientific-practical approach that involves choosing optimal decisions using tools and automated processing of large volumes of information. Depending on the type of mathematical functions underlying the models, the following are distinguished: [10]

a) linear programming — linear dependencies are used in the objective function and the constraints on the values of the sought variables;
b) nonlinear, integer, and combinatorial programming — the functional dependencies in the objective function and the constraining conditions are discrete, integer, or combinatorial in nature;
c) dynamic programming — considers, in dynamics, the process of a step-by-step multi-stage solution of the task and introduces additional variables at individual steps of this process;
d) probabilistic and statistical programming — used for decision-making in systems whose functioning process is associated with random factors, and is implemented on the basis of numerical methods and computer modeling;
e) game-theoretic programming — modeling of situations in which decision-making must take into account the divergence of interests of different parties or participants;
f) simulation programming — modeling of situations aimed at experimentally testing the implementation of various decisions, conditioned by changes in the initial premise and refinement of the requirements for them.
• Specifics of accounting for risk in decision-making'. Economic risk can have different effects on the results of the decision made. If it is observed but, according to expert assessments, will not lead to the destruction of the observed system, its influence is taken into account in the conditions and constraints introduced into one or another decision-making method. However, in the case of a significant impact of the risk on the functioning of the entire system under study, the risk is considered as an independent object of management, requiring the use of specific risk-management methods. The features that determine the classification of risk-management methods include: the content of the available information on the risk; the controlled risk parameter; the realization of the risk in time; the redistribution of responsibility for the risk; the risk-financing option; the option of joint values of risk parameters; the type of risk co-financing agreement.

Note!

The classification of decision-making tasks and the corresponding methods for solving them is based on features describing the specifics and particularities of the decision-making tasks themselves.

Any classification of tasks and DM methods helps to form standard solutions, determined by the values of a certain set of parameters used in constructing this classification.

A classification of decision problems

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Lectures and tutorial on "Decision theory"

Terms: Decision theory