Decision-making applies to objects of various kinds and under various conditions of their existence. The formal methods developed within decision theory reveal that decision-making processes across different spheres of human activity have much in common.
Formal decision-making methods may prove useful in the following cases:
- there exists a problem or a problem situation that requires resolution. Often the desired result is identified with one or several goals that must be achieved in resolving the problem situation;
- there are several options for solving the problem, ways of achieving the goal, actions, or objects among which a choice is made. In decision theory, these options are usually called alternatives. If only one possibility exists and there is no choice, then there is no decision-making problem;
- there are factors that impose certain constraints on the possible ways of solving the problem and achieving the goal. These factors are determined by the problem context and may be of different kinds: physical, technical, economic, social, personal, and others;
- there is a person or a group of persons who are interested in resolving the problem, have the authority to select one or another solution, and bear responsibility for carrying out the decision made.
The life cycle of a decision on a problem consists of several stages and represents a multi-step iterative procedure.
The need for a decision arises when a problem situation appears. In this case, the problem is identified — that is, a substantive description of the problem is given, the desired outcome of its resolution is determined, and existing constraints are assessed.
At the next stage, the decision-making problem is formulated. This requires determining the set of possible solutions (alternatives). Depending on the problem under consideration, the number of possible solutions may range from just a few to dozens, hundreds, or even thousands. Theoretically, the number of alternatives considered may be infinite.
To fully describe all possible solutions, it is usually necessary to collect and analyze various information relating to the problem and the alternative ways of solving it. The absence or inability to obtain the necessary information can render the problem unsolvable. In such cases, one must return to the original statement of the problem and modify its description. Such a need may also arise at all previous stages of the solution process. In complex choice situations, it may also be necessary to develop a specialized model of the problem (usually a mathematical one) to obtain a simplified solution.
The second stage concludes with the formulation of the decision-making problem. It should be noted that a detailed substantive description of the problem being resolved, already at the first stage, largely determines the possible approaches to its solution and may immediately lead to the formulation of the decision-making problem, bypassing all or many of the subsequent stages.
Once the decision-making problem has been formulated, the search for a solution begins. This stage includes, first, selecting an appropriate method for solving the problem from those already known or developing a new method; and second, the solution process itself, which consists of evaluating and analyzing various solution options and selecting the most preferred among them. In some problems, obtaining the final result is not difficult. However, more often these are quite complex and labor-intensive procedures requiring the knowledge and expertise of many people and the capabilities of modern computing technology.
At the same time, even after completing all stages of the problem-solving process, it is not always possible to make a final choice. Situations arise where the best solution cannot be found. The needed option may simply not be available. In that case, one can either modify the formulation of the original problem, or return to previous stages and collect the necessary additional information, make changes to the formal statement of the problem or the model of the problem situation, expand or narrow the number of alternatives considered, or construct new options.
In any case, the search for the best solution, even if it has not led to a positive result, will not have been futile. It may prompt a new understanding of the problem under consideration, highlight new aspects to consider, and suggest other ways to solve it.
If an acceptable option is found, the stage of decision execution begins, during which the adopted decision is implemented, the implementation process is monitored, and the result of resolving the problem situation is evaluated. Strictly speaking, this stage does not belong to the decision-making procedure. However, including decision execution in the overall scheme is important from both methodological and practical standpoints, as this stage closes the life cycle of the problem situation's emergence, resolution, and disappearance. Moreover, implementing an adopted decision may give rise to a new problem that requires its own solution.
The problem of decision-making arises in cases where a problem (task) becomes so complex that no suitable formalization apparatus can be immediately applied to its formulation (statement), and the process of problem formulation requires the participation of specialists from various fields of knowledge.
This leads to a situation in which the formulation of the problem itself becomes problematic, requiring the development of specialized approaches, techniques, and methods. In such cases, it becomes necessary to define the domain of the decision-making problem (the problem situation), identify the factors that influence its resolution, and select techniques and methods that enable the problem to be formulated or stated in a way that allows a decision to be made.
Thus, to make a decision, one needs to obtain an expression that links the goal with the means of its achievement, using introduced criteria for assessing goal attainability and evaluating means. In the various applied fields that developed in parallel, such expressions have received different names: performance criterion; effectiveness criterion or effectiveness indicator; objective function or criterion function; and so on. (In Russian-language literature, these are also referred to as tselevaya funktsiya — literally "goal function" — and funktsiya tseli, both of which correspond to the English term "objective function.")