Let us mention one, rather original method used when choosing a solution in conditions of «bad uncertainty» the so-called method of expert assessments. It is often used in other fields, such as futurology. Roughly speaking, it consists in the fact that a team of competent people («experts») gathers, each of them is asked to answer a question (for example, name the date when this or that discovery will be made); then the answers obtained are processed like statistical material, making it possible (to paraphrase T. L. Saati) «to give a bad answer to a question that cannot be answered in any other way.» Such expert assessments for unknown conditions can also be applied to solving problems of operations research under conditions of «bad uncertainty». Each of the experts evaluates the degree of plausibility of various variants of conditions, attributing to them some subjective probabilities. Despite the subjective nature of the estimates of probabilities by each expert, by averaging the estimates of the whole team, you can get something more objective and useful. By the way, the subjective assessments of different experts do not differ as much as one might expect. In this way, the solution of the problem of studying operations with «bad uncertainty» seems to be reduced to the solution of a relatively benign stochastic problem. Of course, the result obtained cannot be treated too trustingly, forgetting about its dubious origin, but along with others arising from other points of view, it can still help in choosing a solution.
Lets name another approach to choosing a solution in conditions of uncertainty the so-called «adaptive algorithms» of control. Let the operation O in question belong to the category of repeating repeatedly, and some of its conditions are ξ1, ξ2, Unknown in advance, random. However, we do not have statistics on the probability distribution for these conditions and there is no time to collect such data (for example, it takes a considerable amount of time to collect statistics, and the operation needs to be performed now). Then it is possible to build and apply an adapting (adapting) control algorithm, which gradually takes place in the course of its application. At first, some (probably not the best) algorithm is taken, but as it is applied, it improves from time to time, since the experience of application indicates how it should be changed. It turns out something like the activity of a person who, as you know, «learns from mistakes.» Such adaptable control algorithms seem to have a great future.
Finally, we will consider a special case of uncertainty, not just «bad» but «hostile.» This kind of uncertainty arises in so-called «conflict situations» in which the interests of two (or more) parties with different goals collide. Conflict situations are characteristic of military operations, partly for sports competitions; in capitalist society for competition. Such situations are dealt with by a special branch of mathematics game theory. (It is often presented as part of the discipline «operations research.») The most pronounced case of a conflict situation is direct antagonism, when two sides A and B clash in a conflict, pursuing directly opposite goals («us» and «adversary»).
The theory of antagonistic games is based on the proposition that we are dealing with a reasonable and far-sighted adversary, always choosing his behavior in such a way as to prevent us from achieving our goal. In the accepted proposals, game theory makes it possible to choose the optimal solution in some sense, i.e. the least risky in the fight against a cunning and malicious opponent.
However, such a point of view on the conflict situation cannot be absolutized either. Life experience suggests that in conflict situations (for example, in hostilities), it is not the most cautious, but the most inventive who wins, who knows how to take advantage of the enemys weakness, deceive him, go beyond the conditions and methods of behavior known to him. So in conflict situations, game theory provides an extreme solution arising from a pessimistic, «reinsurance» position. Yet, if treated with due criticism, it, along with other considerations, can help in the final choice.
Closely related to game theory is the so-called «statistical decision theory». It is engaged in the preliminary mathematical justification of rational decisions in conditions of uncertainty, the development of reasonable «strategies of behavior» in these conditions. One possible approach to solving such problems is to consider an uncertain situation as a kind of «game», but not with a consciously opposing, reasonable adversary, but with «nature». By «nature» in the theory of statistical decisions is understood as a certain third-party authority, indifferent to the result of the game, but whose behavior is not known in advance.
Finally, lets make one general remark. When justifying a decision under conditions of uncertainty, no matter what we do, the element of uncertainty remains. Therefore, it is impossible to impose too high demands on the accuracy of solving such problems. Instead of unambiguously indicating a single, exactly «optimal» (from some point of view) solution, it is better to single out a whole area of acceptable solutions that turn out to be insignificantly worse than others, no matter what point of view we use. Within this area, the persons responsible for this should make their final choice.
2.4 Multi-criteria Operations Research Tasks
Despite a number of significant difficulties associated with the uncertainty of the conditions of the operation, we have still considered only the simplest problems of operations research, when the criterion by which the effectiveness is evaluated is clear, and it is necessary to turn into a maximum (or minimum) a single indicator of efficiency W. It is he who is the criterion by which one can judge the effectiveness of the operation and the decisions made.
Finally, lets make one general remark. When justifying a decision under conditions of uncertainty, no matter what we do, the element of uncertainty remains. Therefore, it is impossible to impose too high demands on the accuracy of solving such problems. Instead of unambiguously indicating a single, exactly «optimal» (from some point of view) solution, it is better to single out a whole area of acceptable solutions that turn out to be insignificantly worse than others, no matter what point of view we use. Within this area, the persons responsible for this should make their final choice.
Despite a number of significant difficulties associated with the uncertainty of the conditions of the operation, we have still considered only the simplest problems of operations research, when the criterion by which the effectiveness is evaluated is clear, and it is necessary to turn into a maximum (or minimum) a single indicator of efficiency W. It is he who is the criterion by which one can judge the effectiveness of the operation and the decisions made.
Unfortunately, in practice, such tasks, where the evaluation criterion is clearly dictated by the target orientation of the operation, are relatively rare, mainly when considering small-scale and modest-value activities. As a rule, the effectiveness of large-scale, complex operations affecting the diverse interests of participants cannot be exhaustively characterized using a single performance indicator W. To help him, he has to attract other, additional ones. Such operations research tasks are called «multi-criteria».