In practice situations are often found when it is difficult enough to estimate the value of probability of an event. In such cases methods are often times applied which do not involve using numerical values of probabilities: maximax – maximization of the maximum result of the project; maximin – maximization of the minimum result of the project; minimax – minimization of maximum losses; compromise – Gurvitz’s criterion: weighing of minimum and maximum results of the project. For decision-making on realization of investment projects a matrix is built. Matrix columns correspond to the possible states of nature, i.e. situations which are beyond of control of the head of an enterprise. Lines of the matrix correspond to possible alternatives of realization of the investment project – strategies which may be chosen by the director. The matrix cells specify the results of each strategy for each state of nature. Example: The enterprise analyzes the investment civil-engineering design of a line for the production of new kind of product. There are two possibilities: the construction of a high power capacity line or to construct low power line. Net present value of the project depends on the demand for production, whereas the exact volume of demand is unknown, however, it is known that there are three basic possibilities: absence of demand, average demand and great demand. The matrix cells (see table 1) show net present value of the project at a certain state of nature, provided that the enterprise will choose the appropriate strategy. The last line shows what strategy is optimum in each state of nature. The maximax decision would be to construct a high power capacity line: the maximum net present value will thus be 300 which correspond to the great demand situation. The maximum criterion reflects the position of the enterprise director – the optimist ignoring possible losses. The maximin decision, i.e. to construct a low power line: the minimum result of this strategy is the loss of 100 (which is better than possible loss of 200 in case of construction of a high power capacity line). The maximin criterion reflects the position of the director who is in no way disposed towards taking risk and is notable for his/her extreme pessimism. This criterion is quite useful in situations where risk is especially high (for example when the existence of an enterprise depends on the results of the investment project). Threat is determined by two components: possibilities and intention of the contestant.

Table 1. Example of construction of the matrix of strategy and states of nature for the investment project.

To apply the minimax criterion let us construct “a matrix of regrets” (see table 2). The cells of this matrix show the extent/value of “regret”, i.e the difference between actual and the best results which could have been achieved by the enterprise at the given state of nature. “Regret” shows what is being lost by the enterprise as a result of making wrong decision. The minimax decision corresponds to the strategy, whereby the maximum regret is minimal. In our case of low power line maximum regret makes 150 (in great demand situation) and for a high power capacity line – 100 (in the absence of demand). As 100 <150, the minimax decision would be to construct a high power capacity line. The minimax criterion is oriented not so much towards actual as possible damages or loss of profit.

Table 2.

Example of structure of the “matrix of regrets” for minimax criterion

Gurvitz’s criterion consists in that minimum and maximum results of each strategy are assigned “weight”. Evaluation of result of each strategy equals to the sum of maximum and minimum results multiplied by corresponding weight.

Let’s assume that the weight of the minimum result is equal to 0.5, the weight of the maximum result equals to 0.5 as well (it is the probabilistic characteristic; in this case probability of onset of any option of events = 50 %, as far as we have 2 options : 50 % + 50 % = 100 %; if there will be 3 options, then the ratio can be 33,33 (%) for each or, for example, 20 %, 25 % and 55 %). Then the calculation for each strategy will be the following:

Low power line: 0.5 х (-100) + 0.5 х 150 = (-50) + 75 = 25;

High power capacity line: 0.5 х (-200) + 0.5 х 300 = (-100) + 150 = 50.

Gurvitz’s criterion testifies in favor of the construction of high power capacity line (as 50> 25). Advantage and simultaneously disadvantage of Gurvitz’s criterion consists in the necessity of assigning weights to the possible outcomes; it allows taking into account specificity of situation, however, assigning weights always implies some subjectivity. As a result of the fact that in real situations there is often lack of information on the probabilities of outcomes the use of the above methods in engineering of investment projects is quite justified. However, the choice of concrete criterion depends on the specificity of situations and individual preferences of an analyst (the company’s strategy).

“Data mining”, getting/acquisition of information (it should be noted that many modern “data mining” techniques focus mainly on search of information based on key parameters (words, images, matrixes, algorithms), but in that way we will only be able to bring out ties/links that have already been exposed by someone else). According to the theory of information (Stanislav Yankovsky), requisite condition of activity of intellectual (higher) system is the redundancy of incoming and generated information, read and think “to lay up in store/as a reserve”, accumulate “assets” which expands your possibilities and get rid of “liabilities” which reduce your potential. Any phenomenon should be analyzed from the view point of what it gives to you and what it takes from you. Even two most universal resources – money and information (sometimes “time” is added thereto) – also limit to some extent the possibilities of their holder. A very important point in the evaluation of information is reliability of the source of information and credibility of data itself. Specific code of marking information carriers is applied for this purpose. Reliability of source: A – absolutely reliable source; B – usually reliable source; C – quite reliable source; D – not always reliable source; E – unreliable source; F - reliability of source cannot be defined. Credibility of data: 1 – credibility of data is proven by data from other sources; 2 – data are probably correct; 3 – data are possibly correct; 4 – doubtful data; 5 – data are improbable; 6 – credibility of data cannot be established. It should be noted that many elements of scientific, research and analytical activity are weakly formalizable, in which connection practical experience in the concrete field of activity gains great importance.

Issues recommended for independent study: the Game theory, the theory of fields, the theory of crises, the chaos theory, the theory of relativity, the management, strategy and tactics theories, basics of logic and statistics – concepts, substance/essence, stereotypes, paradoxes. See also: Software “Archivarius 3000” http://www.likasoft.com - highly effective searcher in database on the basis of keywords.