Abstract
In the management of the organization, decisionmaking acts as a binding process for main functions: planning, organizing, motivating and control. Selection and justification of specific decisions is based on the concept and methodology of the theory of managerial decisions under uncertainty. An important feature of the processes of managerial decisionmaking is the need to consider the impact of uncertain factors and all possible consequences of alternatives presented for choice. The adoption of any decisions under risk and uncertainty is essential for the management of the organization. Management decision cannot be made without a rational approach to the analysis, substantiating its effectiveness. The article proposes the definitions of “management decisions” and “uncertainty”, based on the study of scientific literature. The authors present: stages of the production process and managerial decisionmaking; main approaches, peculiarities and system of managerial decision making in conditions of uncertainty; algorithm of acceptance of optimum administrative decisions and the “decision matrix” for making managerial decisions in conditions of uncertainty. The authors consider and compare Wald criterion and Hurwitz criterion, used when comparing alternatives in situations of uncertainty.
Keywords: uncertainty, models, matrix, management decisions, risks
Introduction
An important feature of managerial decisionmaking processes is the need to take into account the influence of uncertain factors and consider all the possible consequences of the alternatives that are presented for selection, where, in the face of uncertainty, the development of managerial decisionmaking models is of great practical importance;
Problem Statement
The problem of making managerial decisions in the face of uncertainty is relevant and important for consideration, since it is the main tool for managing influence.
Issues of making managerial decisions in the face of uncertainty are reflected in the works: V.A. Durdenko, S.V. Spiridonova, B.G. Litvak, A.I. Orlova, E.Yu. Kuzmina, L.A. Birman, E.I. Brazhko, A.G. Ivasenko, R.A. Fathutdinova, V.N. Kodina, S.V. Lityagina, L.I. Lukicheva, D.N. Egorycheva, A.P. Chernikova, E.E. Dosuzhevoi, E.V. Potapova.
A managerial decision is a choice that a leader makes in the management process and for solving specific organizational problems. A managerial decision aims to ensure progress towards the goals set for the organization. Therefore, the most effective management decision is an implemented choice that will make the greatest contribution to achieve the ultimate goal (Borodin, 2015).
Managerial decisionmaking process is one of the elements of independent management of the organization and it is significant for Russian entrepreneurs.
The process of making management decisions should be an algorithm that is maximally suited to solving problems in managing the organization. The main problem in this process is the need to choose the best solution from the many possible ones or to order options according to their preference. In this case, the result is the receipt of recommendations and forecasts, which are not a direct indication of further actions (Babushkina, 2015).
According to Potapova E.V. uncertainty is “open tasks in which the decision maker does not know the totality of the factors involved and must formulate many hypotheses before evaluating them.” The situation of complete uncertainty is characterized by the fact that the choice of a specific action plan can lead to any outcome from a fixed set of outcomes, but the probability of their implementation is different (Samotina, 2011). Uncertainty can be caused by sociopolitical, administrativelegislative, production, commercial, financial and other factors, as well as rapidly changing circumstances (Kudryashov, 2016). Uncertainty associated with the possibility of adverse situations and consequences during the implementation of the project is characterized by the concept of risk (Sapunova, 2010). In economic activity, there is almost always uncertainty (Yashchenko, 2013).
Research Questions
Management decisionmaking models help to ensure the structuring and processing of information about the problem and, thus, partially make up the incompleteness of the data available to the head (Golovin, 2013). Nevertheless, recommendations for decision making, obtained with the help of abstract models, can be considered as a way to solve problems only when the uncertainties and risks in these decisions are predicted and taken under control.
Purpose of the Study
The main goals and features of the managerial decisionmaking process in the face of uncertainty are (Busov, 2013): limited source data; large number of restrictions and assumptions, expressed in an explicit form; the absence and inability to mathematically formalize the objective function; the influence of random risk factors; taking into account all possible consequences of alternative assumptions; the choice of mathematical apparatus and the formation of the necessary model (Macheret, 2016).
The system of managerial decisions in the face of uncertainty is presented in Figure 1.
The management decisionmaking process goes through the stages presented in Figure 2.
The main features of management decisions are presented in Figure 3.
The process of production and implementation of management decisions consists of six stages, and is presented in Figure 4.
To develop an optimal management decision, it is necessary to highlight the patterns of development of the situation, to predict the onset of crises and to form strategic rules in accordance with which decisions are made (Vasilenko, 2018).
There are four main approaches to making management decisions in the face of uncertainty: 1) deterministic; 2) probabilistic; 3) fuzzy sets; 4) system (table 1).
The algorithm for substantiating optimal management decisions in the face of uncertainty is presented in Figure 5.
It is worth noting that the uncertainty situation includes several alternative solutions, each of which is a set of outcomes that take into account the corresponding state of the organization’s functioning environment (Sokolov, 2015). For a reasonable comparison of the set of values of each alternative and the choice of the most optimal option, it is effective to apply various selection criteria (Tagiltseva, 2017).
Research Methods
Decision making in the face of risk and uncertainty involves the construction of a “decision matrix” to justify it. The “decision matrix” is presented in table 2 (Shapkin, 2015). In the matrix, the indicated values are A1; A2; ...; An denote options for alternatives to decision making. C1 values; C2; ...; Cn characterize each possible variant of how further events can develop. values of E11; E12; E1 n; E21; E22; E2 n; E n1; E n2; ...; Э nn – A certain level of effectiveness of the decision made, corresponding to a specific alternative in a particular situation, describes the values of B11; B12; B1n; B21; B22; B2n; Bn1; Bn2; ...; Bnn.
The “decision matrix” reflects one of its types, as the “payoff matrix”, as it studies the degree of effectiveness. This matrix helps to reveal the most suitable and favorable solution from the alternatives according to the selected criterion. The results of the analysis show that most decisions, which a manager has to make in the modern world, are associated with uncertainty and risk. The basis for decisionmaking under conditions of uncertainty is the presence of the probability of various scenarios that are unknown (Drozdov, 2018).For a comparative analysis of competing alternatives, it is necessary to perform the steps presented in Figure 6.
There are six main criteria for comparing alternatives in a situation of uncertainty and for calculating the best alternative solution:
1. Wald's criterion (from the possible options of the “decision matrix”, an alternative option is selected, which of all adverse outcomes of events has the largest of the minimum values, in other words, the maximum of the minimum);
2. criterion of “maximax” (minimization of the maximum possible losses);
3. Laplace criterion (the highest mathematical expectation of gain in conditions of uncertainty in the state of nature);
4. Savage criterion (one of all possible options will be chosen, that minimizes the size of the maximum losses for each decision. This method converts the “decision matrix” into a “loss matrix”, in which the efficiency values are replaced by the loss sizes for various scenarios);
5. Hurwitz criterion (the Hurwitz criterion for the coefficients of the characteristic equation of this control system allows us to conclude that the system is stable or unstable);
6. generalized Hurwitz criterion (the generalized criterion takes into account all the outcomes of each alternative) (Tagiltseva, 2017).
Findings
Let us consider the example of management decisions used when comparing alternatives in a situation of uncertainty: the Wald criterion and the Hurwitz criterion.
According to Wald's criterion, the optimal alternative is the one that provides the best outcome among all possible alternatives under the worst of circumstances. According to Wald's criterion, the estimate of the ialternative is its smallest gain, and the optimal alternative is the one with the maximum worst gain.
There are two projects X1 and X2, which, with three possible scenarios for the development of the region (j = 1..3), provide different profits. Profit values are shown in table 1. We must select a project for implementation.
Among the possible projects, there are no dominant ones either absolutely or by state. Therefore, the decision has to be made according to the criteria. If the optimal project is selected according to the Wald criterion, then the decision maker must perform the following actions:
1. Find the minimum outcomes for each alternative (Vald test values):_{}_{}_{}
W_{2} =( x_{2j}), j = 1..3 => W_{2} =(44, 95, 47) = 44
2. Compare the values of the Wald criterion and find the largest value. An alternative with will be considered optimal:
45 > 44 => W_{1} > W_{2} => X* = X_{1}
If the decision was made only by Wald’s criterion, the decision maker would choose project_{} for implementation, since the profit that this project will provide in the worstcase scenario is higher. Having chosen the optimal alternative according to the Wald criterion, the decision maker guarantees himself that in the worst case of circumstances he will not receive less than the value of the criterion.
Decision making according to the Hurwitz criterion for a decision maker – an optimist and a decision maker – a pessimist(table 3). The procedure is as follows:
1. Find the maximum_{} and minimum_{} outcomes for each project:
x_{1}=(50, 45, 58) = 58 x_{1}=(50, 45, 58) = 45
x_{2}=(44, 95, 47) = 95 x_{2}=(44, 95, 47) = 44
2. Calculate the value of the Hurwitz criterion for given values of the optimism coefficient:
Optimist Decision Maker (λ=0.7):
H_{1}(0.7) = λ x_{1} +(1 – λ) x_{1}= 0.7×58 +(1 – 0.7)×45 = 54.1
H_{2}(0.7) = λ x_{2} +(1 – λ) x_{2} = 0.7×95 +(1 – 0.7)×44 = 79,7
Pessimist Decision Maker (λ=0.2):
H_{1}(0.2)= λ x_{1}+(1 λ) x_{1} = 0.2×58 +(1 – 0.2)×45 = 47,6
H_{2 }(0.2) = λ x_{2}+(1 λ)x_{2}= 0.2×95 +(1 – 0.2)×44 = 54,2
3. Compare the obtained values. Optimal for each decision maker will be alternatives withof the Hurwitz criterion:
Optimist Decision Maker (λ = 0.7):
54,1 < 79,7 => H_{1}(0.7) < H_{2}(0.7) => X* = X_{2}
Pessimist Decision Maker (λ = 0.2):
47.6 < 54,2 => H_{1}(0.2) > H_{2}(0.2) => X* = X_{1}
The optimal alternative under the same conditions substantially depends on the attitude of the decision maker towards risk. For a pessimist, both projects are approximately equal, and an optimist, in the hope of the best, will choose the second project. Its high best profit with large values of the coefficientsignificantly increases the value of this project according to the Hurwitz criterion.
As can be seen from the analysis, the procedure for calculating the criterion is objective and does not depend on the person making decision (Tereshina, 2014).
Conclusion
Thus, in conditions of uncertainty, it is very important to act thoughtfully, carefully consider various alternative solutions and assess the options for the development of the event before determining the next direction in the development strategy. The choice made will subsequently affect the result and determine the outcome: win, lose or unchanged situation.
The successful functioning of the organization without analysis of risk and uncertainty is simply impossible since any decision in the organization must pass risk control, otherwise, everything can turn out to be unpredictable consequences for the company.
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Drozdov, N. A., Kuzina, E. L., Vasilenko, M. A., Tagiltseva, J. A., Laponogova, A. A., & Magomedov, S. S. (2021). The System Approach To Making Management Decisions Under Uncertainty. In D. K. Bataev, S. A. Gapurov, A. D. Osmaev, V. K. Akaev, L. M. Idigova, M. R. Ovhadov, A. R. Salgiriev, & M. M. Betilmerzaeva (Eds.), Knowledge, Man and Civilization  ISCKMC 2020, vol 107. European Proceedings of Social and Behavioural Sciences (pp. 26302639). European Publisher. https://doi.org/10.15405/epsbs.2021.05.351