Algorithm and methods for management decision-making based on the theory of latent variables under time conditions
Authors:   Voronezh State Technical University, Voronezh, Russia, Barkalov S.A. , Ananiev A.V. ,   JSC Research and Production Enterprise “Polet”, Nizhny Novgorod, Russia, Ivannikov K.S. ,   JSC Research and Production Enterprise “Radar mms”, St. Petersburg, Russia, Moiseev S.I. ,   Voronezh State Technical University, Voronezh, Russia
Published: August 2022

The paper describes a decision-making algorithm under conditions of dynamically changing external and internal factors that affect the result of decision-making. The main role in this algorithm is played by the stage of assessing the attractiveness of alternatives and, as a result, choosing the most attractive of them. The main problem for solving this problem is the choice of the best alternative under conditions of uncertainty, when there is no information about possible scenarios for the development of the situation. To solve this problem, the paper proposes to apply the Rasch model of estimating latent variables, which allows not only to obtain estimates of alternatives on a linear scale, but also to obtain estimates of the sensitivity of alternatives to possible scenarios that make sense of the risk of loss for each alternative in case of an unexpected change in the scenario of the development of the situation. The results of modeling the process of data refinement for decision-making based on non-stationary Markov random processes are also presented. Aim. The purpose of the study is to develop an algorithm and a dynamic decision-making model that takes into account situational risk management, which is based on the theory of latent variables and non-stationary Markov random processes. Materials and methods. To substantiate the algorithm of the decision-making process, there is a mathematical model for assessing the attractiveness of alternatives, based on the Rasch model for assessing latent variables. To substantiate the evaluation results, computational experiments were carried out, which substantiated the adequacy of the obtained estimates. In addition, to confirm the possibility of using a decision-making algorithm, which involves the use of iterations to collect information, mathematical modeling of the decision-making process was carried out, which showed a high probability of successful completion of the process within the specified time frame. Results. On the basis of the decision-making algorithm presented in the paper under conditions of limited time, the issue of calculating the weights of alternatives under conditions of uncertainty, taking into account dynamically changing external and internal conditions, is raised. An original method for obtaining estimates of the attractiveness of alternatives under uncertainty is described, which takes into account the sensitivity of alternatives to possible scenarios for the development of the situation. For a qualitative analysis of the results when making decisions in accordance with the developed algorithm, a model of dynamic control over the probability of making decisions within a given time frame was presented. Using non-stationary Markov random processes, it is possible to evaluate the success of decision-making in the allotted time and calculate the number of cycles required to refine the initial data. Conclusion. On the basis of the decision-making algorithm presented in the paper under conditions of limited time, the issue of calculating the weights of alternatives under conditions of uncertainty, taking into account dynamically changing external and internal conditions, is raised. An original method for obtaining estimates of the attractiveness of alternatives under uncertainty is described, which takes into account the sensitivity of alternatives to possible scenarios for the development of the situation. For a qualitative analysis of the results when making decisions in accordance with the developed algorithm, a model of dynamic control over the probability of making decisions within a given time frame was presented. Using non-stationary Markov random processes, it is possible to evaluate the success of decision-making in the allotted time and calculate the number of cycles required to refine the initial data.