A mathematical model of the decision-making process by a command group in the case of conflict interaction of the requirements for the efficiency and validity of the decision

The article presents a mathematical model of the decision-making process by a command group in the context of conflict interaction of the requirements for the efficiency and validity of the decision. The proposed mathematical model reflects the physical and practical features of the decision-making process by the command group and takes into account the main factors influencing it. To model the decision-making process, the following are defined: stages of decision-making; the indicator characterizing the qualification of the officials included in the group; the indicator characterizing the quality of information support; an indicator characterizing the novelty of the task; the indicator characterizing the scale of activities, the indicator characterizing process automation. The model introduces a decision-making efficiency coefficient, which helps to link two main indicators of an optimal solution: validity (through the average time of development and analysis of several decision options) and efficiency (through the ratio of the total average decision-making time and the allocated time); this makes it possible to account for the influence of the quality of the decision made for the subsequent planning process. A coefficient of adopted decision obsolescence has been introduced, which helps to assess the relevance of the adopted decision after a certain period of time. Using a mathematical model, analytical expressions are obtained that make it possible to evaluate the effectiveness of decision-making while taking into account the average time of the decision-making stages and the quality factor of the command group.

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