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The field of managing the logistics of agricultural products under significant dynamic changes in today's conditions requires the formation of new approaches using the possibilities of modern information tools. The article presents a systematic mathematical approach to logistics management in agriculture for conditions with an insignificant level of risk and under conditions of significant threats to the logistics processes of the agricultural industry. The presented study also examines the issue of analyzing the effectiveness of management actions in the logistics process, both operationally and strategically. The developed mathematical approach takes into account a wide range of conditions for carrying out logistics activities - both at a low level of risk in the implementation of the logistics process, and in circumstances of significant threats that lead to the minimization of the reliability of logistics in the agricultural sector. This is especially important today, given the significant level of negative impacts on logistics processes due to military threats. The growth of these influences even leads to the destabilization of the world food market, and the threat of famine in some regions of the world. The proposed mathematical approach takes into account both the emergence of new risks, the significantly increased dynamic nature of the effects on logistics activities in the agricultural sector of the economy, and the traditional specificity of the conditions for the implementation of logistics processes in the agricultural sector. The specificity of logistics management in the agricultural sector is due to the peculiarities of the agricultural production process; properties inherent in agricultural products, conditions of distribution of these products. This determines a wide range of tasks that must be performed by the logistics of the agricultural sector. This, in turn, creates a need for a highly adaptive dynamic approach when forming a set and combination of logistics tasks and goals. Algorithms, tools and methods were specially developed to implement this approach. In particular: the unification of target functions; the approach of flexible adaptive changes in the ranks of target functions to ensure the appropriate level of rationality of logistics process management; a compromise approach in the case of the need to simultaneously achieve a group of set goals or a group of goals; the approach of assessing the strategic impact of a management decision for operating not with static values of parameters, but with their trends over time. In general, this makes it possible to achieve the appropriate level of economic efficiency of agricultural logistics management even with dynamic changes in the conditions of its implementation and to ensure a high level of reliability of the logistics process even with an increase in the level of threats.