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A model of queuing is proposed to describe the logistics support process for the state defense forces group. In the model, the transitions of the sample of weapons from one state to another are carried out with intensities, μ or λ dependіs on the influence of the external environment and management. Within the framework of the proposed model, a differential equations system is obtaineddescribes the average numbers of weapons samplesin different states during their operation in the army. The obtained differential system solution corresponding the model is a quantitative estimate of the required number of weapons needed to ensure a given level of combat readiness and serviceability of state defense forcestroops, as well as optimal management of procurement, repair and modernization of weapons over certain time.

The subject matter of the article is the logistical support of the state defence forces.The goalof the study is the is the development of a probabilistic economic and mathematical model of logistics supply management for planning a non-reducing stock of the state defence forceslogistics supply. The tasks to be solved are: to formulate the task of determining the irreducible (reserve) of logistics supply stock size, to providethat the maximum possible value of its probability exhaustion within a certain period will not exceed the limiting value in terms of Wilson economic and mathematical model; by statistical processing of the state defence forces actions observation performingtheir assigned tasks to present the task of determining the optimal non-reducing stock by type of logistics cost without to reducing the level of reliability as a task to test multi-alternative statistical hypotheses; on the basis of solving the problemof continuous linear programming to determine the optimal non-reducible stock according to the nature of expenditures in order to improve the logistics supply management of the state defence forces. General scientific and special methods of scientific knowledge are used. The following resultswere obtained: Loses of the logistics supply stocks the defensestate forces performing their assigned tasks within a certain period of time as a normally distributed random variable with a mathematical expectation and standard deviation calculated from the results of statistical data processing. The problem of determining the optimal irreducible stock by types of loses of the logistics supplywithout reducing the level of reliability is formulated as a problem ofmulti-alternative statistical hypotheses testing and solved as a problem of continuous linear programming. Conclusions. It was determinedthe size of the non-reducing (reserve) stock of logistics supply of state defense units when performing their assigned tasks, provided that the maximum possible value of the probability of its exhaustion during a certain period does not exceed the limit value should be formulated in terms of Wilson economic-mathematical model. The assumption that the expenditure of the logistics supply stocks means when performing the assigned tasks by the state defense forces is a random variable subject to the normal distribution law make it possible to use the well-known theory of probability apparatus and many-alternative statistical hypotheses testing and make calculations based on the existing statistical sampling data. Statistical processing of data obtained during state defense forces preforming assigned tasks allows you to obtain initial data and calculate the predicted optimal probabilities of the logistics supply loses distribution in accordance with current, average, overhaul and irrecoverable losses.

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