The analysis of the country's hostilities against the Russian occupiers and the existing state of providing troops showed the need to improve the management system of providing material means, weapons, and military equipment to military units based on a scientific analysis of the state of the troops, forecasting changes in circumstances, and decision-making. This requirement is largely satisfied by the implementation of the main mechanism of the management system at all levels of supply in the Armed Forces of Ukraine (AFU), namely the «feedback system». The implementation of such a system in the organization and management of the process of logistical (technical, rear and medical) support (MTZ) of training and combat use of the Armed Forces, which is currently in a state of conducting hostilities on the territory of the state, necessitates the development of a new concept of military information and material management - technical flows for use by a more effective structure, which is called the «military logistics system». A key element of the MTZ is a set of measures to accumulate stockpiles of material resources up to the established norms and provide military units and units with them in a timely manner, storage and maintenance in a state of constant readiness for use as intended. The purpose of the article is to determine directions for improving the management system of material resources, weapons and military equipment for their creation and accumulation in peacetime, rational echeloning at all levels of management for their timely and sufficient supply to military units during hostilities. Keywords: inventory management system, main mechanism, inventory, supply, material inventory, logistics, echeloning, operational accounting, inventory management process.

Emphasis is placed on building a complex feedback system that responds objectively to changing circumstances regarding damaged means and forces of combat operations, because otherwise the system becomes self-sufficient and may become incapable of performing tasks. The variants of change of a situation with insufficient working capacity of system in the conditions of stochastic crossing of signs of variants of sets of forces and means for restoration of working capacity of system, after a choice of the best from set of alternative variants are defined. The probabilities of realization of each of the options of measures that are alternatives for the restoration of the system as a whole are determined. The distinction between the options of forces and means for the possible scope of measures is made using the criterion of the ideal observer, taking into account the costs of implementing each of the alternatives with maximum levels of probability in the hypotheses that intersect. The method of determining the predicted estimates of the probability of implementing alternatives to restore a complex system of technical support as a whole, under the conditions of a certain number of identified options for additional forces and additional equipment to intensify the process of restoring the system as a whole. . The method of determining the necessary costs and forecasting the reliability of their implementation, the method of testing statistical hypotheses, was used during the long-term planning of activities to create a more effective system of ensuring any level of hierarchy. Keywords: systems of comprehensive support of troops' actions, adaptive recovery of support system, method of statistical testing of hypotheses, assessment of realization of necessary forces and means, restoration of damaged support system in conditions of intersection of statistical hypotheses on its recovery.