Today, the basis of defense planning in Ukraine should be the principles of forming programs and plans for the development of its law enforcement agencies, based on the needs of ensuring the required level of defense capabilities of the country as a whole by finding the optimal balance between defense needs and economic capabilities. The degree of fulfillment of tasks on equipping the Armed Forces of Ukraine (the AFU) with the latest or modernized models of armaments and military equipment (AME) depends on the state of financing of defense needs. Analysis of the availability of basic models of weapons and military equipment in the AFU, as well as the pace of their renewal showed today the most problematic issues of national scale is the state of existing AFU, as well as the current pace of modernization. The number of weapons that need to be replaced, upgraded and repaired is constantly increasing, and their condition is approaching unsatisfactory every year. The development or purchase of new modern models of AME of domestic or foreign production, modernization of existing complexes and systems, individual models of weapons, testing, serial production and equipping of military units of the AFU is an urgent problem today. considered a state-wide problem. In the article the authors analyze the development of AME of the AFU over the years of independence and reveal the dynamics of the ratio of the number of available and required basic samples of AFU to determine the magnitude of their mismatch. Based on the results, the practical recommendations have been developed on the algorithm of modernization of AME of the AFU. Failure to comply with a certain annual percentage of modernization of AME will sooner or later have a negative impact on the country’s military security level. Keywords: combat capabilities, modernization of armaments and military equipment, financing of defense needs, military-economic factors, state of modernization, volumes of financial resources.

An analysis of wars and military conflicts shows that the effectiveness of operations is influenced by: the introduction of news forms and methods of using troops (forces); organization and conduct of armed struggle in real time; increasing the capabilities of weapons and military equipment; the creation of weapons for various purposes, capable of ensuring effective conduct of hostilities with minimal losses and having a sudden and impressive effect on the enemy due to a qualitative advantage. A significant increase in the operational-tactical capabilities of groupings of troops (forces) and the effectiveness of their use is possible under conditions of broad integration of heterogeneous and diverse means of armed struggle into complex multifunctional systems, such as reconnaissance and strike systems. However, at the same time, the problem arises of choosing the necessary variant (composition) of such a system, since its different elements have different characteristics and capabilities, different costs for their creation, maintenance and use, as well as different times for their development and bringing to combat readiness. Analysis and evaluation of various factors influencing the choice of composition (creation) of reconnaissance-strike systems for conducting operations by troops (forces) will increase the validity of the management decisions taken on the formation of their composition. The assessment of the coefficients of the importance of the influence of factors on the choice of the composition of reconnaissance-strike systems in a particular operation, using the method of an expert survey by pairwise comparisons of the set of all selected factors, will allow us to form groups of the most influential external and internal military factors from their totality. In order to better determine the influence of factors in choosing the composition of reconnaissance-strike systems for use in the operations of troops (forces), an assessment was made of the correlations between the development of weapons and military equipment of the Armed Forces of Ukraine, the combat capabilities of the Armed Forces of Ukraine and the allocated financial resources using regression and correlation analysis methods. The article determines that the greatest indicator of influence on the choice of composition (creation) of reconnaissance-strike systems for their use in the operations of troops (forces) of the many factors presented is carried out by military, economic and time factors. Keywords: choice of option, forms and methods of application, reconnaissance strike system, grouping, weapons and military equipment, UAVs, combat capabilities, efficiency, economic factor, financial resources, pair comparison.

An analysis of the experience of conducting combat operations shows that a significant role in the operations of groupings of troops (forces) belongs to units of mechanized (tank) troops. The existing mathematical model of combat operations of units of mechanized (tank) troops in the simulation model of the operation of a grouping of troops (forces) makes it possible to model the tactical actions of units of mechanized (tank) troops, however, it is somewhat generalized and does not always meet the requirements. The article proposes a methodical approach to improving the mathematical model of combat operations of units of mechanized (tank) troops in a simulation model of an operation (combat operations), the main content of which is to use such an algorithm, which will allow more detailed modeling of the tactical actions of units mechanized (tank) troops. The novelty of the algorithm is the ability to: determine indicators of the priority of targets (enemy objects) on the battlefield during simulation, thereby affecting the order and sequence of fire damage; to simulate the actions of battalion tactical groups, which are widely used in the war; carry out fire maneuver and fire concentration during simulation; the ability to give orders for a fire defeat in manual mode, thereby simulating the target designation of the commander; etc. Keywords: simulation modeling, modeling of tactical actions of subunits, grouping, weapons and military equipment, counter-offensive operation, mechanized (tank) troops, effectiveness of combat operations, grouping of troops (forces) operation, fire engagement, target designation.

Russian armed aggression against Ukraine has intensified research by Ukrainian scientists related to the development of weapons and military equipment and increasing the effectiveness of its combat use. The first months of the war showed that aviation and rocket troops and artillery are one of the key elements in the conduct of most large-scale operations in order to repulse the enemy and destroy his manpower and weapons and military equipment. In order to achieve the necessary results in carrying out various types of military operations, it becomes necessary to constantly make decisions on the use of certain troops (forces), means of destruction in order to destroy the enemy and inflict such losses on him, contributing to the achievement of the main goal of the operation. One of the important issues in the study of the problems of the optimal use of weapons is the solution of problems of target distribution of different content. For example, distribution over homogeneous or heterogeneous targets, protected or not protected, etc. The most relevant for research is the solution of the problem of distributing homogeneous means of attack over a set of objects of destruction, taking into account their degree of protection. Therefore, in the article, the authors propose one approach to the distribution of homogeneous weapons over the totality of enemy objects, taking into account the risks of hitting one's own weapons and the coefficients of importance of enemy objects in case of defeat. The proposed methodological approach is based on a mathematical model of decision-making on the defeat of enemy targets under conditions of risk, that is, their active countermeasures. Further prospects for research on the topic of the article include the need for practical implementation of the proposed approach in the form of calculation programs, as well as the search for the possibility of adapting it to the decision-making environment under conditions of uncertainty. Keywords: means of destruction, means of counteraction, mathematical programming, probability of defeat, weapons and military equipment, decision-making under risk.