Introduction

The changing security environment, the existing challenges, and the current military threats to the Ukrainian state require the Ministry of Defence and the General Staff of the Armed Forces to pay special attention to strategic decision-making during the defence review. Making strategic decisions to determine the strategy for the development of the Armed Forces in conditions of partial uncertainty and risks is one of the most urgent practical problems of strategic planning for the capabilities-based development of the Armed Forces. Incorrect strategic decisions in the future can negatively affect the level of readiness and capabilities of the Armed Forces to defend the state, protect its sovereignty and territorial integrity, and lead to inefficient use of budget funds.

The elaboration of rational strategic decisions based on quantitative assessments to determine an effective strategy for developing the capabilities of the Armed Forces in the long term cannot be conducted without the use of mathematical methods and tools of strategic analysis. The terms "rational", "objective", and "effective", chosen for this study, are interdependent and this is not accidental. "Rational" characterises a strategic decision made to solve the problems of the Armed Forces using indicators and criteria for effectiveness.¹ "Objective" means the use of mainly statistical and mathematical data and calculations, and a minimum of expert assessments and judgments to determine an effective strategy for developing the capabilities of the Armed Forces. "Effective" characterises the expected positive effect of the implementation of the chosen strategy based on a strategic analysis of the development of the Armed Forces.

Strategic analysis for the development of the Armed Forces is one type of strategic analysis, namely a comprehensive study of the current state and strategy for the development of the capabilities of the Armed Forces according to the parameters that determine their future state. Strategic analysis for the development of the Armed Forces should be conducted during defence reform, defence review, and other strategic planning procedures. Contradictions in the construction and development of the Armed Forces are caused by not using the method of strategic analysis, which will consider statistical data and minimise the involvement of experts. This method should allow making rational strategic decisions to determine the strategy for developing the capabilities of the Armed Forces in the long term, while considering resource risks. Certain formalisation of the strategic analysis for the development of the Armed Forces of Ukraine, as well as the definition of a long-term strategy for the development of different types and branches of the Armed Forces is already laid down in legal regulations and military standards.²

Thus, during the defence review it is customary to assess the state and readiness of the Defence Forces to perform tasks related to the defence of the country, the state of their comprehensive logistical support, and of their available capabilities.³ The defence review is commonly conducted in compliance with the following principles: objectivity, systematic measures, scientific validity, etc. The procedure for organising and implementing the defence planning in the Ministry of Defence of Ukraine, the Armed Forces of Ukraine, and other components of the defence forces was approved in 2020.⁴ This procedure defines the authorities involved and the sequence of actions for the organisation of this process and the implementation of certain procedures (capacity assessment, risk management, development of programmes and plans, etc.) in the defence forces.

Also, the military security strategy of Ukraine was approved in 2021⁵, one of whose priorities is to increase the level of combat readiness, and the capabilities of the Armed Forces of Ukraine, as well as of other components of the defence forces to perform tasks as intended. A military standard was also established and approved in 2020⁶, defining the procedure for elaborating strategies for the development of a separate branch of the Armed Forces. It defines the necessary initial data to elaborate strategies (results of the defence review, budget, etc.), those responsiblefor the elaboration, deadlines for developing draft strategies, etc. However, there are no fixed methodological foundations (statistical methods, assessment methods, approaches, and other tools of strategic analysis) for determining options for strategic decisions, which creates a problematic situation when performing this complex strategic task.⁷

The purpose of this study is to elaborate a method for the strategic analysis of the development of the Armed Forces. To achieve this purpose, the following tasks were set forth:

Literature Review

During the defence review, it is customary to use general scientific methods based on expert assessments and strategic analysis to assess possible scenarios for the emergence and development of crisis situations in the military, etc.⁸ It is also customary to use different methods of analysis, such as SWOT analysis, the Delphi method, the hierarchy analysis method, the scenario method, the trend analysis method, the decision tree methodology, the brainstorming method, comparison etc.⁹

For risk assessment the most used methods are¹⁰:

These general scientific methods of expert assessment and strategic analysis differ in their purpose, essence, objects, subjects, stages sequence and content, criteria, indicators, etc. However, all of them, explicitly or implicitly, necessarily include the stage of assessing the options for strategic decisions.¹¹ Expert assessment methods conduct a strategic analysis of the development of the Armed Forces based on the subjective opinion of experts, the results of which may vary depending on various factors (current situation, awareness, etc.). Considering the above, the use of methods of strategic analysis for the long-term development of the Armed Forces remains an urgent practical and scientific problem.

The problem of the objectivity and rationality of strategic decision-making in the areas of defence and military construction has already been considered in the literature, but not solved constructively. In the management literature, ten main scholarly traditions have been identified, which differ in their fundamental view of the strategic management process, have certain shortcomings, and have a specific character in the development and choice of strategy.¹² The complexity of the problem of forming and choosing a strategy for the development of the Armed Forces lies in the fact that its qualitative solution requires the use of multi-criteria optimisation methods to find the maximum and minimum value of the objective function. However, the mechanism for making strategic management decisions in the field of defence and military construction has not yet been sufficiently developed and is ambiguously interpreted in the scientific literature.

In the theory, the national security strategy of the state has been defined as an official set of strategic tasks, measures, actions, and other strategic decisions established by the state¹³. Strategic decisions are those that are complex, large-scale, and with a high level of generalisation and aggregation, aimed at ensuring the protection of national values and national interests and achieving certain national goals. It can be agreed that the defence review and the comprehensive review of the security and defence sector are components of more general processes, such as strategic planning and national security management. Therewith, it is disputable that the defence review is carried out in the interest of developing a strategic defence bulletin.¹⁴ First, the strategic defence bulletin¹⁵ is a strategic document based on the results of the defence review, secondly, it highlights the strategic decision to develop the defence forces in the long term (with strategy).

Massa and Anzera proposed a method for substantiating options for national security strategic decisions, which is not specific of this field.¹⁶ Generating alternative solutions (from three to nine) is usually carried out using special procedures and methods such as brainstorming, Zwicky methods, analogue methods, etc. However, the above method does not comply with the principle of objectivity of assessments, due to the use of expert assessment methods, reducing the objectivity of the process.

Saganyuk et al.¹⁷ consider the existing methodological approaches to determining the strategic development goals of troops (forces) for the development of a strategic defence bulletin based on the results of the defence review. They note that strategic goals must meet certain requirements for measurement (goals must have a quantitative expression); clarity, necessity, and sufficiency; attainability; time parameters; and consistency with the management hierarchy. Defining strategic goals also follows a sequence in a general top-down form. Therewith, the indicators, criteria, and functions by which it is customary to determine the strategic goals for the development of troops (forces) are not given.

Some studies¹⁸ have developed practical recommendations for the application of methods for making strategic management decisions (strategic analysis), which are grouped into seven groups depending on the objects of research. In these studies, it has been noted that the adoption of strategic management decisions cannot be imagined without conducting a strategic analysis, which was considered as the performance of the corresponding management function, focused on the future, and having a high level of uncertainty. Therewith, the researchers did not provide practical recommendations on the application of the existing methods for other management operations and the procedures for making strategic management decisions (identifying possible ways to solve the problem and assessing and choosing the best option).¹⁹

Tagirova²⁰ has described the conceptual foundations of strategic analysis and the methods for grouping and forecasting objects in it. This author notes that strategic analysis is a research process that never stops, closely related to the life cycle of the strategy. Its stages form a closed loop:

This proposed sequence of stages cannot be applied in the strategic analysis of the development of the Armed Forces, as it contains duplicate stages (stages 3 and 5) and needs to be adjusted. Several articles²¹ have examined the essence, approaches, and stages of the strategic analysis in enterprise management, and the forms and mechanism of its implementation. Methods of variant analysis, creative thinking, and expert assessments, and methods of forming an economic portfolio at the stage of strategic planning have been proposed. Therewith, the possibility of using a group of economic and mathematical methods (mathematical programming, mathematical analysis, etc.) has not been investigated, and the proposed algorithm and mechanism for conducting strategic analysis does not allow making rational strategic decisions.

In other articles²², strategic analysis is considered as a comprehensive study of positive and negative factors that can affect the economic situation of the research object in the future, including ways to achieve strategic goals. This research has noted that strategic analysis can be used to formulate a comprehensive strategic plan for the development of the object, while providing a scientifically based, comprehensive, and timely support for strategic decision-making. However, these authors have ignored the question of the principles of strategic analysis and the objectivity of strategic decision-making.

Calabrese et al.²³ considered the strategic manipulation of weight information in the TOPSIS MADM method in two scenarios:

The authors noted that a person who makes a strategic decision can manipulate information about the weight of the selected scenarios to substantiate a certain order of rank categories of alternatives that are of interest. Therefore, a decision-making procedure based on a genetic algorithm has been developed to solve the nonlinear programming model (MINLP). However, the proposed genetic algorithm does not allow processing constant and variable parameters to determine (refine) the strategy for developing the capabilities of the Armed Forces based on performance criteria.

Džeko et al. proposed to use the fuzzy analytic hierarchy process (AHP) to select those sustainability issues that are most relevant for strategic planning and management.²⁴ The authors proposed applying the AHP method in practice, through a step-by-step procedure, and they also discussed its usefulness as a management tool for strategic decision-makers. The method facilitates directly involving diverse types of stakeholders and integrating the principle of sustainability into strategic decision-making. Therewith, it does not allow integrating the principles of objectivity, consistency, rationality, and positive effect of strategic decision-making.

Džeko et al. also presented the main stages concerning the new multicriteria SNAP method and its ERA metamodel. ²⁵The SNAP method combines two methods, namely analytic network process (ANP) and social network analysis (SNA). The integration of these two methods has reduced some of the deficiencies that occur when applying ANP. The role of the ERA-SNAP metamodel is twofold: it helps to understand the steps of SNAP and is also the basis for developing potential support for SNAP software. Therewith, the SNAP method and its ERA metamodel are not suitable for synthesising the results of strategic analysis of the development of the capabilities of the Armed Forces due to the specific features of their use.

Toledo Gandarias and Otegi Olaso²⁶ present a method for making strategic decisions based on the maturity of company management, that is, based on the organization's competencies and procedures to implement projects. This method considers the relationship between three aspects: the maturity level of the main stakeholders (customer and contractor), the complexity of the project, and the success of the project. It also provides additional information for making decisions when new business opportunities arise and trust between the client and contractor is low. Therewith, this method of making strategic decisions is not based on the principles of objectivity, consistency, rationality, and positive effect.

Kadoic et al. developed a method for making strategic decisions in higher education²⁷, which considers the importance of criteria for decision-making. A measure describing how strong a particular criterion is in terms of influences/dependencies is based on the degree of centralisation, one of the most fundamental measures of centrality. However, when determining the importance of criteria, the requirements (limitations) for constructing a mathematical model and synthesis stages are not considered.

Garg developed a new model of decision-making with probabilistic information and the use of immediate probabilities for aggregating information in the environment of a fuzzy Pythagorean set.²⁸ In this model, existing probabilities were changed by introducing the positional character of the decision-maker using an ordered weighted average operator. However, the positional character of a person when making decisions can negatively affect the level of readiness and capabilities of the Armed Forces due to the subjectivity of assessments.

Also, other authors have proposed a method for strategic analysis before decision-making to choose an effective strategy²⁹. These authors presented examples of choosing strategies and demonstrated its feasibility and practicality. However, it is impossible to choose rational strategic decisions using interval-considerable fuzzy information about the level of readiness and capabilities of the Armed Forces.

Quiñones Páez et al.³⁰ present an aggregation method for decision-making using induced aggregation operators and a maximum and minimum level index. Its main advantage is that it can assess complex ordering processes, representing complex relationships of the character of the decision maker, such as psychological or personal factors. The method considers only the subjective attitude and degree of optimism of the decision-maker in the decision-making process.

Korendovich³¹ presents expert methods for multi-criteria analysis of military systems for several strategies to support decision-making about the most acceptable option. Using the methods of expert assessments and analytical methods, this author proposes to solve a wide range of practical problems of rational choice of military means. However, the use of scores by experts in practice carries the risk of choosing the most acceptable option based on the judgments of experts, who may change their opinion depending on the specific situation, awareness, and the influence of other factors.

Other authors have studied the content of strategic decisions in conditions of uncertainty and risk³², like the features and technology of strategic decision-making in a dynamic business environment. This allows the identification of typical risks at the different stages of taking managerial decisions and the methods for their optimisation. These stages are considered when determining the procedure for strategic analysis of the development of the Armed Forces.

Rusnak et al. analyse national and foreign experiences in capabilities-based defence planning and present five detailed stages for defence planning. ³³ The fifth stage is to assess the results every two to three years by conducting a review of the capabilities of the Armed Forces to monitor the implementation of the tasks related to the development of capabilities. However, it is not disclosed how and by what methods the results of the selected stages will be assessed for making strategic decisions to determine the strategy for developing the capabilities of the Armed Forces.

Other researchers have studied the relevance for this subject of mathematical methods and models with economic branches³⁴. Mathematical models, in particular those based on elementary mathematical methods, are used in economic calculations when substantiating resource needs, accounting for production costs, and developing plans and projects. The general properties of the model are clarified, which are chosen to be considered when developing and checking the adequacy of the mathematical model for synthesising the results of strategic analysis of the development of the Armed Forces, and when substantiating the possibility of its practical use.

Other studies have presented models and methods for calibrating and testing the line-of-sight firepower of the Armed Forces (LOS) as one of the main components of capacity-based planning in the field of Armed Forces development³⁵. The sizing and testing model includes a mathematical description of the LOS fire rating for the various components of the Armed Forces, the weapon unit, the carrier unit, and the reference module. These results can be used for subsequent studies on the distribution of components of the Armed Forces in response to a threatening scenario.

Finally, several studies have confirmed the relevance of elaborating a method of strategic analysis for the development of the Armed Forces³⁶, based on the principles of objectivity, consistency, and rationality of strategic decisions.

Materials and Methods

This study assumes that the method of strategic analysis for the development of the Armed Forces should rely on the principles of objectivity, consistency, rationality, and positive effect. Objectivity will be ensured by minimising the use of expert assessments and maximising the use of statistics from the results of defence reform and defence review to develop options and make rational strategic decisions. Consistency will be ensured by using a recursive method of organising the computational process, source data, and assessment results for selected stages.

Rationality will be ensured by applying a system of effective criteria and indicators, a target function to determine (clarify) the strategy for developing the capabilities of the Armed Forces, which will have a positive effect after its implementation. The positive effect of implementing the strategy for developing the capabilities of the Armed Forces will be provided by the expected increase in the level of readiness of the Armed Forces, considering resource risks. The strategy for developing the capabilities of the Armed Forces is a model of defence reform for a certain period, aimed at acquiring the necessary capabilities for the Armed Forces to guarantee the performance of tasks according to possible scenarios.

The previously proposed conceptual approach to the selection of priority areas for the development of the capabilities of the Armed Forces and other components of the defence forces³⁷ consists in applying recursion to certain stages, ordered by level of detail. It considers the relationship between the necessary input and output information for calculations and support for making rational strategic decisions on determining priority areas.

The conceptual approach includes stages for defining (clarifying) strategic goals, necessary capabilities, necessary resources, a promising model (structure), and priority areas, which are conventionally grouped into two assessment procedures. The first procedure allows obtaining the necessary data and assessment results to determine the optimal ratio of the required resources and the maximum result. The second procedure selects specific values of the characteristics of the prospective structure (model) and capabilities of the Armed Forces, and ways to achieve them through the choice of priority areas.

Thus, mathematical modelling of the synthesis of the strategic analysis results of the development of the Armed Forces is usually conducted using this conceptual approach. A mathematical model is a set of mathematical relations that link the initial characteristics of the state of a physical object with input information, initial data, and restrictions imposed on the functioning of the object.³⁸ The purpose of mathematical modelling is to identify rational strategic solutions, assess the effect, determine the properties of the system (sensitivity to changes in the values of characteristics, etc.) and establish the relationship between the characteristics of the system.³⁹ The strategic analysis of the development of the Armed Forces provides for an optimisation approach to determine the effective version of the strategy in the long term in conditions of partial uncertainty and risks. The implementation of the chosen strategy should contribute to the achievement of the necessary capabilities of the Armed Forces during defence reform.

An analysis of the experience of constructing mathematical models and conducting computer modelling allowed setting requirements for a mathematical model for synthesising the results of strategic analysis of the development of the Armed Forces and determining the sequence of actions⁴⁰:

The procedure for the strategic analysis of the development of the Armed Forces is generally conducted in the following stages⁴¹:

The defined sequence of stages 1-4 of the procedure of strategic analysis for the development of the Armed Forces is ordered by importance (from greater to lesser), and is applied to the system of criteria and generalised indicators of performance assessment.

The structure of the mathematical model for synthetizing the strategic analysis results of the development of the Armed Forces includes the following elements⁴³: the object of modelling is a strategy for the development of the capabilities of the Armed Forces for the long term; constant parameters -values that remain unchanged during the entire modelling; variable parameters -values that need to be found when solving the problem using mathematical modelling; complex performance criteria -an indicator of the effectiveness of the strategy, whose value at the maximum significance of the target function determines the rationality of solutions for given conditions, that is, the effective value of the variable parameters of the model; restrictions -areas of possible values under given specific conditions of the strategy which is analysed and for which the best (rational) strategic decision is calculated; and target functions, which link performance criteria to variable and constant parameters.

Results and Discussion

In the process of constructing a structural diagram of the mathematical model for finding rational solutions I _sol (1 - 5), variable parameters I _jn(1 - 5) I _out (1 - 5) are determined that will give the functions Y_1-5, Z_1-5 a minimum value to obtain the maximum effect of the objective function E.

The block diagram of the mathematical model for the synthesis of the strategic analysis results of the development of the Armed Forces is shown in Figure 1.

The block diagram of a mathematical model (Figure 1) characterises the selected stages of the strategic analysis for the development of the Armed Forces and the information relationships between input, output, and internal parameters in the form of a recursive algorithm. To obtain the maximum effect from determining (clarifying) the strategy for developing the capabilities of the Armed Forces in the long term, it is necessary to choose a system of indicators and criteria for the effectiveness of this strategy.

The strategy for developing the capabilities of the Armed Forces is a model of defence reform for a certain period, aimed at achieving the necessary capabilities of the Armed Forces to guarantee the performance of tasks according to possible scenarios. Considering the above general requirements, it is customary to assess the effectiveness of the defence reform and the strategy options according to a system of performance criteria based on generalised indicators and selected considering certain stages:

The selected criteria are used to determine the weight coefficients (C _n) during the analysis of solution options at the 5th stage, through the ratio of their total amount to the corresponding score: . The sum of the weighting coefficients is -1.0 (dimensionless value), which indicates the objectivity and correctness of the definition.

Therefore, the selected performance criteria are based on generalised indicators that characterise the results obtained at the selected stages and have weight when choosing an effective strategy option. The structural elements of complex and generalized indicators are constant and variable quantitative and qualitative indicators (x, y), which characterise⁴⁴:

The system of indicators and criteria for the effectiveness of the strategy for developing the capabilities of the Armed Forces is shown in Figure 2.

It is advisable to conduct the selection of quantitative and qualitative indicators (x, y) to assess partial and generalised indicators with factor analysis, which will allow to consider the selected performance criteria (Figure 2) and to choose an effective strategy. To analyse the effectiveness of defence reform and strategy options, fixed values of performance criteria that characterise the increase in the effect are adopted (Table 1).⁴⁵

The defence reform or the chosen version of the strategy for the development of the Armed Forces will be considered effective, and strategic decisions will be considered rational, provided that (Table 1) their implementation has a positive effect for the Armed Forces of at least 0.3. This will allow achieving the expected increase in the level of readiness and capabilities of the Armed Forces of at least 30% (positive effect) for a certain period of the implementation of the strategy for the development of the capabilities of the Armed Forces.

Strategic analysis of the development of the Armed Forces is a process of reducing uncertainty and minimising resource risks in determining (clarifying) a strategy for developing the capabilities of the Armed Forces in the long term. The process conventionally includes two components: the first is a sequence of analysis stages in which initial data are obtained based on the assessment results; the second is the choice of specific solutions and options for achieving the desired effect.⁴⁶ The procedure for determining (clarifying) the strategy for developing the capabilities of the Armed Forces can be expressed as:

where: is a comprehensive generalised indicator that represents the level of effect of the selected strategy option; I is an information component that describes the necessary input and output data, the solutions, and other information; F is a procedural component that includes recursive functions. It is accepted that the information component characterised by dimensional values will be reduced to dimensionless values during the calculation through the ratio of available to required values.

Recursive functions should include⁴⁷:

Heuristics is a method of solving a problem based on informal rules of experienced experts (specialists), which will reduce the number of calculations or the time to obtain the result when algorithmic methods are useless. Converting an information component into team information for decision-making (Figure 1) is characterised by the expression:

The initial function for determining the effect level of the selected strategy option can be characterised by the expression:

To find rational solutions for the selected stages of analysis, directly dependent functions are defined:

Input information of the 1st stage I _in(1) is composed by variable parameters that characterise the quantitative, qualitative, time, and cost values of the selected quantitative and qualitative indicators for assessing and constructing a recursive function Y ₁ :

where x ₁₁..., x _1n are quantitative and qualitative indicators for assessing the results of defence reform and defence review to determine (clarify) strategic goals.

Quantitative and qualitative indicators are generally calculated by the method of scale comparisons⁴⁸ through the ratio of homogeneous values (quantitative, qualitative, time, and cost):

where X _1i is the dimensionless value obtained from the assessment results, X _n . the actual value, and x _ri the standard (required) value.

The calculated quantitative and qualitative indicators (x ₁₁,...,x _1n) are summarised in tables, for example, those defined in the recommendations⁴⁹ for summarising and analysing the results obtained. As initial 1st stage data, I _out (1), the results of achieving strategic goals are used:

where y ₁₁ ,…,y _1m are the results of achieving strategic goals and defence reform in general.

Input information I _1n(2) will be the results obtained during the defence reform, the defence review to assess the security environment, and the available and necessary capabilities (operational, combat, special) in the form of calculation tables.⁵⁰

The set of input information of the second stage, I _1n(2), as well as the initial data of the 1st stage, I _out(1), form the structure and range of variable parameters for constructing a recursive function Y ₂:

As initial second stage data, I _out(2), a set of necessary capabilities of the Armed Forces that need to be maintained, developed, and created will be obtained:

where y ₂₁,... ,y _2m is the set of necessary capabilities of the Armed Forces.

Input information I _in (3) will be the results from the defence reform and defence resource planning review.

The set of input information of the third stage, I _in (3), and the initial data of the second stage, I _out (2), form the structure and range of variable values for constructing a recursive function Y₃:

As initial third stage, data I _out(3), a set of necessary resources (human, technological, material, financial) for the development (clarification) of the defence budget will be obtained:

where Y ₃₁,... ,Y _3m is the set of necessary resources (human, technological, material, financial).

Set of input information of the fourth stage, I _in(4) , and the initial data of the third stage, ¡_out(3), form the structure and range of variable values for constructing a recursive function Y ₄:

As initial fourth stage data, I _out(4), a set of forces and means and organisational structures to determine priorities for the development and creation of new capabilities of the Armed Forces will be obtained:

where y₄₁,... ,y_4m - is the set of forces and means and organisational structures to be maintained, developed, and created.

Set of input information of the fifth stage, I _n(5) , and the initial data of the fourth stage, I _out(4), form the structure and range of variable values for constructing a recursive function Y ₅:

As initial fifth stage data, I _out(5), a set of data for determining the priority of developing and creating new capabilities of the Armed Forces in the long- and medium-term, considering certain necessary capabilities and resources, will be obtained:

where y ₅₁ ,... ,y _5m is the set of data for prioritising the development and creation of new capabilities of the Armed Forces.

Through the consolidated recursive functions Z_1-5, feedback is provided with the results of the previous stages (Figure 1), for the development of draft decisions at stages 1-5 I _sol(1)- I _sol(5):

The condition for the completion of the recursion by the recursive functions (5) - (20) are the constant parameters, the values of which are determ_-ined_- by the performance criteria and consist in establishing the maximum effect . It is customary to determine the maximum effect based on the target function:

where _e is a generalised indicator that determines the level of definition (clarification) of the strategic goals for the development of the capabilities of the Armed Forces; _c is a generalised indicator of the necessary capabilities of the Armed Forces; _ra is a generalised indicator of the required resources P _co is a generalised indicator of the definition (coordination) of the priority development areas; and c ₁ , c ₂ , c ₃ , c ₄ are the calculated weight coefficients of the selected performance criteria.

As draft decisions in stages 1-5, I _sol(1)- I _sol(5), a coherent set is obtained: defined (clarified) strategic goals; necessary capabilities and resources; priority areas for developing the capabilities of the Armed Forces to determine (clarify) the strategy. Therefore, steps 1-5 (Figure 1) need to be repeatedly referred until rational and consistent solutions are obtained for the selected stages and the maximum (from a certain minimum) effect is achieved. It should be noted that the results of calculations obtained using the corresponding mathematical model for synthesising the strategic analysis results of the development of the Armed Forces cannot be the only basis for making strategic decisions. They are only a basis for an official to make a final strategic decision.

The developed method is based on the objectivity of assessments, consistency, and effectiveness, which allows increasing the rationality of strategic decision-making in determining the strategy for developing the capabilities of the Armed Forces in the long term. The originality of the developed method of strategic analysis of the development of the Armed Forces lies in the following factors:

Thus, it can be asserted that it is possible to use the method of strategic analysis of the development of the Armed Forces (SADAF-RW) in the elaboration of a scientific and methodological apparatus for assessing the effectiveness of strategic planning for the development of the Armed Forces. Further research will be devoted to the elaboration of a comprehensive methodology for determining the strategic goals and priority areas for developing the long-term capabilities of the Armed Forces using the resulting method.

Conclusions

A method of strategic analysis of the development of the Armed Forces was developed based on the principles of objectivity, consistency, the rationality of strategic decisions, and positive effect.

A classical mathematical model of synthesis of the strategic analysis results of the development of the Armed Forces was built for making rational strategic decisions on the selected stages and, accordingly, the system of effective indicators and criteria. This is a flexible model, in which the indicators and criteria can be updated depending on the number of analysis stages. Also, their weight coefficients are calculated considering the priority of the selected stages. Therefore, the model allows a strategic analysis of the development, not only of the Armed Forces, but also of other components of the defence forces, or of defence forces in general. The criteria are based on generalised indicators that characterise the selected solutions by analysis stages. Changing the character of the stages allows determining the appropriate criteria and calculating the weighting factors according to their importance.