















































ISSN 2744-1741 
Defense and Security Studies  Original Research 
Vol. 3, January 2022, pp.83-100 
https://doi.org/10.37868/dss.v3.id199 

This work is licensed under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) that allows others 
to share and adapt the material for any purpose (even commercially), in any medium with an acknowledgement of the work's 
authorship and initial publication in this journal. 

 83 

 
 
Using Data Envelopment Analysis (DEA) for measuring efficiency in 
the Defense Sector 
 
Ivan Okromtchedlishvili1* 
1 PhD student, Business Administration, Faculty of Business and Technology, International Black Sea University, Tbilisi, Georgia 
 
 

*Corresponding author E-mail:  iokro@yahoo.com

Received Oct. 3, 2022 
Revised Nov. 15, 2022 
Accepted Nov. 17, 2022 

Abstract 
The way to improve the efficiency and effectiveness of public spending, which is 
a top priority for any government in any country, implies the introduction of 
Performance-Based Budgeting (PBB). One of the more advanced government-
wide performance budgeting systems that uses performance information 
systematically in the preparation of the government budget is program budgeting. 
It is important to keep in mind that without systematic development and use of 
program performance information and adequate and effective performance 
indicators, program budgeting in the defense sector does not make sense as a tool 
to improve the efficiency and effectiveness of the defense resource management 
process.  
Only by defining and tracking success can it be known if the defense 
organizations and units perform efficiently and effectively. In this article, Data 
Envelopment Analysis (DEA) was considered an instrument that can be used to 
measure, evaluate, and analyze the efficiency of the state and government as a 
whole, as well as commercial and non-profit organizations, including military 
units. It can be used as an instrument to hold managers accountable for their 
performance, which is critical to effective PBB. In this article, DEA has been 
applied to NATO members and some Eastern Europe post-Soviet aspirant and 
partner countries (Ukraine, Georgia and Moldova) to understand how efficient 
each country is at achieving its military power.  
In order to demonstrate the feasibility of using DEA to examine the efficiency of 
the infantry battalions of the infantry brigades under the Eastern and Western 
Commands of the Georgian Defense forces (GDF), an illustrative analysis of the 
efficiency of the aforementioned units was carried out using fictitious data. 

© The Author 2022. 
Published by ARDA. 

Keywords: Program budgeting; Performance; Efficiency; Effectiveness; Data 
Envelopment Analysis. 

1. Introduction 

The introduction of Performance-Based Budgeting (PBB) is a way to improve the efficiency and effectiveness 
of public spending, which is a top priority for any government in any country.  This approach implies focusing 
rather on the results of spending and the achievement of policy objectives than on the management of inputs 
and provides budget decision-makers with greater discretion in the use of resources and in deciding the input 



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84 

mix. However, simultaneously, increased flexibility, and weakened central controls are counterbalanced by 
stronger internal controls and oversight and accountability mechanisms to hold managers accountable for the 
results of their performance. PBB implies the systematic use of performance information in the budget process 
to make results a central determinant of budget funding decisions, and thereby make budgeting a powerful 
instrument for maximizing government’s efficiency and effectiveness. 
Program budgeting is one of the most advanced nationwide performance budgeting systems that 
systematically uses performance information in the preparation of the state budget where expenditures are 
classified into groups of similar activities or projects (i.e. programs) with common outputs and outcomes. 
The main differences between the traditional line-item budget method and the program budget method are 
presented in the Table 1. 

Table 1. The main differences between the traditional line-item budget method and the program budget 
method [26] 

Budget Method Characteristics 
Primary 

Organization 
Feature 

Budget Focus 

Line-Item 
Expenditure Budget 

Expenditure by commodity or 
resource purchased 

Resources Purchased Control of Resources 

Program Budget 
Expenditure Related to Public 
Goals Cost data across 
organizational lines 

Achievements 
(products or outputs) 

Planning 

 
Defense is an important part of the public sector, and its organizations consume large amounts of public 
resources. Improving the efficiency and effectiveness of managing defense funds and ensuring a successful 
defense budgeting process implies introducing the performance-based (program) budgeting approach in the 
defense sector as well.  
The systematic development and use of program performance information is critical to achieving a good 
defense program budget. Without adequate and effective performance indicators and their application to 
assess the performance of program managers, program budgeting in the defense sector does not make sense as 
a tool to improve the efficiency and effectiveness of the defense resource management process; this will only 
make it easier and simpler for the ministry to allocate and use budgetary resources by loosening line item 
controls, without obtaining the core benefits of program budgeting. 
Van Dooren et al. [1, p. 20] argue that “performance can be defined as outputs and outcomes.” The principal 
tool of program budgeting identified by Robinson [2, p. 2], along with “budgetary expenditure classification 
in terms of outcome/output groups (“programs”), is “the systematic gathering of performance information 
(through indicators, evaluation, etc.) to inform decisions about budgetary priorities between competing 
programs.”  Performance-based budgets require information on inputs (measured in monetary terms), outputs 
(units of output), efficiency and productivity data (cost per activity), and effectiveness information (level of 
goal achievement) [3]. 
In the case of the defense ministry, performance information (outputs, outcomes, and indicators) and its 
systematic development and use are critical to achieving a good defense program budget and an effective 
resource allocation. The existence of a clear linkage between resource allocation and desired/produced outputs 
and outcomes is crucial for defense decision-makers to provide them with the ability to compare the costs and 
benefits of alternative spending options and choose the most effective ones, as well as monitor and control 
performance. 
The old management adage “you can’t manage what you can’t measure” applies to the defense sector as well. 
Without defining and tracking success, it is impossible to know if the defense organizations and units are 
successful. 
When considering the defense sector's activities, two aspects can be distinguished. The first concerns the 
products/services (outputs) produced by defense entities through the use of resources and is related to 



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efficiency ("doing things right"). The second aspect, which concerns the impact of the produced products or 
services (outputs) on the objectives set for defense, is related to effectiveness (“doing the right things”). 
As Webb & Angelis [24, p.21] noted, “to measure efficiency, we must understand the relationship between 
the cost of inputs and the amount of outputs […] to measure effectiveness, we must understand the 
relationship between the organization’s goals and objectives [or outcomes] and its outputs […].” 
In order to do the right things (or to achieve effectiveness), defense policy-makers and decision-makers have 
to choose and develop the right mix of subprogram (intermediate) outputs to produce the final output (military 
capability) of the defense program, maximizing their preference value for outcomes, while subprogram 
managers have to do things right when responsible for producing outputs efficiently [13].  
Data Envelopment Analysis (DEA) can be seen as a tool to measure and evaluate the effectiveness and 
efficiency of the state and government as a whole, as well as non-profit and commercial organizations, units 
and subunits (including defense organizations and units). It can be used as an instrument to hold managers 
accountable for their performance which is critical to effective PBB. 
The results of the DEA analysis, in the form of potential improvements, offer management (commanders) 
opportunities to explore in search of higher performance. The process includes identifying the main sources of 
inefficiency, as well as those units that can become a benchmark for others. 
In this study, DEA has been applied to NATO members and some Eastern Europe post-Soviet aspirant and 
partner countries (Ukraine, Georgia and Moldova) to understand how efficient each country is at achieving its 
military power. The efficiency of the decision-making units was measured with a CCR model. 
As for the Georgian Defense Forces (GDF) units, in particular the infantry battalions of the infantry brigades 
under the Eastern and Western Commands, there are significant limitations in conducting such research due to 
the secrecy of detailed information, especially regarding the output of the defense program, namely, the 
military capability and its indicators – readiness levels of units. In addition, due to the peculiarities of the 
current defense program structure, obtaining accurate cost information, such as detailed information on the 
cost per battalion for any given period, should be very problematic. Therefore, in order to demonstrate the 
feasibility of using DEA to examine the efficiency of operational units, an illustrative analysis of the 
efficiency of the aforementioned infantry battalions was carried out using fictitious data. 

2. Data Envelopment Analysis (DEA) 

2.1 The use of the DEA in measuring performance 

An excellent mathematical programming tool that can be used to measure, evaluate, and analyze performance 
is data envelopment analysis (DEA), which has been used to evaluate the performance of many different types 
of organizations, including government, not-for-profit and commercial units and subunits since it was first 
introduced in the late 1970s.  
As a comparative performance measurement tool, DEA is aimed at facilitating “a program to improve 
performance, not to provide a simple grading of service providers” [4]. According to Avkiran, DEA is a non-
parametric method that provides a comparative ratio of weighted outputs to inputs for each decision-making 
unit (DMU), i.e., a relative efficiency score, which is usually reported as a number from 0 to 100% or 0 to 1. 
A unit scoring less than 100% is considered inefficient compared to other units in the sample [5]. 
Efficiency can be defined as a "degree to which the observed use of resources to produce outputs of a given 
quality matches the optimal use of resources to produce outputs of a given quality" [4, p. 14]. Sherman defines 
efficiency as "the ability to produce products or services with the minimum level of resources required" [6, p. 
3]. Farrell recognized the importance of measuring the extent to which outputs could be increased through 
higher efficiency without the use of additional inputs [7]. The Pareto optimality condition for efficient 
production states that a DMU is inefficient if the output can be increased without increasing any input and 
without decreasing any other output; likewise, a DMU is inefficient if the input can be decreased without 
decreasing any output and without increasing any other input [8]. 



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DEA measures the efficiency of decision-making units (DMUs) using linear programming techniques, 
envelops observed input-output vectors as tightly as possible and allows to consider multiple input-output 
vectors at the same time without any assumptions on data distribution. In each case, efficiency is measured by 
proportional changes in inputs or outputs. According to Ji and Lee, “a DEA model can be subdivided into an 
input-oriented model, which minimizes inputs while satisfying at least the given output levels, and an output-
oriented model, which maximizes outputs without requiring more of any observed input values” [9, p. 268].  
 
The original Charnes, Cooper, and Rhodes (CCR) DEA model utilizes linear programming to produce an 
efficiency measure for a DMU, requiring only that the DMUs convert similar inputs to similar outputs and 
that these can be quantified. The logic of the model implies, first, defining the underlying premise that 
efficiency is the sum of weighted outputs over the sum of weighted inputs [10]. The DEA model for the kth 
DMU can be formulated as follows:  
 
             t  

∑ UrYrk  
Max Ek =         r = 1     

                  m  
∑ ViXik  
i = 1  

                 t  
                 ∑ UrYrj    
 s.t.          r = 1    ≤  1      j = 1,……n  
                 m  
                 ∑ ViXij  
                  i = 1   
                  Ur   ≥   0               r = 1,…….t  
                  Vi  ≥   0                i = 1,…….m,  

 
Where:  

 
Objective function    
Ek = the efficiency index of the k

th DMU;  
 

Parameters    
yrj = the amount of the r

th output for the jth DMU;    
xij = the amount of the i

th input for the jth DMU;    
t   = the number of outputs;    
m = the number of inputs; and     
n = the number of DMUs  

 
Decision variables    
ur = the weight assigned to the r

th output; and    
vi = the weight assigned to the i

th input [11]. 

Generally, in the defense sector area, DEA efficiency and productivity studies have focused on various 
support functions such as maintenance and recruitment, as well as operational units, the core area of defense 
(see Table 2). 

 
 



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87 

Table 2. Bibliography of DEA in the military [12] 

Paper  Field  Inputs  Outputs  Observa
tions  

Lewin and Morey (1981) Recruitment 10  2  43  
Charnes et al. (1985)  Maintenance  8  4  42  

Bowlin (1987)  Maintenance  3  4  21  

Bowlin (1989)  Accounting and finance  1  5  18  

Ali et al. (1989)*  Recruitment  n/a  n/a  n/a  

Roll et al. (1989)  Maintenance  3  2  10-35  

Clarke (1992)  Maintenance  4  2  17  

Ozcan and Bannick (1994) Hospitals 6 2 23 
Bowlin (2004)  Civil reserve air fleet  4  7  37-111  

Brockett et al. (2004)  Recruitment  1  10  n/a  

Sun (2004)  Maintenance  6  5  30  

Farris et al. (2006) Engineering design projects 4  1  15  
Lu (2011)  
Kalin (2021) 
Hanson (2012) 
Hanson (2019) 

Outlets  
Logistics 
Operational units 
Combat units 

4 
4 
3 
3 (1) 

2  
1 
1 
1 (1) 

31 
34 
11 
12  

*Paper not available.  

Hanson conducted interesting research that examined the productivity and efficiency of the core area of the 
Norwegian armed forces, operational units, using Data Envelopment Analysis (DEA). A model has been 
developed to analyze the productivity and efficiency by DEA for the operational units of the armed forces. As 
Hanson noted, “By aggregating activity standards and quality measures the model enables a meaningful and 
measurable expression for the output of an operational unit” [12, p. 25].  
In another study, Hanson used a scenario-based planning approach to develop an effectiveness measurement 
model for situations where traditional methods such as two-stage regression fail due to long time lags and lack 
of variation in the variables. According to Hanson, “from a sample of 12 combat units in the Norwegian 
Armed Forces, producing different outputs, [it was found] that inefficiencies in output mix can explain most 
of the changes in overall effectiveness over a four-year period of time” [13, p. 1]. 

2.2 Examining the efficiency of NATO members and some partner countries in achieving military 
power by using DEA 

DEA has been applied to NATO members and some Eastern Europe post-Soviet aspirant and partner countries 
(Ukraine, Georgia and Moldova) to understand how efficient each country is at achieving its military power. 
The efficiency of the decision-making units was measured with a CCR model.  

2.2.1 Specification of Data and Variables  

A total of 31 DMUs were selected for the study. These DMUs focused on NATO members and some Eastern 
Europe post-Soviet aspirant and partner countries (Ukraine, Georgia and Moldova). The study was aimed at 
measuring how efficiently each country achieved its military power. Four variables were retrieved from the 
open sources [28], [29], [30], [31]: two input variables - Defense Expenditure, Current prices and exchange 
rates US dollars for 2020; Defense Expenditure as a share of real GDP (%) for 2020; and two output 
variables - Military Personnel for 2020; and Military Strength Ranking for 2022 (reversed).  



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Defense expenditure refers to all current and capital spending on the armed forces of a state and in theory, the 
higher the level of defense expenditure, the better the military power of the state.  
The commitment made in 2014 by members of the North Atlantic Treaty Organization (NATO) to increase 
their Defense expenditure as a share of real GDP to 2 % by 2024 is still the subject of debate about military 
spending in NATO [25]. 
In my recent article, I proposed to define the main output of a defense program as “Military Capability as a 
comprehensive force structure consisting of its constituent force elements/capabilities […] with an integrated 
set of aspects categorized as doctrine, organization, training, materiel, leadership development, personnel, and 
facilities, and with an appropriate readiness level assessed at a concrete time” [23, p. 94].  
Therefore, in this case, it is crucial that Military Personnel be considered as an integral part of military 
capability (combat-ready forces), i.e., the “production” of military personnel implies the simultaneous 
development of the military capability as a whole (across the entire DOTMLPF spectrum).  
In principle, the GFP rating (Military Strength Ranking) is a kind of indicator of the performance of the 
defense organization of a state, and an improved position in the ranking is evidence of increased efficiency 
and effectiveness of the defense programs. For this study, the reverse military power index (Global Firepower, 
2022) was used, so it was assumed that the higher the military power index, the better the country. At the 
initial measure, the lower the military index, the better. 

2.2.2 DEA Model and Results  

The DEA analysis was carried out using DEA-Solver-PRO 5.0 software [22] developed by W.W. Cooper, 
L.M. Seiford and K. Tone. This study performed a CCR input-oriented DEA model, and the main focus was 
to see how efficient each country was at producing military capability and achieving its military power index, 
given its resources or inputs.  
Table 3 and Table 4 below show the results of running the model.  

Table 3. DEA Test Results 

Rank DMU Score   Rank DMU Score 

1 Moldova  1 17 Netherlands 0,57707535 

1 United States 1 18 Bulgaria 0,570603056 

1 Spain 1 19 Poland 0,569492872 

1 Türkiye 1 20 Hungary 0,55453459 

5 Czech Republic 0,971773347 21 United Kingdom 0,548049942 

6 Ukraine  0,932569009 22 Belgium 0,533707754 

7 Italy 0,909221694 23 Croatia 0,528911822 

8 Portugal 0,8447062 24 Slovenia 0,5158751 

9 Georgia 0,792712503 25 Slovak Republic 0,476957309 

10 France 0,697923222 26 Albania 0,376089889 

11 Romania 0,665795625 27 North Macedonia 0,368317769 

12 Germany 0,662166375 28 Lithuania 0,28768714 

13 Greece 0,634367881 29 Latvia 0,20825904 

14 Norway 0,631334284 30 Montenegro 0,197800912 

15 Canada 0,610115983 31 Estonia 0,157514612 

16 Denmark 0,578313316 

 
 
 
 



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Table 4. Projections by the CCR Model 

No DMU Score       

   I/O Data Projection Difference   % 

1 United States 1       

  Defense Expenditure 7,84952E+11 7,84952E+11 0 0,00% 

  
Defense Expenditure as a share of 

real GDP (%) 
3,72 3,72 0 0,00% 

  Military Personnel 1346000 1346000 0 0,00% 

  Military Strength Ranking (reversed) 35,8958 35,8958 0 0,00% 

2 France 0,697923222       

  Defense Expenditure 52727000000 36799397750 -15927602250 -30,21% 

  
Defense Expenditure as a share of 

real GDP (%) 
2,03 1,416784142 -0,613215858 -30,21% 

  Military Personnel 208000 208000 0 0,00% 

  Military Strength Ranking (reversed) 5,7275 5,7275 0 0,00% 

3 United Kingdom 0,548049942       

  Defense Expenditure 61925000000 33937992687 -27987007313 -45,20% 

  
Defense Expenditure as a share of 

real GDP (%) 
2,29 1,255034368 -1,034965632 -45,20% 

  Military Personnel 156200 175283,8318 19083,83183 12,22% 

  Military Strength Ranking (reversed) 5,2184 5,2184 0 0,00% 

4 Italy 0,909221694       

  Defense Expenditure 26071000000 23704318784 -2366681216 -9,08% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,38 1,254725938 -0,125274062 -9,08% 

  Military Personnel 175500 175500 0 0,00% 

  Military Strength Ranking (reversed) 4,7871 4,7871 0 0,00% 

5 Türkiye 1       

  Defense Expenditure 13396000000 13396000000 0 0,00% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,86 1,86 0 0,00% 

  Military Personnel 437200 437200 0 0,00% 

  Military Strength Ranking (reversed) 4,4351 4,4351 0 0,00% 

6 Germany 0,662166375       

  Defense Expenditure 58902000000 39002923817 -19899076183 -33,78% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,55 1,026357881 -0,523642119 -33,78% 

  Military Personnel 186900 186900 0 0,00% 

  Military Strength Ranking (reversed) 4,3067 4,3067 0 0,00% 

7 Spain 1       

  Defense Expenditure 12828000000 12828000000 0 0,00% 

  
Defense Expenditure as a share of 

real GDP (%) 
1 1 0 0,00% 

  Military Personnel 122500 122500 0 0,00% 

  Military Strength Ranking (reversed) 3,7337 3,7337 0 0,00% 

8 Ukraine  0,932569009       

  Defense Expenditure 5924000000 5524538808 -399461191,8 -6,74% 



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90 

  
Defense Expenditure as a share of 

real GDP (%) 
4,1 3,823532936 -0,276467064 -6,74% 

  Military Personnel 209000 209000 0 0,00% 

  Military Strength Ranking (reversed) 3,4016 6,261898544 2,860298544 84,09% 

9 Canada 0,610115983       

  Defense Expenditure 23595000000 14395686628 -9199313372 -38,99% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,44 0,878567016 -0,561432984 -38,99% 

  Military Personnel 71000 111398,8073 40398,80729 56,90% 

  Military Strength Ranking (reversed) 3,3736 3,3736 0 0,00% 

10 Poland 0,569492872       

  Defense Expenditure 13590000000 7739408124 -5850591876 -43,05% 

  
Defense Expenditure as a share of 

real GDP (%) 
2,28 1,298443747 -0,981556253 -43,05% 

  Military Personnel 120000 120000 0 0,00% 

  Military Strength Ranking (reversed) 3,1759 3,1759 0 0,00% 

11 Greece 0,634367881       

  Defense Expenditure 5019000000 3183892393 -1835107607 -36,56% 

  
Defense Expenditure as a share of 

real GDP (%) 
2,65 1,681074884 -0,968925116 -36,56% 

  Military Personnel 107600 107600 0 0,00% 

  Military Strength Ranking (reversed) 2,8681 2,8681 0 0,00% 

12 Norway 0,631334284       

  Defense Expenditure 7272000000 4591062910 -2680937090 -36,87% 

  
Defense Expenditure as a share of 

real GDP (%) 
2,01 1,26898191 -0,74101809 -36,87% 

  Military Personnel 20800 54698,49719 33898,49719 
162,97

% 

  Military Strength Ranking (reversed) 2,6527 2,6527 0 0,00% 

13 Netherlands 0,57707535       

  Defense Expenditure 13125000000 7574113967 -5550886033 -42,29% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,47 0,848300764 -0,621699236 -42,29% 

  Military Personnel 40000 75401,12632 35401,12632 88,50% 

  Military Strength Ranking (reversed) 2,5771 2,5771 0 0,00% 

14 Romania 0,665795625       

  Defense Expenditure 5051000000 3362933704 -1688066296 -33,42% 

  
Defense Expenditure as a share of 

real GDP (%) 
2,03 1,351565119 -0,678434881 -33,42% 

  Military Personnel 66400 66400 0 0,00% 

  Military Strength Ranking (reversed) 2,5072 2,5072 0 0,00% 

15 Czech Republic 0,971773347       

  Defense Expenditure 3201000000 3110646484 -90353515,56 -2,82% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,31 1,273023085 -3,70E-02 -2,82% 

  Military Personnel 26800 41984,69203 15184,69203 56,66% 

  Military Strength Ranking (reversed) 2,3944 2,3944 0 0,00% 

16 Portugal 0,8447062       



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91 

  Defense Expenditure 3306000000 2792598697 -513401303 -15,53% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,43 1,207929866 -0,222070134 -15,53% 

  Military Personnel 28700 38467,306 9767,306 34,03% 

  Military Strength Ranking (reversed) 2,2436 2,2436 0 0,00% 

17 Hungary 0,55453459       

  Defense Expenditure 2770000000 1536060814 -1233939186 -44,55% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,79 0,992616916 -0,797383084 -44,55% 

  Military Personnel 22700 25069,63378 2369,63378 10,44% 

  Military Strength Ranking (reversed) 1,7083 1,7083 0 0,00% 

18 Denmark 0,578313316       

  Defense Expenditure 4979000000 2879422001 -2099577999 -42,17% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,4 0,809638643 -0,590361357 -42,17% 

  Military Personnel 18100 34469,74292 16369,74292 90,44% 

  Military Strength Ranking (reversed) 1,6836 1,6836 0 0,00% 

19 Slovak Republic 0,476957309       

  Defense Expenditure 2050000000 977762482,9 -1072237517 -52,30% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,96 0,934836325 -1,025163675 -52,30% 

  Military Personnel 12900 19568,30014 6668,300138 51,69% 

  Military Strength Ranking (reversed) 1,5252 1,5252 0 0,00% 

20 Croatia 0,528911822       

  Defense Expenditure 1031000000 545308088,2 -485691911,8 -47,11% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,8 0,952041279 -0,847958721 -47,11% 

  Military Personnel 15200 16045,33197 845,3319659 5,56% 

  Military Strength Ranking (reversed) 1,4729 1,4729 0 0,00% 

21 Bulgaria 0,570603056       

  Defense Expenditure 1075000000 613398285,7 -461601714,3 -42,94% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,55 0,884434738 -0,665565262 -42,94% 

  Military Personnel 25600 25600 0 0,00% 

  Military Strength Ranking (reversed) 1,3664 1,3664 0 0,00% 

22 Belgium 0,533707754       

  Defense Expenditure 5427000000 2896431982 -2530568018 -46,63% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,05 0,560393142 -0,489606858 -46,63% 

  Military Personnel 25200 31646,37661 6446,376605 25,58% 

  Military Strength Ranking (reversed) 1,3265 1,3265 0 0,00% 

23 Lithuania 0,28768714       

  Defense Expenditure 1176000000 338320076,6 -837679923,4 -71,23% 

  
Defense Expenditure as a share of 

real GDP (%) 
2,11 0,607019865 -1,502980135 -71,23% 

  Military Personnel 16300 16300 0 0,00% 

  Military Strength Ranking (reversed) 0,8633 0,924254558 6,10E-02 7,06% 

24 Slovenia 0,5158751       



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  Defense Expenditure 568000000 293017056,6 -274982943,4 -48,41% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,08 0,557145108 -0,522854892 -48,41% 

  Military Personnel 7000 9164,882239 2164,882239 30,93% 

  Military Strength Ranking (reversed) 0,8573 0,8573 0 0,00% 

25 Georgia 0,792712503       

  Defense Expenditure 292000000 231472050,9 -60527949,13 -20,73% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,8 1,426882505 -0,373117495 -20,73% 

  Military Personnel 20650 20650 0 0,00% 

  Military Strength Ranking (reversed) 0,8169 2,09945964 1,28255964 
157,00

% 

26 Latvia 0,20825904       

  Defense Expenditure 743000000 154736466,7 -588263533,3 -79,17% 

  
Defense Expenditure as a share of 

real GDP (%) 
2,22 0,462335069 -1,757664931 -79,17% 

  Military Personnel 7000 7000 0 0,00% 

  Military Strength Ranking (reversed) 0,6953 0,6953 0 0,00% 

27 Moldova  1       

  Defense Expenditure 44500000 44500000 0 0,00% 

  
Defense Expenditure as a share of 

real GDP (%) 
0,4 0,4 0 0,00% 

  Military Personnel 5150 5150 0 0,00% 

  Military Strength Ranking (reversed) 0,5859 0,5859 0 0,00% 

28 Estonia 0,157514612       

  Defense Expenditure 719000000 113253006,3 -605746993,7 -84,25% 

  
Defense Expenditure as a share of 

real GDP (%) 
2,32 0,365433901 -1,954566099 -84,25% 

  Military Personnel 6600 6600 0 0,00% 

  Military Strength Ranking (reversed) 0,5455 0,5455 0 0,00% 

29 Albania 0,376089889       

  Defense Expenditure 188000000 70704899,2 -117295100,8 -62,39% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,27 0,47763416 -0,79236584 -62,39% 

  Military Personnel 6700 6700 0 0,00% 

  Military Strength Ranking (reversed) 0,4276 0,701893273 0,274293273 64,15% 

30 Montenegro 0,197800912       

  Defense Expenditure 83000000 16417475,73 -66582524,27 -80,22% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,73 0,147572816 -1,582427184 -91,47% 

  Military Personnel 1900 1900 0 0,00% 

  Military Strength Ranking (reversed) 0,1695 0,216157282 0,046657282 27,53% 

31 North Macedonia 0,368317769       

  Defense Expenditure 154000000 56720936,47 -97279063,53 -63,17% 

  
Defense Expenditure as a share of 

real GDP (%) 
1,25 0,460397212 -0,789602788 -63,17% 

  Military Personnel 6100 6100 0 0,00% 

  Military Strength Ranking (reversed) 0,1283 0,67508041 0,54678041 426,1% 



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2.2.3 Summary and Recommendations 

The study showed that some states were efficient at producing their military capability and achieving the 
military power index utilizing the inputs provided, while others needed to improve. According to the test 
results, 4 out of the 31 countries (United States, Spain, Türkiye and Moldova) outputted 1.00 or 100 percent 
efficiency across the DEA model and can be used as benchmarks. The CCR input-oriented model we applied 
measures technical efficiency, or how resources are used during the production/delivery of an output (doing 
the things right). Since the scores of other states were below 1.00 or 100 percent, this means that the ministries 
of defense should look for ways to utilize the allocated budgetary resources more efficiently to achieve higher 
results and improve positions in the Military Strength Ranking.   

2.3 A sample DEA model for measuring the efficiency of the GDF infantry battalions 

In the case of the Georgian Defense Forces (GDF), the DEA can be used, for example, to examine the 
efficiency of operational units, particularly the infantry battalions of the infantry brigades under the Eastern 
and Western Commands, on delivery of readiness. However, a significant limitation in conducting such 
research is the secrecy of detailed information, especially regarding the output of the defense program, 
namely, the military capability and its indicators – readiness levels of units. Also, due to the peculiarities of 
the current defense program structure, it should be quite problematic to obtain accurate information regarding 
the inputs, for example, detailed costs per battalion for any particular period. Consequently, in order to 
demonstrate the possibility of using DEA for the above purposes, an illustrative analysis of the efficiency of 
battalions was carried out using fictitious data. 
 

 

Figure 1. Units, equipment, and personnel in an Army Infantry Brigade Combat Team, excluding support 
battalion [17] 



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According to Strategic Defense Review (SDR) 2021-2025 [14], the GDF Future Force Structure, along with 
other military units, includes four infantry brigades under the Eastern and Western Commands. 
Due to the unavailability of relevant information regarding the structure of brigades of the GDF from open 
sources, data on the structure of brigades of the US Army were used as an example. Infantry Brigade Combat 
Teams (IBCTs) constitute the Army’s “light”, primarily foot-mobile ground forces that can move by foot, 
vehicle, or air (either air landed or by helicopter) [15]. According to the Army’s Field Manual (FM) 3-96, the 
IBCTs are employed as follows: “The role of the IBCT is to close with the enemy by means of fire and 
movement to destroy or capture enemy forces, or to repel enemy attacks by fire, close combat, and 
counterattack to control land areas, including populations and resources” [16, p. 1-2]. 
IBCTs are relatively independent tactical formations that are designed to include approximately 4,400 
personnel [17]. As can be seen from Figure 1, there are three infantry battalions in the IBCT. 

Since there are four infantry brigades in the GDF Future Force Structure, it can be assumed that there will be a 
total of 12 infantry battalions that will be treated as decision making units (DMUs) in our sample DEA model. 
Two input variables can be defined for the use of personnel and equipment: (1) Personnel Costs - pay and 
benefits for military personnel, compensation for civilian employees, health care costs, and travel expenses for 
military and civilian personnel; and (2) Material Costs - daily expenses of operating a unit, such as equipment 
maintenance, training, support contractors, and so on. Readiness indicators by category can be used as 
outputs: personnel (P-level), equipment availability (S-level), equipment readiness (R-level) and training (T-
level) (see Figure 2). 

 

Figure 2. Data model for the DEA 

It should be mentioned that according to Avkiran, “there are some rules of thumb on the number of inputs and 
outputs to select and their relation to the number of DMUs” [5, p. 115]. Boussofiane, Dyson and Thanassoulis 
argue that to obtain good discriminatory power out of the CCR and BCC models, the lower bound on the 
number of DMUs must be a multiple of the number of inputs and the number of outputs. For example, if there 
are 2 inputs and 4 outputs, the minimum total number of DMUs must be 8 for some discriminatory power to 
exist in the model [18]. 



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Golany and Roll propose a rule of thumb that the number of units should be at least twice the number of 
inputs and outputs under consideration [19]. Bowlin mentions the need to have three times as many DMUs as 
there are input and output variables [20].  
According to Dyson et al., a total of two times the product of the number of input and output variables is 
recommended [21]. For example, for a 3-input, 4-output model, Golany and Roll recommend 14 DMUs, while 
Bowlin recommends 21 DMUs. In any case, these figures should probably be used as the minimum for 
baseline performance models. 
As can be seen, the variants of DMUs, inputs and outputs proposed in our example basically meet the above 
requirements. 
Table 5 below shows the fictitious data for conducting the DEA. 

Table 5. Fictitious data for conducting the DEA 

DMU name 
Input 1 

Personnel 
costs GEL 

Input 2 
Material 

costs GEL 

Output 1 
P-level 

(%) 

Output 2 
S-level 

(%) 

Output 3 
R-level 

(%) 

Output 4 
T-level 

(%) 

1st Infantry battalion 10 800 000 5 000 000 85 91 70 85 

2nd Infantry battalion 10 200 000 5 500 000 75 82 75 85 

3rd Infantry battalion 11 760 000 6 000 000 88 74 96 87 

4th Infantry battalion 11 160 000 7 000 000 74 96 84 78 

5th Infantry battalion 10 680 000 6 500 000 96 97 99 95 

6th Infantry battalion 10 920 000 5 850 000 81 75 82 76 

7th Infantry battalion 10 788 000 5 100 000 68 85 78 82 

8th Infantry battalion 11 520 000 5 350 000 92 86 91 95 

9th Infantry battalion 11 040 000 5 120 000 77 88 99 87 

10th Infantry battalion 10 560 000 4 950 000 85 91 75 81 

11th Infantry battalion 10 320 000 6 200 000 86 69 85 73 

12th Infantry battalion 11 568 000 6 850 000 91 92 94 93 

 
The exemplifying analysis was carried out using DEA-Solver-PRO 5.0 software [22]. As can be seen from the 
DEA test results depicted in Table 6 and 7, five of the twelve infantry battalions are efficient, while the rest 
show some inefficiency. 

Table 6. DEA test results 

  Rank DMU Score 

1 10th Infantry battalion 1 

1 1st Infantry battalion 1 

1 9th Infantry battalion 1 

1 8th Infantry battalion 1 

1 5th Infantry battalion 1 

6 2nd Infantry battalion 0,970912603 

7 7th Infantry battalion 0,954380827 

8 4th Infantry battalion 0,947123379 

9 3rd Infantry battalion 0,939071369 

10 11th Infantry battalion 0,93254636 

11 12th Infantry battalion 0,911386993 

12 6th Infantry battalion 0,87500128 



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Table 7. Projections by the CCR Model 

No. DMU Score       

   I/O Data Projection Difference   % 

1 1st Infantry battalion 1       

  Personnel costs GEL 10800000 10800000 0 0,00% 

  Material costs GEL 5000000 5000000 0 0,00% 

  P-level (%) 85 85 0 0,00% 

  S-level (%) 91 91 0 0,00% 

  R-level (%) 70 70 0 0,00% 

  T-level (%) 85 85 0 0,00% 

2 2nd Infantry battalion 0,970912603       

  Personnel costs GEL 10200000 9903308,547 -296691,4534 -2,91% 

  Material costs GEL 5500000 5340019,314 -159980,6857 -2,91% 

  P-level (%) 75 84,23988411 9,239884114 12,32% 

  S-level (%) 82 82,23862868 0,238628682 0,29% 

  R-level (%) 75 85,26924191 10,26924191 13,69% 

  T-level (%) 85 85 0 0,00% 

3 3rd Infantry battalion 0,939071369       

  Personnel costs GEL 11760000 11043479,3 -716520,7003 -6,09% 

  Material costs GEL 6000000 5634428,214 -365571,7859 -6,09% 

  P-level (%) 88 88 0 0,00% 

  S-level (%) 74 90,00404513 16,00404513 21,63% 

  R-level (%) 96 96 0 0,00% 

  T-level (%) 87 92,00663008 5,006630078 5,75% 

4 4th Infantry battalion 0,947123379       

  Personnel costs GEL 11160000 10569896,91 -590103,0928 -5,29% 

  Material costs GEL 7000000 6432989,691 -567010,3093 -8,10% 

  P-level (%) 74 95,01030928 21,01030928 28,39% 

  S-level (%) 96 96 0 0,00% 

  R-level (%) 84 97,97938144 13,97938144 16,64% 

  T-level (%) 78 94,02061856 16,02061856 20,54% 

5 5th Infantry battalion 1       

  Personnel costs GEL 10680000 10680000 0 0,00% 

  Material costs GEL 6500000 6500000 0 0,00% 

  P-level (%) 96 96 0 0,00% 

  S-level (%) 97 97 0 0,00% 

  R-level (%) 99 99 0 0,00% 

  T-level (%) 95 95 0 0,00% 

6 6th Infantry battalion 0,87500128       

  Personnel costs GEL 10920000 9555013,98 -1364986,02 -12,50% 

  Material costs GEL 5850000 5118757,489 -731242,5106 -12,50% 

  P-level (%) 81 81 0 0,00% 

  S-level (%) 75 78,99387085 3,993870847 5,33% 

  R-level (%) 82 82 0 0,00% 

  T-level (%) 76 81,84403062 5,84403062 7,69% 



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7 7th Infantry battalion 0,954380827       

  Personnel costs GEL 10788000 10295860,37 -492139,6349 -4,56% 

  Material costs GEL 5100000 4867342,219 -232657,7807 -4,56% 

  P-level (%) 68 78,80442417 10,80442417 15,89% 

  S-level (%) 85 85 0 0,00% 

  R-level (%) 78 78 0 0,00% 

  T-level (%) 82 82 0 0,00% 

8 8th Infantry battalion 1       

  Personnel costs GEL 11520000 11520000 0 0,00% 

  Material costs GEL 5350000 5350000 0 0,00% 

  P-level (%) 92 92 0 0,00% 

  S-level (%) 86 86 0 0,00% 

  R-level (%) 91 91 0 0,00% 

  T-level (%) 95 95 0 0,00% 

9 9th Infantry battalion 1       

  Personnel costs GEL 11040000 11040000 0 0,00% 

  Material costs GEL 5120000 5120000 0 0,00% 

  P-level (%) 77 77 0 0,00% 

  S-level (%) 88 88 0 0,00% 

  R-level (%) 99 99 0 0,00% 

  T-level (%) 87 87 0 0,00% 

10 10th Infantry battalion 1       

  Personnel costs GEL 10560000 10560000 0 0,00% 

  Material costs GEL 4950000 4950000 0 0,00% 

  P-level (%) 85 85 0 0,00% 

  S-level (%) 91 91 0 0,00% 

  R-level (%) 75 75 0 0,00% 

  T-level (%) 81 81 0 0,00% 

11 11th Infantry battalion 0,93254636       

  Personnel costs GEL 10320000 9623878,44 -696121,5601 -6,75% 

  Material costs GEL 6200000 5781787,435 -418212,5652 -6,75% 

  P-level (%) 86 86 0 0,00% 

  S-level (%) 69 87,15708111 18,15708111 26,31% 

  R-level (%) 85 88,04103148 3,041031479 3,58% 

  T-level (%) 73 84,94507688 11,94507688 16,36% 

12 12th Infantry battalion 0,911386993       

  Personnel costs GEL 11568000 10542924,74 -1025075,26 -8,86% 

  Material costs GEL 6850000 6243000,905 -606999,0952 -8,86% 

  P-level (%) 91 93,56101001 2,561010012 2,81% 

  S-level (%) 92 93,80856701 1,808567007 1,97% 

  R-level (%) 94 96,07991476 2,079914761 2,21% 

  T-level (%) 93 93 0 0,00% 

 
Sherman [27] argues that the DEA is best used as a tool that can focus the attention of managers. In the 
infantry battalions example above, potential improvements suggest opportunities for managers (commanders) 



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to explore in search of higher performance. The process includes identifying the main sources of inefficiency 
as well as those units that can become reference DMUs for others. 

3. Conclusions 

The way to improve the efficiency and effectiveness of public spending, which is a top priority for any 
government in any country, implies the introduction of Performance-Based Budgeting (PBB). Program 
budgeting is one of the most advanced government-wide performance budgeting systems that systematically 
uses performance information in the preparation of the state budget where expenditures are classified into 
groups of similar activities or projects (i.e., programs) with common outputs and outcomes. 
It is important to keep in mind that without systematic development and use of program performance 
information and adequate and effective performance indicators, program budgeting in the defense sector does 
not make sense as a tool to improve the efficiency and effectiveness of the defense resource management 
process. Only by defining and tracking success can it be known if the defense organizations and units perform 
efficiently and effectively. 
In this article, DEA was considered an excellent mathematical programming and a powerful management tool 
that can be used to measure, evaluate, and analyze the efficiency of the state and government as a whole, as 
well as commercial and non-profit organizations, including military units. DEA can be applied as an 
instrument to hold managers at all levels accountable for their performance which is critical to effective 
Performance-Based Budgeting (PBB). 
In this study, Data Envelopment Analysis (DEA) has been applied to NATO members and some Eastern 
Europe post-Soviet aspirant and partner countries (Ukraine, Georgia and Moldova) to understand how 
efficient each country is at achieving its military power. The efficiency of the decision-making units was 
measured with a CCR model. 
Due to the secrecy and peculiarities of the current defense program structure, there are significant limitations 
in obtaining detailed information on the main output of the defense, namely, the military capability and its 
indicators – readiness levels of units and accurate cost information, such as detailed information on the cost 
per battalion for any given period. Therefore, in order to demonstrate the feasibility of using DEA to examine 
the efficiency of operational units, an illustrative analysis of the efficiency of the aforementioned infantry 
battalions was carried out using fictitious data. 
I believe that one of the main barriers to using DEA as a valid tool for measuring and evaluating the 
performance of the GDF units is the current structure of the defense program. 
The introduction of the defense program structure proposed in my recent article [23], which will include the 
Major Force Program developed on a Force Capabilities basis; the definition of capabilities embodied in a 
force element as the main output of the defense subprograms; and the identification of force (program) 
elements (e.g., departments, commands, brigades, and battalions) as cost centers, will facilitate the use of the 
DEA and other statistical tools to measure and evaluate the performance of the GDF units and develop 
proposals for its improvement. 
A key precondition for the successful application of the DEA and other statistical tools in measuring and 
evaluating performance in the Ministry of Defense is the development of effective computerized financial 
management information systems (FMIS), including computerized accounting systems. 
One of the challenges for the Ministry is to implement an effective management accounting system to provide 
managers (unit commanders) with timely, accurate, meaningful, and insightful information without which an 
effective decision-making process is impossible. Well-organized accounting systems are the main original 
source of the best quality and ultimately the most reliable primary data for the life cycle costing to support 
decision-making process as well as performance measurement and evaluation. 
It is also crucial to include the “readiness level” as an output indicator in the defense program structure of the 
Georgian Ministry of Defense. The target readiness levels of the GDF units should also be specified in the 
Defense Program Guidance (DPG) and other planning documents of the MOD of Georgia (in the secret part of 



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the documents), as well as procurement objectives and descriptions of acceptable risk. Defense program 
managers who are accountable for the resources provided must monitor the balance of inputs to readiness and 
the state of readiness achieved. 

Disclaimer 

The views represented in this paper are those of the author and don’t reflect the official policy or position of 
the Ministry of Defense of Georgia. 

Declaration of competing interest 

The authors declare that they have no any known financial or non-financial competing interests in any 
material discussed in this paper. 

Funding information 

No funding was received from any financial organization to conduct this research. 

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