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ASSESSMENT OF EFFICIENCY OF MILITARY TRANSPORT UNITS USING THE DEA AND SFA METHODS

Dejan R. Despica, Nebojsa J. Bojovicb, Milorad J. Kilibardac, Marko V. Kapetanovicd

Ministry of Defence of the Republic of Serbia, w Material Resources Sector, Department for General Logistics,

Belgrade, Republic of Serbia, O e-mail: dejandespic79@gmail.com,

^ ORCID iD: ©https://orcid.org/0000-0001-5256-3436

< b University of Belgrade, Faculty for Transport and Traffic Engineering, ° Belgrade, Republic of Serbia, x e-mail: nb.bojovic@sf.bg.ac.rs, ft ORCID iD: ©https://orcid.org/0000-0001-5600-3807

c University of Belgrade, Faculty for Transport and Traffic Engineering, o^ Belgrade, Republic of Serbia

< e-mail: m.kilibarda@sf.bg.ac.rs, ORCID iD: ©https://orcid.org/0000-0003-3794-7380 University of Belgrade, Faculty for Transport and Traffic Engineering, Belgrade, Republic of Serbia,

_ e-mail: m.kapetanovic@sf.bg.ac.rs,

w ORCID iD: https://orcid.org/0000-0002-5703-6536

CD DOI: 10.5937/vojtehg67-18508; https://doi.org/10.5937/vojtehg67-18508

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>o FIELD: Mathematics, Logistics, Traffic Engineering

ARTICLE TYPE: Original Scientific Paper ¡5 ARTICLE LANGUAGE: English

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Summary:

^ The aim of the paper is to make an analysis of the efficiency of selected

transport units in the military logistics and military vehicles in carrying out the tasks of cargo transport using the method of stochastic frontier analysis (SFA) and the data envelopment analysis (DEA), and creating the basis for further investigation of the parameters that influence the efficiency of military transport units and military vehicles. The research was carried out in ten military transport units intended for the realization of tasks dealing with the logistic function of movement and transportation. The efficiency analysis was done for military vehicles used for carrying out cargo transportation tasks for the needs of supply and special needs of command, units and military institutions. The data was obtained from the software package used to monitor the exploitation of military motor vehicles in the period of one calendar year. The results show that the method selection has a major impact on the obtained technical efficiency

assessments, and therefore on possible management decisions based on the performed efficiency analysis.

Key words: efficiency, military transport units, military vehicles, data envelopment analysis, stochastic frontier analysis.

Introduction

A modern military organization together with its missions and tasks in the function of state defense cannot be imagined without its dynamic determinant i.e. its transport and transportation system that allows it to be mobile in its totality or in its parts. Increasing transport needs and demands as products of more dynamic engagement of the military in modern conditions, with a tendency of increasing efficiency and reducing operating costs, make it complicated because of the existing organizational structure of the management and transport units.

In the economy and society in general as well as in the military, logistic processes are an important factor in the functioning of the organization. The performance of the entire logistic system depends largely on the performance of the transport system as its segment. The efficiency of transport is thus imposed as a necessity in order to create a predisposition of the defense system in response to the contemporary challenges and threats to security in accordance with the needs and possibilities of the state.

Efficiency is a very important indicator of a company business analysis and it is one of the most basic and most used performances (Andrejic et al, 2016). The essence of measuring efficiency in transport is to improve efficiency.

The aim of this paper is to carry out an analysis of the efficiency of selected transport units in the military logistics and military vehicles in carrying out cargo handling tasks using the method of stochastic frontier analysis (SFA) and the data envelopment analysis (DEA) in order to create a basis for further research of the parameters that influence the efficiency of the work of the military transport units and military vehicles.

The research was, therefore, carried out in ten military transport units intended for the realization of tasks in the logistic function of movement and transportation. The efficiency analysis was carried out for military vehicles used for carrying out cargo transportation tasks for the needs of supply and special needs of command, units and military institutions. The actual data obtained from the software package used to monitor the use and exploitation of military motor vehicles were used, and they relate to a period of one calendar year.

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The efficiency analysis was realized at three levels: first level -efficiency of transport units, second level - vehicle efficiency, and third level - vehicle efficiency within defined classes (clusters). The DEA and SFA methods were used to evaluate and analyze the efficiency of transport units and vehicles. First, the selected decision units (DMUs) of relative efficiency were also defined. Then, the input and output parameters suitable for assessing the relative technical efficiency of the selected DMUs were determined, and then the corresponding DEA and SFA models were selected. Finally, the DEA and SFA models were solved and the results analyzed and interpreted.

Besides the introduction, the paper consists of four chapters. The second chapter provides the basic remarks on the functioning of transport in the defense system and defines the concept of efficiency. The third chapter describes the SFA and DEA methods used in the work to evaluate efficiency. The selection of the input and output parameters and the results of the analysis are given in the fourth chapter. Finally, the conclusion and directions for future research are given in the last chapter.

Transportation function in the defense system and the definition of the concept of efficiency

In accordance with the Rulebook on Transportation of Personnel and Assets in the Ministry of Defense and the Serbian Armed Forces (hereinafter: the Rulebook on Transportation) (Sluzbeni vojni list, 9/2013), transportation of personnel and assets in the Ministry of Defense and the Serbian Armed Forces (hereinafter: transport) is performed by units and institutions of the Serbian Armed Forces and the Ministry of Defense dealing with the tasks of transporting personnel and assets for their own needs, or for the needs of other units and institutions in the Ministry of Defense and the Serbian Armed Forces.

According to the Rulebook on Transportation (Sluzbeni vojni list, 9/2013), the objectives of the movement and transportation function are to provide conditions for satisfying transport needs of the Ministry of Defense and the Serbian Armed Forces, the continuous performance of transport tasks, as well as the economy, efficiency and effectiveness of transport.

The general tasks of the movement and transportation management encompass monitoring, analyzing and proposing measures for improving the organization and use of transport and transport capacities of the army (Dozet et al, 1988).

According to the Rule on Transportation (Sluzbeni vojni list, 9/2013), the principles of effectiveness and efficiency are:

- the principle of effectiveness which means that the planning and realization of transport allow full satisfaction of the transport needs of the military;

- principle of efficiency, which means that the transportation needs of the army are met in a timely and efficient manner by using the comparative advantages of each of the aspects and modes of transport.

On the other hand, in the Vujaklija's Leksikon stranih reci i izraza (Vujaklija, 1980), efficiency (lat. Efficacitas) is "action, activity, craftiness, success"; while the term "effectiveness" is not mentioned. Gleason and Barnum (1982) emphasize that the term "effectiveness" often means the degree of accomplishment of goals ("doing the right things"), and under the term efficiency - achieving these goals in the best way ("doing things in the right way") (Andrejic & Kilibarda, 2017).

The efficiency of the vehicle refers to the minimal energy consumption achieved by the design of the vehicle, but also by the technologies of their use. (Andrejic & Kilibarda, 2017).

The use of military vehicles is carried out on the basis of acts of command (orders, commands, instructions) or approved plans of use or extracts from these plans. By coordinating the planning of the use of military vehicles, the capabilities of the planner and the needs of the users are coordinated, so that the same number of military vehicles accomplishes a greater number of tasks during the day.

Planning in peace, organization and monitoring of the operation of transport means are performed in accordance with tasks such as transport of people and transport of cargo.

The paper analyzes the efficiency of only vehicles used for the realization of cargo transportation tasks for the needs of supply and the special needs of the commands, units and institutions of the Ministry of Defense and the Serbian Armed Forces, all of which are freight cars and terrain vehicles for towing and transport, regardless of their specific purpose, and according to the plan of the competent body for organization and planning of transport and transport.

Methods

Data Envelopment Analysis - DEA

In addition to using traditional measures, the assessment of the organization's performance can be carried out using parametric and non-parametric techniques. In practice, it is often necessary to consider

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multiple inputs and outputs that are diverse by their nature (financial, technical, environmental) and are expressed in different measuring units. Farel's technical efficiency measure (Farrell, 1957) allows the inclusion of £ either multiple inputs or multiple outputs in the analysis. This ° macroeconomic theory served as the basis for the development of the Data Envelopment Analysis (DEA) as a methodology for assessing efficiency.

oc The DEA method creators (Charnes et al, 1978) assumed that in

assessing the efficiency of units there should not be an objective procedure for determining the values of weight coefficients. By

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< are efficient and which are not. The DEA is a mathematical programming ° technique that allows determining whether the entity, based on data on 5 its inputs and outputs, is efficient or not, relative to other entities involved m in the analysis.

There are a large number of models, given in detail in the overview

< published on the occasion of 30 years of the development of the DEA method (Cook & Seiford, 2009). The basic models and basic extensions are described in detail in the doctoral dissertation (Martic, 1999) published at the Faculty of Organizational Sciences.

!5 DEA models with constant returns to scale

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0, i = 1,2,...,m, j= 1,2,...,n), and yij the observed amount of the output r-th J type of DMUj (yrj > 0, r = 1,2,...,s, j = 1,2,...,n). Charnes, Cooper and ¡5 Rouds proposed in (Charnes et al, 1978) that for each DMUk, k=1,2,...,n, the optimization task, known as CCR model, MODEL (M.1), should be ^ solved:

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to be compared; m - the number of inputs; s - the number of outputs; ur - the weight coefficient for the output r; vi - the weight coefficient for the o

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The relative efficiency of hK for DMUk is defined as the ratio of the £ weights of its outputs (virtual output) and the weights of its inputs (virtual input). The CCR ratio model calculates total technical efficiency that ^ includes both pure technical efficiency and efficiency as a result of different business volumes.

Since condition (2) is valid for the k-th DMU required for the maximum efficiency (1), it is obvious that 0 < hK <1. If the value for hK in the function of the target is equal to 1, then the DMU is relatively efficient, and if it is less than 1, the DMUK is relatively inefficient and the value of hK shows how many percent of this unit needs to reduce its inputs. o

The linear fractional programming problem, described by relations (1) - (4), can be reduced to an equivalent linear program using simple Charns-Cooper transformations (Cooper et al, 1999) - MODEL (M.2):

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DEA model with variable returns to scale

The first extension of the core CCR DEA model was introduced by Banker, Charnes and Cooper (Banker et al, 1984). The BCC model measures pure technical efficiency, i.e. it gives an efficiency measure that ignores the impact of the volume of operations by comparing the k-th DMU with other units of the same size.

In relation to the CCR model, the primary BCC model contains an additional variable in u* which defines the position of an auxiliary hyper plane that lies on or above each DMU included in the analysis. The value of the parameter u* directly indicates the nature of the economies of scale allowed by the DEA model. This is shown in the theorem that Banker and Thrall proved in (Banker & Thrall, 1992).

The primary BCC DEA model proposed in (Banker et al, 1984) has the following form - MODEL M.3:

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CCR efficiency limit

BCC efficiency limit

Figure 1 - Forms of efficiency limit Рис. 1 - Пределы эффективности Слика 1 - Облици границе ефикасности

For example, the input values are displayed on the x-axis and the output values on the y-axis. The firm A uses the input xA to generate the output qA (indicated by x), while the firm B uses the input xB to generate the output qB (shown by x). If there are no inefficiency effects, i.e. if (uA=0, uB=0), then the so-called exits of the frontier area are

qA = exp(^o +Aln x

A + vA ) and qB = exp(^0 +^jln XB + vB ) . In Figure

2, these values are represented by the sign ®. Obviously, the frontier exit of A is above the deterministic part of the frontier region because the effect of the statistical noise is positive vA>0, and the B-frontier output is

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The orientation of the DEA model (input or output) determines the g direction of the ineffective DMU projection to the efficiency limit. In an input-oriented model, efficiency improves through a proportional input reduction, and the output orientation requires a proportional increase in output.

Stochastic Frontier Analysis - SFA |

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The original specification of the model included the production function defined for crosssectional data, and later it received a number of different modifications and shapes. The function contained an error component, consisting of two elements - noise (random errors) and technical inefficiency. This model, in the case of Cobb-Douglas frontier | function, has the following form:

ln(y) = P0 +Y&ln(Xik) + v -Ui j?

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q A=exp(Po+PilnxA+VA) q*B=exp(Po+PilnxB+VB)

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Figure 2 - Kob-Douglas model Рис. 2 - Модель Кобба-Дугласа Слика 2 - Коб-Дагласов модел

Function modifications included additional assumptions regarding the distribution of technical inefficiencies ui, such as a truncated normal or gamma distribution; other forms of the frontier function; consideration of panel data and technical efficiencies variability in time; expanding models with cost functions, etc.

Although it contains a number of parameters to be assessed against the Cobb-Douglas function, the transcedental logarithmic form of the frontier form of the function is much more flexible and provides more consistent technical efficiency estimates. It represents the generalization of the Cobb-Douglas function, and has the following form (Knezevic et al, 2015):

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In(y) = p0 ln(xlk) + ££^kk, ln(xlk)ln(xik,) + V,. -ut

k=1 k=1 k • =1

The main disadvantage of standard SFA models is the inability to observe multiple outputs, i.e. the existence of only one output. Coelli and Perelman (Coelli & Perelman 1996, 2000), Knezevic, Bojovic,

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Selection of parameters and the efficiency analysis

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In order to improve the efficiency of the organization's work, it is .2 necessary to select relevant indicators whose monitoring and analysis can provide the necessary information in order to generate actions to improve the process and improve the efficiency of the organization's operation. |

Transport is a process characterized by high costs: number of vehicles and drivers, energy consumption, realized transport work, space and time use of the vehicle, are just some of the factors that influence the efficiency of the transport process.

The goal of transportation planning, due to the specific nature of the military organization, is to find the conditions for meeting the transport < needs of units and military institutions, regardless of the respect of other transport principles: rationality, economy, etc. For these reasons, there are cases of inefficient use of vehicles.

The basic efficiency criteria should contribute to meeting the goal of the existence of a system - meeting the transport needs of the army in q peace, during the mobilization period and in the war. The basic criteria of transport in general can be taken as the basic criteria of efficiency for achieving these goals - the performance of the fleet and the cost of transport services, since most of the parameters of the transport process are related to them. The performance of the transport fleet of transport units is assessed with two interconnected parameters of the incineration

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criterion; the volume of transported cargo (volume of transport) in tonnes and the number of tonne-kilometers achieved (cargo traffic) in tkm (Dozet et al, 1988).

The indicators of efficiency in transport in literature:

Byrne and Markham (1991): tkm / total transport costs, transported quantity / total transport costs, total transport capacity / capacity costs.

Cruijssen et al (2010): labor power (salaries, driver experience, total hours of work, number of employees), equipment (number of trucks, number of trailers, total capacity), intangible assets (market information, contact with users), profit.

Kim (2010): costs of employees, fuel costs, lubricant costs, taxes, insurance, mileage, transported quantity, transport distance.

The division of the indicators of the efficiency of logistics processes can also be carried out according to the subsystem or process described by Andrejic and Kilibarda (2017). Thus, groups of indicators can be distinguished:

- storage indicators;

- transport indicators (number of vehicles, total number of kilometers traveled, realized transport work, fuel consumption, etc.);

- stock indicators.

The data used in the paper were collected through an application intended for automated processing of data on the condition and use of non-combat vehicles and connecting vehicles and other fuel consumers in the information system of the traffic service in the military. This application allows tracking the traveled route, fuel used, the number of persons transported and the amount of transported cargo for a specified period of time (month, year) for the vehicle or the entire unit.

Data on the performance indicators of military transport units and vehicles which can be obtained from the above application coincide with the often used indicators of efficiency in transport in the literature, first of all in the book Efficiency of Logistic Processes (Andrejic & Kilibarda, 2017). For this reason, the following data were used in the analysis of the efficiency of the observed military transport units and vehicles - Table 1.

Two input parameters were used to evaluate the efficiency of the transport units: the number of vehicles used for the transport of cargo and the total fuel consumption of these vehicles (l). Two parameters were also used as output indicators: the total distance driven by vehicles used for transport of goods (km) and the total quantity of transported cargo (t).

For the assessment of the efficiency of vehicles (in total and by classes), the parameters were used - two inputs: total fuel consumption per vehicle (l) and total available vehicle load for the days of use in the

observed time (t) and two outputs: distance driven per vehicle (km) and the total quantity of cargo carried per vehicle (t).

Table 1 - Aspects of measuring the efficiency of transport Таблица 1 - Аспекты измерения эффективности транспорта Табела 1 - Аспекти мерена ефикасности транспорта

Efficiency of transport unit Efficiency of the vehicle Vehicle efficiency by class

Management level Operating level Tactical level Tactical level

Input indicators 1. number of vehicles 2. fuel (l) 1. fuel (l) 2. the total available vehicle load in the observed time (t) 1. fuel (l) 2. the total available vehicle load in the observed time (t)

Output indicators 1. distance driven(km) 2. transported cargo (t) 1. distance driven (km) 2. transported cargo (t) 1. distance driven (km) 2. transported cargo (t)

DMU number 10 transport units 173 vehicles 6 class vehicles: 24 vehicles up to 3t capacity 78 vehicles up to 6t capacity 17 vehicles up to 12t capacity 11 vehicles over 12t capacity 21 vehicle ACG 22 vehicles ACV

Applied model DEA and SFA analysis

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The vehicle classes are defined according to load capacity (up to 3t, from 3t to 6t, from 6t to 12t and over 12t) and the specific type of cargo being transported by them (ACG - fuel tanks and ACV - water tank), Table 2. In this analysis, vehicles used for fewer than 10 working days and covering fewer than 500 kilometers during the year were not observed.

The paper analyzes the relative technical efficiency of ten military transport units and 173 vehicles engaged in cargo transportation tasks for supplies and special needs of the army.

It should be emphasized that until now, to a certain extent, mainly through the annual analysis of logistics in the military, the problem of organization and structure of transport units and their efficiency was partially taken into account, but not comprehensively approached in the research of the subject matter.

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Table 2 - Overview of the number of vehicles by classes and units Таблица 2 - Обзор количества транспортных средств по классам и единицам Табела 2 - Преглед броjа возила по класама и jединицама

up to 3t up to 6t up to 12t over 12t ACG ACV TOTAL

DMU 1 2 9 1 5 0 0 17

DMU 2 0 12 1 0 1 2 16

DMU 3 0 7 3 3 3 0 16

DMU 4 2 4 3 2 3 0 14

DMU 5 3 5 1 1 1 3 14

DMU 6 2 8 1 0 0 3 14

DMU 7 2 10 4 0 5 9 30

DMU 8 3 7 1 0 6 2 19

DMU 9 3 4 0 0 1 2 10

DMU 10 7 12 2 0 1 1 23

TOTAL 24 78 17 11 21 22 173

Table 3 - Descriptive input and output statistics for transport units Таблица 3 - Описательная статистика ввода и вывода транспортных единиц Taбела 3 - Дескриптивна статистика улаза и излаза за транспортне jединице

I/O Parameter Var Obs Mean Std. Dev. Min Max

DMU output distance driven (km) У1 10 137133.3 68275.3 62682 296695

output transported cargo (t) y2 10 4156.7 4694.2 808 15763

input fuel (l) x1 10 35138.5 19019.4 16717 78223

input the number of vehicles x2 10 17.3 5.6 10 30

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The calculation of the efficiency of transport units and vehicles was done whith:

- Input CCR and BCC DEA models - DEAP Version 2.1 software used for calculating (Softver DEAP Version 2.1., 2018).

- SFA model (using (6)), halfnormal and truncatednormal distribution - STATA13 software used for calculating (Softver STATA13, 2018).

The input-oriented model was selected as transport unit managers can influence more the reduction of input (the number and type of vehicles used, i.e. fuel consumption and vehicle load), and less the increase of output (quantity of transported cargo).

The DEA CCR model, which shows only three efficient units, has the greatest discriminatory power. On the other hand, the SFA model, with the assumed distribution of technical inefficiency, recognizes all units as effective.

As said, the SFA model, with the hnorm and tnorm distribution, recognizes all units as efficient. The DEA BCC model recognizes three (conditionally two) inefficient units, while the DEA CCR model recognizes only three units as effective - DMU3, DMU6 and DMU8 and therefore has the highest discriminatory power - Table 4.

Table 4 - Results of the analysis of the efficiency of transport units Таблица 4 - Результаты анализа эффективности транспортных единиц Taбела 4 - Резултати анализе ефикасности транспортних jединица

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DEA CCR DEA BCC SFA tnorm SFA hnorm DEA CCR DEA BCC SFA tnorm SFA hnorm

rank

DMU1 0.727 0.798 0.998363 0.999526 10 10 1 10

DMU2 0.771 1 0.998362 0.999545 9 1 7 2

DMU3 1 1 0.998362 0.999547 1 1 7 1

DMU4 0.997 1 0.998363 0.999526 4 1 1 9

DMU5 0.856 0.961 0.998363 0.999534 7 1 6

DMU6 1 1 0.998362 0.999528 1 1 7 8

DMU7 0.983 1 0.998363 0.999535 5 1 1 5

DMU8 1 1 0.998362 0.999536 1 1 7 4

DMU9 0.773 1 0.998363 0.999537 8 1 1 3

DMU10 0.968 0.999 0.998363 0.999531 6 8 1 7

Thus, the comments on the results obtained are as follows. The average efficiency of transport units by models is: DEA CCR-0.91 <DEA BCC-0.98 <SFA tnorm ~ 1.00 <SFA hnorm ~ 1.00 DMU8 and DMU6, as efficient, do not have a high-capacity vehicle (tow truck). The greatest contribution to the efficiency of DMU8 is a vehicle marked mv127 ACG which was used to transport by far the largest amount of cargo - 13613t (i.e. liters of fuel). Without the mentioned vehicle, DMU8 would have had efficiency of 0.847 under the CCR model, and 0.849 according to the BCC model, i.e. it would not be at the limit of efficiency. DMU8 transported the largest amount of cargo.

DMU3 does not have a vehicle carrying capacity of up to 3t or ACV. Only one of the four units with high-capacity vehicles was declared effective (DMU3). It is interesting to note that the lowest efficiency in both the CCR and BCC model is DMU1, with a percentage of the largest number of heavy-duty vehicles (trucks) being 29% of the vehicle unit.

DMU2 is inefficient even though there are no vehicles with high load capacity, and the highest number of used vehicles is 3t to 6t capacity (75%). Also, DMU2 covered the fewest number of kilometers and transported the smallest amount of cargo. The reason for relative

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inefficiency of DMU9 can be the size of the unit (the smallest number of vehicles), besides being the third transport unit in one region. The largest number of kilometers covered is in DMU7, but it is not at the limit of efficiency because it is the unit with the largest number of vehicles used.

If the efficiency of transport units is analyzed through the average efficiency of the observed vehicles of the transport units, given in Table 5, the lowest results of efficiency are still given by the DEA CCR: DEA CCR-0.37 <DEA BCC-0.46 <SFA hormone -0.74 <SFA tnorm -0.8

Table 5 - Average efficiency of vehicles by transport units Таблица 5 - Средняя эффективность транспортных средств по транспортным

единицам

Taбела 5 - Просечна ефикасност возила по транспортним jединицама

DEA DEA SFA SFA DEA DEA SFA SFA

CCR BCC tnorm hnorm CCR BCC tnorm hnorm

rank

DMU1 0.33 0.42 0.82 0.75 8 8 5 5

DMU2 0.31 0.51 0.85 0.79 10 3 1 1

DMU3 0.31 0.37 0.83 0.77 9 10 2 3

DMU4 0.42 0.51 0.76 0.67 2 2 9 9

DMU5 0.37 0.49 0.81 0.74 5 4 7 7

DMU6 0.46 0.53 0.71 0.65 1 1 10 10

DMU7 0.41 0.45 0.79 0.72 3 7 8 8

DMU8 0.39 0.47 0.81 0.74 4 5 6 6

DMU9 0.33 0.41 0.83 0.76 6 9 3 4

DMU10 0.33 0.47 0.83 0.78 7 6 4 2

Somewhat higher results of vehicle efficiency in the SFA model are obtained for the assumed truncatednormal relative to the halfnormal distribution of technical inefficiency. The DEA CCR model yields less efficacy results than the DEA BCC, as it assumes constant returns to scale.

By analyzing the obtained average efficiency of vehicles used by transport units, it is noticed that DMU6 is still the most efficient for both DEA models, but according to the SFA models it has the worst results. Observing the results in this way, the SFA models rated DMU2 as the most efficient, which, according to DEA CCR, I has the worst results of vehicle efficiency, and the opposite case is with DMU3.

When the number of vehicles used is taken as the input parameter, the results of the efficiency of transport units differ from the results obtained when the average values of the efficiency of the vehicles used for the transport within the unit are observed.

It is noted that the efficiency of the vehicles is small, which can be explained by using a vehicle for transporting freight often without the criterion of better utilization of the load (the need for transport has the quantity of cargo within the defined time limit). Out of 173 vehicles observed:

- according to the DEA CCR model, only three vehicles are efficient, as many as 146 vehicles have an efficiency of less than 0.5, and the average efficiency is 0.37.

- according to the DEA BCC model, 8 vehicles are effective, 124 vehicles have efficiency lower than 0.5, and the average efficiency is 0.46.

- according to the SFA tnorm model, the highest efficiency of 0.94 was found in two vehicles, 54 vehicles have efficiency below average, and the average efficiency is 0.8.

- according to the SFA hnorm model, one vehicle has the highest efficiency of 0.93, 72 vehicles have efficiency below average, and the average efficiency is 0.74.

The vehicle carrying capacity up to 3t with the mark mv172 is efficient according to the DEA CCR and BCC models, while it is among the two worst ones in the efficiency evaluation of the SFA models. On the other hand, the ACG vehicle with the mv152 tag has the best efficiency according to the SFA models, while according to the DEA CCR it has the lowest efficiency, and according to the DEA BCC, it is among the least efficient.

Among the most efficient vehicles, there are no vehicles with greater capacity (from 6t to 12t and over 12t), and the reasons for this should be sought in the fact that their efficiency is more reflective of the inexorability of their load capacity.

When considering the efficiency of all vehicles in the entire group of 173 vehicles per cluster, Table 7, it is noted that the vehicles with a minimum carrying capacity of up to 3t have the highest average efficiency according to the DEA methods, which can be explained with the smallest loss of available load capacity and lower average fuel consumption.

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Table 6 - Descriptive statistics of inputs and outputs for vehicles Таблица 6 - Описательная статистика вводов и выводов транспортных

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Табела 6 - Дескриптивна статистика улаза и излаза за возила

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I/ O Parameter Var Obs Mean Std. Dev. Min Max

All 173 vehicles O distance driven (km) a1 173 7927 8249 423 40576

O transported cargo (t) a2 173 240 1057 5 13613

I fuel (l) b1 173 2031 2059 110 11531

I available vehicle load (t) b2 173 379 443 33 3984

Vehicles up to 3t capacity O distance driven (km) til 24 9918 10663 779 39908

O transported cargo (t) ti2 24 70 82 5 344

I fuel (l) tu 1 24 1347 1243 238 4728

I available vehicle load (t) tu2 24 215 180 39 843

Vehicles up to 6t capacity O distance driven (km) si1 78 7430 7354 423 35330

O transported cargo (t) si2 78 71 77 6 446

I fuel (l) su1 78 1874 1653 110 8107

I available vehicle load (t) su2 78 290 172 35 800

Vehicles up to 12t capacity O distance driven (km) di1 17 7255 3975 176 7 15544

O transported cargo (t) di2 17 109 80 19 292

I fuel (l) du1 17 1981 1106 523 4349

I available vehicle load (t) du2 17 418 243 147 960

Vehicles over 12t capacity O distance driven (km) oil 11 11099 11248 927 31102

O transported cargo (t) oi2 11 557 651 40 1748

I fuel (l) ou1 11 4172 4145 385 11397

I available vehicle load (t) ou2 11 970 811 180 2574

Vehicles ACG O distance driven (km) gil 21 7873 11330 479 40576

O transported cargo (t) gi2 21 870 2938 14 13613

I fuel (l) gul 21 2162 2832 213 11531

I available vehicle load (t) gu2 21 592 894 35 3984

Vehicles ACV O distance driven (km) vi1 22 6498 5168 487 17195

O transported cargo (t) vi2 22 370 268 25 980

I fuel (l) vu1 22 2177 1786 256 6005

I available vehicle load (t) vu2 22 344 226 33 952

Table 7 - Average efficiency of all vehicles by defined groups Таблица 7 - Средняя эффективность всех транспортных средств по

определенным группам Табела 7 - Просечна ефикасност свих возила по дефинисаним групама

Vehicles DEA DEA SFA SFA DEA DEA SFA SFA

capacity CCR BCC tnorm hnorm CCR BCC tnorm hnorm

rank

up to 3t 0.56 0.70 0.68 0.61 1 1 6 6

up to 6t 0.32 0.40 0.83 0.76 5 4 2 3

up to 12t 0.33 0.38 0.81 0.74 4 5 4 4

over 12t 0.27 0.31 0.88 0.83 6 6 1 1

ACG 0.33 0.45 0.83 0.76 3 3 3 2

ACV 0.45 0.58 0.78 0.72 2 2 5 5

According to the SFA method, the vehicles up to 3t capacity have the lowest efficiency. Completely opposing ranking is found in the vehicles carrying over 12t. According to the SFA method, they have the highest efficiency, while according to the DEA methods in both cases they have the lowest average efficiency. Conditional consistency, as far as the average vehicle efficiency rating is concerned, is found in all methods in the case of the groups of ACG vehicles and the vehicle with a carrying capacity from 6t to 12t. The highest standard deviation of the results is with the vehicles with a carrying capacity up to 3t, ACV and ACG.

It is noteworthy that the results of the DEA and SFA models vary greatly; therefore, decision makers must be aware of that and choose the model in which they want to perform an efficiency assessment.

The results of vehicle efficiency, when calculations were made for vehicles within defined groups (clusters), are given in Table 8.

In small vehicle groups, the SFA models show all vehicles within the group as efficient, and there is certain discrimination only in larger vehicle groups. In this sense, the SFA model will not be commented on in this part of the paper.

The most homogeneous group of vehicles (and the smallest one) consists of the vehicles over 12t capacity - with the average efficiency of 0.92. According to the DEA CCR, the efficient vehicles are those with mv7, mv44 and mv61 markings, and the least efficient is the mv8 vehicle, while the BCC model has 7 efficient vehicles.

In the group of the vehicles up to 12t of capacity, there are 6 or 10 efficient vehicles according to the DEA models and they are evenly distributed in transport units.

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Table 8 - Average efficiency of vehicles per class Таблица 8 - Средняя эффективность транспортных средств по классам Табела 8 - Просечна ефикасност возила по класама

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capacity CCR BCC tnorm hnorm

up to 3t 0.66 0.83 1.00 0.71

up to 6t 0.60 0.65 0.86 0.74

up to 12t 0.89 0.93 1.00 1.00

over 12t 0.92 0.96 0.99 0.99

ACG 0.62 0.77 1.00 1.00

ACV 0.80 0.91 0.91 0.91

A group of vehicles with a minimum mean efficiency of 0.60 and 0.65 consists of the vehicles of 3t to 6t capacity, respectively, most of them being in group 78.

The vehicles with a carrying capacity up to 3t may have unexpectedly low mean efficiency. Six vehicles have an efficiency of less than 0.5 which says they are often used to transport very small loads.

ACGs within the group have 2 or 4 efficient vehicles, and, according to the DEA CCR model, 7 vehicles have efficiency below 0.5. All ACVs have efficiency within a group higher than 50%.

The comparison of the average efficiency of transport units in relation to the vehicle groups was not considered in the work due to the relatively small number of vehicles by defined groups in transport units. In other words, it could not be concluded where and in which transport units certain groups of vehicles are used better.

The comparison of the efficiency of vehicles in general and by defined groups showed that only three vehicles were declared effective in both cases: mv63 to 3t capacity, mv127 ACG and mv152 ACG.

The dependence of data on input and output parameters of transport units and vehicles was tested using the Spearman and Pearson correlation tests. The test results show that the input and output data are independent for all pairs of input and output data except in the case of input data for the vehicles with a capacity of 6t to 12t.

The results show that the choice of the method of evaluation of technical efficiency has a major impact on the obtained efficiency estimates, and, consequently, on the decisions made and implemented after the efficiency analysis.

Conclusion

The paper presents the application of the DEA and SFA methods for evaluating the efficiency of the work of the selected ten military transport units and 173 military motor vehicles used in cargo transportation tasks for the needs of supply and special needs of the army, individually and within six defined classes. It can be deduced from the estimate that the CCR DEA model has the highest discriminatory power that shows the lowest number of efficient units and gives the lowest mean value of efficiency of both transport units and vehicles.

The CCR DEA estimates that three transport units are efficient (with an average efficiency of 0.91), as well as three vehicles (average vehicle efficiency 0.37). The BCC DEA model estimates seven transport units as efficient as well as eight vehicles (average vehicle efficiency 0.46). No transport unit has been declared extremely inefficient (DMU1 has the lowest calculated efficiency with a score of 0.727 per CCR DEA model). Since the carrying capacity of the used vehicles has a large impact on the results of the efficiency of transport units, only one unit with high-capacity vehicles was declared effective, while the least efficient unit has the largest proportion of these vehicles.

With the SFA model, all transport units are rated as efficient. The same is the case with the assessment of the efficiency of vehicles in groups with few vehicles. For this reason, in assessing the efficiency of transport units and military vehicles, the SFA model is applicable in measuring the efficiency of a larger number of DMUs. Of all vehicles, two have the highest efficiency of 0.94, while the average vehicle efficiency according to the SFA models is 0.74 and 0.8. Low-capacity vehicles are rated as more efficient according to the DEA models, while the SFA models rate vehicles with higher load capacity as more efficient.

The choice of the method for calculating efficiency can be a determining factor for making management decisions, as it has been shown that the results of the DEA and SFA models differ significantly, about which decision makers must be informed in order to choose the model in which they want to perform efficiency assessment.

The DEA method makes it easier to compare DMUs across multiple inputs or outputs, and for each inefficient unit, it defines respectable units and required changes to the input or output in order to achieve efficiency. The CCR DEA model gives the lowest efficacy results because it allows a constant return to scale and measures the overall technical efficiency and efficiency of the business volume, while the BCC model measures

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only pure technical efficiency, which makes a number of units more efficient.

Since this paper deals with the military context, certain specific information related to the organization, as well as the actual names of transport units, and data on the marks, kind and type of specific vehicles could not be included.

It has been shown that the conducted analysis and efficiency assessment provide a basis for a different approach to the problems of military transport management and more efficient use of vehicles. This paper explores the efficiency of military transport units in a different way than usual. The obtained efficiency results indicate that there is a space for increasing the efficiency of the transport units, especially the efficiency of vehicles. Increased efficiency can be achieved by better vehicle selection in relation to the amount of cargo in order to better utilize the vehicle's capacity. Also, the planning of return transport and better planning of freight transport through reduction of off-plan tasks, with fewer engaged vehicles and, consequently, lower fuel consumption, can increase output, i.e. quantity of transported cargo. By equipping newer vehicles with lower fuel consumption and greater reliability, the input resource needed to complete the tasks can also be reduced.

By choosing an appropriate method for assessing efficiency, input / output parameters and a good analysis of the obtained results, one can obtain a model of transport in the army that would increase the efficiency of transport units and vehicles to a higher level in order to achieve better operational capabilities of the military.

Numerous parameters influence transport efficiency, both at the level of transport units and vehicles. In this sense, the direction of further research on efficiency measurement,would be the influence of the parameters not observed in this paper: type of cargo, vehicle and driver time, organizational structure of the transport unit, distances to which goods are transported, the age of the vehicle, etc. Also, in further work, the influence of the factors on which the organization does not have influence i.e. weather conditions, road conditions, etc, can be investigated.

The work should be the initial phase of the research devoted to the parameters of the efficiency of the military transport units and military vehicles. The efficiency analysis is an important tool that can enable military organization management and transport management to find common solutions in order to achieve the goals of the organization. This would identify proposals for optimizing the use of vehicles for the transport of cargo as well as the engagement of the transport unit as a

whole, which would increase the quality and quantity of execution of transport tasks in support of the missions and tasks of the Serbian Armed Forces.

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ОЦЕНКА ЭФФЕКТИВНОСТИ ТРАНСПОРТНЫХ СРЕДСТВ ВООРУЖЕННЫХ СИЛ МЕТОДАМИ DEA И SFA

Деян Р. Деспича, Небойша Й. Борвич6, Милорад Й. Килибарда6, Марко В. Капетанович6

а Министерство обороны Республики Сербия, Сектор материальных ресурсов, Управление логистикой, г. Белград, Республика Сербия б Белградский университет, Транспортный факультет, г. Белград, Республика Сербия

ОБЛАСТЬ: математика, логистика, транспорт ВИД СТАТЬИ: оригинальная научная статья ЯЗЫК СТАТЬИ: английский

Резюме:

Целью данной работы являлось проведение анализа эффективности выбранных транспортных средств и военных боевых машин для осуществления заданий по перевозке груза при применении метода стохастической границ (SFA), а также анализа оболочки данных (DEA), создавая тем самым основание для дальнейших исследований параметров, влияющих на эффективность работы транспортных средств Вооруженных сил и военных боевых машин. Исследование проведено на основании десяти транспортных средств Вооруженных сил, предназначенных для осуществления логистических задач по транспорту и перевозкам. Анализ эффективности проведен для военных машин, используемых для выполнения заданий по транспорту и перевозкам груза для нужд снабжения и нужд специального назначения командования, воинских частей и учреждений Вооруженных сил. В работе использованы данные, полученные благодаря программному обеспечению, с помощью которого ведется наблюдение за пользованием и эксплуатацией военных машин в течение одного календарного года. Результаты показали, что выбор метода оказывает большое влияние на полученную оценку технической эффективности, и соответственно на возможные управленческие решения, принимаемые на основании проведенного анализа эффективности.

Ключевые слова: эффективность, транспортные средства Вооруженных сил, военные боевые машины, анализ оболочки данных, метод анализа стохастической границы.

ПРОЦЕНА ЕФИКАСНОСТИ ТРАНСПОРТНИХ JЕДИНИЦА BOJCKE МЕТОДАМА DEA И SFA

Деjан Р. Деспипа, Небоша J. Борвип6, Милорад J. Килибарда , Марко В. Капетановипб

а Министарство одбране Републике Срби]е, Сектор за матери]алне

ресурсе, Управа за општу логистику, Београд, Република Срби]а

б Универзитет у Београду, Саобрапа]ни факултет, Београд, Република Срби]а

ОБЛАСТ: математика, логистика, саобрапа] ВРСТА ЧЛАНКА: оригинални научни чланак JЕЗИК ЧЛАНКА: енглески

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Цил> рада }есте да се изврши анализа ефикасности изабраних транспортних jединица у логистици Во]ске и воних возила у реализации задатака транспорта терета применом метода

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анализе стохастичких граница (SFA) и анализе обав^аша података (DEA), као и ствараше основе за даъе истраживаше параметара щи утичу на ефикасност рада транспортних jединица Воjске и во]них возила.

Истраживаше jе извршено у десет транспортних jединица Воjске, намешених за реализац^у послова из логистичке функц^е саобраЩ и транспорт. Анализа ефикасности извршена jе за воjна oj возила коришЯена за реализац^у задатака транспорта терета за

ос потребе снабдеваша и посебне потребе команди, jединица и

^ установа Воjске. КоришЯени су подаци доб^ени из програмског

g пакета щим се прати коришЯеше и експлоатац^а во]них

0 моторних возила у периоду од jедне календарске године. ^ Резултати показуjу да избор методе има велики утицаj на — доб^ене оцене техничке ефикасности, а самим тим и на

1 евентулане управл>ачке одлуке на основу извршене анализе EC ефикасности.

I>- Къучне речи: ефикасност, транспортне jединице Воjске, воjна

< возила, анализа обав^аша података, анализа стохастичких граница.

Paper received on / Дата получения работы / Датум приема чланка: 04.08.2018. Manuscript corrections submitted on / Дата получения исправленной версии работы / и Датум достав^а^а исправки рукописа: 25.09.2018.

< Paper accepted for publishing on / Дата окончательного согласования работы / Датум О коначног прихвата^а чланка за об]ав^ива^е: 27.09.2018.

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© 2019 Авторы. Опубликовано в «Военно-технический вестник / VojnotehniCki glasnik / Military О Technical Courier» (www.vtg.mod.gov.rs, втг.мо.упр.срб). Данная статья в открытом доступе и > распространяется в соответствии с лицензией «Creative Commons» (http://creativecommons.org/licenses/by/3.0/rs/).

© 2019 Аутори. Обjавио В^нотехнички гласник / VojnotehniCki glasnik / Military Technical Courier (www.vtg.mod.gov.rs, втг.мо.упр.срб). Ово jе чланак отвореног приступа и дистрибуира се у складу са Creative Commons licencom (http://creativecommons.org/licenses/by/3.0/rs/).