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1
Railway stations in the Republic of Serbia in the function of transportation of goods: efficiency according to the DEA system
Dubravka R. Vukovic
"Srbija Kargo" JSC, Traffic and Transport Department,
Belgrade, Republic of Serbia,
e-mail: dub.vukovic@gmail.com,
ORCID iD: 1i https://orcid.org/0000-0003-1341-2568
DOI: https://doi.org/10.5937/vojtehg72-45975
FIELD: mathematics
ARTICLE TYPE: original scientific paper Abstract:
Introduction/purpose: Data Envelopment Analysis (DEA) is commonly used to calculate the efficiency of similar Decision-Making Units (DMUs), which as such are elements of one set. In the article, it is considered that each such element of a set (of similar elements) is at the same time an element of a system (of various elements). An example of DMUs are 27 railway stations in the Republic of Serbia (RS) as an element of a set of railway stations and as an element of the railway transportation system, in the function of transporting goods, after division of the company Serbian Railways in 2015 (into "passengers" and "goods"). For the sake of better service, attraction and retention of clients, in the newly opened, free, transport market, the purpose of this article is to find the efficiency of the RS stations iin the period of 20182022.
Methods: Set-systemic-model comparative DEA analysis of railway stations as a DMUs. A unit is an element of the set, a unit is an element of the system, and a unit is the subject of the mathematical DEA-CCR/BCC/SE model.
Results: The final efficiency, the average of all average values, is 0.7666, as a result of a triple comparative DEA analysis: 27 DMU, three DEA models and five years of functioning.
Conclusion: Stations are functionally different in terms of efficiency and each station functionally differs by years and by model. The final aim is an input-output balance and the 27/27 option which is achieved with corrective actions - reduction/addition, input or output.
Key words: efficiency, DEA-CCR/BCC/SE, railway stations, set-system, transportation of goods.
Introduction
Set-systemic DEA analysis
È
The article is intended to those aiming to achieve as much as possible with as little investment as possible, especially in wider and wider environments.
The environment here refers to the system, the structure of various ys elements-subsystems and more structures in the supersystem. A concrete a element-subsystem is a railway station, as an object of research, in the function of transporting goods.
Efficiency is the issue here. It is a property of someone or something, on the one hand, and a mathematical quantity, on the other. Hence, it is 8 treated here in two levels: (1) practically, shown through the examples of other authors and the example of the RS railway stations, and (2) theoretically, shown by the first DEA mathematical method, the cCr s§ model, named after its authors - Charnes, Cooper and Rhodes (Charnes et al, 1978). Later, the method was innovated over several decades, through numerous mathematical models by other authors.
In terms of such a tendency, a new idea is presented here, which is J an upgrade to a known method. The emergence of a new idea - setsystem DEA analysis - originates from the reality and that is now open free transport market.
But why railways, why railway stations and why efficiency assessment? The railway, as a complex, profit-making system, is a good sample for this kind of research. Furthermore, railway stations, as a numerous set, are a true example of decision-making units. Furthermore, after more than eight years from the division of the Serbian Railways company (in 2015) and the start of the new business, further system changes follow, according to the guidelines of developed countries, according to the principles of dynamic market economy. On the basis of the guidelines and the transition process there are business indicators as input-output parameters. Hence the topic of efficiency, evaluation of the & efficiency of railway stations and measures for better competitiveness in the newly opened, free, transport market. This article deals with a DEA analysis from the time of its creation, the railway stations of the RS from the recent era and the multi-year transition process of the ZS (Serbian Railways).
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Set-systemic DEA analysis is a combination of the DEA method and o system theory, and the important determinants are:
1. Set analysis, where the decision-making unit is an element of the set, and an important step is the correct selection of the set size, i.e., the number of analyzed units.
2. System analysis, where the decision-making unit is an element of the system, which according to system theory has many diverse elements (subsystems) and complex connections between them, and an important step is the correct selection of inputs and outputs.
3. DEA analysis - a mathematical DEA model which solves the problem of linear programming; for a concrete sample from practice and for each decision-making unit, it determines whether a particular is either efficient or inefficient in regard to the remaining units. There are two options for the functioning of decision-making units - they are either followed by other (inefficient) units or they are followers of other (efficient) units. The numerical value of efficiency is from zero to one. Efficient units are best practice units, where Eff=1. The other, opposite, inefficient units, where 0<Eff<1, emulate the efficient units, the best practice units, as their role model. The logic of inefficient units reads: Under the same conditions, here in the same set and with the same input-output variables, inefficient units can be efficient, because the model (best practice) is realistic (already achieved) and relative (valid for a concrete sample, i.e., one and the same set of decision units). One can go further and ask which one is the most exemplary.
Set-systemic DEA analysis is mathematically represented by models where the mathematical model consists of:
1. Set DEA models (a unit is an element of a set of similar elements): - CCR CRS model is with constant returns to scale (Charnes et al, 1978):
max ho =f=lMryr0 (1)
¿.£=1 ViXi0
s.t. §¡^£1,7 = 1.....n
¿. i=1
Ur, Vi > 0; r = l,...,s; i = 1, ...,m
where:
h0 - relative efficiency of the 0th DMU;
n - number of DMU; m - number of inputs; s - number of outputs; ur - weight coefficient of the rth output; Vi - weight coefficient of the ith input.
- BCC VRS is a model with variable returns to scale or the extended CCR model (1) for an additional variable uo, in the numerator of the efficiency ^ formula (Banker et al, 1984):
max h = (2) J
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where (Banker et al, 1984, p.1087): Si
- Increasing returns to scale <=> uo* < 0, Q
- Constant returns to scale <=> uo* = 0, and
- Decreasing returns to scale <=> uo* > 0.
DMU1,..., DMUn e SISTEMA (E1, E2,...,EN) (4)
where are the links between N elements:
E1~E2, E1~E3.....EI^EN, E2~E3.....E2^EN,...
Railway station as an element of a set and a system
A railway station is seen here as an element of a set of railway stations and, more broadly, as an element of the railway transportation system.
A railway station is an element of a set of official places on the railway network, which consists of a set of supervisory and a set of subordinate
- SE model (Panwar et al, 2022) is: %
Scale efficiency = Eccr/Ebcc, (3)
where: Eccr- CCR efficiency and Ebcc- BCC efficiency.
2. System DMU model (a unit is an element of a system of N diverse elements, among which there are connections): I
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In the set approach, the DEA mathematical method and the classical DEA models - CCR, BCC and SE - are applied. In the systems approach, system theory and a multi-component transportation system are applied. How to adequately mathematically model railway stations? Defining inputs and outputs in the DEA procedure is a complex and crucial issue. In the example of railway stations, it is known that inputs and outputs are economic, commercial activities, invested or realized, in the goods transport sector. How to select, re-select or not select them? What are inputs and outputs? Indeed, what is a railway station? |
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official places, Figure 1. Official places that deal with loading/unloading (in tons of transported goods) in the respective year of the analyzed period are called active official places.
The end stations of the traffic route are called terminuses and determine the type of traffic:
1. Domestic traffic (initial and final terminuses in the RS);
2. International traffic:
- import (initial terminus abroad, final terminus in the RS);
- export (initial terminus in the RS, final terminus abroad); and
- transit (both terminuses abroad).
RAILWAY STATIONS (Mostly supervisory)
Subordinate official places: - transport forwarding (TO) transport loading point (TT)
Figure 1 - Railway station as an element of the set of railway stations of RS
The railway station is an element of the transportation system according to model (4), where the transportation system has N=5 basic elements (Filipovic, 2013):
1. Vehicles (V);
2. Traffic roads (TR);
3. Terminals (T);
4. Energy (E); and
5. Organization and management (OM).
Specifically, in the goods transport sector, the railway transportation system has the following five elements, Figure 2: V - freight cars; TR - railway lines;
T - railway stations (there are 27 stations on the RS railway network); E - diesel and electric energy, facilities, equipment and people; and OM - station (executive) staff.
V (vehicles)
railway freight cars various serious and type
OM (organization and management)
employees (station chief, storekeepers, goods cashiers...)
TR (traffic roads) railway lines
T (Terminals) railway stations DMU 1, 2 ,3.....27
E (energy) diesel and electro
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Figure 2 - The railway station as an element of the RS transportation system
"A transportation system has several components. First, it can be defined in terms of infrastructure, vehicles, operations, and policies." (Sinha, 2007, p.3)
The assessment of the efficiency and re-efficiency of the railway station (T) in the business course of the newly formed company is an assessment of the ratio of activities achieved and invested, for each decision-making unit, by years. If the station, T, is defined as an element of the transportation system, then the activities invested and the service provided are simply determined.
The invested activities are:
- resource activities: work of employees, in the number of executors, OM and E; and
- operational activities: reception/dispatch of freight cars, in the number of cars, V.
The accomplished activities are:
- transport flows - transport service: import, export, transit and domestic transport of goods, in tons of transported goods, as a transport indicator; and
- traffic flows - tariff kilometers per car, as a traffic indicator, TR.
Therefore, as an element of the set, as an element of the system and as a unit of efficiency decision making, when applying the DEA method, the railway station has two inputs and two outputs.
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Literature review
Efficiency and DEA begin with the first DEA authors: Charnes, Cooper and Rhodes, and the first DEA paper from 1978, as well as the first basic CCR model. (Charnes et al, 1978) Many decades later, the first published paper is the first in the ranking list of cited papers. As stated in the bibliometric report: "The most cited paper is also the most cited paper of all time in the field of OR and MS and was published by Charnes, Cooper and Rhodes". (Laengle et al, 2017, p.812) A brief review of the literature contains the papers published in the relatively recent period of 2013-2023 from the field of DEA, a subfield of traffic and transport engineering, with data on efficiency decision-making units as a research subject, listed in Table 1.
Table 1 - Literature review
Journal Autor(s) No. DMU DMU Sample
Military Technical Andrejic (2013) 20 Distribution centers1 in
Courier/VojnotehniCki Serbia
glasnik
Transportation Park et al. 50 The transport sector
Research Part D (2018) of the US states
Transport Policy Kyriacou et al. 34 Transport
(2018) infrastructure
investments of
countries
Transport Zeng et al. 20 Airports in Eastern
(2020) China
International Journal Ghanem et al. 28 Turkish and EU
Technology, Policy (2020) railways
and Management
Case Studies on Fancello et al. 9 Italian city roads
Transport Policy (2020)
Axioms Nguyen et al. 24 Maritime transport in
(2022) EU countries
Discrete Dynamics in Shang et al. 40 Airports in China
Nature and Society (2022)
Journal of Navigation Bernal et al. 17 Container terminals in
and Port Research (2022) Spain
Procedia Computer Jiang et al. 30 Transport in Chinese
Science (2022) provinces
1 A distribution center consists of (Andrejic, 2013): a storage subsystem and a transport subsystem.
Journal Autor(s) No. DMU DMU Sample
Transport Policy Tomikawa & 6 Railway passenger
Goto (2022) companies
Research Square Niu et al. 38 Railway operators
(2022)
Energy Lee & Kim 6 Road passenger
(2023) vehicles in EU
countries
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In a broader sense, the listed similar units from each sample are additionally similar to the units of the other samples as components of the o transportation system, which according to Sinha (2007) constitute: §
1. Infrastructure: distribution centers (Andrejic, 2013), airports (Zeng et al, 2020), (Shang et al, 2022), roads (Fancello et al, 2020) and container terminals (Bernal et al, 2022);
2. Vehicles: electric vehicles and internal combustion engine vehicles (Lee sdo & Kim, 2023); "
3. Operations: rail transport of passengers and goods (Ghanem et al, 2020), (Tomikawa & Goto, 2022), (Niu et al, 2022) and maritime transport | of passengers and goods (Nguyen et al, 2022); and
4. Policies: transport infrastructure investments (Kyriacou et al, 2018), or the entire transport sector (Park et al, 2018), (Jiang et al, 2022).
According to Andrejic (2013, p.86), "it is possible to make a difference among the following efficiency measurement aspects in logistic: activity efficiency, process efficiency, subsystem efficiency, system efficiency and chain efficiency", viewed vertically, from the bottom up. But the activities, processes, subsystems and systems themselves are different, for the same level of observation, viewed horizontally. Therefore, we distinguish vertical and horizontal structures when measuring efficiency of diverse and few/many decision-making units. £
Thanks to the research studies of earlier authors, today there are numerous multivariate DEA models and numerous theoretical/practical examples of application. At the world level, according to the State of the J Art from 2011 (Markovits-Somogyi, 2011), the share of studies with the DEA application in the railway transport sector, in the total number of studies in the field of transport, is 9 out of 69 analyzed. J
In the article, a triple comparative analysis was chosen, the determinants of which are: 27 real decision-making units, three DEA ^ models and five years of business. Hence, this article is a new theoretical J contribution to the application of the DEA method in the field of railway transport - (1) a new real sample: railway stations, transport of goods,
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2018-22, (2) knowledge about efficiency, and (3) the possibility of corrective actions, to improve the company's operations and survival in the open market.
And the concrete challenge in the theoretical contribution is to know the individual practical contribution of each railway station to the functioning of the company. Accordingly, which stations should only be considered as role models, and which should be actively improved for the efficient operation of the company as a whole.
This article examines the efficiency of 27 railway stations in the RS in the function of transporting goods after the division of the ZS company, in the five-year period of 2018-2022. More precisely, the efficiency of railway stations, in relation to the remaining stations in the set, and the remaining elements in the system and the model applied following the complex mathematical DEA system achieved/invested.
The next section deals with another example in the Republic of Serbia, a new non-monopoly company "Srbija Kargo" JSC, in the official places in the function of goods transportation: railway stations and the issue of efficiency.
Railway stations in the Republic of Serbia
In this article, the subject of research are concrete railway stations on the railway network of the Republic of Serbia, open for the transportation of goods. According to the latest data, there are 27 railway stations in the RS, in the function of transporting goods, most of which are supervisory for subordinate official places (transport forwarding and transport loading points) on the railway network of the RS.
Introductory analysis
Railway station, train station, Bahnhofe, Les gares, Stazioni ferroviarie, Ii5npo5po^iKoi ота6^о1, Vasutallomasok, Zeleznicne stanice, Zelezniske postaje, Железнодорожные станции, Jarnvagsstationer, Estaciones de ferrocarril2 - the words are different but they all mean the same: railway stations. In accordance with the system theory, they are part of the economic subsystem, part of the transportation subsystem, part of the transport subsystem, and here we analyze them as part of the railway, more precisely the railway transport subsystem.
2 Respectively, in the languages: British English, American English, German, French, Italian, Greek, Hungarian, Slovak, Slovenian, Russian, Swedish and Spanish.
The subject of analysis - the railway stations (in the Republic of Serbia) - has been singled out for operational research theoreticians as well as traffic and transport practitioners. Since the first railway station until today, through decades of continuous innovation, the most modern ,m stations have been built in developed European and world countries. In terms of such a tendency, the example that follows reflects a more recent s A state and is not a rounded whole, but open to new ideas, new examples, ED and future stations as the most valuable and prominent objects of the railway infrastructure, the beginning and the end of the transport service -loading and unloading stations in the process of transporting goods.
3 (Min & Jong Joo, 2006), (Andrejic, 2015)
The main means of transporting goods are railway freight cars with different capacities (maximum amount of goods in tons). Hence, in the sample that follows, there are adequate inputs and outputs for each iffe railway station:
- inputs: the number of executors and the number of received/dispatched ° freight cars from loading/unloading, and °
- outputs: the quantity of transported goods (as a transport indicator) and the number of tariff kilometers traveled (as a traffic indicator). tro
As practitioners, we look for operational efficiency i.e., efficiency of functioning3 where real empirical data is used, to find out the effects of disintegration. We look for the situation in the practice of rail transport of goods after the milestone in 2015 in order to identify target actions.
As an example of an activity where the creation of a service has ^ several mutually competitive options, the activity of transport is given here, namely: (1) road transport, (2) rail transport, (3) air transport, (4) water transport, and (5) integral transport. Each of the listed transports has a passenger transport sub-option and a goods transport sub-option.
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In practice, transport companies usually provide transport service exclusively in one way, e.g. rail transport service through railway transport technology. Further channeling of rail transport or disintegration into passenger transport and goods transport is a new practice in Serbia, understudied and insufficiently known. Hence, a challenge in the new period is to assess the situation after the disintegration in terms of the £ efficiency of each particular station in the years after the division.
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Numerical pre-analysis
Merged into the rail transportation system, the passenger rail transport subsystem and the goods rail transport subsystem existed in the railway network of the Republic of Serbia until August 10, 2015, as the company Serbian Railways (ZS). Since then, four separate companies have been operating: Srbija Kargo JSC (Joint Stock Company for Railway Transport of Goods), here the subject of research, Srbija Voz JSC (Joint Stock Company for Railway Passenger Transport), as well as ZS Infrastructure (IZS) and ZS Holding.
In the sample that follows, the decision-making units are all 27 railway stations in the function of goods transportation (including their subordinate offices: TO and TT on the IZS. The analyzed official places are terminuses, i.e., final official places of traffic routes in the RS (departure and/or end in the process of vehicle movement; departure or destination; entry and/or exit to/from the system4). The research includes: internal traffic (starting and ending places are at IZS), import (ending places are at IZS) and export (starting places are at IZS).
How to divide one set (of 27 units) into two sets (a set of efficient units and a set of inefficient units)? Theoretically, this is possible to be achieved in 27 ways; therefore, there are 27 options, i.e., potential solutions, Table 2.
Table 2 - Potential solutions
Option Efficient Inefficient Total Efficient
units units units /Total units
Oi 1 26 27 1/27
O2 2 25 27 2/27
O3 3 24 27 3/27
O4 4 23 27 4/27
O5 5 22 27 5/27
O6 6 21 27 6/27
O7 7 20 27 7/27
O8 8 19 27 8/27
O9 9 18 27 9/27
O10 10 17 27 10/27
O11 11 16 27 11/27
O12 12 15 27 12/27
O13 13 14 27 13/27
O14 14 + 13 = 27 14/27
O15 15 12 27 15/27
O16 16 11 27 16/27
O17 17 10 27 17/27
4 An entry or an exit station is a place where goods enter or leave the selected transport system. (Filipovic, 2013)
Option Efficient Inefficient Total Efficient
units units units /Total units
O18 18 9 27 18/27
O19 19 8 27 19/27
O20 20 7 27 20/27
O21 21 6 27 21/27
O22 22 5 27 22/27
O23 23 4 27 23/27
O24 24 3 27 24/27
O25 25 2 27 25/27
O26 26 1 27 26/27
O27 27 0 27 27/27
At the very beginning of the research, the business indicators are known - total results by year: tons of transported goods, the number of traffic cars (which generate income) and the number of active official places on the railway - which slightly decrease from year to year, according to data normalized between zero and one, Figure 3.
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The optimal option is O27, with all 27 efficient units, followed by option O26, with 26 efficient units, then O25, O24... In the numerical sample, the | efficiency is calculated for each of 27 decision-making units, a set of efficient units and a set of inefficient units are obtained, and a particular oo option is identified. o
In the process of the movement of freight cars, the aim is to transport as many loaded cars as possible (Output1 maximum) and on the longest possible distance (Output2 maximum5). At the same time, it should be achieved with as few executors as possible and as few cars as possible -Input1 and Input2 should be minimal. Therefore, for calculating efficiency '■§ with classic DEA models, there are two inputs and two outputs here.
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In general, various types of goods are transported by rail: articles of m human nutrition, military equipment, containers, various types of oil, ores, coal, etc., in various series and types of cars, for various clients/shippers in import, export, domestic traffic, and transit. Empty cars also run, sent for loading or returning from unloading.
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2018 2019 2020 2021 2022
^^»tons of goods 1 0,9553 0,8496 0,8236 0,7780
freight cars 1 0,9326 0,8234 0,7727 0,5453
active official places 1 0,7984 0,6667 0,5891 0,4806
Figure 3 - Business indicators, 2018-22
In more detail, the percentage share of freight car traffic by year is divided by type of traffic, Table 3. A higher share of international traffic is observed, which is in line with growing globalization.
Table 3 - Freight car transportation, by year and type of traffic
Type of traffic 2018 2019 2020 2021 2022
Domestic 34 33 31 26 26
International 66 67 69 74 74
- import 23 24 23 25 29
- export 19 20 21 24 23
- transit 24 23 25 25 22
7 100 100 100 100 100
The initial data (inputs and outputs) are real statistical data for the five-year period of 2018-22. Transit was not analyzed because there are no loading/unloading operations at the stations on the IZS railway network (the final official places, loading or unloading, are abroad). The table of descriptive statistics of the initial data consists of (Aparicio & Zofio, 2021): minimum, median, average, maximum, and standard deviation. For the sample of the RS railway stations, descriptive statistics are given by year for the five-year period 2018-22, Table 4.
For a better trend, it is necessary to determine exactly which units of the organization are not functioning optimally. Hence, in the next section, the efficiency of each railway station is analysed, as follows: Effstation = f [Input1, Input2, Output1, Output2, u1, u2, u1, u2, model (1), (2), (3)]. At the same time, the dependence function is not known, and consequently, the non-parametric DEA method is applied.
Table 4 - Descriptive statistics of the initial data for 2018-22
Type 2018 2019 2020 2021 2022
Minimun
Input1 5 5 5 5 5
Input2 193 108 26 0 0
Output1 4,617 2,964 1,224 0 0
Output2 50,764 23,714 11,414 0 0
Median
Input1 19 21 21 21 21
Input2 11,809 8,214 7,840 5,058 3,189
Output1 266,382 247,441 249,238 192,106 136,539
Output2 2,212,381 1,486,651 1,636,987 918,934 559,322
Average
Input1 22 21 21 21 21
Input2 15,032 14,004 12,387 11,618 10,901
Output1 463,853 443,365 394,314 382,254 371,003
Output2 2,741,357 2,368,649 2,255,948 2,111,191 2,095,982
Maximum
Input1 55 53 53 53 53
Input2 115,084 120,416 84,054 90,766 90,807
Output1 4,100,475 4,209,062 2,938,645 3,240,929 3,261,823
Output2 15,247,532 14,410,170 10,088,444 10,782,367 11,594,050
Standard deviation
Input1 12 12 12 12 12
Input2 21,597 22,477 16,211 18,084 17,883
Output1 772,382 784,148 562,298 630,782 645,382
Output2 3,139,907 2,908,017 2,413,276 2,763,524 2,911,553
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Source: (1) information: own research, (2) data: "Srbija Kargo" JSC, Traffic and Transport Sector, Center for Commercial Affairs, Center for Calculation and Control of Income.
Numerical DEA analysis
This subsection calculates the numerical value of the efficiency of 27 railway stations in the Republic of Serbia in the function of transporting goods after the 2015 division of the company Serbian Railways (ZS) for the period of 2018-22.
The computational procedure was performed using the noncommercial software OSDEA-GUI (an acronym for Open Source Data Envelopment Analysis Graphical User Interface), version 0.2, more precisely, the CCR input and BCC input models (Open Source DEA, nd). For the specific sample of railway stations, where n=27, m=2, and s=2, a series of 27 linear programming (LP) problems is programmed. Each LP for each decision-making unit and each resulting unit efficiency, relative to the remaining DMUs. Inputs and outputs are the elements of the system, according to model (4), where N=5, namely: N1=V, N2=TR, N3=T, N4=E and N5=OM.
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In order to have a broader overview, a three-way comparative analysis was performed with the above-mentioned, so-called classical6 DEA models, Table 5.
Table 5 - Triple comparative analysis
Station Year Model
Acronym of Orientation Result
1 2018 CCR Charnes- input Technical
2 2019 Cooper- efficiency
3 2020 Rhodes TE
... 2021
... 2022 BCC Banker- input Pure
27 Charnes- technical
Cooper efficiency
PTE
SE Scale input TE/PTE
Efficiency
The result of the mentioned triple comparative analysis is the information on the efficiency (for station 1, year 2018, model CCR...), the average efficiency, as well as the number of the efficient units, Table 6.
Table 6 - Efficiency, input-oriented, stations-models-years
No. DMUName CCR BCC SE Average No. efficient
2018
1 Beograd R. 0.4830 0.4878 0.9902 0.6537
2 Bor Teretna 0.5736 0.5738 0.9997 0.7157
3 Brasina 0.4352 0.5652 0.7700 0.5901
4 Crveni Krst 0.8919 0.8942 0.9974 0.9278
5 Dimitrovgrad 0.6500 0.6595 0.9856 0.7650
6 Kragujevac 0.5986 0.6003 0.9972 0.7320
7 Kraljevo 0.5583 0.6318 0.8837 0.6913
8 Lapovo R. 0.9857 0.9977 0.9880 0.9905
9 Nis R. 0.5129 0.5254 0.9762 0.6715
10 Novi Sad R. 0.6484 0.6594 0.9833 0.7637
11 Pancevo G. 1 1 1 1 1
12 Pozega 0.9420 0.9591 0.9822 0.9611
13 Prahovo P. 0.8725 0.8878 0.9828 0.9144
14 Prijepolje T. 0.9867 1 0.9867 0.9911
15 Radinac 1 1 1 1 2
16 Ristovac 1 1 1 1 3
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No. DMU Name CCR
BCC
SE
Average No. efficient
10 11 12
13
14
15
16
17
18
19
20 21 22
23
24
25
26 27
Novi Sad R.
Pancevo G.
Pozega
Prahovo P.
Prijepolje T.
Radinac
Ristovac
Ruma
Sombor
S. Mitrovica
Subotica
Surcin
Sabac
Sid
Vrbas
Vreoci
Vrsac
Zrenjanin
Average
0.3127 0.6754 0.3983 1 1
0.8494 0.5316 0.5267 1 1 1
0.4452 1
0.2526 0.7520 0.5365 1
0.6109 0.6310
0.3616 0.9194 0.4148 1 1 1
0.5538 0.7846 1 1 1
0.5416 1
0.2851 1
0.5937 1
0.6904 0.7201
0.8648 0.7346 0.9602 1 1
0.8494 0.9599 0.6713 1 1 1
0.8220 1
0.8860 0.7520 0.9037 1
0.8848 0.8580
0.5130 0.7765 0.5911 1 1
0.8996 0.6818 0.6609 1 1 1
0.6029 1
0.4746 0.8347 0.6780 1
0.7287 0.7364
1 2
3
4
5
6
7
8
9
10 11 12
13
14
15
16
17
18
19
20 21 22
23
24
25
26 27
Beograd R. Bor Teretna Brasina Crveni Krst Dimitrovgrad Kragujevac Kraljevo Lapovo R. Nis R.
Novi Sad R.
Pancevo G.
Pozega
Prahovo P.
Prijepolje T.
Radinac
Ristovac
Ruma
Sombor
S. Mitrovica
Subotica
Surcin
Sabac
Sid
Vrbas
Vreoci
Vrsac
Zrenjanin
Average
0.1695 0.6320 1
0.5436 0.1677 0.6837 0.2968 0.4073 0.2497 0.3450 0.8091 0.3562 1
0.4226 0.9788 0.0451 0.4226 1 1 1
0.4043 1
0.2789 0.6763 0.3898 0
0.3464 0.5417
2021 0.1851 1 1
0.7680 0.3481 0.7330 0.3158 0.4164 0.2867 0.3501 0.9332 0.3567 1
0.5556 1
0.3846 0.7225 1 1 1
0.5364 1
0.2874 1
0.4029 0.8333 0.4229 0.6607
0.9157 0.6320 1
0.7078 0.4818 0.9327 0.9398 0.9781 0.8709 0.9854 0.8670 0.9986 1
0.7606 0.9788 0.1173 0.5849 1 1 1
0.7537 1
0.9704 0.6763 0.9675 0
0.8191 0.8125
0.4234 0.7547 1
0.6731 0.3325 0.7831 0.5175 0.6006 0.4691 0.5602 0.8698 0.5705 1
0.5796 0.9859 0.1823 0.5767 1 1 1
0.5648 1
0.5122 0.7842 0.5867 0.2778 0.5295 0.6716
2022
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No. DMUName CCR BCC SE Average No. efficient
1 Beograd R. 0.4088 0.4109 0.9949 0.6049
2 Bor Teretna 1 1 1 1 1
3 Brasina 1 1 1 1 2
4 Crveni Krst 0.8496 0.8602 0.9877 0.8992
5 Dimitrovgrad 0.0052 0.3846 0.0135 0.1344
6 Kragujevac 0.6518 0.7542 0.8642 0.7567
7 Kraljevo 0.8999 0.9089 0.9901 0.9330
8 Lapovo R. 1 1 1 1 3
9 Nis R. 0.2503 0.2618 0.9561 0.4894
10 Novi Sad R. 0.7038 0.7111 0.9897 0.8015
11 Pancevo G. 0.9031 0.9272 0.9740 0.9348
12 Pozega 0.9106 0.9141 0.9962 0.9403
13 Prahovo P. 0.8898 0.8987 0.9901 0.9262
14 Prijepolje T. 0.9049 0.9258 0.9774 0.9360
15 Radinac 0.9484 1 0.9484 0.9656
16 Ristovac 0.4508 0.4618 0.9762 0.6296
17 Ruma 0.8351 0.8799 0.9491 0.8880
18 Sombor 1 1 1 1 4
19 S. Mitrovica 0.7411 0.8125 0.9121 0.8219
20 Subotica 0.5833 1 0.5833 0.7222
21 Surcin 0.5091 0.5154 0.9878 0.6708
22 Sabac 0.6873 0.8034 0.8555 0.7821
23 Sid 0.3598 0.3746 0.9605 0.5650
24 Vrbas 0.7970 1 0.7970 0.8647
25 Vreoci 0.8822 0.8964 0.9842 0.9209
26 Vrsac 0 0.8333 0 0.2778
27 Zrenjanin 0.6089 0.6172 0.9866 0.7376
Average 0.6956 0.7834 0.8768 0.7853
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The integration of multiple models can be important in determining corrective actions in order to achieve efficiency. For inefficient units, target actions? They are those that affect the complex input-output connection, to which the stations are differently sensitive, and the actions are smaller or larger. Also, actions are smaller or larger depending on the applied model. Opting for multiple models, this can be understood as a phased (gradual) increase in efficiency, from smaller to larger changes. Hence, for each inefficient station, the best target actions are determined post-DEA by Sensitivity Analysis. This results in a decrease in input and/or an increase in output, with which the inefficient station achieves its efficiency.
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Table 7 - Efficiency, input, stations - average models - years
DMU No. Average model Average Figure 4
2018 2019 2020 2021 2022
1 0.6537 0.5758 0.4831 0.4234 0.6049 0.5482
2 0.7157 0.7179 0.6384 0.7547 1 0.7653
3 0.5901 1 1 1 1 0.9180
4 0.9278 0.7910 0.8083 0.6731 0.8992 0.8199
5 0.7650 0.3580 0.2967 0.3325 0.1344 0.3773
6 0.7320 0.7455 0.7056 0.7831 0.7567 0.7446
7 0.6913 0.6341 0.5667 0.5175 0.9330 0.6685
8 0.9905 0.7797 0.6132 0.6006 1 0.7968
9 0.6715 0.5614 0.3279 0.4691 0.4894 0.5039
10 0.7637 0.6503 0.5130 0.5602 0.8015 0.6577
11 1 0.8560 0.7765 0.8698 0.9348 0.8874
12 0.9611 0.6998 0.5911 0.5705 0.9403 0.7526
13 0.9144 1 1 1 0.9262 0.9681
14 0.9911 0.6067 1 0.5796 0.9360 0.8227
15 1 1 0.8996 0.9859 0.9656 0.9702
16 1 1 0.6818 0.1823 0.6296 0.6987
17 1 0.8135 0.6609 0.5767 0.8880 0.7878
18 1 1 1 1 1 1
19 0.7245 0.9670 1 1 0.8219 0.9027
20 0.6872 1 1 1 0.7222 0.8819
21 0.7285 0.5504 0.6029 0.5648 0.6708 0.6235
22 1 1 1 1 0.7821 0.9564
23 0.8254 0.5972 0.4746 0.5122 0.5650 0.5949
24 0.7613 0.8648 0.8347 0.7842 0.8647 0.8219
25 0.9950 0.8436 0.6780 0.5867 0.9209 0.8048
26 1 0.8414 1 0.2778 0.2778 0.6794
27 0.9386 0.7839 0.7287 0.5295 0.7376 0.7437
Average 0.8529 0.7866 0.7364 0.6716 0.7853 | 0.7666 |
Table 8 - Efficiency, input, average, years-models
CCR BCC SE Average
Year Figure 5
2018 0.7840 0.8017 0.9729 0.8529
2019 0.6937 0.7798 0.8863 0.7866
2020 0.6310 0.7201 0.8580 0.7364
2021 0.5417 0.6607 0.8125 0.6716
2022 0.6956 0.7834 0.8768 0.7853
Average 0.6692 0.7491 0.8813 | 0.7666 |
Based on Tables 7 and 8, for each station, the average efficiency per station and the average efficiency per year of the analyzed period are shown graphically, Figures 4 and 5, respectively. The research showed
that the analyzed period of 2018-22 is characterized by an annual change in the number of efficient units in the set of railway stations as decisionmaking units. The result is a relatively small number of efficient units (7, 7, 8, 6 and 4, respectively, out of 27 units) in an open, dynamic market, where the number of licensed/active freight operators is growing year by year (14 licensed / 5 active in 2018, 14/6, 15/9, 16/10 and 19/13 of the operators in 2022). (Directorate for Railways, 2019; 2020; 2021; 2022; 2023). Efficiency was decreasing by year until 2021, and then it increased slightly. If the result is connected with the pandemic, then a return of the average annual efficiency to the pre-pandemic level can be noticed for the year 2022.
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Finally, the obtained information on efficiency is also relative to the assigned weight coefficients of the input-output parameters, Table 9. For the analyzed years and from the aspect of particular stations, the most important is the number of freight cars loaded or unloaded at respective stations, and the least important is the number of kilometers traveled by car. This means that with such assigned input-output weights, the efficiency is maximal. For further improvement of efficiency (up to the value "1", in the case of inefficient units) a change of the initial (input/output) data is required, i.e., a change in business practices.
Table 9 - Weights of the input-output parameters
Year Model U1 U2 01 02
staff cars tons km
2018 CCR 0.4637 2.6454 0.0559 0.0078
2019 0.6902 2.9984 0.0299 0.0192
2020 1.0638 6.4583 0.0339 0.0210
2021 1.1511 1.3942 0.0173 0.0187
2022 0.3510 7.9415 0.1800 0.0053
I 3.7198 21.4378 0.3170 0.0720
2018 BCC 0.6612 1.4292 0.0269 0.0140
2019 0.7828 1.9940 0.0198 0.0045
2020 0.9163 5.9992 0.0307 0.0183
2021 1.1181 1.4230 0.0141 0.0098
2022 0.6540 3.8519 0.0795 0.0103
7 4.1324 14.6973 0.1710 0.0569
This can be seen in Figures 4 and 5, where the efficiency as a indicator of the business practice of the railway station - as a decisionmaking unit, as a set and as a system - can be further improved, up to the value of "1". From a transport functional to an efficiently functional unit, assembly and system, it is necessary to balance the input-output connection.
However, while the required information for several years has been obtained by applying different DEA models and while corrective actions
are part of the results of the used program, DEA still does not solve the question: how to practically implement the measures? "While DEA can be used to set targets for improvement of desired outputs, it does not instruct the user on how to reach those targets." (Avkiran, 2001, p.74) e
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In the newly opened free transport market, operators need to function efficiently in order to better serve, attract, and retain clients.
The purpose of this article is to calculate the efficiency of the decisionmaking units in relation to the remaining elements of the set, the selected elements of the system and the applied DEA models. Specifically, the aim is the set-system-model DEA analysis of a set of 27 railway stations in the RS, in the function of transporting goods, including subordinate official ¡§ places, on the five-year path after the reorganization, from 2018 to 2022. Each railway station was observed threefold, namely, as: doo
1. An element of the set of IZS stations, in the function of transporting goods (set analysis); J
2. An element of the RS railway transportation system (system analysis); and
3. A DMU efficiency decision-making unit (mathematical DEA analysis).
Such a demanding goal was achieved by obtaining triple-relative efficiency which comes to the fore through the application of 27 decision-making units, four input-output parameters and three mathematical models.
The initial data (inputs and outputs) with which the efficiency is calculated, are the reflection of the state in the set, in the system and outside the system. Specifically, the inputs are the number of executors and the number of freight cars (for which the respective station is loading/unloading). The outputs are transport and traffic services: tons of £ goods loaded/unloaded and tariff kilometers traveled per car. The data on inputs and outputs are at the 2018-22 annual level.
The mathematical models (CCR/BCC/SE), used to calculate the | efficiency based on the initial data, express an average technical/pure-technical/scale efficiency of 0.6692, 0.7491, and 0.8813, respectively.
At the very end of the research, by applying the set-system-model £ DEA analysis, as a result of the overall situation in practice, the following is obtained: (1) final efficiency value of 0.7666 as an average of 27 DMU, five analyzed years of operation, and three DEA models (2) total weights
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of the initial data, where the number of cars has the highest weight, and the number of kilometers has the lowest.
For full efficiency (27/27), a new business practice and additional, corrective, target actions are advised as a proposal for future research.
The target actions are the amount (reduction and/or addition) of the same considered activities (inputs or outputs) with which inefficient decision-making units become efficient; thus re-efficiency or regained efficiency is obtained, which is now equal to the one, and railway stations in the function of transporting goods by traffic and transport function efficiently. However, there is no unique efficiency. It is always an assessment, relative to the analyzed set of similar decision-making units, the analyzed multi-component system of various elements and the applied Data Envelopment Analysis model.
An extension of the sample, in addition to the implemented setsystem-model DEA analysis of railway stations, is a step forward that considers the railway (1) against other, competitive modes of transport, such as road, water and air transport, and (2) together with other, complementary modes, such as combined, multimodal transport, primarily rail-road and rail-water, with a multifaceted advantage.
"For both passenger and freight movements, portal-to-portal transportation should be considered that may include various modes and interfaces. This is particularly crucial for freight, domestic as well as international." (Sinha, 2007, p.12)
The final and common conclusion is that in order to work successfully, strengthen efficiency and increase competitiveness, as well as after the implemented measures, it is necessary to monitor business parameters over and over again, refresh information, and innovate efficiency measures.
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TIPO DE ARTICULO: artículo científico original
Zeng, Z., Yang, W., Zhang, S. & Witlox, F. 2020. Analysing airport efficiency ¡2
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Estaciones de ferrocarril en la República de Serbia en la función de g
transporte de mercancías: eficiencia según el sistema DEA
Dubravka R. Vukovic "Srbija kargo" JSC, Departamento de Tráfico y Transporte,
Belgrado, República de Serbia «
CAMPO: matemáticas ™
o c o
Resumen: H
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CP
Introducción/propósito: El Análisis Envolvente de Datos (DEA - por sus siglas en inglés) es comúnmente utilizado para calcular la eficiencia de Unidades de Toma de Decisiones similares (DMU - por sus siglas en inglés), que como tales son elementos de un conjunto. En el artículo, se considera que cada elemento de un conjunto (de elementos similares) es al mismo tiempo un elemento de un sistema (de varios elementos). Un ejemplo de DMU son 27 estaciones de ferrocarril en la República de Serbia (RS) como elemento de un conjunto de estaciones de ferrocarril y j¡ como elemento del sistema de transporte ferroviario, en función de transporte de mercancías, tras la división de la empresa Serbian Railways (en pasajeros y mercancías). Por el bien de un mejor servicio, atracción y retención de clientes, en el nuevo, libre, mercado del transporte, el g. propósito de este artículo es encontrar la eficiencia de las estaciones de la & RS en el periodo 2018-2022.
Métodos: Análisis DEA comparativo de modelos sistémicos de sistemas m ferroviarios. estaciones como DMU. Una unidad es un elemento del J conjunto, la unidad es un elemento del sistema, y una unidad es el tema de -la matemática. Modelo DEA-CCR/BCC/SE. Análisis DEA comparativo de modelos sistémicos de sistemas de estaciones ferroviarias como DMU. Una unidad es un elemento del conjunto, la unidad es un elemento del sistema y una unidad es el tema del modelo matemático DEA-CCR/BCC/SE. |
ra CU
Resultados: La eficiencia final, el promedio de todos los valores medios, es 0.7666, como resultado de un triple análisis comparativo de la DEA: 27 DMU, tres modelos DEA y cinco años de funcionamiento. Conclusión: Las estaciones son funcionalmente diferentes en términos de eficiencia, y cada estación difiere funcionalmente, por años y por modelo. El objetivo final es lograr un equilibrio entrada - salida y la Opción 27/27 que se logra con acciones correctivas de reducción/adición, entrada o salida.
Palabras clave: eficiencia, DEA-CCR/BCC/SE, estaciones ferroviarias, sistema de configuración, transporte de mercancías.
Железнодорожные станции в Республике Сербия в функции грузоперевозок: эффективность по системе DEA
Дубравка Р. Вукович
АО "Србия карго", подразделение дорожного движения и транспорта, г. Белград, Республика Сербия
РУБРИКА ГРНТИ: 27.47.19 Исследование операций 28.29.00 Системный анализ
73.29.21 Железнодорожные станции и узлы. Вокзалы, 73.29.51 Грузовое хозяйство железнодорожного транспорта ВИД СТАТЬИ: оригинальная научная статья
Резюме:
Введение/цель: Анализ охвата данных (DEA) обычно используется для расчета эффективности аналогичных подразделений по принятию решений (DMU), которые как таковые являются элементами одного множества. В данной статье такие элементы рассматриваются как часть множества (из сходных элементов), но одновременно и как часть системы (из различных элементов). Примером DMU в данной статье являются 27 железнодорожных станций в Республике Сербия в качестве элемента множества железнодорожных станций, а также в качестве элемента системы железнодорожного транспорта, которая выполняет функцию грузоперевозок, после разделения компании «Сербские железные дороги» (на «пассажирские» и «товарные»). Целью данной статьи является определение эффективности работы станций Сербских железных дорог в период с 2018 по 2022 год для улучшения обслуживания, привлечения и удержания клиентов на недавно открывшемся свободном транспортном рынке.
Методы: В ходе исследования проведен сравнительный DEA-анализ групповых системных моделей железнодорожных станций как DMU. Причем, единица - это элемент множества, единица - это
элемент системы, и единица - это объект математической модели DEA-CCR/BCC/SE.
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Результаты: В результате тройного сравнительного анализа DEA: 27 железнодорожных станций, трех моделей DEA в течение ¡= пяти лет работы получена итоговая эффективность, выраженная средним значением всех средних значений, которое составляет 0,7666. ш
Заключение: Станции функционально различаются с точки зрения эффективности. Каждая станция функционально отличается в зависимости от года и модели. Конечной целью является баланс доходов и расходов и опция 27/27, которая достигается о корректирующими действиями: уменьшением/увеличением, и доходов и расходов.
Ключевые слова: эффективность, DEA-CCR/BCC/SE, Ц железнодорожные станции, система множеств, грузоперевозки.
Железничке станице у Републици Срби]и у функции превоза ^
робе: ефикасност по систему DEA
Дубравка Р. Вуковип .g
„Срби]а карго" АД, Сектор за саобрапа] и транспорт, Београд, Република Срби]а
ОБЛАСТ: математика
КАТЕГОРША (ТИП) ЧЛАНКА: оригинални научни рад Сажетак:
Увод/циъ: Data Envelopment Analysis (DEA) y06u4ajeH0 се користи за израчунаваше ефикасности истоврсних jeduHuца одлучиваша (DMU), ще су елементи jедног скупа. У раду се сматра да je сваки такав скуп (истоврсних елемената) у/едно и елемент система (разноврсних елемената). Пример DMU представка 27железничких станица у Републици Срб^и (РС), као елемент скупа железничких станица и као елемент система железничког транспорта, у функции превоза робе после поделе предузеЬа Железнице Срб^е (ЖС) (одвоjeно „путници" и „роба"). Ради квалитетн^ег опслуживаша, привлачеша и задржаваша комитената на .Q новоотвореном, слободном и транспортном тржишту, цил> овог -рада био je налажеше ефикасности станица РС, у периоду 20182022. година. га
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Методе: У раду je примешена скуповно-системска моделна компаративна DEA анализа железничких станица као DMU. Jeдиница je елемент скупа, елемент система и предмет о математичког DEA-CCR/BCC/SE модела.
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Резултати: Коначна ефикасност, просек свих просека, износи 0,7666, као резултат троjне компаративне DEA анализе: 27 железничких станица, три DEA модела и пет година пословаъа. ™ Закъучак: Станице су различито функционалне по питаъу
с5 ефикасности; jедна иста станица jе различито функционална по
>v годинама и по моделу. Краjfoи цил> jе баланс улаз-излаз и опц^а 27/27
g ща се постиже уз корективне акц^е - смак>ек>е/повепак>е улазa,
02, односно излаза. си
ш Къучне речи: ефикасност, DEA-CCR/BCC/SE, железничке
з станице, скуп-систем, превоз робе.
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y Paper received on: 14.08.2023.
^ Manuscript corrections submitted on: 04.03.2024.
o Paper accepted for publishing on: 05.03.2024.
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© 2024 The Author. Published by Vojnotehnicki glasnik / Military Technical Courier cn (www.vtg.mod.gov.rs, BTr.MO.ynp.cp6). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.Org/licenses/by/3.0/rs/).
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