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BEST PRACTICE AS ACTUAL AND RELATIVE BENCHMARK TO INEFFICIENT UNITS:
MULTISET DEA ANALYSIS ^
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Dubravka R. Vukovic is
"Srbija kargo" JSC, Traffic and Transport Department, <
Belgrade, Republic of Serbia, a
e-mail: dub.vukovic@gmail.com, ORCID iD: http://orcid.org/0000-0003-1341-2568
DOI: 10.5937/vojtehg66-16155; https://doi.org/10.5937/vojtehg66-16155
FIELD: Mathematics, Logistics, Traffic Engineering ARTICLE TYPE: Original Scientific Paper ARTICLE LANGUAGE: English
Summary:
The direction in research of the efficiency of decision-making units in this o paper is an efficient^muiti-inefficient^muiti-efficient unit. So, the general purpose of this paper is twofold: (1) identification of «hidden» inefficient e units within a multi-set, among efficient units of the basic set, and (2) "§ achieving the efficiency in such identified inefficient units. This indicates (warns of!) a negative efficient^inefficient process, so as to provide a timely response and thereby prevent multi-inefficiency. The specific goal is is to assess the efficiency of the Serbian railway passenger stations, first within the basic set of the Passenger Transport Section Belgrade, then in the multi-set of the Passenger TransportSections, and finally in the superset, the Passenger Transport Sector. This is achieved by means of
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the multi-set DEA (Data Envelopment Analysis) method, which is a
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system for: (i) relative efficiency assessment, in the first iteration, through ^ the basic set analysis, and (ii) decrease in efficiency of potentially inefficient units, in subsequent iterations, through the multi-set analysis. ¡£ The result is that the efficient stations Pozarevac and Pancevo Bridge are at the initial level, and the (newly) efficient Pozarevac, Novi Sad and Indija at the final level. The best practice station remains the Pozarevac Station, which is multi-efficient, and therefore the role model to inefficient stations. The conclusion is drawn that the solution resulting from the multi-set DEA analysis is more realistic, and less relative, because it applies to a wider analysed set of decision-making units, i.e., a larger coverage when considering the issue. This is important for fitting into the new era of growing globalization, and therefore our recommendation is the integral multi-set, as opposed to the individual single set approach.
Key words: Efficiency, Data Envelopment Analysis, Multi-Set Analysis, Railway Stations.
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Introduction
A number of same-type organisational units within a single organisation jointly accomplish the objective of the organisation, thereby contributing to a higher or lesser extent. In order for the organisation to be successful, it is necessary for all of its units to be successful. Success is a multidimensional concept, with efficiency being one of its dimensions.
Efficiency is a feature of someone or somebody (people, institutions, organisations, companies, processes and other) to produce maximum output (products, services) using minimum input (resources, activities). Expressed in the simplest mathematical terms, it is the ratio of an output and an input. From a more complex mathematical point of view, it is a ratio between the weighted sum of multiple outputs and weighted sum of multiple inputs. For this purpose, the Data Envelopment Analysis, (DEA) was created in 1978 by Charnes, Cooper and Rhodes as a method of calculating the efficiency of the so-called Decision Making Units, abbreviated DMU), (Charnes et al, 1978).
The idea of this paper is to decrease the relativity and to increase the reality of the best practice through the iterative procedure "efficients-inefficient" (efficient unit in the basic set, inefficient in the multiset). Thus, success is a relative and changeable category and requires caution and constant reconsideration. With the view to the future, the goal of this paper is an early discovery of potentially inefficient so-called "hidden" units, and their respective timely redirecting.
Among numerous examples of best practices of similar companies, both local and foreign, the most suitable example is a so-called personal example, and that is the example of the same analysed set of measuring units. This is because all the units of the same company as means of their teamwork, under the same conditions, contribute to the accomplishment of a single goal. Logical conclusion is the requirement for all the units to proportionally contribute to this objective, whereby inefficient units imitate the efficient ones. And when those efficient units, acting as models for the inefficient ones, are "among us" or "ours", we believe that the efficiency can really be achieved.
On the one hand, the Sensitivity analysis of a single same set of decision making units, but applying different input/output data and opposite DEA models, results in the same efficiency (Vukovic, 2016). On the other hand, the stated Multiset DEA analysis of the same data of decision-making units in a number of different, ever bigger sets, results in smaller or equal efficiency, so some efficient units become inefficient. By
application of the post DEA sensitivity analysis, newly efficient units become efficient in a wider set, a so-called multiset. Thus the research direction is efficient^multiinefficient^multiefficient units. From this point of view, the goal is two steps ahead: recognition of potentially inefficient units and achieving efficiency in a wider set. Multiset efficiency is more weighted than the monoset, as is it obatined by further decrease of input and/or increase of output, thereby improving the operation of units, which defines the contribution of our paper.
The following chapters include the overview of references, the short descriptions of the DEA method and the Multiset DEA analysis, as well as a numerical example, while the conclusion has been provided based on the stated information.
Overview of references
Having reviewed the newly published worldwide and local literature, we herewith provide the following observations:
1. Efficiency is monoset-oriented, where each decision-making unit is analysed in the same set. Examples of such sets include: 208 clinical commissions in England (Takundwa et al, 2017), 42 bus routes in Brisbane, Australia (Tran et al, 2017), and 55 universities in the state of Mexico (Sagarra et al, 2017). While in these works each unit is analysed in the same set, we here observe a unit in a wider scale, as an element of every bigger set. It is thus possible to compare the efficiency results obtained through multisets and to provide a more realistic assessment of efficiency.
2. The problem of the multiset prediction is not well known in the literature. According to certain authors, the problem is solved by consecutive decision-making, where a new multiset function of loss is proposed as a parameter of predictive policy (Welleck et al, 2017). According to others, the multiset approach is used to predict the average daily temperature, as shown by the Taipei example in Taiwan (Vamitha & Rajaram, 2015). In our paper, the Multiset DEA analysis of units is used for predicting inefficient results, which meant increasing the set of decision-making units by adding a new set. In this way, potentially inefficient units are more accurately predicted, which is helpful in solving the problems of multiset prediction.
3. The multiset theory differentiates between conventional and fuzzy logic. Conventional logic defines whether an element belongs to a set by "yes or no", whereas fuzzy logic does so by "more or less" (Pamucar et al, 2016). The Multiset DEA analysis is a connection between the
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multiset theory and the DEA method. The stated analysis defines the simultaneous belonging of elements to a larger number of sets by "yes", with multiset efficient units. In addition, it also uses "yes", with multiset inefficient units. Realistically, a multiset is a family of a set of efficient and a set of inefficient units. Units "more or less" belong to a multiset, where units closer by efficiency belong to a multiset "more", and with the deviation "less".
4. Efficiency is dealt with without burdening the external society, but individually instead, within the scope of internal potential. The example of this case are premises used by institutions, command departments and units of the Serbian Army, where the application of thermal isolation is proposed to solve the problem of energy efficiency (Zivkovic & Banjac, 2016). By applying the stated idea of using internal potential, we are solving a complex problem of efficiency of railway stations, with an additional idea of using its diverse potential, not just material but also organisational, and thereby achieving certain savings.
5. Organisational efficiency is impossible without the evaluation of the work of employees, which requires management so that it could be managed (maximised) in this way (Lukovac et al, 2014). Measurement of work at different levels by a multiset approach is a higher stage of comparison.
Core principles of DEA (Data Envelopment Analysis)
DEA is a method of mathematical programming for the calculation of efficiency and it is used, from a wider perspective, in economy, and more precisely, in different kinds of economics, depending on the type of decision making units. This is supported by numerous and diverse examples from the world and local literature, covering different types of Economics:
- Health Economics, where the effectiveness of health organizations is being decided upon (an example of this type of units is the public health system and the medical protection system of the OECD countries (Ozcan & Khushalani, 2017);
- Traffic Economics, where the effectiveness of transport organizations is being decided upon (examples are the Brazilian intermodal terminals), (Peixoto et al, 2017);
- Sports Economics, where the decision on the efficiency of sports organizations is being decided upon (for example, the football team of Serbia), (Petrovic Bordevic, 2015);
- Tourism Economics, involving decision making on the efficiency of tourism organizations (e.g. ecotourism parks), (Lin et al, 2017);
- Business Economics, where the effectiveness of business organizations is being decided upon (for example, Taiwanese insurance companies), (Chen & Zhu, 2017);
- Economics of Education, where the decision making on the effectiveness of educational organizations is being decided upon (examples are Chinese educational organizations, from pre-school to higher education), (Si & Qiao, 2017);
The algorithm of the selection process with the DEA method application includes five steps, as presented in Figure 1.
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Step 1: \ Selection of a set of units DMU
Step 2: Selection of the parameters of INPUT/ OUTPUT
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Step 4: Selection of a mathematical DEA model
Step 5: Selection of a computing LP
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Figurel - DEA method application algorithm Рисунок 1 - Алгоритм применения АОД метода Слика 1 - Алгоритам примене ДЕА методе
According to Figure 1, each example of a particular DEA method is characterised by the concrete: decision making units (DMU), input-output parameters (INPT/OUPT), numerous values of input and output, mathematical DEA model (Charnes et al, 1978), (Banker et al, 1984), (Yang et al, 2000), and a computer program (MS Excel Solver, LINDO, LINGO and other) for solving linear programming (LP) tasks, whose result is the efficiency value for each decision making unit.
By the application of the DEA method, decision making units are divided into two groups: efficient (Eff=1) and inefficient (0<Eff<1), while according to their numerical values they have a number of comparison stages, so it is possible to establish a ranking (complete or incomplete) of decision making units. Efficient units obtained based on the actual data are realistically best practice units, but they are also a substandard of efficiency as they are valid only for a concrete example (case study). Opposite to this is a generally applied standard which does not exist in this case, as there is no absolute efficiency.
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Multiset DEA analysis
The Multiset DEA analysis is based on the fact that sets are not of exact size, but can be changed depending on the number of elements. Hence, the limit i.e. the final size of a set remains unknown. And it is exactly the issue of the limit of the set, being the analysis framework, which is significant for the efficiency value. The above analysis contains the principle that all the units outside the basic set break the ranking of the units of the basic set, by the value of efficiency, by analysing them in sets, which are at different (organizational, hierarchical) levels. A complete set is not known, so it is unknown which is the highest possible efficiency i.e. only experiential efficiency is known.
Similar to Savic's idea (Savic, 2017) that the algorithm should be applied several times, whereby a single input or output is added in each iteration, the idea of our paper is to add more decision-making units to each iteration, i.e. a new set of DM Us which represent a single organizational unit. However, while in the previously stated reference "turning" points among the iterations referred to the inputs/outputs (qualitative characteristics of the DMU), the "turning" points here are the sets of DMUs (quantitative characteristics). Changing qualitative features or changes of content are a feature of a systemic approach, while the change in quantitative characteristics or changes in the size of a set of features, discussed herewith, is a multi-set approach.
The multiset DEA analysis estimates the efficiency of the decision-making unit, where a unit is an element in each iteration of a new wider set. The first DEA model which we will use, from which many modified models are devised, is the CCR model (Charnes et al, 1978) whose multiset mathematical formulation consists of sets of decision making units in which the goal function is maximized with the set limits, Table 1.
According to Table 1, the Multiset DEA analysis is an iterative process of maximizing the function of the objective h0 (efficiency) under the given restrictions, in ever increasing set till the final total sum set of all p basic sets (BSp).
The idea of the Multiset analysis is contrary to the idea of the post DEA Sensitivity Analysis. The Sensitivity analysis yields targeted activities (target values of inputs and outputs), which by the realization of an inefficient unit become effective. Contrary to this, the Multiset analysis is a kind of prediction that produces non-targeted (undesirable) inefficient units, by making some efficient units inefficient in the multiset, Figure 2.
Table 1 - Multi-Set DEA Analysis Mathematical Model Таблица 1 - Математическая модель Мульти-множественного АОД анализа Табела 1 - Математички модел мултискуповне ДЕА анализе
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DMUjG{OS1}V{OS2}V... {OSp} {OS1}U{OS2}U ... U{OSp}={NS} OS1={DMU1, DMU2, ..., DMUa} OS2={DMUa+1,..., DMUb}
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h0 -efficiency of DMU for which is calculated yrj - output of j DMU Xjj - input of j DMU n - number of DMU m - number of input s - number of ourput Ur - weighted coefficient of r output Vi - weighted coefficient of i input p - no. of OS a,b,c...,,d,..,g - no. of elements of BS
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Figure 2 - Two-way process of efficiency change Рисунок 2 - Двунаправленный процесс изменения эффективности Слика 2 - Двосмерни процес промене ефикасности
According to Ljubisav Rakic: "The position of science in the century which has begun is to change the methodology. Instead of studying why something happened, we should move in the direction of predicting and studying of what could happen." (Rakic, 2017)
The essence of the Sensitivity analysis is as follows: (1) improving the efficiency of decision making units, and (2) aiming at proportionally equal contribution of all units of a set to the common goal of the company. The essence of opposite, multiset approach is viewing the units in a wider context.
The philosophy of the multiset approach may be explained by a modern theory included in the quotation of Stuart Diamond: "Each ceiling is a new floor", expressed in such a way to say that we could always get more (but not everything), which is also the name of his book (Diamond, 2015, p.36). Applied to the topic of our paper, provided efficiency is the
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ability to maximise the results with the least possible investment - it means that by widening the analysed set by inclusion of new units we can get the efficiency of higher weight (the efficiency of the units of the basic set decreases or remains the same with multiset efficient units).
Within the context of the multiset DEA analysis of efficiency, this means that the current efficiency is disturbed by inclusion of new units and may always be overcome by new units included in the set of the analysed units, and thus new efficient units are being formed.
If, according to Marjanovic (Vesovic et al, 2007), the basic goals of the company are survival, facilitation of survival (efficiency of operation) and progress, then within the context of the multiset approach:
1. The current state of the set indicates: the survival (the organisation is operating with both efficient and inefficient units).
2. Targeted state of the set obtained by the Sensitivity analysis marks: Facilitating survival (as a result of targeted activities, all inefficient units become efficient).
3. Higher targeted state of the set obtained by Multiset DEA analysis marks: Progress (as the result of increase in the size of the set, the criterion for reaching efficiency has become more demanding, as the former efficient units with the same values of input-output parameters become inefficient). Therefore, the efficiency in a larger set is more weighted than the efficiency in smaller set.
Real evaluation of the efficiency for the previous period is performed by solving the preferred DEA model, or Ex-post evaluation of efficiency (backwards evaluation) for each of the analysed units of decision making. The sensitivity analysis provides the desired estimation for the future period or Ex-ante evaluation of efficiency (forward evaluation), only for inefficient units of decision making (efficient decision making units already have the desired efficiency for the unit).
Case study: Railway stations of IZS Company
The Multiset DEA analysis is a universal system for the evaluation of efficiency of entities and their arrangement according to a given efficiency, within diverse numeric examples. However, with each individual application, it is necessary for entities to be of the same kind, as it is widely known and logical that comparison makes sense only in such circumstances. A realistic example of such entities are Serbian railway passenger stations, which are subject of our research with the aim of illustrating the stated analysis. But, why railway, why railway stations and why at this moment?
Railway is a type of transport for passengers and goods, used for civil purposes, for transporting people and equipment, and also for military purposes. Theoretically, its advantages are numerous and important in terms of transport power, traffic safety, spatial acquisition, consumption of energy, emissions of harmful substances, noise and other, which make it competitive. Railway stations are important infrastructure facilities in the transport process; apart from this, they are numerous, and financially valuable. They are also important to us as a place of departures and arrivals, loadings and unloadings. In the new era of business, according to the principle of a liberal, supranational market, it is compulsory for companies to be efficient and trending for continuous improvement. Hence, it is necessary to continuously monitor and comply with complex and expensive interoperability flows. To this purpose, a case study: Serbian Railway Passenger Stations.
On the one hand (theoretically), Serbian railway passenger stations are decision making units (DMU) within the DEA method, and on the other hand (practically), railway stations (RS) are infrastructural facilities within the Infrastruktura zeleznica Srbije Company (IZS), Table 2. Six-set DEA analysis following the enlargement of a single-set example (Vukovic, 2016).
Table 2 - Example in practice of the Serbian railways Таблица 2 - Пример из практики сербских железных дорог Табела 2 - Пример из праксе српских железница
DEA method IZS company
DMU as element of DEA RS as element of IZS
Superset Set Subset Railway station Section Sector
LS BS1 DMU1 Belgrade 1.Passanger Passenger
73 DMU 16 DMU DMU2 Mladenovac Transport Section Belgrade (including OU Pancevo Transport Sector
DMU3 Rakovica
DMU4 Zemun
DMU5 Batajnica
DMU6 Novi Belgrade and OU
DMU7 Pancevo Bridge Pozarevac)
DMU8 Resnik
DMU9 Pancevo Main
DMU10 Vrsac
DMU11 Pancevo Town
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DEA method IZS company
DMU as element of DEA RS as element of IZS
Superset Set Subset Railway station Section
DMU12 Pozarevac
DMU13 Smederevo
DMU14 Mala Krsna
DMU15 Vranovo
DMU16 Radinac
BS2 DMU17 Lapovo 2.
12 DMU DMU18 Jagodina Passanger Transport Section Lapovo (including
DMU19 Stalac
DMU20 Paracin
DMU21 Velika Plana
DMU22 Cuprija OU Kraljevo)
DMU23 Cicevac
DMU24 Palanka
DMU25 Kraljevo
DMU26 Kragujevac
DMU27 Raska
DMU28 Cacak
BS3 DMU29 Nis 3.
12 DMU DMU30 Leskovac Passenger Transport Section Nis (with OU Zajecar)
DMU31 Pi rot
DMU32 Dimitrovgrad
DMU33 Vranje
DMU34 Palilulska Rampa
DMU35 Crveni Krst
DMU36 Aleksinac
DMU37 Zajecar
DMU38 Knjazevac
DMU39 Negotin
DMU40 Bor
BS4 DMU41 Novi Sad 4.
18 DMU DMU42 Beska Passenger Transport Section Novi Sad
DMU43 Cortanovci
DMU44 Sremski Karlovci
DMU45 Vrbas (including
DMU46 Odzaci OU Ruma
DMU47 Zmajevo and OU Zrenjanin)
DMU48 Petrovaradin
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DEA method IZS company
DMU as element of DEA RS as element of IZS
Superset Set Subset Railway station Section Sector
DMU49 Ruma
DMU50 Sabac
DMU51 Sid
DMU52 Indija
DMU53 Stara Pazova
DMU54 Nova Pazova
DMU55 Sremska Mitrovica
DMU56 Zrenjanin
DMU57 Zrenjanin Factory
DMU58 Kikinda
BS5 DMU59 Subotica 5.
8 DMU DMU60 Sombor Passenger Transport Section Subotica
DMU61 Sonta
DMU62 Prigrevica
DMU63 Senta
DMU64 Bogojevo
DMU65 Zednik
DMU66 Horgos
BS6 DMU67 Uzice 6.
7 DMU DMU68 Pozega Passenger Transport Section Uzice
DMU69 Priboj
DMU70 Valjevo
DMU71 Prijepolje
DMU72 Lazarevac
DMU73 Lajkovac
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Based on Table 2, there are 73 railroad stations within the network of Serbian Railways. They are organized in two levels: (1) Passenger Transport Sector, at a higher organizational level; and (2) Passenger Transport Section, at a lower organizational level. The sector includes six sections, four of which have organizational units (OU), as a lower organizational level. The seats of the Sections (Belgrade, Lapovo, Nis, Novi Sad and Subotica) are important railway hubs, where more lines are obtained, with more intensive traffic volumes, and are commercially significant places. By the very nature of their operation, the mutual cooperation of the Sections is very important because they are connected: (1) physically, by railroad tracks; (2) organizationally, by
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traffic connections (both railways and connections are usually administered by two or more Sections). Hence, it is important that they are all efficient, in order to maintain the continuity of the technological process of work. Namely, the inefficiency of one of them jeopardizes the efficiency of any other.
If we select the following input/output parameters as follows:
- The man: "basic factor of each production, including the production of transport or post office service. It simultaneously appears as its organiser, manager and executor." (Vesovic et al, 2007. p.186),
- Produced service: "Standard measure of the volume of the whole economy is the gross domestic product (GDP), which represents the value of all gods and services produced in an economy within a year." (Stiglitz, 2008, p.38),
- Wok performance: the purpose, and therefore the point of performing the works, is to gain profit,
then the following parameters are selected in our case according to the given logic: (i) number of cashiers (entry 1), (ii) number of dispatched trains (entry 2), (iii) number of dispatched passengers (exit). The sources of the concrete data for our case include:
- Job classification within the company in 2010: number of cashiers, (Zeleznice Srbije, 2010);
- Timetable 2013/2014: number of trains, (Zeleznice Srbije, 2013);
- Statistics of Serbian Railways 2013: number of passengers, (Zeleznice Srbije, 2014).
The option A of the multi-set DEA analysis analyses units in each basic set individually (left side of Table 3) and units in the total sum superset (right side of Table 3). The application of the CCR DEA model from Table 1 results in the values of efficiency of decision making units evaluated by MS Excel Solver to six decimal numbers, Table 3.
According to Table 3, the application of the Section analysis resulted in the total of 12 efficient units, which are the best practice units, whereas the Sector analysis resulted in only three efficient units: Pozarevac, Novi Sad and Indjija. The remaining nine, DMU7,18,24,25,30,37,59,66 and 67, so called ''hidden'' inefficient units, have been discovered by the analysis of the superset of Sectors, where they become inefficient.
This indicates the sensitivity of the DEA method to a change in a set size. A quotation of Andersen and Petersen states (Andersen & Petersen, 1993, p.1261): A weakness of DEA is that a considerable number of observations typically is characterized as efficient, unless the sum of the number of inputs and outputs is small relative to the number of observations.
Table 3 - Decision-making unit efficiency in the basic sets and in a superset Таблица 3 - Эффективность единиц принятия решений в основном множестве и
надмножестве
Табела 3 - Ефикасност ]единица одлучиваша у основним скуповима и надскупу
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VARIANT A
No of BS. DMU no. Efficiency (0-1] Quantity of efficient units SS DMU no. Efficiency (0-1] Quantity of efficient units
DMU1 0.879175 DMU1 0.798903
DMU2 0.192230 DMU2 0.170841
DMU3 0.206022 2 DMU3 0.175874
DMU4 0.164341 DMU4 0.140289
DMU5 0.361602 DMU5 0.308687
DMU6 0.181727 DMU6 0.155137
DMU7 1.000000 DMU7 0.961284
DMU8 0.093544 DMU8 0.079853
DMU9 0.359357 DMU9 0.341007
DMU10 0.862869 DMU10 0.765826
DMU11 0.323213 DMU11 0.298594
DMU12 1.000000 DMU12 1.000000
DMU13 0.603945 DMU13 0.533680
Ф DMU14 0.302814 DMU14 0.258497
о DMU15 0.100037 DMU15 0.087856
ro m DMU16 0.139338 DMU16 0.122371
DMU17 0.113290 DMU17 0.039702
DMU18 1.000000 DMU18 0.350449
DMU19 0.248430 3 DMU19 0.075714
DMU20 0.757351 DMU20 0.164219
DMU21 0.589529 DMU21 0.148776
DMU22 0.312563 DMU22 0.100666
DMU23 0.267623 DMU23 0.083624
DMU24 1.000000 DMU24 0.345956
CM DMU25 1.000000 DMU25 0.256134
' Ф DMU26 0.633900 DMU26 0.137451
о <л го m DMU27 0.466613 DMU27 0.123317
DMU28 0.913229 DMU28 0.304692
со DMU29 0.982846 DMU29 0.674760
ф DMU30 1.000000 t Ф DMU30 0.660572
о DMU31 0.306841 2 Ф DMU31 0.204181
го m DMU32 0.259709 ю DMU32 0.172817 3
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VARIANT A
No of BS. DMU no. Efficiency (0-1] Quantity of efficient units SS DMU no. Efficiency (0-1] Quantity of efficient units
DMU33 0.439482 DMU33 0.148063
DMU34 0.249361 DMU34 0.165932
DMU35 0.555812 DMU35 0.187271
DMU36 0.647396 DMU36 0.367192
CO DMU37 1.000000 DMU37 0.877614
<u DMU38 0.490002 DMU38 0.320747
o DMU39 0.472408 DMU39 0.303723
ro m DMU40 0.767057 DMU40 0.468147
DMU41 1.000000 DMU41 1.000000
DMU42 0.488504 DMU42 0.488504
DMU43 0.266385 2 DMU43 0.266385
DMU44 0.148627 DMU44 0.148627
DMU45 0.544243 DMU45 0.544243
DMU46 0.126275 DMU46 0.126275
DMU47 0.307956 DMU47 0.307956
DMU48 0.133064 DMU48 0.133064
DMU49 0.215982 DMU49 0.215982
DMU50 0.327164 DMU50 0.327164
DMU51 0.340419 DMU51 0.340419
DMU52 1.000000 DMU52 1.000000
DMU53 0.732659 DMU53 0.732659
DMU54 0.522205 DMU54 0.522205
DMU55 0.422567 DMU55 0.422567
<u DMU56 0.387019 DMU56 0.387019
o DMU57 0.022979 DMU57 0.022979
ro m DMU58 0.041560 DMU58 0.041560
DMU59 1.000000 DMU59 0.477291
DMU60 0.721202 2 DMU60 0.321932
DMU61 0.558896 DMU61 0.178442
DMU62 0.584930 DMU62 0.186759
LO DMU63 0.166865 DMU63 0.074945
<u DMU64 0.063039 DMU64 0.020127
o DMU65 0.873175 DMU65 0.278792
ro m DMU66 1.000000 DMU66 0.443437
VARIANT A
No of BS. DMU no. Efficiency (0-1] Quantity of efficient units SS DMU no. Efficiency (0-1] Quantity of efficient units
DMU67 1.000000 DMU67 0.774963
DMU68 0.602181 1 DMU68 0.296396
DMU69 0.691438 DMU69 0.470662
CD DMU70 0.955143 DMU70 0.508139
<U DMU71 0.661295 DMU71 0.419728
О DMU72 0.521605 DMU72 0.191992
ro m DMU73 0.135552 DMU73 0.049899
Totally efficient units 12 Totally efficient units 3
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DMU67 Uzice 12 DMU66 Horgos 11 DMU59 Subotica 10 DMU52 Indija 9 DMU41 Novi Sad 8 DMU37 Zajecar 7 DMU30 Leskovac 6 DMU25 Kraljevo 5 DMU24 Palanka 4 DMU18 Jagodina 3 DMU12 Pozarevac 2 DMU7 Pancevacki Most 1
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Figure 3 - Best practice units in the Section (12 units) and the Sector (3 units) Рисунок 3 - Единицы передовой практики в Секции (12 единиц) и Секторе
(3 единицыi)
Слика 3 - Jединице наjбоъе праксе у секции (12 jединица) и сектору (3 jединице)
The ratio between the Sector efficiency (Eff<1) and the Section efficiency (Eff=1), for 12 efficient units in the Section, may be seen from the graph presented in Figure 3. The highest span is of DMU25 which is on the verge of efficiency (0.256134/1), with the achieved 25.6% of the goal. The lowest span is with the DMU7, which is firmly efficient (0.961284/1), with the achieved 96.1% of the target.
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For the variant B of the multiset DEA analysis, through the iterative procedure, the number of DMUs gradually increases by adding the units of the following basic unit to Basic set 1, up to the superset size, Table 4.
Table 4 - Efficiency of decision-making units in BS1 and aggregate sets Таблица 4 - Эффективность единиц принятия решения в ОМ1 и суммарных
множествах
Табела 4 - Ефикасност ]единица одлучиваша у ОС1 и збирним скуповима
VARIANT B
DMU Efficiency
no. 1st iteration 2nd 3rd 4th 5th 6th
(16DMU) iteration iteration iteration iteration iteration
(28DMU) (40DMU) (58DMU) (66DMU) (73DMU)
DMU1 0.879175 0.879175 0.879175 0.798903 0.798903 0.798903
DMU2 0.192229 0.192229 0.192229 0.170841 0.170841 0.170841
DMU3 0.206021 0.206021 0.206021 0.175874 0.175874 0.175874
DMU4 0.164340 0.164340 0.164340 0.140289 0.140289 0.140289
DMU5 0.361602 0.361602 0.361602 0.308687 0.308687 0.308687
DMU6 0.181726 0.181726 0.181726 0.155137 0.155137 0.155137
DMU7 1.000000 1.000000 1.000000 0.961284 0.961284 0.961284
DMU8 0.093543 0.093543 0.093543 0.079853 0.079853 0.079853
DMU9 0.359357 0.359357 0.359357 0.341007 0.341007 0.341007
DMU10 0.862869 0.862869 0.862869 0.765826 0.765826 0.765826
DMU11 0.323213 0.323213 0.323213 0.298594 0.298594 0.298594
DMU12 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000
DMU13 0.603944 0.603944 0.603944 0.533680 0.533680 0.533680
DMU14 0.302814 0.302814 0.302814 0.258497 0.258497 0.258497
DMU15 0.100036 0.100036 0.100036 0.087856 0.087856 0.087856
DMU16 0.139337 0.139337 0.139337 0.122371 0.122371 0.122371
DMU17 0.044929 0.044929 0.039702 0.039702 0.039702
DMU18 0.396589 0.396589 0.350449 0.350449 0.350449
DMU19 0.088672 0.088672 0.075714 0.075714 0.075714
DMU20 0.177537 0.177537 0.164219 0.164219 0.164219
DMU21 0.157789 0.157789 0.148776 0.148776 0.148776
DMU22 0.111534 0.111534 0.100666 0.100666 0.100666
DMU23 0.092086 0.092086 0.083624 0.083624 0.083624
DMU24 0.389268 0.389268 0.345956 0.345956 0.345956
DMU25 0.287488 0.287488 0.256134 0.256134 0.256134
DMU26 0.148598 0.148598 0.137451 0.137451 0.137451
DMU27 0.143906 0.143906 0.123317 0.123317 0.123317
DMU28 0.349139 0.349139 0.304692 0.304692 0.304692
VARIANT B
DMU Efficiency
no. 1st iteration (16DMU) 2nd iteration (28DMU) 3rd iteration (40DMU) 4th iteration (58DMU) 5th iteration (66DMU) 6th iteration (73DMU)
DMU29 0.809804 0,674760 0,674760 0,674760
DMU30 0.762116 0,660572 0,660572 0,660572
DMU31 0.237283 0,204181 0,204181 0,204181
DMU32 0.200835 0,172817 0,172817 0,172817
DMU33 0.173450 0,148063 0,148063 0,148063
DMU34 0.192833 0,165932 0,165932 0,165932
DMU35 0.219377 0,187271 0,187271 0,187271
DMU36 0.408825 0,367192 0,367192 0,367192
DMU37 0.922098 0,877614 0,877614 0,877614
DMU38 0.369195 0,320747 0,320747 0,320747
DMU39 0.348028 0.303723 0.303723 0.303723
DMU40 0.529783 0.468147 0.468147 0.468147
DMU41 1.000000 1.000000 1.000000
DMU42 0.488504 0.488504 0.488504
DMU43 0.266385 0.266385 0.266385
DMU44 0.148627 0.148627 0.148627
DMU45 0.544243 0.544243 0.544243
DMU46 0.126275 0.126275 0.126275
DMU47 0.307956 0.307956 0.307956
DMU48 0.133064 0.133064 0.133064
DMU49 0.215982 0.215982 0.215982
DMU50 0.327164 0.327164 0.327164
DMU51 0.340419 0.340419 0.340419
DMU52 1.000000 1.000000 1.000000
DMU53 0.732659 0.732659 0.732659
DMU54 0.522205 0.522205 0.522205
DMU55 0.422567 0.422567 0.422567
DMU56 0.387019 0.387019 0.387019
DMU57 0.022979 0.022979 0.022979
DMU58 0.041560 0.041560 0.041560
DMU59 0.477291 0.477291
DMU60 0.321932 0.321932
DMU61 0.178442 0.178442
DMU62 0.186759 0.186759
DMU63 0.074945 0.074945
DMU64 0.020127 0.020127
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DMU Efficiency
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DMU65 0.278792 0.278792
DMU66 0.443437 0.443437
DMU67 0.774963
DMU68 0.296396
DMU69 0.470662
DMU70 0.508139
DMU71 0.419728
DMU72 0.191992
DMU73 0.049899
According to Table 4, in the 1st, 2nd and 3rd iteration the units DMU7 and 12 are efficient. The fourth iteration is ''decisive", as in further 4th, 5th and 6th iterations, the efficient units include DMU12, 41 and 52.
The comparative results of the research of the Variants A and B of the Multiset DEA analysis indicate the units which should be further improved (highlighted), and the unit which remains efficient (bold), Table 5. This further indicates the relativity of efficiency, as practices are best, some in supersets, some however in basic sets.
Considering the efficient units from the monoset viewpoint, set BS1 should be partially improved, i.e. just one efficient unit (DMU7), sets BS2, BS3, BS5 and bS6 should completely improve their efficient units, while set BS4 "strong" is a set with both multiefficient units.
Unit DMU7 is multiinefficient due to the fact that it has been discovered as potentially inefficient within the multiset of fourth iteration and further to the superset. Based on this, target activities resulting from the Sensitivity analysis are proposed based on deceasing the input and/or increasing the output. Opposite to this, DMU12 unit is a multiset efficient unit, as it still remains as efficient as in the first set after the increase of the analysed set.
As the Passenger Transport Sector does not include the decision making units by which the analysed set would be enlarged, it is possible to add hypothetical units with hypothetical data in future observations and thus establish the complete ranking. In such future iterations, with new hypothetical units, it is necessary to further decrease the investment and/or increase the result for achieving efficiency.
Table 5 - Result of the Multiset DEA analysis (Variant A, Variant B) Таблица 5 - Результат мульти-множественного АОД анализа (Вариант A,
Вариант Б)
Табела 5 - Резултат мултискуповне ДЕА анализе (варианта А, варианта Б)
о ю ю ю см ю !± Ci
Variant A Variant B
Basic set Efficient Basic set and aggregate basic sets Efficient Multi-efficient Multi inefficie nt
BS1 DMU7 DMU12 BS1 DMU7 DMU12 DMU12 DMU7
BS2 DMU18 DMU24 DMU25 BS1+BS2 DMU7 DMU12 DMU12 DMU7
BS3 DMU30 DMU37 BS1+BS2+BS3 DMU7 DMU12 DMU12 DMU7
BS4 DMU41 DMU52 BS1+BS2+BS3+BS4 DMU12 DMU41 DMU52 DMU12
BS5 DMU59 DMU66 BS1+BS2+BS3+BS4+BS5 DMU12 DMU41 DMU52 DMU12
BS6 DMU67 BS1+BS2+BS3+BS4+BS5+BS6 DMU12 DMU41 DMU52 DMU12
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In conclusion, based on the numerical example, the following three definitions are provided:
- Definition 1: When a DMU is analysed in relation to other units in a bigger set, the DMU efficiency numerical value is smaller or equal to the efficiency obtained when a DMU is analysed in relation to other units in a smaller set. The estimation by the Multiset DEA analysis in a wider set is more restrictive than the evaluation by the monoset approach: Effmultiset< Effset.
- Definition 2: When a DMU is analysed in relation to other units in an aggregate set, the number of efficient units is smaller than the total number of efficient units when units are analysed in relation to other units within the basic set:
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- Definition 3: Multiset efficient unit is efficient in both a basic set and a superset: EffMSEff = 1(BS, SS).
Additional clarification of efficiency, apart from the numerical value of efficiency, also includes the number of decision making units of the analysed set. It is a kind of weighted efficiency according to which efficient units are different and therefore comparable.
Conclusion
After reading the papers of the first and subsequent authors on the subject of the DEA method, it can be learnt that efficiency is a relative feature, as it varies depending on the data analysed. Additionally, the fact that this change may not only be positive (from inefficient to efficient unit), but also a negative one (from efficient to inefficient) has been ignored. Hence, the result of efficiency is only an estimate, and not an evaluation, that is, a final approximate value of efficiency.
With such more profound knowledge in mind, the objective of this paper is to acknowledge potentially inefficient units in order to avoid the previously stated negative process (efficient - inefficient), and sustain efficiency in such a way. In this regard, the Multiset DEA analysis has been proposed, which has also been explained from the theoretical point of view and practically illustrated, while in the end the research results were presented.
Theoretically, the Multiset DEA analysis is a mathematical way of calculating the efficiency of business operations of entities from different areas. The efficiency evaluations obtained by the Multiset analysis are re-evaluated, whereby new estimations of efficiency are equal or smaller than the previous ones, which implies very important information on potentially inefficient units.
Practically, the Multiset DEA analysis is illustrated at an actual example of Serbian railway passenger stations, which are an important part of both the railway segment and the environment. As a part of the changing environment, military sector is a more or less significant customer of transport services. We would like to mention in our paper the best practice units, Pancevacki Most (DMU7) and Pozarevac (DMU12) stations, within the Passenger Transport Section Belgrade, as well as Pozarevac, Novi Sad and Indjija within the Passenger Transport Sector. The stated stations are: (i) an actually achievable model for inefficient units, (ii) a "live" proof of potential efficiency, and (iii) a confirmation of the application of the DEA method. The Pozarevac station is a multiset
efficient station, as it is efficient in the Sector, while DMU7 is potentially inefficient as it becomes inefficient in the Sector.
Based on the results, with certain units we expect a negative process (efficient^multineffecinet). Now that we know what awaits us, our future research will definitively be the Sensitivity analysis. This is the logical order (or a post DEA analysis) as it provides concrete target values of input-output parameters (smaller inputs and/or higher outputs), which is necessary to realise in practice so that multiinefficient units can become multiefficient. Targeted activities are different in each iteration and every time, and in any larger set. There is no doubt that with them in the future, efficient units of the basic set become stable, and they remain as efficient in the end as in the beginning. Therefore, the actual efficiency indicator is not only a pure numerical value, but also the number of units included in the analysis, which makes efficiency additionally defined. The extension of the case would include new inputs and outputs as characteristics of other subsystems, i.e. an analysis of the so-called DAT approach using sets and systems.
Additionally, future research refers to providing measures which encourage activities, and then measures possible to apply in concrete conditions. Now we will make a general proposal for better conversion input/output:
- New rational technology for the operation of stations (rational number of station personnel, rational redistribution of work, modernisation of operations, etc.);
- New rational organisation of railway transport (rational number of shares i.e. fewer trains, more departures, fewer "empty" lines, shorter stays and turning and line stations, which is to be achieved by a quality made timetables, etc.);
- Improved quality of transport service (timely departures, regular trains, comfort, providing information to passengers, travel without changing trains, accessibility of stations, diverse fee-related benefits etc.).
According to the presented system and the analogy to the case shown, the efficiency of entities from other activities may also be calculated, with completely different types of data (apart from the applied traffic-transport and demographic, economic and other statistical data). In the spirit of this magazine, we will mention organisational units, institutions and individuals of the Serbian Army, which is, similarly to the railway, a significant and complex, and above all, extremely important organisational system.
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Through constant innovation lasting for a number of decades, the DEA model of mathematical programming has become a subject of significant and important number of works which present the modified models and contemporary examples. In terms of such tendency, the presented subject of DEA is not a completely closed issue, but it instead eagerly waits for new ideas and new examples, all with a wider comprehension of the notion of efficiency.
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^ Zeleznice Srbije. 2014. Statistika 2013. Belgrade: Bajka 87 (in Serbian).
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* ПЕРЕДОВАЯ ПРАКТИКА В КАЧЕСТВЕ РЕАЛИСТИЧНОГО И
ОТНОСИТЕЛЬНОГО ПРИМЕРА ДЛЯ ПОДРАЖАНИЯ ДЛЯ НЕЭФФЕКТИВНЫХ ЕДИНИЦ: МУЛЬТИ-МНОЖЕСТВЕННЫЙ АОД АНАЛИЗ
S
< Дубравка Р. Вукович
О «Сербия карго» AО, Транспортный сектор, г. Белград, Республика Сербия
'У ОБЛАСТЬ: математика, логистика, пути сообщения
ВИД СТАТЬИ: оригинальная научная статья
ш ЯЗЫК СТАТЬИ: английский
I-
0 Резюме:
^ Исследования эффективности единиц принятия решения в
настоящей работе проводились в следующем направлении: эффективная^мульти-неэффективная^мульти-эффективная единица. Следовательно, цель настоящей работы -предусмотреть несколько шагов заранее, таких как: (1) идентификация "скрытых" неэффективных единиц в мультимножестве, среди эффективных единиц в основном множестве, (2) осуществление эффективности в случаях идентифицированных неэффективных единиц. Таким образом указывается (предупреждается!) на отрицательный процесс эффективная^неэффективная, и создается возможность для своевременного реагирования, в том числе и для предупреждения мульти-неэффективности. Конкретной целью настоящей работы является оценка эффективности сербских вокзалов и железнодорожных пассажирских станций, прежде всего в основном
о ю ю
Ю
см ю
множестве Секции пассажирского транспорта Белград, а затем в мульти-множестве Секции пассажирского транспорта, и в конце в надмножестве - Секторе пассажирского транспорта. Это осуществляется с помощью применения мульти-множественного АОД метода (Анализ охвата данных), который представляет собой систему: (и) оценки относительной эффективности, в первой итерации, путем анализа основного множества, (ии) снижения эффективности потенциально неэффективных единиц, в последующих итерациях, путем анализа мульти-множества. В ш результате - эффективные станции Пожаревац и Панчевачки мост находятся на начальном уровне, а (ново)эффективные Пожаревац, Нови Сад и Инджия, на последнем уровне. Станция Пожаревац на практике остается лучшей станцией, и по своей мульти-эффективности является примером для подражания неэффективным единицам. Можно сделать вывод, что решение мульти-множественного АОД анализа в большей степени реалистично и в меньшей степени относительно, поскольку применимо к более широкому анализируемому множеству единиц принятия решения, то есть к большему охвату рассмотрения проблемы. Данные показатели являются весьма значимыми, особенно, если учитывать тенденции возрастающей глобализации, в данной связи мы рекомендуем интегральный мульти-множественный подход, в отличии от индивидуального
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единично-множественного подхода. >
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Ключевые слова: эффективность, анализ среды ф функционирования, мульти-множественный анализ,
железнодорожные станции.
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НАJБО^А ПРАКСА КАО РЕАЛАН И РЕЛАТИВАН УЗОР ^
НЕЕФИКАСНИМ JЕДИНИЦАМА: МУЛТИСКУПОВНА ДЕА 8
АНАЛИЗА
Дубравка Р. Вукови^ го
„Срби]а карго" АД, Сектор за саобра^но-транспортне послове, Београд, Република Срби]а
(Л ф
СО
ОБЛАСТ: математика, логистика, саобра^ ВРСТА ЧЛАНКА: оригинални научни чланак -о
иЕЗИК ЧЛАНКА: енглески §
Сажетак:
Правац истраживаъа ефикасности }единица одлучиваъа у овом раду }есте ефикасна^мултинеефикасна^мултиефикасна 1'единица, а општи цил> су два корака напред: (1) откриваъе „скривених" неефикасних }единица у мултискупу, ме^у ефикасним ]единицама у основном скупу и (2) постизак>е ефикасности код
откривених неефикасних ¡единица. Тиме се указке (упозорава!) на негативан процес ефикасна^неефикасна, како би се правовремено реаговало и тиме предупредила мултинеефикасност. Конкретни § цил> }есте да се процени ефикасност железничких путничких
станица у Србщи, на]пре у основном скупу Секци}е за превоз путника Београд, затим у мултискупу Секци]а за превоз путника и, на кра}у, у надскупу Сектор за превоз путника. То се постиже
° мултискуповном методом ДЕА (Data Envelopment Analysis), што }е
ос систем за: (и) процешиваше релативне ефикасности, у првоj
^ итерации, анализом основног скупа, (ии) смашеше ефикасности
g потенци]ално неефикасних ]единица, у наредним итераци}ама,
0 анализом мултискупа. Резултат jе да су ефикасне станице ^ Пожаревац и Панчевачки мост на почетном нивоу, а — (ново)ефикасне Пожаревац, Нови Сад и ИнГ)и]а на крадем нивоу.
1 На]бол>а пракса }е у станици Пожаревац, ко}а ]е мултиефикасна и ш представка узор неефикасним ]единицама. Закя>учу]е се да jе
решете мултискуповне ДЕА анализе више реално, а маше ос релативно, }ер важи за шири анализирани скуп jединица
одлучиваша, тj. веЯи обухват сагледаваша проблема. То jе значаjно за уклапаше у ново доба растуПе глобализац^е, те jе наша препорука целовит мултискуповни приступ насупрот поjединачном моноскуповном приступу.
< Къучне речи: ефикасност, Data Envelopment Analysis,
щ мултискуповна анализа, железничке станице.
^
>о Paper received on / Дата получения работы / Датум приема чланка: 27.12.2017.
Manuscript corrections submitted on / Дата получения исправленной версии работы / ш Датум достав^а^а исправки рукописа: 22.02.2018. ^ Paper accepted for publishing on / Дата окончательного согласования работы / Датум коначног прихвата^а чланка за об]ав^ива^е: 24.02.2018.
> © 2018 The Author. Published by Vojnotehnicki glasnik / Military Technical Courier
(www.vtg.mod.gov.rs, втг.мо.упр.срб). 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/).
© 2018 Автор. Опубликовано в «Военно-технический вестник / Vojnotehnicki glasnik / Military 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/).
© 2018 Аутор. 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/).
