Stability of the Classifications of Returns to Scale in Data Envelopment Analysis: A Case Study of the Set of Public Postal Operators

Transcription

1 Acta Plytechnica Hungarica Vl., N., 0 Stability f the Classificatins f Returns t Scale in Data Envelpment Analysis: A Case Study f the Set f Public Pstal Operatrs Predrag Ralevic, Mmčil Dbrdlac, Dean Markvic, Matthias Finger PhD Candidate at Faculty f Transprt and Traffic Engineering, University f Belgrade, Vvde Stepe Street 0, 000 Belgrade, Serbia p.ralevic@sf.bg.ac.rs Faculty f Transprt and Traffic Engineering, University f Belgrade, Vvde Stepe Street 0, 000 Belgrade, Serbia m.dbrdlac@sf.bg.ac.rs, mdean@sf.bg.ac.rs Ecle Plytechnique Fédérale de Lausanne (EPFL), Odyssea, Statin, 0 Lausanne, Switzerland matthias.finger@epfl.ch Abstract: A significant theme in data envelpment analysis (DEA) is the stability f returns t scale (RTS) classificatin f specific decisin making unit (DMU) which is under bserved prductin pssibility set. In this study the bserved DMUs are public pstal peratrs (PPOs) in Eurpean Unin member states and Serbia as a candidate cuntry. We demnstrated a sensitivity analysis f the inefficient PPOs by DEA-based apprach. The develpment f this analytical prcess is perfrmed based n real wrld data set. The estimatins and implicatins are derived frm the empirical study by using the CCR RTS methd and the mst prductive scale size cncept (MPSS). First, we estimated the RTS classificatin f all bserved PPOs. After that, we determined stability intervals fr preserving the RTS classificatin fr each CCR inefficient PPO under evaluatin. Finally, scale efficient inputs and utput targets fr these PPOs are designated. Keywrds: data envelpment analysis; returns t scale; stability; scale efficient targets; public pstal peratrs Intrductin Data envelpment analysis (DEA) is a nn-parametric technique fr evaluating the relative efficiency f multiple-input and multiple-utput f a decisin making units (DMUs) based n the prductin pssibility set. DEA methd is intrduced

2 P. Ralevic et al. Stability f the Classificatins f Returns t Scale in Data Envelpment Analysis: A Case Study f the Set f Public Pstal Operatrs by Charnes et al. and extended by Banker et al.. There are varius DEA mdels that are widely used t evaluate the relative efficiency f DMUs in different rganizatins r industries. Additinaly, DEA is recgnized as a pwerful analytical research tl fr mdeling peratinal prcesses in terms f perfrmance evaluatins, e.g., cmpetiteveness, e.g. and decisin making e.g.. A taxnmy and general mdel framewrks fr DEA can be fund in,. The stability f the classificatins f returns t scale (RTS) is an imprtant theme in DEA and was first examined by Seifrd and Zhu. There are several DEA appraches cnsidering this tpic. One apprach is the stability analysis f a specific DMU which is under evaluatin see, 0. Anther apprach is the stability f a specific DMU which is nt under evaluatin see,. Additinally, sme authrs used free dispsal hull (FDH) mdels (unlike the cnvex DEA mdels, FDH mdels are nn-cnvex) fr estimating RTS see,,. The stability f RTS and the methds fr its estimating in DEA prvides imprtant infrmatin n the data perturbatins in the DMU analysis. These infrmatin prvide discussins that can be develped in perfrmance analysis. This enables t determine the mvement f inefficient DMUs n the frntier in imprving directins. In,, the authrs develped several linear prgramming frmulatins fr investigating the stability f RTS classificatin (cnstant, increasing r decreasing returns t scale). These authrs cnsidered data perturbatins fr inefficient DMUs. The authrs f indicated that smetimes a change in input r utput r simultaneus changes in input and utput are nt pssible. In the papers f Jahanshahl et al. 0 and Abri develped an apprach fr the sensitivity analysis f bth inefficient and efficient DMUs frm the bservatins set. The current article prceeds as fllws: In Sectin, the determinatin f RTS in the CCR mdels is reviewed. Additinally, in this Sectin are intrduced utputriented RTS classificatin stability and scale efficient targets inputs and utputs f DMUs. In Sectin, we applied methds frm Sectin n real wrld data set f public pstal peratrs (PPOs). Finally, cnclusins are given in Sectin. Methds. RTS Classificatin In the DEA literature there are several appraches fr estimating f returns t scale (RTS). Seifrd and Zhu in demnstrated that there are at least three

3 Acta Plytechnica Hungarica Vl., N., 0 equivalent RTS methds. The first CCR RTS methd is intrduced by Banker 0. The secnd BCC RTS methd is develped by Banker et al. as an alternative apprach using the free variable in the BCC dual mdel. The third RTS methd based n the scale efficiency index is suggested by Fare et al.. The CCR RTS methd is based upn the sum f the ptimal lambda values in the CCR mdels f DEA, and is used in this study t the RTS classificatins f bserved PPOs. The CCR is riginal mdel f DEA fr evaluating the relative efficiency fr a grup f DMUs prpsed by Charnes et al.. The CCR stands fr Charnes, Cper and Rhdes which are the last names f this mdel creatrs. Suppse there are a set ( A ) f DMUs. Each DMU ( A ) uses m inputs x i ) t prduce s utputs y r ( r,,,..., s ). The CCR mdel A, with respect t a set E { 0 fr sme ptimal slutins fr ( i,,,..., m evaluates the relative efficiency f a specific DMU, f CCR frntier DMUs defined DMU }. One frmulatin f a CCR mdel aims t minimize inputs while satisfying at least the given utput levels, i.e., the CCR input-riented mdel (see the M mdel). Anther frmulatin f a CCR mdel aims t maximize utputs withut requiring mre f any f the bserved input values, i.e., the CCR utputriented mdel (see the M' mdel). The CCR mdels assume the cnstant returns t scale prductin pssibility set, i.e. it is pstulated that the radial expansin and reductin f all bserved DMUs and their nnnegative cmbinatins are pssible and hence the CCR scre is called verall technical efficiency. If we add E in the M and M' mdels, we btain the BCC input-riented and the BCC utput-riented mdels, respectively prpsed by Banker et al.. The name BCC is derived frm the initial f each creatr's last name (Banker-Charnes- Cper). The BCC mdels assume that cnvex cmbinatins f bserved DMUs frm the prductin pssibility set and the BCC scre is called lcal pure technical efficiency. It is interesting t investigate the surces f inefficiency that a DMU might have. Are they caused by the inefficient peratins f the DMU itself r by the disadvantageus cnditins under which the DMU is perating? Fr this purpse the scale efficiency scre (SS) is defined by the rati, SS CCR BCC. This apprach depicts the surces f inefficiency, i.e. whether it is caused by inefficient peratins (the BCC efficiency) r by disadvantageus cnditins displayed by the scale efficiency scre (SS) r by bth. M mdel min ()

4 P. Ralevic et al. Stability f the Classificatins f Returns t Scale in Data Envelpment Analysis: A Case Study f the Set f Public Pstal Operatrs Subec t: E x i x i, i,,,..., m E y r y r, r,,,..., s 0, E M' mdel max () Subect t: E x E i y r x i y, i,,,..., m r, r,,,..., s 0, If E E A The DMU ( aspect. These DMU (, then the M mdel is riginal frm f the input-riented CCR mdel. E ) are called CCR efficient and frm a specific CCR efficient ) appear in ptimal slutins where 0. The E E in the M mdel when evaluating DMU enables fact that 0 fr all perfrming the CCR mdel in frm f M mdel r M' mdel. By using the M r M' mdel, we can estimate the RTS classificatin based n the fllwing therem by Banker and Thrall : Therem. Let ( E ) be the ptimal values in M r M' mdel, returns t scale at DMU can be determined frm the fllwing cnditins: (i) If in any alternate ptimum then cnstant returns-t-scale (CRS) prevails. E 0

5 Acta Plytechnica Hungarica Vl., N., 0 (ii) If fr all alternate ptima then decreasing returns-t-scale (DRS) prevails. E (iii) If fr all alternate ptima then increasing returns-t-scale (IRS) prevails. E Seifrd and Thrall in derived the relatinship between the slutins f the M mdel and M' mdel. Suppse ( E ) and is an ptimal slutin t M mdel. There exists a crrespnding ptimal slutin ( t the M' mdel such that and. E ) and A change f input levels fr DMU in the M mdel r a change f utput levels in the M' mdel des nt change the RTS nature f DMU. These mdels yield the identical RTS regins. Hwever, they can generate different RTS classificatins. In this study we chse the M mdel t determine the RTS classificatin.. Stability f the RTS Classificatins The stability f the RTS classificatins prvides sme stability intervals fr preserving the RTS classificatin f a specific DMU. It enables t cnsider perturbatins fr all the inputs r utputs f DMU. Input-riented stability f RTS classificatins allws utput perturbatins in DMU, and utput-riented stability f RTS classificatins enables input perturbatins. In this study stability intervals f each CCR inefficient PPO under evaluatin are derived frm utput-riented RTS classificatin stability because we aim t cnsider input increases and decreases fr each CCR inefficient PPO. Lwer and upper limit f stability intervals determined by using tw linear prgramming mdels (see the M and M' mdels) where is the ptimal value t the M' mdel when evaluating DMU. M mdel min E ()

6 P. Ralevic et al. Stability f the Classificatins f Returns t Scale in Data Envelpment Analysis: A Case Study f the Set f Public Pstal Operatrs Subec t: E x E i y r x i y, i,,,..., m r, r,,,..., s 0, E M' mdel max E () Subec t: E x E i y r x i y, i,,,..., m r, r,,,..., s 0, E By using the M and M' mdels, we can define lwer and upper limit f stability intervals f DMUs based n the fllwing therems by Seifrd and Zhu : Therem. Suppse DMU exhibits CRS. CRS If R min, max, :. The CRS classificatin cntinues t hld, where represents the prprtinal change f all inputs, xˆ ( i,,,..., m), and i x i mdels, respectively. and are defined in the M and M' Therem. Suppse DMU exhibits DRS. The DRS classificatin cntinues t hld fr R DRS decrease f all inputs, M mdel. : i i, where represents the prprtinal xˆ x ( i,,,..., m), and is defined in the

7 Acta Plytechnica Hungarica Vl., N., 0 Therem. Suppse DMU exhibits IRS. Then the IRS classificatin cntinues t hld fr R IRS change f all inputs, M' mdel. : xˆ x ( i,,,..., m), and i i, where represents the prprtinal is defined in the. Scale Efficient Targets Scale efficient targets (inputs and utputs) fr DMUs can be derived by using the mst prductive scale size cncept prpsed by Banker 0. This cncept in DEA is knwn as acrnym MPSS (see the M and M' mdels). Bth mdels are based n utput-riented CCR mdel. The M mdel prduces the largest MPSS targets (MPSS max ), and the M' mdel the smallest (MPSS min ). M mdel min () E Subect t: 0 E x E i y r x i y, i,,,..., m r, r,,,..., s 0, E M' mdel max () E Subect t: 0 E x E i y r x i y, i,,,..., m r, r,,,..., s 0, E

8 P. Ralevic et al. Stability f the Classificatins f Returns t Scale in Data Envelpment Analysis: A Case Study f the Set f Public Pstal Operatrs The largest MPSS fr DMU ( x, the smallest MPSS fr DMU are i y r ) are x i x x i i x i and y i and y yr r yr, and. Seifrd and Thrall in demnstrated that MPSS max and MPSS min remains the same under bth rientatins. Results and Discussin In this study we bserved the sample f DMUs. The bserved DMUs are public pstal peratrs (PPOs) in the cuntries f Eurpean Unin (Austria, Bulgaria, Cyprus, Czech Republic, Denmark, Estnia, Finland, France, Germany, Great Britain, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxemburg, Malta, Netherlands, Pland, Prtugal, Rmania, Slvakia, Slvenia, Spain, Sweden) and the PPO in Serbia. We emplyed inputs (the number f full-time staff ( x ), the number f part-time staff ( x ) and ttal number f permanent pst ffices ( x )) and ne utput (the number f letter-pst items, dmestic services ( y )) fr evaluating the stability f the RTS classificatins and scale efficient targets f PPOs. There are tw types f reasns fr selecting these particular input and utput. The first and essential reasn is that chsen input parameters (human capital and infrastructure) imply the largest part f the ttal csts fr public pstal peratr functining. On the ther hand, the utput that refers t the letter pst prduces the largest part f revenue. The secnd reasn lies in the fact that we had an intentin t use available data frm the same database which was a cnstraint in the selectin f input and utput. Input and utput data are listed in Table. PPO N. PPO Name Table Data f public pstal peratrs x x x y PPO Austria PPO Bulgaria PPO Cyprus 0 0 PPO Czech Republic PPO Denmark surce: Universal Pstal Unin (0),

9 Acta Plytechnica Hungarica Vl., N., 0 PPO Estnia PPO Finland PPO France PPO Germany PPO 0 Great Britain 0 0 PPO Greece PPO Hungary 0 PPO Ireland 0000 PPO Italy 0 0 PPO Latvia 0 PPO Lithuania 0 PPO Luxemburg PPO Malta 0 PPO Netherlands PPO 0 Pland PPO Prtugal PPO Rmania 0 0 PPO Slvakia 0 0 PPO Slvenia 00 PPO Spain PPO Sweden PPO Serbia Given data were btained frm Universal Pstal Unin fr the year 0. Cnsidering the Eurpean Unin member states, there is nly ne PPO that was nt included in the research. It is PPO in Belgium fr which there were n fficial data n the website f Universal Pstal Unin in the mment f this research. Beside that PPO in Serbia as a candidate cuntry was included in bserved prductin pssibility set cnsisting f PPOs in Eurpean Unin member states. By reviewing the literature n Thmsn Reuters Web f Science, cnsidering years frm t 0, we have nt fund the examples f using a RTS in DEA in pstal sectr. This was an inspiratin fr the authrs t demnstrate the applicability f this analytical prcess in this field. All calculatins in the study are perfrmed by using the sftware DEA Excel Slver develped by Zhu. It is a Micrsft Excel Add-In fr slving data envelpment analysis (DEA) mdels.

10 P. Ralevic et al. Stability f the Classificatins f Returns t Scale in Data Envelpment Analysis: A Case Study f the Set f Public Pstal Operatrs By using the M and the Therem we derived RTS classificatin f bserved PPOs. The M mdel evlved accrding t the selected input and utput and applied t the sample frm Table, e.g. the PPO in Czech Republic is: min Subec t: θ ,,,, The ptimal slutin fr this PPO is: CCR 0. CCR θ

11 Acta Plytechnica Hungarica Vl., N., 0 0., ther 0 the PPO in Czech Republic exhibits IRS. Since, the reference fr this PPO is the PPO in Austria. The BCC scre ( mdel: BCC 0 The BCC scre fr this PPO is: BCC 0.0 ) is btained by adding the fllwing cnditin in the M In the same manner, the M mdel shuld be evlved fr all ther PPOs. The CCR, BCC and returns t scale characteristics f each PPO are listed in Table. PPO N. RTS Regin Table Analytical results derived frm the M mdel BCC CCR Scale Scre ( SS ) Scre Scre Inputriented SS CCR ) ( ) Reference CCR E RTS ( BCC PPO II Cnstant PPO I PPO Increasing 0.0 PPO I PPO 0.00 Increasing 0. PPO VI PPO 0. Increasing 0. PPO I PPO 0. Increasing 0.0 PPO I PPO, PPO 0.00 Increasing 0.0 PPO I PPO 0. Increasing 0. PPO III PPO, PPO, PPO.0 Decreasing 0.0 PPO III PPO. Decreasing 0. PPO 0 III PPO.0 Decreasing 0. PPO I PPO, PPO 0. Increasing 0. PPO VI PPO, PPO 0. Increasing 0. PPO I PPO, PPO 0. Increasing 0. PPO III PPO, PPO. Decreasing 0. PPO I PPO 0.00 Increasing 0. PPO I PPO 0.00 Increasing 0.0 PPO I PPO 0.0 Increasing 0.00 PPO I PPO 0.00 Increasing 0. PPO I PPO 0.0 Increasing 0. BCC

12 P. Ralevic et al. Stability f the Classificatins f Returns t Scale in Data Envelpment Analysis: A Case Study f the Set f Public Pstal Operatrs PPO 0 VI PPO, PPO 0. Increasing 0.0 PPO VI PPO, PPO 0. Increasing 0.0 PPO VI PPO, PPO 0. Increasing 0. PPO I PPO 0.00 Increasing 0. PPO II Cnstant PPO II Cnstant PPO VI PPO, PPO, PPO 0.0 Increasing 0. PPO VI PPO, PPO 0. Increasing 0. Average Based n the results in Clumn f Table the PPOs are lcated in fur RTS regins I, II, III and VI as shwn in Figure. The regins IV and V are empty. Figure PPOs lcating within the RTS regins The results frm Table shw that there are three PPOs which have the CCR scre equal t. This scre indicates verall technical efficiency when evaluated n the cnstant returns t scale assumptin. These are PPOs in Austria, Slvenia and Spain. PPO in Austria is ne f three best perfrmers, and furthermre it is the PPO mst frequently referenced fr evaluating inefficient PPOs. The BCC scre prvide efficiency evaluatins using a lcal measure f scale, i.e. under variable returns t scale. In this empirical example fur PPOs are accrded efficient status in additin t the three CCR efficient PPOs which retain their previus efficient status. These fur PPOs are in Germany, Great Britain, Greece and Malta. Fr example, it can be cncluded that PPO in Greece has the efficient peratins ( ). Additinally, it can be cnsidered that all PPOs having BCC

13 Acta Plytechnica Hungarica Vl., N., 0 the BCC scre abve average (0.) have the efficient peratins. These are PPOs in Austria, Cyprus, France, Germany, Great Britain, Greece, Luxemburg, Malta, Netherlands, Slvenia and Spain. Based n the results f scale scres frm Table the fllwing PPOs perate in the advantageus cnditins: Austria, Czech Republic, Denmark, Finland, Germany, Hungary, Ireland, Italy, Netherlands, Pland, Prtugal, Slvakia, Slvenia, Spain and Sweden. Their scale scres are higher than average value (0.0). Sme f them althugh wrking in the advantageus cnditins have the inefficient peratins. We can ntice the examples f PPOs in Czech Republic, Pland and Prtugal. There are the ppsite cases where PPOs wrk in the disadvantageus cnditins but their peratins are abve average, fr example PPOs in Cyprus and Luxemburg. Further there are PPOs perating in the disadvantageus cnditins and having the inefficient peratins such as PPOs in Bulgaria, Estnia, Latvia, Lithuania, Rmania, Slvakia and Serbia. By using the M and M' mdels and the Therem, and we derived lwer and upper limit f stability intervals f PPOs. Fr example, the PPO in Czech Republic exhibits IRS, therefre it needs t use the Therem and the M' mdel shuld be evlved: max Subec t:

14 P. Ralevic et al. Stability f the Classificatins f Returns t Scale in Data Envelpment Analysis: A Case Study f the Set f Public Pstal Operatrs ,,,, Inputs lwer limit f stability interval f this PPO is Accrding t Therem, inputs upper limit f stability interval f this PPO is equal t. Analgusly, we can define stability regin fr inputs f all ther PPOs. The analytical results are shwn in Table. Table Stability regin fr inputs f PPOs PPO N. Stability interval PPO N. Stability interval PPO ( , ) PPO ( ,.0) PPO ( ,.) PPO ( ,.0) PPO ( ,.) PPO ( ,.00000) PPO (0.00, ) PPO ( ,.) PPO ( ,.) PPO ( ,.) PPO ( ,.) PPO 0 (0., ) PPO ( ,.0) PPO (0.0, ) PPO (0.00, ) PPO (0.00, ) PPO (0., ) PPO ( ,.0) PPO 0 (0.0, ) PPO ( , ) PPO ( ,.0) PPO ( , ) PPO (0.0, ) PPO (0., ) PPO ( ,.) PPO (0., ) PPO (0.00, ) The results frm Table indicate that PPOs in Austria, Slvenia and Spain d nt need input perturbatins. PPOs in Czech Republic, France, Germany, Great Britain, Hungary, Italy, Pland, Prtugal, Rmania, Sweden and Serbia shuld cnsider decreasing inputs. PPOs in Bulgaria, Cyprus, Denmark, Estnia, Finland, Greece, Ireland, Latvia, Lithuania, Luxemburg, Malta, Netherlands and Slvakia shuld cnsider increasing inputs. 0

15 Acta Plytechnica Hungarica Vl., N., 0 By using the M and M' mdels we derived scale efficient inputs and utput targets fr each CCR inefficient PPOs. Thus, the M and M' mdels fr PPO in Czech Republic are: M mdel min Subec t: M' mdel max ,,,, The ptimal slutin fr this PPO is:

16 P. Ralevic et al. Stability f the Classificatins f Returns t Scale in Data Envelpment Analysis: A Case Study f the Set f Public Pstal Operatrs The smallest inputs fr the PPO are: x x x x. 0. x x The largest utput fr the PPO is: y y Analgusly, the M and M' mdels shuld be evlved fr all ther PPOs. The analytical results are shwn in Table. PPO N. Table Analytical results derived frm M and M' mdels PPO Name x x x x x x y y PPO Bulgaria PPO Cyprus PPO Czech R PPO Denmark PPO Estnia PPO Finland PPO France PPO Germany PPO 0 GB PPO Greece PPO Hungary 00 0 PPO Ireland PPO Italy PPO Latvia PPO Lithuania PPO Luxem PPO Malta PPO Nether PPO 0 Pland 0 000

17 Acta Plytechnica Hungarica Vl., N., 0 PPO Prtugal PPO Rmania 0 0 PPO Slvakia PPO Sweden PPO Serbia Cnsidering the results frm Table, PPOs that need t perfrm input perturbatins can be divided in three grups. The first grup cntains f PPOs with the input excess and the utput deficit. Based n the results frm Table these PPOs are in Czech Republic, Hungary, Pland, Prtugal, Rmania, Sweden and Serbia. Fr example, PPO in Serbia has the input excess f the number f fulltime staff, the number f part-time staff and ttal number f permanent pst ffices, x x, x x, x x, respectively. Additinally, this PPO has the utput deficit f the number f letter-pst items, dmestic services, y y 00. In the secnd grup there are PPOs having the input excess. This means they culd achieve the current utput level with less inputs. The examples f this kind f PPOs are in France, Germany, Great Britain and Italy. The rest f PPOs are in the third grup. The main characteristic f these PPOs is the pssibility f increasing utput by increased inputs. These PPOs are in Bulgaria, Cyprus, Denmark, Estnia, Finland, Greece, Ireland, Latvia, Lithuania, Luxemburg, Malta, Netherlands and Slvakia. Obtained values frm Table shuld be cnsidered cnditinally having in mind the public expectatins abut pstal systems, first f all the bligatin t prvide pstal services n the whle territry f a state. Thus, in rder t implement the prpsed mdel further research shuld be perfrmed fr each specific cuntry cnsidering the legal limitatins. Cnclusins Many DEA researchers have studied the sensitivity analysis f efficient and inefficient decisin making unit classificatins. This study develps a RTS in DEA and the methds t estimate it in the pstal sectr. The sensitivity analysis is cnducted fr the CCR inefficient public pstal peratrs in Eurpean Unin member states and Serbia as a candidate cuntry. The develpment f this analytical prcess is perfrmed based n the public data btained frm the same surce frm Universal Pstal Unin. The fcus f this study was n the stability f the RTS classificatins and scale efficient inputs and utputs targets f bserved PPOs. It has been carried ut by using the CCR RTS methd and the MPSS. In rder t determine lwer and upper limit f stability intervals f the CCR inefficient PPOs we used utput-riented RTS classificatin stability when input perturbatins ccur in PPOs.

18 P. Ralevic et al. Stability f the Classificatins f Returns t Scale in Data Envelpment Analysis: A Case Study f the Set f Public Pstal Operatrs In rder t implement the btained results, PPOs shuld have in mind their legal bligatins specific fr the pstal sectr in their cuntries. This culd be ne f the pssible guidelines fr future research. In this paper we used crss-sectin type f data. As a pssible directin fr the future research panel data culd be used invlving the efficiency measurement ver time. This shuld be carried ut in rder t cnfirm the btained results. Acknwledgement This research was supprted by Serbian Ministry f Educatin, Science and Technlgical Develpment with prect TR 0. References [] Charnes, A., Cper, W. W., Rhdes, E.: Measuring the Efficiency f Decisin Making Units, Eurpean Jurnal f Operatinal Research, Vl., N., pp. -,. [] Banker, R. D., Charnes, A., Cper, W. W.: Sme Mdels fr Estimating Technical and Scale Inefficiencies in Data Envelpment Analysis, Management Science, Vl. 0, N., pp. 0-0, [] Dalfard, V. M., Shrabian, A., Naafabadi, A. M., Alvani, J.: Perfrmance Evaluatin and Priritizatin f Leasing Cmpanies Using the Super Efficiency Data Envelpment Analysis Mdel, Acta Plytechnica Hungarica, Vl., N., pp. -, 0 [] Kabk, J., Kis, T., Csuelleg, M., Lendak, I.: Data Envelpment Analysis f Higher Educatin Cmpetitiveness Indices in Eurpe, Acta Plytechnica Hungarica, Vl. 0, N., pp. -0, 0 [] Ertay, T., Ruan, D.: Data Envelpment Analysis-based Decisin Mdel fr Optimal Operatr Allcatin in CMS, Eurpean Jurnal f Operatinal Research, Vl., N., pp. 00-0, 00 [] Gattufi, S., Oral, M., Reisman, A.: A Taxnmy fr Data Envelpment Analysis, Sci-Ecnmic Planning Sciences, Vl., N. -, pp. -, 00 [] Kleine, A.: A General Mdel Framewrk fr DEA, Omega: Internatinal Jurnal f Management Science, Vl., N., pp. -, 00 [] Seifrd, L. M., Zhu, J.: Sensitivity and Stability f the Classificatin f Returns t Scale in Data Envelpment Analysis, Jurnal f Prductivity Analysis, Vl., N., pp. -, [] Cper, W., Seifrd, L., Tne, K., Thrall, R. M, Zhu, J.: Sensitivity and Stability Analysis in DEA: Sme Recent Develpments, Jurnal f Prductivity Analysis, Vl., N., pp. -, 00

19 Acta Plytechnica Hungarica Vl., N., 0 [0] Jahanshahl, G. R., Ltfi, F. H., Sha, N., Thidi, G., Razavian, S.: A One-mdel Apprach t Classificatin and Sensitivity Analysis in DEA, Applied Mathematics and Cmputatin, Vl., N., pp. -, 00 [] Charnes, A., Russeau, J., Semple, J.: Sensitivity and Stability f Efficiency Classificatins in Data Envelpment Analysis, Jurnal f Prductivity Analysis, Vl., N., pp. -, [] Seifrd, L. M, Zhu, J.: Sensitivity Analysis f DEA Mdels fr Simultaneus Change in all the Data, Jurnal f the Operatinal Research Sciety, Vl.. N. 0, pp. 00-0, [] Pdinvski, V. V.: On the Linearizatin f Reference Technlgies fr Testing Returns t Scale in FDH Mdels, Eurpean Jurnal f Operatinal Research, Vl., N., pp. 00-0, 00 [] Sleimani-damaneh, M., Jahanshahl, G. R., Reshadi, M.: On the Estimatin f Returns t Scale in FDH Mdels, Eurpean Jurnal f Operatinal Research, Vl., N., pp. 0-0, 00 [] Lee, G., Yu, M. M., Wang, L. C.: Dea-based Integrated Relatinship f Returns t Scale - An Applicatin t Rad Maintenance in Taiwan, Jurnal f Civil Engineering And Management, Vl., N., pp. 0-, 0 [] Jahanshahl, G. R., Ltfi, F. H., Sha, N., Abri, A. G., Jeldar, M. F., Firuzabadi, K. J.: Sensitivity Analysis f Inefficient Units in Data Envelpment Analysis, Mathematical and Cmputer Mdelling, Vl., N. -, pp. -, 0 [] Charnes, A., Cper, W. W., Glany, B., Seifrd, L. M, Stutz, J.: Fundatin f Data Envelpment Analysis fr Paret-Kpmans Efficient Empirical Prductin Functins, Jurnal f Ecnmetrics, Vl. 0, N. -, pp. -0, [] Abri, A. G.: An Investigatin n the Sensitivity and Stability Radius f Returns t Scale and Efficiency in Data Envelpment Analysis, Applied Mathematical Mdelling, Vl., N., pp. -, 0 [] Seifrd, L. M., Zhu, J.: An Investigatin f Returns t Scale Under Data Envelpment Analysis, Omega: Internatinal Jurnal f Management Science, Vl., N., pp. -, [0] Banker, R. D.: Estimating Mst Prductive Scale Size Using Data Envelpment Analysis, Eurpean Jurnal f Operatinal Research, Vl., N., pp. -, [] Fare, R., Grsskpf, S., Lvell, C. A. K.: Prductin Frntiers, Cambridge University Press, Cambridge, [] Banker, R. D., Thrall, R. M.: Estimatin f Returns t Scale Using Data Envelpment Analysis, Eurpean Jurnal f Operatinal Research, Vl., N., pp. -,

20 P. Ralevic et al. Stability f the Classificatins f Returns t Scale in Data Envelpment Analysis: A Case Study f the Set f Public Pstal Operatrs [] Seifrd, L. M., Thrall, R. M.: Recent Develpments in DEA: The Mathematical Prgramming Apprach t Frntier Analysis, Jurnal f Ecnmetrics, Vl., N. -, pp. -, 0 [] Zhu, J.: Quantitative Mdels fr Perfrmance Evaluatin and Benchmarking: Data Envelpment Analysis with Spreadsheets and DEA Excel Slver, Kluwer Academic Publishers, Bstn, 00