A proxy approach to dealing with the infeasibility problem in super-efficiency data envelopment analysis

Transcription

1 MPRA Muich Persoal RePEc Archive A proxy approach to dealig with the ifeasibility problem i super-efficiecy data evelopmet aalysis Gag Cheg ad Paagiotis Zervopoulos Jue 2012 Olie at MPRA Paper No , posted 19. October :59 UTC

2 A proxy approach to dealig with the ifeasibility problem i super-efficiecy data evelopmet aalysis Gag Cheg Chia Ceter for Health Developmet Studies, Peig Uiversity, 38 Xueyua Rd, Beiig, Chia cheggag@bmu.edu.c Paagiotis D. Zervopoulos Chia Ceter for Health Developmet Studies, Peig Uiversity, 38 Xueyua Rd, Beiig, Chia Departmet of Busiess Admiistratio of Food ad Agricultural Eterprises Uiversity of Ioaia, 2 Georgiou Seferi St, Agriio, Greece pzervopoulos@uoi.gr Abstract Super-efficiecy data evelopmet aalysis (SE-DEA) models are expressios of the traditioal DEA models featurig the exclusio of the uit uder evaluatio from the referece set. The SE-DEA models have bee applied i various cases such as sesitivity ad stability aalysis, measuremet of productivity chages, outliers idetificatio, ad classificatio ad raig of decisio maig uits (DMUs). A maor deficiecy i the SE-DEA models is their ifeasibility i determiig super-efficiecy scores for some efficiet DMUs whe variable, o-icreasig ad o-decreasig returs to scale (VRS, NIRS, NDRS) prevail. The scope of this study is the developmet of a orieted proxy approach for SE-DEA models i order to tacle the ifeasibility problem. The proxy itroduced to the SE-DEA models replaces the origial ifeasible DMU i the sample ad guaratees a feasible optimal solutio. The proxy approach yields the same scores as the traditioal SE-DEA 1

3 models to the feasible DMUs. Keywords: Data evelopmet aalysis (DEA); Super-efficiecy (SE); Ifeasibility; Orietatio 2

4 1. Itroductio Data Evelopmet Aalysis (DEA) is a comparative efficiecy measuremet methodology put forth by Chares et al. (1978) that serves as a quatitative bechmarig techique. DEA draws o liear programmig for distiguishig the relatively efficiet from the iefficiet operatioal uits of a particular sample. Nevertheless, the distictio betwee efficiet ad iefficiet uits is ot the oly preset as there are further dissimilarities i the productio process of the efficiet uits. These dissimilarities are ot detected by traditioal DEA models. Super-efficiecy DEA (SE-DEA) models, iitially developed by Baer et al. (1989), ad Aderse ad Peterse (1993), are appropriate for idetifyig premium efficiecy amog efficiet uits ad raig efficiet DMUs. I the SE-DEA, the uit uder evaluatio is excluded from the referece set, so that its efficiecy may be greater tha 100%. A maor drawbac of the SE-DEA models is their ifeasibility i defiig super-efficiecy scores for some efficiet DMUs uder VRS techology. Several scholars (Dula & Hicma, 1997; Seiford & Zhu, 1999; Xue & Harer, 2002) discussed the coditios for ifeasibility i SE-DEA models uder VRS. Dula ad Hicma (1997) ad Seiford ad Zhu (1999) proved the ecessary ad sufficiet coditios for ifeasibility i the VRS SE-DEA model. Taig ito accout these coditios, a umber of methods have bee developed to solve the ifeasibility problem(che et al., 2011; Che, 2005; Coo et al., 2009; Lee et al., 2011; Lovell & Rouse, 2003; Ray, 2008). I this paper, we propose a ew proxy approach which successfully overcomes the ifeasibility problem. The ovelty of the ew approach is that it completely holds the origial orietatio of the SE-DEA model (iput-orietatio or output-orietatio) by idetifyig a virtual proxy uit i the frotier. The proxy uit is located at the earest poit to the origial ifeasible efficiet uit ad it has a feasible super-efficiecy score. The paper is orgaized as follows. Sectio 2 describes the ifeasibility problem i iput- ad output-orieted models. Sectio 3 presets existig VRS super-efficiecy models ad discusses both the procedure applied for overcomig the ifeasibility problem ad the appropriateess of the results of these models, i order to provide a basis for compariso betwee the existig models ad the ew approach preseted i this paper. Sectio 4 aalyses the proposed approach. Sectio 5 3

5 compares alterative approaches for taclig the ifeasibility problem through a umerical example. The umerical example is based o a real-world dataset foud i Bal et al. (2010). Coclusios are preseted i the fial sectio of the paper. 2. Ifeasibility problem for SE-VRS model 2.1 Ifeasibility for iput-orieted SE-VRS model The iput-orieted VRS model for the evaluated DMU ca be formulated as (Baer et al., 1984): m i s.t. x x, i 1, 2,..., m 1 i i 1 y y, r 1, 2,..., s r r 1 1 0, 1, 2,..., (1) For a efficiet DMU, the SE-VRS model becomes (Aderse & Peterse, 1993): m i s.t. x x, i 1, 2,..., m 1 i i 1 y y, r 1, 2,..., s r r 1 1 0, 1, 2,..., ( ) (2) 4

6 The ecessary ad sufficiet coditio for ifeasibility i the iput-orieted VRS SE-DEA is that the evaluated DMU has at least oe output greater tha the covex combiatio formed by all the other DMUs. I such a coditio, the efficiet DMU caot reach the frotier formed by the remaiig DMUs because the costrait for outputs i (2) is ifeasible, i.e. y y is r r 1 ifeasible. A sufficiet coditio for ifeasibility i the iput-orieted VRS SE-DEA is that the evaluated DMU has at least oe output greater tha the correspodig output for all the other DMUs. 2.2 Ifeasibility for output-orieted SE-VRS model The output-orieted VRS model ca be formulated as: max s. t. x x, i 1, 2,..., m 1 i i 1 y y, r 1, 2,..., s r r 1 1 0, 1, 2,..., (3) For a efficiet DMU, the SE-VRS model is: max s. t. x x, i 1, 2,..., m 1 i i 1 y y, r 1, 2,..., s r r 5

7 1 1 0, 1, 2,..., ( ) (4) The ecessary ad sufficiet coditio for ifeasibility i the output-orieted VRS SE-DEA is that the evaluated DMU has at least oe iput less tha the covex combiatio formed by all the other DMUs. I such a coditio, the efficiet DMU caot reach the frotier formed by the rest of the DMUs because the costrait for iputs i (4) is ifeasible, i.e. 1 x x i i is ifeasible. A sufficiet coditio for ifeasibility i the output-orieted VRS SE-DEA is that the evaluated DMU has at least oe iput less tha the correspodig iput for all the other DMUs. 3. Modified SE-DEA models dealig with ifeasibility Lovell ad Rouse (2003) proposed a orieted method for taclig the ifeasibility problem of traditioal SE-DEA models. This method draws o a scalig procedure applied either to the iputs (iput orietatio) or the outputs (output orietatio) of the efficiet uits for which the calculatio of a super-efficiecy score, based o traditioal SE-DEA models, is ifeasible. For the scalig procedure, a arbitrarily selected factor that is sufficietly large (iput orietatio), or a sufficietly small factor (output orietatio) is utilized. The scalig procedure removes the uit from the referece set to avoid ay ifeasibility problem. The super-efficiecy score of the modified uit is calculated after rescalig the assiged score. The method itroduced by Lovell ad Rouse (2003) copes with the ifeasibility problem. However, cocers are raised about the desirability of the results of this method ad the role of exogeous itervetio to the procedure (Che et al., 2011; Coo et al., 2009; Ray, 2008). To be more precise, the super-efficiecy scores of the efficiet DMUs with ifeasible solutios are idetical to the scalig factor. Therefore, these particular results should ot be iterpreted while the target levels for iputs ad outputs are fictitious. The results obtaied solely reflect a arbitrary choice of the scalig factor. I additio, Lovell ad Rouse s method fails to classify the efficiet uits i that the 6

8 ifeasible DMUs are assiged equal super-efficiecy scores. Che (2005) s model relies o the substitutio of the iefficiet uits with their efficiet proectios, uder the assumptio of variable returs to scale (VRS). Che argues that ifeasibility is elimiated either i the iput- or the output-orieted expressio of super-efficiecy models, though, ot i both simultaeously. As a result, both orietatios should be applied to tacle the ifeasibility problem ad calculate the overall super-efficiecy score of a uit. The overall super-efficiecy score derives from the combiatio of the two SE-DEA orietatios with suitable weights. Che s method provides partial solutio to the ifeasibility problem of SE-DEA models because i some cases it fails to defie a feasible solutio i both orietatios (Che et al., 2011; Ray, 2008). Coo et al. (2009) itroduced a approach which proposes oe-directioal iput-output movemets (i.e. decreases whe iput-orietatio is applied, ad icreases i case of output-orietatio) so that the uit uder evaluatio that experieces ifeasibility i super-efficiecy models reaches the frotier formed by the rest of DMUs. Lee et al. (2011) exteded Coo et al. s method by itroducig a two-stage method to achieve Coo et al. s solutio. I additio to the above orieted solutios for ifeasibility, Ray (2008) put forth a o-orieted super-efficiecy model drawig o the directioal distace fuctio itroduced by Chambers et al. (1996). Ray s approach allows sychroous proportioal output reductios ad iput expasios by a urestricted factor which is determied by the optimizatio procedure. Despite this particular method resolvig the ifeasibility problem, it is ot a orieted aalysis. Che et al. (2011) proposed a combiatorial iput- ad output-orieted method that provides targets for the evaluated DMU with radial movemets of both iputs ad outputs. The aggregated super-efficiecy score is defied as a ratio of optimal iput- ad output-orieted super-efficiecy compoets. Hece, it is the result of a optimizatio procedure without requirig arbitrary selectios o a factor. Che et al., as Ray, itroduce a o-orieted aalysis for taclig the ifeasibility problem at VRS SE-DEA models. 7

9 4 A proxy approach to dealig with ifeasibility of SE-VRS model 4.1 A proxy approach to iput-orieted SE-VRS model As discussed i the previous sectio, the essetial reaso for the ifeasibility i the iput-orieted SE-VRS model is that the efficiet DMU does ot belog to the output set S y formed by the remaiig DMUs. y r (5) y S { y : y y, 1} 1 1 The cocept of the proxy approach is to fid a virtual proxy uit for the efficiet DMU. The proxy of the DMU (x,y ) is idicated by DMU (x,y ).The DMU is the earest poit to DMU at the frotier, ad its outputs y belog to the output set S y. The process applied for determiig the proxy of the efficiet DMU has two steps. I the first step, a itermediate DMU (x,y ) is defied. The itermediatio process is expressed by a vertical movemet from poit K to K i Fig. 1, or, a scalig dow of the output levels of DMU holdig the iputs fixed. I this cotext, the first step of the proxy approach ca be writte as follows mi s. t. (1 ) y y r 1 r 1 1, 0 (6) The iputs ad outputs of the itermediate DMU are defied by x i '' x, y (1 ) y ''. i r r Havig already idetified the itermediate DMU, we solve the followig liear programmig i order to determie the iputs ad outputs of the proxy DMU i a secod step 8

10 m ax s. t. x (1 ) x i 1, 2,..., m 1, i i '' 1 y y, r 1, 2,..., s r r '' 1 1 0, 1, 2,..., (9) The iputs ad outputs of the proxy DMU are defied as follows x i ' (1 ) x, y y r ' r '' i ''. The above discussio is expressed graphically by the horizotal movemet from poit K to K i Fig. 1. If the efficiet DMU is feasible i the traditioal SE-DEA model, its proxy DMU will be the same poit as DMU, i.e., there are either vertical or horizotal movemets i the above two steps. At last, by replacig the origial DMU with its proxy uit DMU i the sample ad by solvig the followig super-efficiecy model we defie a feasible super-efficiecy score for every efficiet DMU m i s. t. x x i 1, 2,..., m 1 ', i i ' 1 ' y y r 1, 2,..., s, r r ' (10) 1 ' 1 0, 1, 2,..., ( ') 9

11 3.5 3 K 2.5 y 2 B K' K'' C A Figure 1. Proxy approach to ifeasibility i iput-orieted SE-DEA uder VRS x 4.2 A proxy approach to output-orieted SE-VRS model I the output-orieted VRS SE-DEA model, ifeasibility is preset i case a efficiet DMU does ot belog to the iput set S x determied by the rest of DMUs. x r (11) x S { x : x x, 1} 1 1 Similarly, a proxy of DMU is defied, as idicated by DMU, whose iputs belog to the iput set S x. I the first step, a itermediate DMU (x,y ) is idetified after scalig up the iputs of DMU holdig the outputs fixed. As illustrated i Fig. 2, the itermediate DMU is determied after a rightward shift from K to K so that the iputs of the itermediate DMU to be idetical to the lowest iput level of the referece set. To achieve this, we solve the followig liear programmig model mi s. t. (1 ) x x i i 1 10

12 1 1, 0 (12) The iputs ad outputs of the itermediate DMU are defied by x i (1 ) x, y y. '' i r '' r I the secod step, the proxy uit DMU is idetified by proectig the itermediate DMU to the origial frotier with the followig programmig max s. t. x x i 1, 2,..., m 1, i i '' 1 y (1 ) y r 1, 2,..., s r r '', 1 1 0, 1, 2,..., (13) The above procedure is depicted by the upward movemet from K to K i Fig. 2. The iputs ad outputs of the proxy DMU are defied by x x, y (1 ) y i ' i '' r ' r ''. Lie the iput-orieted proxy approach, DMU replaces DMU i the sample ad is evaluated agaist the super-efficiecy referece set m ax s. t. x x, i 1, 2,..., m 1 ' i i ' 11

13 1 ' y y, r 1, 2,..., s r r ' 1 ' 1 0, 1, 2,..., ( ') (14) A 2.5 y 2 K' B K K'' C Figure 2. Proxy approach to ifeasibility i output-orieted SE-DEA uder VRS x 5. Illustrative example I Sectio 4, we apply our approach to a dataset used i Bal et al. (2010) (see Appedix 1). This dataset cosists of 30 OECD coutries that utilize three iputs (Iput 1: uemploymet ratio (2006), Iput 2: rate of iflatio (2005), ad Iput 3: ifat mortality (2005)) i order to geerate five outputs (Output 1: atioal icome per capita (US dollars, 2006), Output 2: huma developmet idex: life expectacy from birth (2006), Output 3: huma developmet idex: educatio idex (2006), Output 4: cotributio rate to labor force of female populatio (2006), ad Output 5: health expediture per capita (US dollars, 2005)). 12

14 Table 1. Super-efficiecy measures DMU Traditioal SE-DEΑ Lovell & Rouse Ray Che et al. Proxy Approach Iput-orieted Output-orieted Iput-orieted Output-orieted No-orieted No-orieted Iput-orieted Output-orieted θ φ θ φ ψ θ φ ρ θ φ 1 Ifeasible Ifeasible Ifeasible Ifeasible Ifeasible Ifeasible Ifeasible Ifeasible Ifeasible Ifeasible Ifeasible Ifeasible

15 Ifeasible Ifeasible Ifeasible I Table 1, the secod ad third colums report super-efficiecy scores measured by the traditioal iput- ad output-orieted SE-DEA models (2) ad (4), respectively. Colums four ad five represet iput- ad output-orieted SE-DEA scores obtaied by Lovell ad Rouse (2003) s measure. The ext colum presets super-efficiecy scores accordig to Ray (2008) s approach. Colums seve to ie report the movemets of iputs ad outputs ad the super-efficiecy scores, as defied by Che et al. (2011) s measure. The fial two colums illustrate the iput- ad output-orieted super-efficiecy scores yielded by the proxy approach. The ew approach successfully overcomes the ifeasibility problem of the traditioal SE-DEA method i both orietatios ad its results are fully cosistet with those of the traditioal method for feasible DMUs. The super-efficiecy scores assiged to the ifeasible DMUs by the proxy SE-DEA model are displayed i bold umbers i the last two colums of Table 1. The ew proxy approach provides differetiated scores for every DMU eablig their raig. To be more precise, whe iput orietatio is selected, the most efficiet DMU amog the thirty couties of the sample is Japa (DMU 16) which obtais , followed by Switzerlad (DMU 28) with , ad Norway (DMU 21) with Whe output orietatio is applied, the most efficiet coutry is Switzerlad (DMU 28), receivig a score of , followed by the Uited States (DMU 30) ad Icelad (DMU 13), obtaiig scores of ad , respectively. The Uited States (DMU 30), which is a feasible DMU i the output-orieted traditioal SE-DEA method, is raed No. 2, above the ifeasible DMU 13 (i.e., Icelad). I additio, there are 5 feasible DMUs which are raed higher tha the ifeasible DMU 7 (i.e., Eglad). Such cases ca also be foud i the results of the iput-orieted proxy model. This reveals that ifeasibility uder the traditioal SE-DEA models does ot always mea extreme super-efficiecy. A similar coclusio is deduced by Ray s ad Che et al. s measures. 14

16 The iput- ad output-orieted proxy approach yields completely cosistet super-efficiecy scores with the respective traditioal SE-DEA models for every feasible uit. As a result, the ew approach provides raigs idetical to that obtaied by the traditioal measures for the feasible DMUs. Lovell ad Rouse (2003) method elimiates ifeasibility but fails to provide a orderig procedure for the DMUs deemed ifeasible by the traditioal SE-DEA models. For istace, uder iput-orieted Lovell ad Rouse s measure, uits that are deemed ifeasible, accordig to covetioal SE-DEA measures, obtai a uique score of ; ad uder the respective output-orieted measure, the three ifeasible uits are assiged a score of Both scores reflect the scalig factor that is arbitrarily decided rather tha the results of the super-efficiecy assessmet process. Therefore, the obtaied scores for the traditioally ifeasible efficiet DMUs are uliely to be iterpreted. Additioally, this method yields cosistet results for the DMUs that are regarded as feasible by the traditioal SE-DEA method. This is ust because those feasible DMUs are actually ot ivolved i the scalig procedure. Essetially, Lovell ad Rouse s method is applied exclusively to the ifeasible DMUs. Ray (2008) measure has a twofold iterpretatio referrig both to iputs ad outputs. For istace, Eglad obtais a super-efficiecy score of , which deotes that the iputs of this coutry ca be icreased by 15.5% ad its outputs reduced by 15.5% without affectig its efficiecy status. Acowledgig that this method is o-orieted, it is ot desirable to compare its results with the traditioal SE-DEA ad the Lovell & Rouse s measures, which are orieted. Similar to Ray s measure, Che et al. (2011) developed a o-orieted method which defies the super-efficiecy score (ρ) as a ratio of the iput chage (θ) to the output chage (φ). Drawig o the results obtaied by Che et al. s method, Switzerlad (DMU 28) is raed secod, receivig a overall super-efficiecy score (ρ) of By decomposig the super-efficiecy score, we fid that Switzerlad will remai efficiet by scalig up its iputs by 54.85% ad simultaeously scalig dow its outputs by 2.35%. The results yielded by Che et al. s method are ot comparable with those of the traditioal SE-DEA models due to the icompatible orietatio cocepts that uderlie the two approaches. 15

17 The super-efficiecy scores displayed i Table 1 are evidece of the icompatibility of Ray s ad Che et al. s measures with the traditioal SE-DEA models. Table 2. Step-by-step results of the proxy approach DMU Iput Orieted Output Orieted Step 1 Step 2 Proxy Approach Step 1 Step 2 Proxy Approach Beta Alpha θ Alpha Beta φ N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

18 24 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A Detailed results of the proxy approach are preseted i Table 2. I particular, colums two ad three demostrate the movemets of outputs (betas) ad iputs (alphas) of both the ifeasible ad the feasible efficiet DMUs to their proxies whe the iput-orieted proxy SE-DEA model is applied. The colums five ad six display the movemets of iputs (alphas) ad outputs (betas) to their proxies whe the output-orieted proxy model is utilized. Note that there are o movemets for the feasible efficiet DMUs, which meas that the proxies of the feasible efficiet DMUs are themselves. The ifeasible DMUs, as defied by the traditioal SE-DEA models, are displayed i bold umbers i Table 2. Taig a example i the iput-orieted proxy approach, Japa (DMU 16) is origially deemed ifeasible by the traditioal iput-orieted SE-DEA model. If it decreases its outputs by 0.97% ad scales dow its iputs by 8%, its proxy ca obtai a feasible super-efficiecy score of For feasible efficiet DMUs, i.e., Eglad (DMU 7) ad Swede (DMU 27), there is o eed for iput ad output adustmets. I such a case, the proxy uit is the same as the origial oe, ad the proxy approach will yield cosistet super-efficiecy scores as the traditioal iput-orieted SE-DEA model. Turig to a example i the output-orieted proxy approach, Switzerlad (DMU 28) should scale up its iputs by 28.89% without adustig its output levels to fid its proxy, ad the proxy ca get a feasible super-efficiecy score of

19 6. Coclusios The curret paper deals with the ifeasibility problem that is preset i traditioal VRS SE-DEA models. Our approach holds the origial orietatio of the SE-DEA model ad idetifies a optimal virtual proxy uit that replaces the origial ifeasible DMU i the evaluatio process. The proxy uit is defied by applyig a two-stage procedure which secures that the proxy uit is a optimal derivative of the origial uit. By applyig the proposed method, 1) The proxy approach ca yield a super-efficiecy score i cases where the traditioal super-efficiecy model is ifeasible; ad 2) The proxy approach yields the same results as the traditioal super-efficiecy model whe it is applied to cases where the traditioal super-efficiecy model is feasible. The properties of the proposed approach are preseted i a umerical example. Utilizig a dataset foud i Bal et al. (2010), we demostrate the advatages of the proxy approach over some existig methods developed for taclig the ifeasibility problem. Refereces Aderse, P., & Peterse, N. C. (1993). A procedure for raig efficiet uits i data evelopmet aalysis. Maagemet Sciece, 39, Bal, H., Örcü, H. H., & Çelebioglu, S. (2010). Improvig the discrimiatio power ad weights dispersio i the data evelopmet aalysis. Computers & Operatios Research, 37, Baer, R. D., Chares, A., & Cooper, W. W. (1984). Some models for estimatig techical ad scale iefficiecies i data evelopmet aalysis. Maagemet Sciece, 30, Baer, R. D., Das, S., & Datar, S. (1989). Aalysis of cost variaces for maagemet cotrol i Hospitals. Research i Govermetal ad Noprofit Accoutig, 5, Chambers, R. G., Chug, Y., & Färe, R. (1996). Beefit ad Distace Fuctios. Joural of Ecoomic Theory, 70, Chares, A., Cooper, W. W., & Rhodes, E. (1978). Measurig the efficiecy of decisio maig uits. Europea Joural of Operatioal Research, 2, Che, J.-X., Deg, M., & Gigras, S. (2011). A modified super-efficiecy measure based o simultaeous iput output proectio i data evelopmet aalysis. Computers & Operatios Research, 38, 18

20 Che, Y. (2005). Measurig super-efficiecy i DEA i the presece of ifeasibility. Europea Joural of Operatioal Research, 161, Coo, W. D., Liag, L., Zha, Y., & Zhu, J. (2009). A modified super-efficiecy DEA model for ifeasibility. Joural of the Operatioal Research Society, 60, Dula, J. H., & Hicma, B. L. (1997). Effects of excludig the colum beig scored from the DEA evelopmet LP techology matrix. Joural of the Operatioal Research Society, 48, Lee, H.-S., Chu, C.-W., & Zhu, J. (2011). Super-efficiecy DEA i the presece of ifeasibility. Europea Joural of Operatioal Research, 212, Lovell, C. A. K., & Rouse, A. P. B. (2003). Equivalet stadard DEA models to provide superefficiecy scores. Joural of the Operatioal Research Society, 54, Ray, S. C. (2008). The directioal distace fuctio ad measuremet of super-efficiecy: a applicatio to airlies data. Joural of the Operatioal Research Society, 59, Seiford, L. M., & Zhu, J. (1999). Ifeasibility of super-efficiecy data evelopmet aalysis models. Ifor, 37, Xue, M., & Harer, P. T. (2002). Note: Raig DMUs with ifeasible super-efficiecy DEA models. Maagemet Sciece, 48, Appedix 1 Table A1. Iput ad output data of 30 OECD coutries DMU No Coutries Iput1 Iput2 Iput3 Output1 Output2 Output3 Output4 Output5 DMU01 Australia DMU02 Austria DMU03 Belgium DMU04 Caada DMU05 Czech Republic DMU06 Demar DMU07 Eglad DMU08 Filad

21 DMU09 Frace DMU10 Germay DMU11 Greece DMU12 Hugary DMU13 Icelad DMU14 Irelad DMU15 Italy DMU16 Japa DMU17 Luxembourg DMU18 Mexico DMU19 New Zealad DMU20 Netherlads DMU21 Norway DMU22 Polad DMU23 Portugal DMU24 South Korea DMU25 Slova Republic DMU26 Spai DMU27 Swede DMU28 Switzerlad DMU29 Turey DMU30 USA