RANKING INDIAN DOMESTIC BANKS WITH INTERVAL DATA THE DEA APPLICATION

Transcription

1 INDIAN JORNA OF MANAGEMENT SCIENCE (IJMS) EISSN X ISSN RANKING INDIAN DOMESTIC BANKS WITH INTERVA DATA THE DEA APPICATION D. T. Subaanya, Guet Faculty, Dept. of Stattc, Pondchey nvety, Pondchey, Inda. D. R.V.Vadhan, Atant Pofeo, Dept. of Stattc, Pondchey nvety, Pondchey, Inda. ABSTRACT Data Envelopent Analy (DEA) a non-paaetc appoach ued to eaue the elatve effcency of oganzatonal unt whee ultple nput and output ae copaon dffcult. The peent tudy a at evaluatng the elatve effcency of decon ang unt (DM) wth nteval data. In th cae the elatve effcency wll le wthn an nteval. In th pape we contucted the elatve effcency bound. The DM wee clafed nto dffeent categoe. A anng ethod wa popoed to an the DM n each categoy to dentfy the bet pefong ban n each categoy. Th new ethodologcal technque wee appled fo the data elatng to the Indan Doetc Ban. Keywod: Ban, Data Envelopent Analy, Inteval Data, Ranng, Effcency. Vol. III, Iue 3, July 2013

2 INDIAN JORNA OF MANAGEMENT SCIENCE (IJMS) EISSN X ISSN Intoducton: Data Envelopent Analy the optzaton ethod of atheatcal pogang, baed on lnea pogang technque fo eaung the pefoance of oganzatonal unt whee the peence of ultple nput and output ae copaon dffcult. DEA wa ft ntoduced by Chane et.al, n the yea 1978 to eaue the elatve effcency of DM. Theoetcal developent of DEA ha been qute eaable, becaue of t ue n dffeent publc and pvate ecto ue. In DEA, CCR (1978) and BCC (1984) ae the bac odel to eaue the effcency of DM n contant (CRS) and vaable etun to cale (VRS) envonent epectvely. DEA alone clafe the DM nto two dchotoou goup: effcent and neffcent. Effcent goup eceve the coe 1 and neffcent goup coe le between 0 and 1. Thee bac odel have oe weane n anng the DM. Snce all the effcent DM havng the equal coe 1, one cannot decde whch DM havng the bette an n the epectve envonent. In ode to dffeentate the effcent unt Andeon & Peteon (A&P) developed upe effcency anng ethod. In pte of t populaty thee wee eveal ctc about the A&P anng ethod. Coope & Tone developed anothe anng ethod baed on the lac vaable of the dual poble. All thee ethod wee utlzed to evaluate the effcency and an the DM ung accuate data. If the data an naccuate, thee odel dallowed to calculate the effcency and to an the DM. Inaccuate data ay be pobabltc, nteval, odnal o fuzzy. In th cae the effcency of a patcula DM wll le wthn an nteval. In ecent yea, n dffeent applcaton of DEA, nput and output have been obeved whoe value ae ndefnte. Such ndefnte data ae called naccuate data. A Few nube of eeache devoted the fndng to develop the theoetcal ethodology wth nteval data to dentfy the bound of the elatve effcency of the DM (Depot et.al, 2002; Jahanhahloo et.al, 2004). The peent pape focued on evaluatng the effcency and anng the DM ung nteval data. To an the DM the bac ethod appled A&P upe effcency anng ethod. The peent pape dvded nto x ecton. Afte ntoducton, ecton-i nclude a bef evew of lteatue about the bac CCR-DEA odel. The DEA odel wth nteval data ae dcued n ecton-ii. Secton-III devoted to dcu the DEA anng ethod ung nteval data. In ecton IV we dcued about the Indan Doetc ban and nput, output electon. An epcal applcaton wth Indan Doetc ban dcued n ecton-v. Secton-VI peent the concludng ea of the peent tudy. Bac Data Envelopent Analy Model: Chane, Coope and Rhode (1978) ntoduced a lnea pogang technque to eaue the effcency of Decon Mang nt (DM) n a copettve envonent whee la nput ae eployed to poduce la output. Suppoe, we have n decon ang unt (DM) wth nput and output. et DM, 1,2,..., n to be evaluated unde nvetgaton wth the nput and output vecto X x1, x2,... x Y y y,... y whee X 0 and Y 0. 1, 2 and The bac CCR odel to evaluate the nput techncal effcency of DM Max u y : u y vx 0; vx 1;u, v ε; 1,2,...n; 1,2,...,; 1,2,...,n (1) v and u ae the nput and output weght coputed by olvng the equaton (1). The DM ad to be an effcent wth the optu weght u *,v * f and only f * 1, othewe DM ad to be an neffcent. Inteval Data Envelopent Analy Model: Fo any, t poble to contuct a cla nteval by dentfyng the lowe and uppe bound of the gven nput and output vaable. The lowe and uppe bound of the th nput of the DM be x and x. et y and y be the Vol. III, Iue 3, July 2013

3 INDIAN JORNA OF MANAGEMENT SCIENCE (IJMS) EISSN X ISSN lowe and uppe bound of the th output of the condton ae to be atfed. The CCR Model fo evaluatng the effcency of DM epectvely. Fo evey lowe and uppe bound the followng x x and y y..e., x x, x and y, y y DM wth the gven nteval data a follow: y, y : u y, y v x, x 0, v x, x u 1,u, v ε ; Max ,2,...n; 1,2,...,; 1,2,..., n (2) The above poble doen t allow the eeache to evaluate the effcency. Wheneve a eeache deal wth an nteval data the effcency telf le wthn an nteval. Fo each and evey DM t poble to dentfy two elatvely effcent bound..e., lowe and uppe bound. The followng ae the two PP odel to evaluate the two bound. ppe Bound of the Relatve Effcency: The uppe bound of the elatve effcency of DM evaluated by olvng the followng lnea pogang poble: u y : u y v x 0, u y v x 0; v x 1;u, v ε Max ,2,...n, ; 1,2,...,; 1,2,...,n (3) In th poble, the patcula DM evaluated n t bet condton and the othe DM ae evaluated n the wot condton, uch that. owe Bound of the Relatve Effcency: To obtan the lowe bound of the elatve effcency of DM, we olve the followng lnea pogang poble: u y : u y v x 0, u y v x 0, v x 1;u, v ε Max ,2,...n, ;, 1,2,...,; 1,2,...,n (4) In the above poble the DM evaluated n t wot condton and the othe DM n the bet condton. The obtaned effcency wll alway atfy the condton Theefoe, we obeve that,. Clafcaton of DM:. We clafy the DM nto thee categoe. In categoy-i, all the DM ae effcent both n the bet and wot condton 1, whch denoted by E++. In categoy-ii, the DM ae effcent n the bet condton and neffcent n the wot condton 1, 1 whch epeented a E+ and categoy-iii contan all neffcent DM whch ae neffcent n the bet and wot condton 1, 1 and denoted by E-. Vol. III, Iue 3, July 2013

4 INDIAN JORNA OF MANAGEMENT SCIENCE (IJMS) EISSN X ISSN Ranng DMS: Ranng of DM wth nteval data ee to be vey dffcult. In othe wod, f two o oe DM fall unde ae categoy, how one can decde whch ban functonng n bette envonent wth the bette an than the othe? To ovecoe th dffculty we ugget a two tage DEA ethod eovng the boundedne condton fo the geneal PP ethod (3) and (4). The followng ae the two tage to evaluate the poble effcency coe. Stage-I: DM unde evaluaton n t wot condton and the othe DM n the bet condton. u y : u y v x 0, v x 1; u, v ε; 1,2,...n, 1 Max ,2,..., ; 1,2,..., n Stage-II: DM unde evaluaton n t bet condton and the othe DM n the wot condton. u y : u y v x 0, v x 1;u, v ε; 2 Max ,2,...n, ; 1,2,...,; 1,2,...,n In the above two poble, we elaxed the boundedne condton of the obectve functon fo the contant to get the poble axu coe of the obectve functon. The aveage coe calculated by ung the elaton 1 2 R, 1,2,,n 2 Fo the above ctea we uggeted that, f any DM havng the geate effcency wll be awaded wth a bette an and o on. Indan Doetc Ban: In Inda coecal ban wee opeatng unde thee dffeent ownehp, naely, govenent, pvate and foegn. In publc ecto we have 27 coecal ban, n pvate 23 coecal ban and 28 coecal ban wee functonng unde foegn ownehp. Accodng to the epot of ICRA lted, a atng agency, the publc ecto ban hold ove 75 pecent of total aet of banng nduty. It ndcate the potance of the Indan doetc ban. To now whch doetc ban functonng unde effcent envonent, we ut evaluate the effcency. To gauge the effcency of a coecal ban, ft we odel a coecal ban appopately to eet the need and obectve of the analyt. To odel a coecal ban we have two bac appoache..e., nteedate and poducton appoach. In nteedate appoach ban vewed a nteedate fund between depoto and boowe. In poducton appoach a coecal ban eouce poduce evce to the cutoe. In the peent tudy we puued poducton appoach to odel a coecal ban. The nput that t eploy ae Nube of Eployee, Fxed Aet, output that poduce ae Depot, Advance, and Invetent. Input 1. No. of Eployee 2. Fxed Aet Output 1. Depot 2. Advance 3. Invetent Epcal Applcaton: The peent tudy devoted to nvetgate the effcency of Indan Doetc Ban. In Inda 27 publc ecto ban wee opeatng unde the govenent ownehp. The data collected fo the RBI Bulletn fo the acadec yea 2008 and The pefoance of each ban evaluated wth the nteval data. The bac odel to evaluate the lowe and uppe bound CCR-CRS odel. The eult ae hown n the Table (1). We evaluated the elatve effcency bound by aung 2008 and 2009 data a lowe and uppe bound epectvely. Vol. III, Iue 3, July 2013

5 INDIAN JORNA OF MANAGEMENT SCIENCE (IJMS) EISSN X ISSN The DM wee clafed nto thee categoe on the ba of the effcency coe of the lowe and uppe bound. Fo the table (1), we obeve that the only one ban,.e., IDBI, td., fully effcent whch fall unde the categoy E++. nde categoy E+ we have 52 pecent (14 out of 27) ban and 44 pecent ban (12 out of 27) fall unde the categoy E -. Categoy E++ E+ E- Total Ban No. of Ban The two tage DEA odel eployed to gauge the poble effcency coe of the DM n each categoy. We calculated the aveage effcency coe fo each DM and bang on th aveage coe coepondng an ae alo gven n Table (1). Concluon: Th tudy attept to nvetgate the effcency and anng the Indan Doetc ban wth nteval data. The an a of th pape to contuct the elatve effcency bound of effcency coe and alo to an the DM whch fall unde the ae categoy. Th anng ethod help u to now whch ban functonng n the effcent envonent copang to the othe ban n the ae categoy. The tudy tate that the only one ban IDBI, td. the fully effcent ban aong all the Indan Doetc ban whch agned wth Ran one. The eanng ban n nube 14 and 12 fall unde the categoy E+ and E- epectvely. Oveall, the peent tudy facltate the anng ethod wheneve the nteval data appea n the lteatue. Th wll help a the bae fo anng the decon ang unt wth nteval data. Refeence: [1] Andeen A and Peteen, N.C., A pocedue fo anng effcent unt n data envelopent analy.mgt.sc.39, [2] Bane, R.D., Chane, A., Coope, W.W., (1984), Soe Model fo etatng techncal and cale neffcence n data envelopent analy: Manageent Scence 30, pp [3] Beg, S.A., Found, F.R., Halaon.., and Suonen, M Banng effcency n the Nodc counte, Jounal of Banng and Fnance 17: [4] Chane, A., Coope, W.W., and Rhode, E Meaung the effcency of decon ang unt, Euopean Jounal of Opeatonal Reeach 2, [5] Depot, D.K., Sl, Y.G., Data Envelopent Analy wth Ipece data, Euopean Jounal of Opeatonal Reeach 140, [6] Jahanhahloo, G.R., Hoenzadeh otf, F., and Moad, M., Sentvty Analy and tablty analy n DEA wth nteval data, App. Math. Coput, 156, [7] Mla, A.P., Halaon,., Meaueent of Input and Output n the Banng nduty. Tanzanet Jounal 3(1): [8] Sealey, J. C.W., and ndley, J.T., Input, output and a theoy of poducton and cot at depotoy fnancal nttuton. Jounal of Fnance 4: Ban Nae Table (1) Categoy Vol. III, Iue 3, July R Ran State Ban of Inda E State Ban Bane & Japu E State Ban of Hydeabad E State Ban of Indoe E State Ban of Myoe E State Ban of Patala E State Ban of Tavancoe E Allahabad Ban E

6 INDIAN JORNA OF MANAGEMENT SCIENCE (IJMS) EISSN X ISSN Andha Ban E Ban of Baoda E Ban of Inda E Ban of Mahaahta E Canaa Ban E Cental Ban of Inda E Copoaton Ban E Dena Ban E IDBI td E Indan Ban E Indan Oveea Ban E Oental Ban of Coece E Punab & Snd Ban E Punab Natonal Ban E Syndcate Ban E CO Ban E non Ban of Inda E nted Ban of Inda E Vaya Ban E **** Vol. III, Iue 3, July 2013