PROPOSING A NEW MODEL ON DATA ENVELOPMENT ANALYSIS BY CONSIDERING NON DISCRETIONARY FACTORS AND A REVIEW ON PREVIOUS MODELS. University,Tehran, Iran.

Transcription

1 Maheacal ad Copuaoal Applcao, Vol. 5, No. 3, pp , 200. Aocao fo Scefc Reeach PROPOSING A NEW MODEL ON DATA ENVELOPMENT ANALYSIS BY CONSIDERING NON DISCRETIONARY FACTORS AND A REVIEW ON PREVIOUS MODELS G.R. Jahahahloo, F. Hoezadeh Lof, N. Shoa 2, A.Ghola Ab *, M. Fallah Jeloda, Kaa Jaal fouzabad 2 Depae of Maheac, Scece ad Reeach Bach,Ilac Azad Uvey,Teha, Ia. 2 Depae of Maheac, Foozooh bach, Ilac Azad Uvey, Foozooh, Ia. Agholaab@gal.co Abac- Dceoay odel of daa evelope aaly (DEA) aue ha all pu ad oupu ae dceoay,.e., coolled by he aagee of each deco ag u (DMU) ad vaed a dceo. I ay ealc uao, howeve, hee ay ex exogeouly fxed o o-dceoay pu o oupu ha ae beyod he cool of a DMU, aagee. Thee ae oe odel ha copoae o-dceoay pu o DEA odel. Th pape evew hee appoache, povdg a dcuo of egh ad weaee ad hghlghg poeal lao. Moeove, a ew ehod developed ha ovecoe exg weaee. Key Wod- Daa Evelope Aaly,No-Dceoay, Effcecy, Exogeouly. INTRODUCTION Daa evelope aaly (DEA) whch oduced by Chae e al. [4] (CCR) ad exeded by Bae e al. [] (BCC), a ueful ehod o evaluae elave effcecy of ulple-pu ad ulple-oupu u baed o obeved daa. O he ba of vaou poduco poce aupo, a ube of dffee odel ha bee developed. Sadad DEA aue ha he aeed u (DMU) ae hoogeeou,.e. hey pefo he ae a wh la obecve, coue la pu ad poduce la oupu, ad opeae la opeaoal evoe. Ofe he aupo of hoogeeou evoe volaed ad faco ha decbe he dffeece he evoe eed o be cluded he aaly. Thee faco, ad ohe oude he cool of he DMU, ae fequely called o-dceoay faco. Thee ae oe appoache whch ee o be oe geeal. Thee appoache ae developed fo coollg he o-dceoay pu. The DEA odel coed by Bae ad Moey [2] fo fulfllg wha above ad. Covexy a aupo by codeg ehe dceoay o o-dceoay pu. Thee clae of pu wee eaed dffeely, howeve, by o allowg adal educo he odceoay pu. Ruggeo [] exeded h odel by doppg he covexy coa aocaed wh he o-dceoay pu. Rahe, o-dceoay pu wee eaed a hf faco leadg o ulple foe ad eco wee placed o he wegh o

2 G.R. Jahahahloo, F. H. Lof, N. Shoa, A.G. Ab, M. F. Jeloda ad K. J. Fouzabad 345 exclude DMU wh oe favoable level of he o-dceoay faco. The appoach ha codeed hee a a hd oe oduced by Ray [9], whch doe o code he o-dceoay pu he DEA odel he f age. The o-dceoay pu ae coolled he ecod age of egeo, whch pe a adued eaue of echcal effcecy o ee he odel. A hybd odel aouced by Ruggeo [3] ha have hee age fo allowg he ulple odceoay pu o be pad aeo. Sulao aaly (Ruggeo [3]) howed ha ulple age odel of Ray ad Ruggeo have a upeo level copao wh Bae ad Moey odel, ad ae aced bee. I ode o copae Bae ad Moey odel wh he ochac foe odel wh oe exogeou vaable,a ulao aaly ued by Yu [4]. The co-ecoal ochac foe appoach ha bee depced by Odch ad Ruggeo [8] o be of led value ce doe o eally allow eauee eo. Ohe cocluded eul by Yu ae coe wh Ruggeo []. Moeove, a eved odel wll be popoed ha wll poduce a udoed effcecy eaue by Ruggeo [2]. A dcued ha pape ad lluaed wh ulao aaly, he pefoace of he exg odel decle a he elaohp bewee o-dceoay pu ad ue bu uobeved effcecy ge oge. I addo o dcug he poble, ha pape oduced a ew DEA odel whch ovecoe he defed poble. Oe hocog, howeve, wa he elace o paaec echque o defy h elaohp. The pupoe of h pape o copae he hee appoache, hghlghg poeal egh ad weaee. A ew odel developed ha ovecoe defed weaee. The cue pape poceed a follow. eco 2 dcue he bac DEA odel ad develop a ehodology fo eag o-dceoay ad eco 3 povde a paccal exaple. Fally, cocluo ae gve. 2. PRELIMINARIES AND DEVLOPMENT OF THE DEA MODELS IN THE PRESENCE OF NON-DISCRETIONARY INPUTS Daa Evelope Aaly (DEA) a echque ha ha bee ued wdely he upply cha aagee leaue. Th o-paaec, ul-faco appoach ehace ou ably o capue he ul-deoaly of pefoace dcued eale. Moe foally, DEA a aheacal pogag echque fo eaug he elave effcecy of deco ag u (DMU) whee each DMU ha a e of pu ued o poduce a e of oupu. Code DMU,( =, K, ), whee each DMU coue pu o poduce oupu. Suppoe he obeved pu ad oupu veco of DMU be X ( x, K, x ) = ad Y ( y, K, y ) epecvely, ad le X 0 ad X 0 ad Y 0 ad Y 0. = I DEA, he CCR odel oe of he o poa adal odel, evaluae he elave effcecy of a pecfc DMU o, o (, K, ), wh epec o a e of CCRfoe DMU. We ca we a pu-oeed CCR odel a follow:

3 346 Popog a New Model o Daa Evelope Aaly M θ.. = = λ 0 o o, =, K,, =, K,, =, K, () Moeove a pu-oeed BCC odel a follow: M θ S. = = = λ 0, λ =, o o,, =, K, =, K, =, K, (2) Oe ao poble wh a adal eaue of echcal effcecy ha, doe o eflec all defable poeal fo ceag oupu ad educg pu. I ecooc, he cocep of effcecy aely elaed o he dea of paeo opaly. A pu-oupu budle o paeo opal f hee ea he pobly of ay e ceae oupu o e educo pu. Whe pove oupu ad pu lac ae pee a he opal oluo of a CCR LP poble, he coepodg adal poeco of a obeved pu-oupu cobao doe o ee he ceo of paeo opaly ad hould o be qualfed a a effce po. A o-adal Paeo-Koopa eaue of echcal effcecy of he pu-oupu pa X, ) ca be copued a: ( Y o o M Γ =.. = = θ x λ 0 θ φ = = θ φ φ y o o, =, K,, =, K,, =, K,, =, K,, =, K, (3)

4 G.R. Jahahahloo, F. H. Lof, N. Shoa, A.G. Ab, M. F. Jeloda ad K. J. Fouzabad 347 * I h odel X, ) Paeo-Koopa effce f ad oly f φ = fo each oupu ( o Yo * ad θ = fo each pu plyg Γ =. The obecve fuco h aheacal pogag poble olea. Bu poble o leaze a [0]. Up o h po, we have aued ha all pu ad oupu ca be vaed a he dceo of aageeoe ohe ue. Thee ay be called dceoay vaable. No-dceoay vaable, o ubec o aagee cool, ay alo eed o be codeed. Aue ha hee ae DMU, whee each DMU ( =, K, ), ue dffee dceoay pu, ( =, K, ), ad dffee o-dceoay pu, x z ( =, K, ), whee + =, o poduce dffee oupu y ( =, K, ). Thee ae oe odel ha copoae o-dceoay pu o DEA odel. Bae ad Moey povded he f odel by odfyg he coa o he fxed faco wh he DEA odel. Th odel dffe fo he ogal DEA odel by beag he l bewee o-dceoay pu ad effcecy. Th odel a follow: M θ.. = = = = λ z λ = λ 0 z o o o, =, K,, =, K,, =, K,, =, K, (4) Thee a gea lay bewee fxed faco coa ad coa o he dceoay pu; boh ae odfed, howeve, o bea he l bewee effcecy ad he fxed faco, he fxed faco of poduco ae beg ude cool by he odfcao. The ece ubec doe by equg a covex cobao of he efee poduco poble ode o ga a evoe whch o bee ha he DMU ha gog o be aalyzed. I howed, by Ruggeo [] ha he efee "poduco pobly" ay o be feable. Th eul, becaue of eu o cale, hould be defed elave oly o dceoay pu. Epha o covexy wh codeao he o-dceoay pu coclude o pope eco of he poduco pobly e ad doed effcecy eauee. The eveal auho have popoed ehod fo aalyzg pefoace he peece of o-dceoay pu. Oe of he odel have popoed by Ruggeo []

5 348 Popog a New Model o Daa Evelope Aaly a follow : M S. θ = = = λ 0 λ = 0, λ = o o f z > z o, =, K,, =, K,, =, K,, =, K, (5) The odel explcly expla oe lao fo he copao e o exclude DMU whch ecoue a oe pleaa ad bee evoe. Le he odel (4), h odel eed o have a poy pecfcao of he couou o-dceoay vaable. By ceag he ube of fxed faco cououly, he lelhood of defyg a DMU, a effce by defaul, ceae. Th doe o code he copao bewee a gve DMU ad aohe DMU ha a a whole, ha he ae o o bee evoe, eve hough ha a oe favoable level of a lea oe odceoay pu. The ae ae u a uggeo a hee weae of he Ruggeo odel. To eove hee weaee, Ray [9] developed a aleave wo-age. I he f age he BCC odel eployed ug oly he dceoay pu. Ray [9] howed ha egeo aaly ca be ued he ecod age o faco ou he effec ha he evoe ha o poduco. I h udy, he f-age dex FS wa egeed o he fxed faco of poduco. Igog obevao ubcp, he ecod-age egeo odel pecfed a FS = α β z + K + β + ε (*) + z Noe ha f he pove chage dz z epee a oe favoable evoe, he β > 0. Baed o he egeo eul, Ray' eaue RAY of echcal effcecy copued a RAY = FS α β z K β z. Due o he aue of egeo, h dex wll have ea 0. The dex, howeve, ca be afoed by adug he ecep α o ha RAY o-egave. The doo oduced he ogal DEA odel fo he excluo of he evoeal vaable facoed ou va egeo aaly [3]. The f advaage of he wo-age appoach ha ca be copued. The woage appoach eque olvg he ogal DEA odel oce. Th offe codeable flexbly ad pe evy aaly he ecod age. So, vaou e of odceoay pu ca be exaed. The added flexbly ovecoe weaee defed Ruggeo' publc eco DEA odel a well. If ueou vaable of odceoay ex, he egeo aaly povde he ea o plcly wegh he cobuo each vaable ha o he f-age eae.

6 G.R. Jahahahloo, F. H. Lof, N. Shoa, A.G. Ab, M. F. Jeloda ad K. J. Fouzabad 349 The wo-age appoach ha alo oe poeal weaee. The ecod age of egeo eed a po ccuace of fucoal fo. If he fucoal fo pecfed, he Ray' eaue wll be doed. I h way, Ray' odel ecoue poble le egeo baed appoache. Moeove, poble ha effcecy wll be oveaed, becaue of adug ae ade baed o he wo-ded eo. A howed above, he Ruggeo odel o able copleely o wegh he poace of each o-dceoay vaable poduco. Theefoe, wh ceag he ube of o-dceoay pu cee pabu, he Ruggeo odel wll be oe lely o oveae effcecy. The poace of hee o-dceoay pu, howeve, evealed he ecod-age egeo of Ray' odel. Gve he paaee, poble o oba a oveall dex Z of evoeal hahe a Z = = β z Gve h dex of evoeal hahe, he Ruggeo pu-oeed (vaable eu o cale) effcecy eaue fo DMU o ca be pecfed a a hee-age pocedue. F, he BCC odel olved ad he ecod-age egeo (*) pefoed. Afe couco of Z, he followg hd-age lea poga olved: M θ.. = = = λ 0 λ = λ = 0 f o o Z > Z o, =, K,, =, K,, =, K, Thee ae a few advaage o ug h ew odel. A f, uppoe ha he ecod-age egeo oduce ubaed eae of he paaee wegh, he odel ga he deable popee of he Ruggeo odel. Secod, he odel ae he defed weae of defyg DMU a effce by defaul ae he Ruggeo odel. Iead, h odel capable fo weghg he poace of he odceoay pu. Ray' odel ue alo he eo e fo eaug he effcecy ad coequely, wll be eve o -pecfcao. Th odel oly ue he paaee wegh o couc he evoeal hahe dex. A a eul, dbuoal aupo ae o ade egadg effcecy. Fuhe, h ew odel (ule Ray' odel) aa ohe deable popee of he ogal DEA odel. I pacula, h odel cool fo odceoay faco ad ucove he effce efee e. A a eul, he aue of cale ecooe ca be evealed. Fally, poeally ueful foao egadg caue of effcecy o lo ce effce DMU ca be copaed o effce efee e [3]. Oe ey aupo odel (6) ha ue effcecy o coelaed wh odceoay faco. To ovecoe hee dffcule, Ruggeo odfed he above odel followg: (6)

7 350 Popog a New Model o Daa Evelope Aaly M.. = = = θ λ 0 λ = λ = 0 f o o Z > Z o, =, K,, =, K, + δ ( z),, =, K, δ ( z) > 0 Model (7) dffe fo odel (6) by elaxg he coa ha ec DMU wh a hghe level of he o-dceoay pu fo he efeece goup. Now, DMU wh hghe level of he o-dceoay pu ca be cluded a log a he dffeece bewee o-dceoay level o geae ha δ (z). By elaxg h coa, DMU wh a oe favoable evoe ca be cluded he efee e, whch eeally cool fo he coelao bewee effcecy ad he o-dceoay evoe, [2]. Ufouaely, he eved odel eque a addoal aupo o he poduco echology ad paaec pecfcao a ecod age. Moeove, a poed above, h appoach heoecally ha ay dffculy, bu applyg paccally ad obag δ (z) wll o be ply pefoed. I ode o ovecoe ay dffcule, we wll develop a ehod ha ply wll be ulzed appled apec. I addo o olve he foe poble, deco ag u wll acqued a eal effcece peece of o-dceoay pu. Fo h pupoe, f, we wll ewe odel (3) peece of o-dceoay * * pu a follow ad we fd δ K δ. M ( Γ = = θ + = φ o,, o = δ ) (7).. = = = λ z λ 0 θ δ φ θ x δ z φ y o o o, =, K,, =, K,, =, K,, =, K,, =, K,, =, K,, =, K, (8)

8 G.R. Jahahahloo, F. H. Lof, N. Shoa, A.G. Ab, M. F. Jeloda ad K. J. Fouzabad 35 I coue, we apply he followg odel : M Γ = = θ = φ.. = = λ =0 θ φ θ x φ y f λ 0 o = o * δ z o < = * δ z, =, K,, =, K,, =, K,, =, K,, =, K,, =, K, Follow o he la odel, we oba ue effcecy of evaluaed DMU. Ug he popoed ehod, oe advaage would be appeaed. Th ehod ovecoe he defed weae of defyg DMU a effce by defaul hee he Ruggeo odel. Ipoaly, a he ube of o-dceoay faco ceae, h ehod ca copae all o-dceoay faco, o h ehod oba ue effcecy. Specally, he popoed ehod ca be ulzed ply paccal exaple. 3. A PRACTICAL EXAMPLE I h eco, we wo ou a appled exaple o lluae he popoed odel. So code 30 ba bache Ia wh 3 dceoay pu ad 2 o-dceoay pu ad 4 oupu. F we apply odel (8) fo each DMU,( =, K, ) ad we * fd δ,( N. D). I wha follow, we apply odel (9) ad oba ue effcecy of evaluaed DMU. Daa ad eul ae uazed able : (9)

9 352 Popog a New Model o Daa Evelope Aaly Table. Daa ad Reul DMU Dceoay No- Oupu Popoed Dceoay Ruggeo Model I I2 I3 Z Z2 O O2 O3 O CONCLUDING REMARKS I ay ealc uao, howeve, hee ay ex exogeouly fxed o odceoay pu o oupu ha ae beyod he cool of a DMU, aagee. Th pape ha focued o he peece of o-dceoay pu poduco pocee ad he pogag odel ued o eaue effcecy. Fve exg odel wee dcued ad he egh ad weaee wee defed. Moeove, h pape oduced a ew DEA odel ha ovecoe he defed poble. Thee ae oe advaage by ug h popoed ehod. Th ehod ovecoe he defed weae of defyg DMU a effce by defaul hee he odel whch have bee popoed. Moeove, a he ube of o-dceoay faco ceae, h ehod ca copae all o-dceoay faco, o h ehod oba ue effcecy. Specally, he popoed ehod ca be ulzed ply paccal exaple.

10 G.R. Jahahahloo, F. H. Lof, N. Shoa, A.G. Ab, M. F. Jeloda ad K. J. Fouzabad REFERENCES. Bae, R.D., Chae, A., Coope, W.W., Soe odel fo eag echcal ad cale effcece daa evelope aaly. Maagee Scece 30 (9), , Bae, R.D, Moey, R.C, Effcecy aaly fo exogeouly fxed pu ad oupu. Euopea Joual of Opeaoal Reeach , Badfod, D., Mal, R., Oae, W., The g co of local publc evce.soe evdece ad efleco, Naoal ax Joual , Chae, A., Coope, W.W., Rhode, E., Meaug he effcecy of deco ag u. Euopea Joual of Opeaoal Reeach 2, , Fae, R., Goof, S., Lovell, C.A.K., Poduco foe, Cabdge Uvey Pe, New Yo, Fae, R., Goof, S., Lovell, C.A.K., The aagee of effcecy of poduco. Klowe-Nhoff, Boo, MA, Faell, M.J, The eauee of poducve effcecy. Joual of he oyal acal cece ee A, Geeal 20, , Odch,J;Ruggeo,J, Effcecy eauee he Sochac foe odel. Euopea Joual of Opeaoal Reeach 29, , Ray, S.c., Reouce ue efcecy publc chool. A udy of coeccu daa, Maagee Scece 37, , Ray, Subhah.c., Daa evelope aaly: heoy ad echque fo ecooc ad opeao eeach. Publhed by he pe ydcae of he uvey of Cabdge, Ruggeo, J., O he eauee of echcal effcecy he publc eco, Euopea Joual of Opeaoal Reeach , Ruggeo, J., Pefoace evaluao whe o-dceoay faco coelae wh echcal effcecy. Euopea Joual of Opeaoal Reeach, 59, , Ruggeo, J., No-dceoay pu daa evelope aaly. Euopea Joual of Opeaoal Reeach, , Yu,C, The effec of exogeou vaable effcecy eauee-a Mo Calo udy. Euopea Joual of Opeaoal Reeach 05, , 998.