Management Science Letters

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1 }} Manageent Scence Lette 2 (202) Content lt avalable at GowngScence Manageent Scence Lette hoepage: A obt AHP-DEA ethod fo eang the elatve effcenc: An applcaton of apot ndt An Foogh a* and Mohaad Javad Efahan b a Depatent of Indtal Engneeng, Ilac Azad Unvet, Naagh Banch, Naagh, Ian b Yong Reeache Clb, Naagh Banch, Ilac Azad Unvet, Naagh, Ian A R T I C L E I N F O A B S T R A C T Atcle hto: Receved Jl 6, 20 Receved n Reved fo Septebe, 3, 20 Accepted 8 Septebe 20 Avalable onlne 29 Septebe 20 Kewod: Data envelopent anal Analtcal heach poce DEA-AHP Robt optzaton Meang the elatve effcenc of la nt ha been an potant topc of eeach aong an eeache. Data envelopent anal ha been one of the ot potant technqe fo eang the effcenc of dffeent nt. Howeve, thee ae oe ltaton on ng ch technqe and oe people pefe to e othe ethod ch a analtcal heach poce to eae the elatve effcence. Bede, ncetant n the npt data anothe e, whch ake oe leadng elt. In th pape, we peent an ntegated obt DEA-AHP to eae the elatve effcenc of la nt. The popoed odel of th beleved to capable of peentng bette elt n te of effcenc copaed wth exclve age of DEA o AHP. The pleentaton of the popoed odel deontated fo a eal-wold cae td of Apot ndt and the elt ae analzed. 202 Gowng Scence Ltd. All ght eeved.. Intodcton Data envelopent anal (DEA) ntodced b Chane et al. (978, 994) one of the ot popla technqe fo eang the elatve effcenc of la non-fnancal nt. The ethod e vao npt/otpt and copae the elatve effcence of all nt thogh the optal olton of lnea pogang poble. The ethod ha been wdel ed aong an eeache and thee ae lteall vao veon of th technqe ch contant etn to cale (CRS) and vaable etn to etn (VRS). Thee ae alo an eal-wold applcaton of DEA ethod n dffeent ndte. Sadad and Oan (2008), fo ntance, ed DEA ethod fo eang the elatve effcenc of eneg copane n Ian. Sadad and Oan (2009) pleented DEA technqe to detene the ot effcent nt of teleconcaton f n Ian. Roghanan and Foogh (200) pleented DEA fo Apot ndt n Ian and ng dffeent npt/otpt, the copaed all egonal and ntenatonal apot n Ian. * Coepondng atho. Tel: E-al addee: an.foogh@gal.co (A. Foogh) 202 Gowng Scence Ltd. All ght eeved. do: /.l

2 94 One of the ot potant e aocated wth DEA the ncetant aocated wth the npt data. Snce the elted poble folaton of DEA technqe n fo of lnea pogang, one can e tadtonal entvt anal n cae thee one o a few nknown paaete. Howeve, when all npt data ae bect to ncetant, t pactcall poble to e old fahon ethod to handle ncetant. Thank to ecent advance of optzaton technqe, we a e the dea of obt optzaton fo lnea pogang to handle ncetant, ve eal. Sote (972) beleved to be the ft who ntodced obt optzaton to handle ncetant bt h appoach wa too petc. Ben-Tal and Neovk (999) ntodced a eakable technqe baed on the at of cone pogang and t ee that the ethod povde ve elable olton wth lted aont of penalt. The ethod convet a ple lnea pogang poble nto a nonlnea poble whee one can e the ecent advance of cone pogang technqe to fnd the optal olton. The ethod beleved to be one of the bet technqe fo handlng ncetant bt one t be fala wth the concept of nonlnea pogang to e thee poble. Beta and S (2003) popoed anothe veon of the obt optzaton wthot changng the tcte of the elted poble,.e. fo the cae of DEA ethod the obt DEA antan the lnea fo of the ognal poble. Sadad and Oan (2008) ae alo the ft one who ntodced the dea of obt DEA fo handlng ncetant n the data. The exaned both obt ethod ntodced b Ben-Tal and Neovk (999) and Beta and S (2003) to handle ncetant fo two applcaton fo eneg and teleconcaton ndte and copaed the elt wth the nonal olton. The conclded that the pce of obtne doe not have gnfcant pact of the qalt of fnal elt bt t ne the fnal olton agant data ncetant, gnfcantl. Thee ae eveal dadvantage aocated wth the DEA technqe and oe people t to e anothe lt-ctea technqe to eove an poble hotcong. Saat (980) ntodced analtcal heach poce (AHP) fo ankng dffeent altenatve baed on dffeent attbte. The dea to ake a pawe copaon between each two altenatve fo ankng choce. The ntegated DEA and AHP ha been wdel ed aong an eeache. Fo ntance, Che et al. (200) pleented an ntegaton of Fzz analtcal heach pocede (AHP) and DEA a a decon akng faclt fo akng bank loan decon. The popoed odel of th pape attept to e the dea of obt optzaton a well a AHP n an ntegated faewok to eae the elatve effcenc of dffeent nt of alne n Ian. Th pape oganzed a follow. We ft peent the poble tateent of DEA ethod n ecton 2. Secton 3 peent an n-depth dcon of the pleentaton of the popoed DEA-AHP odel. Fnall, concldng eak ae gven n the lat ecton to aze the contbton of the pape. 2. Poble tateent Let x be the npt fo a decon nt wth =,, and be the otpt wth,, and =,,n. Let and cale DEA odel folated a follow, v be the dal vaable aocated wth x and, epectvel. The contant to ax z = = v x..

3 A. Foogh / Manageent Scence Lette 2 (202) 95 bect to = v x., v 0, =,..., n () Model () the ba of DEA and t olved te to detene the elatve effcence of dffeent nt. Howeve, nce () nonlnea n tcte, Chale et al. (983) ecoend a ple odfcaton of the obectve fncton to plf the tcte of the elted poble a follow, ax bect to z = = = v x v x. =.., v 0, =,..., n (2) Note that the ft contant alo becoe lnea ng a ple anplaton. Poble (2) ha been wdel ed fo the pat thee decade and the elt ae coonl accepted a a tool to eae the elatve effcenc of dffeent nt. Howeve, when thee ncetant wth the npt and the otpt, one a e dffeent technqe to ake e that a all change on npt/otpt data doe not change the otpt ankng. 2.. Robt optzaton Conde a lnea pogang poble of the followng fo, n c w bect to Aw = b, (3) w 0, whee w R n n the vecto of nknown vaable, A R and b R and ae bect to ncetant. Theefoe, Eq. (3) can be efolated a follow, c R n. Let A and c n c ~ w ~ bect to A w = b, (4) w 0, ~ whee ~ denote the ncetant wth A = [ ~ ]. The obt optzaton appoach peented b Beta and S (2004) convet Eq. (4) nto the followng poble, a

4 96 n c w bect to a w Γ p q p + q p, q w R w 0, n, J ea 0,,,, (5) whee Γ detene the ncetant aocated wth each npt paaete. When = 0 thee no ncetant. A Γ nceae, the ncetant alo nceae. The e alo the vecto of ncetan vale. The DEA odel ognall developed b Chane et al. (983) a follow, Γ (CCR) ax z = ~ ~ bect to. v ~ x = = v ~ x. =., v 0, =,..., n (6) whee x ~ and ~ ae the ncetan npt and otpt whch ae aocated wth x and, epectvel. In Eq. (6) each ncetan paaete le n an nteval of ncetant. Applng Eq. (5) to Eq. (6) eld, (RCCR)ax Z bect to = v x. =,. z Γ. p. q J. 0,. Γ p q 0, =,..., n =,, 0,, 0. v J (7) Poble (7) lnea pogang poble whee e a vecto of ncetan vale, Γ the bdget of ncetant, p and q ae new d non-negatve vaable aocated wth ncetan paaete n (6). A we explaned eale, thee ae two advantage aocated wth Beta and S' obt odel. Ft, the obt DEA tll lnea n the tcte althogh we need to add oe addtonal axla vaable. Second, Γ adt the ncetant aocated wth all paaete. Next ecton, we exane two odel (2) and (7) and copae the elt ng oe tattcal technqe.

5 A. Foogh / Manageent Scence Lette 2 (202) DEA-AHP In analtcal heach poce (AHP), one a olve a DEA poble onl b condeng pawe copaon of dffeent nt. Snan-Sten et al. (2000) ae beleved to be the ft who ntodced the dea of DEA-AHP n a copehenve fo. The popoed odel of th pape peent a obt DEA-AHP ehod to handle the ncetant aocated wth the npt/otpt data. Conde, fo ntance, two nt of A and B, whee the obt DEA-AHP odeled a follow, RE AA Max Z A ZΓ A A q A 0,, x A, v x B B Γ B P B q B 0,,,, 0, 0. (8) whee Г defned a Г. The odel ed fo eang the elatve effcenc of nt A copaed wth nt B. Sla odel can be ed fo eang the elatve effcenc of nt B a follow, RE Max Z,, B ZΓ B B q B 0, x B, E AA v x A A Γ A P A q A 0,,,, 0,, 0. (9) Note that we t olve RE BB and RE AB odel and then we can aange the pawe atx of AHP a follow, a RE RE RE,. Now, we can pefo ankng polc ng AHP technqe (Saat, 980).

6 98 3. The elt In th ecton, we peent the pleentaton of o popoed odel fo a eal-wold cae td fo Apot ndt. Table how the npt and the otpt ed fo o DEA pleentaton. Table The npt and the otpt of RDEA-AHP odel Ttle Decpton Mean Std Nbe of Eploee S of the people who wok n the apot Inpt Tenal aea Aea of tenal Length of nwa Sface of the aphalt oad Nbe of Flght of doetc & ntenatonal Otpt oveent Nbe of Paenge paenge Aont of Cago Cago Table 2 deontate detal of o npt/otpt paaete. Baed on the nfoaton povded n Table 2 and Table 2 The npt and the otpt of 2 apot Apot Aont Nbe of of Cago Paenge Ia Khoen Mehabad Mahad Tabz Efahan Adebl Bandaaba Shaz Zahedan Kean Abadan Ahvaz Raht Yazd Sa Boheh Ooeh Keanhah Gogan Laetan Band Nbe of oveent Length of nwa Tenal aea Nbe of Eploee Table 3 we an the popoed the DEA-AHP and the elt of o ankng ae azed n Table 4. Table 4 The elt of ankng of DEA-AHP Apot Effcenc (%) Rankng

7 A. Foogh / Manageent Scence Lette 2 (202) 99 We have alo pleented the popoed obt DEA-AHP ethod to eae the elatve effcenc of apot and the elt ae azed n Table 5. Table 5 The elt of ankng of obt DEA-AHP Apot Effcenc (%) Rankng A we can obeve fo the elt of Table 5, thee ae not ch dffeence between the ankng of thee two ethod. In ode to conf th obevaton, we have pleented Speaan coelaton between the elt of egla and obt DEA-AHP and the elt , whch conf o cla. 4. Conclon In th pape, we have peented an poved DEA-AHP ethod whee the npt/otpt paaete ae bect to ncetant. The popoed odel of th pape not onl eno the advantage of egla DEA-AHP bt alo t can ncopoate the ncetant aocated wth all the data. Theefoe, the fnal ankng of the elt wll not be changed a the npt data ae changed. The popoed odel of th pape ha been pleented fo a eal-wold cae td of apot ndt and the elt ae copaed wth tadtonal DEA-AHP. Acknowledgent Th pape wa fnancall ppoted b Ilac Azad nvet of Naagh and the atho wold lke to nceel thank the fo the fnancal ppot. The atho ae gatefl on contctve coent of the evewe on eale veon of th wok. Refeence Ben-Tal, A., Neovk, A. (999). Robt olton of ncetan lnea poga, Opeaton Reeach Lette, 25 (), 3. Beta, D., & S, M. (2003). Robt dcete optzaton and netwok flow. Matheatcal Pogang See B, 98, Chane A, Coope, W. W., & Rhode, E. (978). Meang the effcenc of decon akng nt. Eopean Jonal of the Opeatonal Reeach, 2, Chane A, Coope W. W., Lewn, A., & Sefod, L. M. (994). Data envelopent anal: theo, ethodolog and applcaton. Maachett: Klwe Acadec Pblhe. Che, Z. H., Wang, H. S., & Chang, Ch-L. (200). A fzz AHP and DEA appoach fo akng bank loan decon fo all and ed entepe n Tawan. Expet Ste wth Applcaton, 37(0), Roghanan, E., & Foogh, A. (200). An epcal td of Ianan egonal apot ng obt data envelopent anal. Intenatonal Jonal of Indtal Engneeng Coptaton, (), Saat, T. L. (980). The Analtc Heach Poce: Plannng, Pot Settng, Reoce Allocaton, ISBN , McGaw-Hll. Sadad, S.J., & Oan, H. (2008). Data envelopent anal wth ncetan data: An applcaton fo Ianan electct dtbton copane, Eneg Polc 36, Sadad, S.J., & Oan, H. (2009). A boottapped obt data envelopent anal odel fo effcenc etatng of teleconcaton copane n Ian, Teleconcaton Polc, 34(4),

8 00 Sote, A.L. (973). Convex pogang wth et-nclve contant and applcaton to nexact lnea pogang, Opeaton Reeach, 2, Snan-Sten, Z., Mehez, A., & Hadad, Y. (2000). An AHP/DEA ethodolog fo ankng decon akng nt. Intenatonal Tanacton n Opeatonal Reeach, 7(2),