S |'X' ( 9 20l l Opem ti onalR es ear c h oc i er yLtd. Al l r i ghr sr es ew ed.0l 60- 56S2i |...
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s | 'X' ( 9 20l l Opem ti onalR es ear c h oc i er yLtd. Al l r i ghr sr es ew ed.0l 60- 56S2i | lournal of the Operational Research Society (20 | l) 62, | 585-1595 w.palgmve-journals.com/jors/ A new approach for weight derivation using data envelopmentanalysisin the analytic hierarchyprocess SM Mirhedayatianl and R Farzipoor Saen2* t antit' Azatl [Jniversi1rQazt'in Branch, Qazvirt,Iran; and2Islantic Azttcl Unit'ersit)t-I{uraj Branch, Kuruj, Iran Recently, sone researcheshave been carried out in the context of using data envelopment analysis (DEA) moclels to generate local weiglits of alternatives from pairwise comparison matrices_used in the analytic hierarchy process (AFIP). One of these n.rodelsis the DEAHP. The main drawback of the pairwise cotnparisotl DEAHP is that it generatcs countcr-intuitive priority vectors for ir.rconsistent matrices. To overcome the drawbacks of the DEAHP, this paper proposes a new procedure entitled Revised DEAHP, and it will be showr] that this procedure generates logical weights that are consistent with the {ecision maker's judgernents and is sensitiveto changes in data of the pairwise colnpalison matr.ices. Through a numerical cxample, it will be shown that the Revised DEAHP'. not only.produces correct weights flr incofiEistent matriies but also does not sulfer from rank reversal when an irrelev:rnt ,o alternative is a"ddedor removed. Society(2OIl) 62,1585 1595.doi:10.1057fors.2010.105 Journul of the OperationulReseorch pu b lish edo rlirre l r Augr pt 2010 ,, ,.r,,.,, ,, . analytic hierarchypfocess; DEAHP; rairk revcrsal Keywords: data envelopnient analysis; matlices are irrational and counter-intuitive. In this paper, | . I nt r oduc t ion a ncw procedure entitled Revised DEAHP is proposed to The derivation of priority vectorsfrom pairwisecolrpar- overcorne these drawbacks. and show that this method iu ison matricesis one of the importarttissues theiandylic gcnel'atesrational weights lor inconsistcnt pairwisc com- hierarchyprocess(AHP) literature.Aftcr propo$iig the parison matrices, rvhilc it retains the DEAIIP advantages method (EM ) by Saaty t2ffi0). nutnerous ergenvulue on the rank reveral problen. resealches were couductedin this area,such as weighted Tlie papcr is organized as follows. In Section 2, the -logarithrnic lcast square mcthod (Chu el al, 1979j; the DEAFIP is reviewed and its drawbacks are numerically method (Crarvlbrd,1987), geometticleast the leastsquare illustrated. In Scction 3, the proposed method for weight squarc metirod (Islei :ind L?iikett, 1988), the fuzzy derivation is discusscd. Numcrical examples arc providcd prograrnming method(Mikhailov,2000),the gradienteigen in Section4. The paper is concluded in Scction 5. weightmethod (Coggerand Yu, 1985),the robust estima- singular value and Conklin,2002), tion method(Lipovetsky 2. DIIAHP 2004). decomposition approach(Gassand Rapcsak, Rarrranathan (2006) proposed an approach Recer.rtly, The DEAHP method uses two similar mcthods for local analysis callcd the DEAHP, in which data envelopment rveights and final weights derivation from pairwise (DEA) is usedfor priority derivationof pairwisecornpar- cornparisor.r matrice s, in which local weights are the in ison matrices the AFIP. Although,the DEAIIP hastlte rveights of criteria (or alternatives with respect to each problernwhen ati advantage lcmoving the rank reversal of criterion) :rnd iinal weights are the weigl.rtsof alternatives irrelevant alternativeis added or removed,it has some that cxist in thc lowest lcvel ol thc hielarchical structure. drawbacks.First of all, it only uscssomeinformation of pairwise comparison matricesand it is not sensitivcto ttsing the DEAIIP 2.1. Obtaininglocal w,eights matrices. Second,the clranges somedata of judgemeut in Let pairwisecontparisou generlrted weightsfrom inconsistent (l ln an 0t2 * a2t u22 02n Correspondente:R Far:i1toor Suen,Deparlnrcttt of hulustrial Matnge- ( l) A:(n4),,u- nutt, Iiacuhy of trfanagententund Accouttlittg, ]slunic Azud Uttit'etsitl'- i hun. Karaj Rrunch,Kuraj, P.O. Bor. 3148-5-313. dnl Lln2 0nn yahocl.corn E-n.rai farzipour(a' l:
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Transcript of S |'X' ( 9 20l l Opem ti onalR es ear c h oc i er yLtd. Al l r i ghr sr es ew ed.0l 60- 56S2i |...
s | 'X'( 9 20l l Opem ti onalR es ear c h oc i er yLtd. Al l r i ghr sr es ew ed.0l 60- 56S2i |lournal of the Operational Research Society (20 | l) 62, | 585-1595
w.palgmve-journals.com/jors/
A new approach for weight derivation usingdata envelopmentanalysisin the analytic
hierarchyprocessSM Mirhedayatianl and R Farzipoor Saen2*
t Islantit' Azatl [Jniversi1rQazt'in Branch, Qazvirt,Iran; and2Islantic Azttcl Unit'ersit)t-I{uraj Branch, Kuruj, Iran
Recently, sone researcheshave been carried out in the context of using data envelopment analysis(DEA) moclels to generate local weiglits of alternatives from pairwise comparison matrices_used in the
analytic hierarchy process (AFIP). One of these n.rodelsis the DEAHP. The main drawback of thepairwise cotnparisotlDEAHP is that it generatcs countcr-intuitive priority vectors for ir.rconsistent
matrices. To overcome the drawbacks of the DEAHP, this paper proposes a new procedure entitledRevised DEAHP, and it will be showr] that this procedure generates logical weights that are consistent
with the {ecision maker's judgernents and is sensitiveto changes in data of the pairwise colnpalison
matr.ices. Through a numerical cxample, it will be shown that the Revised DEAHP'. not only.producescorrect weights flr incofiEistent matriies but also does not sulfer from rank reversal when an irrelev:rnt
,oalternative is a"ddedor removed.Society(2OIl) 62,1585 1595.doi:10.1057fors.2010.105Journul of the OperationulReseorch
pu b lish edo rlirre l r Augr pt 2010,, ,.r,,.,,
,, .analytic hierarchypfocess; DEAHP; rairk revcrsalKeywords: data envelopnient analysis;
matlices are irrational and counter-intuitive. In this paper,| . I nt r oduc t iona ncw procedure entitled Revised DEAHP is proposed to
The derivation of priority vectorsfrom pairwisecolrpar- overcorne these drawbacks. and show that this methodiuison matricesis one of the importarttissues theiandylic gcnel'atesrational weights lor inconsistcnt pairwisc com-
hierarchyprocess(AHP) literature.Aftcr propo$iig the parison matrices, rvhilc it retains the DEAIIP advantagesmethod (EM ) by Saaty t2ffi0). nutnerousergenvulue on the rank reveral problen.
resealches were couductedin this area,such as weighted Tlie papcr is organized as follows. In Section 2, the-logarithrniclcast square mcthod (Chu el al, 1979j; the DEAFIP is reviewed and its drawbacks are numericallymethod (Crarvlbrd,1987), geometticleasttheleastsquare illustrated. In Scction 3, the proposed method for weight
squarc metirod (Islei :ind L?iikett, 1988), the fuzzy derivation is discusscd. Numcrical examples arc providcdprograrnming method(Mikhailov,2000),the gradienteigen in Section4. The paper is concluded in Scction 5.weightmethod (Coggerand Yu, 1985),the robust estima-
singularvalueand Conklin,2002),tion method(Lipovetsky2. DIIAHP2004).decomposition approach(Gassand Rapcsak,
Rarrranathan (2006) proposed an approachRecer.rtly, The DEAHP method uses two similar mcthods for localanalysiscallcd the DEAHP, in which data envelopment rveights and final weights derivation from pairwise
(DEA) is usedfor priority derivationof pairwisecornpar- cornparisor.r matrice s, in which local weights are theinison matrices the AFIP. Although,the DEAIIP hastlte rveights of criteria (or alternatives with respect to each
problernwhen atiadvantage lcmoving the rank reversalof criterion) :rnd iinal weights are the weigl.rtsof alternativesirrelevant alternativeis added or removed,it has some that cxist in thc lowest lcvel ol thc hielarchical structure.drawbacks.First of all, it only uscssomeinformation ofpairwise comparison matricesand it is not sensitivcto ttsing the DEAIIP2.1. Obtaininglocal w,eights
matrices.Second,theclranges somedata of judgemeutinLetpairwisecontparisougenerlrted weightsfrom inconsistent
(l lnan 0t2* a2t u22 02nCorrespondente:R Far:i1toor Suen,Deparlnrcttt of hulustrial Matnge-
( l)A:(n4),,u-nutt, Iiacuhy of trfanagententund Accouttlittg, ]slunic Azud Uttit'etsitl'-ihun.Karaj Rrunch,Kuraj, P.O. Bor. 3148-5-313.dnl Lln2 0nnyahocl.cornE-n.rai farzipour(a'l:
