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Ap p lie dMathemati cal. Model l i ng (2011)5794_5803. 35. **#ffiHfl$ffi#. JJ ti. :11. A two-phaseapproachfor setting targetsln DEAwith negativedata. Rezal(azemiMatin *, RozaAzizi. lslamicAzad lJniversity,Karaj Branch,Department Mathemattcs,. oJ. Karai. Iran. ARTICTE. INF O.

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## Ap p lie dMathemati cal

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**Ap p lie dMathemati cal**Model l i ng (2011)5794_5803 35 **#ffiHfl$ffi# JJ ti :11 A two-phaseapproachfor setting targetsln DEAwith negativedata Rezal(azemiMatin *, RozaAzizi lslamicAzad lJniversity,Karaj Branch,Department Mathemattcs, oJ Karai. Iran ARTICTE INF O ABST R A C T Article history: Conv e n t i o n a l D E A m o d e l s h a v e b e e n i n t r o d u c e d t o a " " t *f f i Received September 8 2010 world, in someoccasions, have outputs and/or inputs,which we can take negativedata.In Received revisedform 4 May 201l in DEAliteraturesome approaches havebeenpresentedfor evaruatingperform"anc" Accepted8 May 201 1 ofunits, which operatewith negativedata. In this paper,firstry, we give A v a i l a b l e n l i n e2 7 M a y 2 0 1 1 o a Lrief review of these works, then we presenta new additive basedapproachin this framework.The proposed model is designedto provide a target with non-negativevarue associated Keywords: with negative componentsfor each observedunit, failed by other methods.An Data envelopmentanalysis empirical applicationin bankingis then usedto show the applicability the proposed Negativedata of methodand make a com- parisonwith the other approaches the literature. Targetsetting in Substitution @ 2011 Elsevier Inc.All rightsreserveo. l. Introduction (DEA) moders a.ssume non_negative for inputs ourpurs. varues and However, :::::T:"::i:::,T:l:l",lT.::,,:ily"' . vr s^ sttr Pr L evaluationofthe universities an area,the rate ofeducationalgrowth could be considered ^ in as an oufput which negative valuein a university duringa periodof time.A simitarsituationcould seen be whenin performance of n aclnnercial ntes returns rtrns ndustry of forinvestnents variable ioi ioiiriii;;;";;;;; ' as uutput nt"t dn we with variabtes, including applications these, be inwhich faced lurpur ofDEA,like could found ValUU, rul wuld Mlany (DMs) interestedbenchmarks posi- with in aLe decision makers values in most thecases, and of positive negative and both levels such of outputs. tive ln DEA literature, there have been various approaches for dealing with negative data. Scheel [1] suggested an ap- proach which considers the absolute values of negative inputs as outputs and the absolute values of outputs as inputs. This method cannot be applied for the case in which DMUs include both negative and positive inputs and/or outputs. Portela et al. [2] have also provided a model in which a variable can take both positive and negative values. They have developed Range Directional Measure (RDM) model in efficiency measurement and improving performance of the units based on a directional distance function. The results of their approach come close to radial DEA measures. Sharp et al. [3] proposed modified slack-based measure (MSBM) in which both negative outputs/inputs can be handled; this model is a modification of slacks-basedmeasure of efficiency (SBM) by Tone [4]. Recently, Emrouznejad [5] proposed Semi-Ori- entetl Radial Measure (SORM) to handle variables that take both positive and negative values over the units. This model treats each input/output variable essentially as a sum of two variables, one taking its negative and the other its Dositive v alu es. * C o r r e s p o n d i n g a u th o r .Ad d r e ss:De p a r tm e n to fth e mati cs, ami cA zadU ni versi ty, Ma Isl I(araj B ranch,p.O.B ox3.l 4g5-3l 3,K arai , l ran E-mail addresses: rkmatin@kiau.ac.ir KazemiMatin), aziziroza@gmail.com Azizi). (R. (R. 0307-904X/$- see front matter O 2011 ElsevierInc. All righrs reserved. d o i :10 .10 l 6 / j . a p m . 2 01 .0 5 .0 0 2 1

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