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3 Appendix A2: The DEA Mdels The Basi R Mdel hames, et al., (978) prpsed the basi data envelpment analysis (DEA) mdel, referred t as the R mdel, fr evalating the relative effiienies f a hmgens set f deisin making nits (DMUs). The R mdel inrprates mltiple inpts and tpts in evalating the relative effiienies f alternative DMUs, where effiieny an be defined as the rati f weighted tpt t inpt. In this paper eah DMU will be a spplier fi-m the seletin set. The general effiieny rati fr a DMU is defined by expressin (). where: (Eks) is the effiieny r prdtivity measre f spplier s, sing the weights f "test" spplier k, where the test spplier is the DMU whse effiieny is t be evalated; (Osy) is the vale f tpt y fr spplier s; (Isx) is the vale fr inpt x f spplier s; (viy) is the weight assigned t spplier k fr tpt jy; and (kx) is the weight assigned t spplier k fr inpt x. Fr the basi R mdel, the bjetive is t maximize the effiieny vale f a test spplier k, frm amng a referene set f spplier s, by seleting the ptimal weights assiated with the inpt and tpt measres. The maximm effiienies are nstrained t. The frmlatin is represented in expressin (2). 28

4 maximize 'kyh sbjet t: Ei<\ V Spplier s «fa'n> This nn-linear prgramming frmlatin (2) is eqivalent t the fllwing linear prgramming frmlatin (): maximize E=Y,,v,. () >' sbjet t: Ei<\ V Spplier s The transfrmatin is mpleted by nstraining the effiieny rati denminatr frm (2) t a vale f. This is represented by the nstraint: The reslt f frmlatin () is an ptimal "tehnial effiieny" vale {Ekk*) that is at mst eqal t. If «* =, then it means that n ther spplier is mre effiient than spplier k fr its seleted weights. That is, Ekk* = has spplier k n the ptimal frntier and is nt dminated by any ther spplier. If Ekk* < then spplier k des nt lie n the ptimal frntier and there is at least ne ther spplier that is mre effiient fr 282

5 the ptimal set f weights determined by (). The frmlatin () is exeted 5 times, ne fr eah spplier. Sine the R Mdel may prvide a nmber f alternative sppliers that are effiient, it wld be diffilt fr a deisin-maker r rganizatin t deide n a single spplier if there is mre than ne effiient spplier. T help disriminate amng effiient sppliers and t help rank these sppliers, DEA ranking apprahes may be sed. One sh apprah is remmended here. A Ranking DEA Mdel A DEA apprah that helps fr ranking is a variatin f the R mdel prpsed by Andersn & Petersen (99). In their mdel, they simply eliminate the test nit frm the nstraint set. The new frmlatin is represented by (4). maximize «=<A,A> (4) V sbjet t: ' < V Spplier sk Expressin (4), whih we will all the "reded" R (RR) frmlatin, allws fr tehnially effiient sres t be greater than. This reslt will allw fr a mre disriminating set f sres fr tehnially effiient nits and an ths be sed fr ranking prpses. 28

6 Integrating Managerial Preferene int the DEA Ranking Apprah nstraining the "flexibility" r range f weights ( and v) prvides an apprah fr integrating managerial preferenes int the RR mdels. The se f assrane regins (AR) fr restritin f weights is ne apprah t better map managerial preferenes t DEA and t handle the prblem f Zer mltipliers (weights). The nept f AR is desribed in detail by Thmpsn, et al., (99). The press f setting AR begins with by defining pper and lwer bnds fr eah inpt and tpt weight. The pper and lwer bnds fr eah weight an help define nstraints that relate the weight vales f varis fatrs. These LB and UB vales may be ranges fr preferene weights fr eah f the fatrs as defined by the deisin-makers. The AR nstraints relate the weights and their bnds t eah ther while nsidering inpts/tpts f DEA mdel in pair. The generalized AR nstraint sets that are derived frm LB and UB data are: LB, UB v> -V. and v. < v. (5) ' UBj ' ' LBj ' These nstraints an be added t expressin (4) t frm the RR with assrane regins (RR/AR) mdel. Frm a mptatinal perspetive, the nmber f additinal /*(/-!) *{-V\ nstramts reqired t help define the AR is eqal t +, where / and O represent the nmber f inpts and tpts, respetively. 284

7 Appendix A: LINDO Prgrams fr DEA! Fllwing is the LINDO prgram fr R Mdel (DEA) fr allating the relative effiieny f DMU.! Fr RR mdel, erase the rrespnding line f bjetive fntin frm nstraints MAV+V2+.74V ST VI > V2> V> U> U2> V+V2+.74 V-. Ul -.25U2<=.99 VI +.99 V V -.2 Ul -.25 U2 <=.97 VI +. V V -. Ul -.67 U2 <=. VI +.99 V2 +.9 V - Ul -.25 U2 <= VI +. V2 +.8 V -.99 Ul -.25 U2 <=.97 VI +.97 V2 +.9 V -. Ul -.8 U2 <=.2 VI +. V2 +.8 V -.97 Ul -.8 U2 <=. VI +.98 V2 +.5 V -.98 Ul -.42 U2 <=. VI + V2 +. V -.98 Ul -.42 U2 <=. U +.25 U2=l END 285

8 ! Fllwing is the LINDO prgram fr RR/AR Mdel (DEA) fr allating the relative effiieny f DMU. MAV+V2+.74V ST VI > V2> V> U> U2>! VI + V V -. Ul -.25 U2 <=.99 VI +.99 V V -.2 Ul -.25 U2 <=.97 VI +. V V -. Ul -.67 U2 <=. VI +.99 V2 +.9 V - Ul -.25 U2 <= VI +. V2 +.8 V -.99 Ul -.25 U2 <=.97 VI +.97 V2 +.9 V -. Ul -.8 U2 <=.2 VI +. V2 +.8 V -.97 Ul -.8 U2 <=. VI +.98 V2 +.5 V -.98 Ul -.42 U2 <=. VI + V2 +. V -.98 Ul -.42 U2 <=. Ul +.25 U2=.8U-.2U2>=. Ul U2 <=.286 VI -. V2>=.222 VI -.57 V2<=.667V-. V>=.4 VI -.57 V<-.667 V V >=.4 V V<= END 286

9 Appendix A4: Zer-One Integer Gal Prgram Zer-One Integer Gal Prgram MINIMIZEid +d," +d{ + d; + (//) Satisfy all Gals Gals SUBJET TO.4 xl +.98 xl xl Selet a mbinatin f Vs with lwest NET PRIE x x x2 +.9 x +.47x2 +.24x- d,* =. xl +.24 xl2 +. xl +.24 Selet a mbinatin f Vs with highest QUALITY x2 +. x x2 +. x +.24x2 +.x+ d{ =.25 xl +.2 xl xl +.29 x x22 +. x2 +.9 x + Selet a mbinatin f Vs with highest SERVIE.24 x x + d; = \.698 xl +.58x xl Selet a mbinatin f Vs with lwest LEAD x x x2 +.9 x + TIME.7 x2 +.9 x ~d, =\.596 xl xl xl Selet a mbinatin f Vs with highest x x x x + QUALITATIVE BENEFITS.45x2 +.45x+ df = xll +xl2 + xl= x2 +x22 + x2 = x+x2 + x= xll+x2 = l x22 + x2 = x2 + 5x22 + 2x2>=2 END INT xl, xl2, xl, x2, x22, x2, x, x2, x Selet nly ne Designer Press V Selet nly ne Manfatring Press V Selet nly ne Distribtr (Lgistis) Press V V f Press (Designer) is nt mpatible with V f Press 2 (Manfatring) V 2 f Press 2 (Manfatring) is nt mpatible with V 2 f Press (Lgistis) Selet a Manfatring press V that has the apaity f simltanesly manfatring 2 r mre mahines (mfg. press Vs, 2, & have the apaity f simltanesly mfg., 5, & 2 mahines respetively) 287

10 Appendix A5: Papers Pblished / mmniated frm this Researh () A paper titled "Spplier Seletin in an Agile Manfatring Envirnment sing DEA and ANP" has been aepted fr pbliatin in the "Internatinal Jrnal f Lgistis Systems and Management". (2) A paper titled "A Stdy f Barriers t Agile Manfatring" has been aepted fr pbliatin in the "Internatinal Jrnal f Agile Systems and Management". () A paper titled "Virtal mpany frmatin fr agile manfatring sing ANP & Gal Prgramming" has been aepted fr pbliatin in the "Internatinal Jrnal f Operatinal Researh " and frthming in Vl. 4, N. 6, 29. (4) A paper titled "Prdtin system seletin fr the agile manfatring f mdlarly designed prdts" has been aepted fr pbliatin in the "Internatinal Jrnal f Manfatring Tehnlgy and Management". (5) A paper titled "A Stdy f Enablers f Agile Manfatring" has been mmniated fr pbliatin nsideratin in the "Internatinal Jrnal f Indstrial and Systems Engineering (IJISE) ". 288

11 Appendix A6: Bigraphial Prfile f Researher (As n Agst, 27) Aademis 27: rrently prsing fr the degree f Dtr f Philsphy as a teaher andidate at Aligarh Mslim University (AMU), Aligarh, India (spervisr frm AMU and spervisr frm Indian Institte f Tehnlgy, Delhi, India). 996: Pst-Gradated frm Zakir Hssain llege f Engineering & Tehnlgy (Z.H..O.E.T.), AMU, Aligarh, India, with a Master's degree in Mehanial Engineering (speializatin in Indstrial Engineering). 992: Gradated frm Z.H..O.E.T., AMU, India, with a Bahelr's degree in Mehanial Engineering. Experiene Wrking as a falty f Mehanial Engineering at University Plytehni, AMU, India, sine