FREE SOFTWARE FOR DECISION ANALYSIS A Software Package for Data Envelopment Models

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1 FREE SOFTWARE FOR DECISION ANALYSIS A Softwae Package fo Data Envelopment Model Lda Anglo Meza Inttto de Cênca e Tecnologa, Unvedade Vega de Almeda, Ra Ibtna 08, Maacanã,Ro de Janeo, Bal Lz Bond Neto Depto. de Engenhaa Elétca e de Telecomncaçõe Unvedade do Etado do Ro de Janeo, Ra São Fancco Xave, 524, Bl. A, Sala 5036, Maacanã, Ro de Janeo, Bal João Calo Coea Baptta Soae de Mello Depto. de Engenhaa de Podção Unvedade Fedeal Flmnene, Ra Pao da Páta, 56, São Domngo, Nteó, Bal Elane Gonçalve Gome Pogama de Engenhaa de Podção Unvedade Fedeal do Ro de Janeo & Embapa Montoamento po Satélte, Av. D. Júlo Soae de Ada, 803, Paqe São Qno, Campna, SP, Bal Pedo Henqe Govêa Coelho Depto. de Engenhaa Elétca e de Telecomncaçõe Unvedade do Etado do Ro de Janeo, Ra São Fancco Xave, 524, Bl. A, Sala 5036, Maacanã, Ro de Janeo, Bal Kewod: Abtact: Softwae, Data Envelopment Anal. Data Envelopment Anal baed on lnea pogammng poblem (LPP) n ode to fnd the effcenc of Decon Makng Unt (DMU). Th poce can be comptatonall ntene, a a LPP ha to be n fo each nt. Bede, a tpcal DEA LPP ha a lage nmbe of edndant contant concenng the neffcent DMU. That elt n degeneate LPP and n ome cae, mltple effcent olton. The developed wok ntend to to fll ot a gap n cent DEA oftwae package.e. the lack of a pece of oftwae capable of podcng fll elt n clac DEA model a well a the capablt of ng moe advanced DEA model. The oftwae package nteface a well a the model and olton algothm wee mplemented n Delph. Both bac and advanced DEA model ae allowed n the package. Bede the man modle that nclde the DEA model, thee an addtonal modle contanng ome model fo decon ppot ch a the mltctea model called Analtc Heachc Poce (AHP). The developed pece of oftwae wa coned a FSDA Fee Softwae fo Decon Anal. INTRODUCTION Data Envelopment Anal (DEA) an appoach to evalate effcenc that e Lnea Pogammng Poblem (LPP) whoe elt ae the pefomance of Decon Makng Unt (DMU). In ecent ea thee ha been nceang nteet fo DEA and t coepondng LPP. Seveal eal cae applcaton have led to a need fo new development n the clac model, the CCR (Chane et. al. 978) and BCC (Banke et al. 984 model, n ode to nclde new taton. Th eveal eeache have been awae to the elt elded b the model n tem of effcenc ndexe, benchmak and taget. On the othe hand, a LPP ha to be olved fo each DMU. So the tak fo effcenc evalaton can Anglo Meza L., Bond Neto L., Calo Coea Baptta Soae de Mello J., Gonçalve Gome E. and Henqe Govêa Coelho P. (2005). FREE SOFTWARE FOR DECISION ANALYSIS - A Softwae Package fo Data Envelopment Model. In Poceedng of the Seventh Intenatonal Confeence on Entepe Infomaton Stem, page DOI: / Copght c ScTePe 207

2 ICEIS ARTIFICIAL INTELLIGENCE AND DECISION SUPPORT SYSTEMS be had and ve tme conmng wthot an adeqate pecfc pece of oftwae, patclal fo a lage nmbe of DMU. Seveal oftwae package wee developed o to mnmze thoe poblem. Howeve, n eveal taton, the elt podced b thoe package ethe ae not complete o ae not content to the one podced b othe pece of oftwae fo the ame model. That lead to ome qeton abot the coectne of the comptng mplementaton of the model n thoe oftwae. That motvate the need fo developng a elable oftwae package eldng complete elt and coveng new theoetcal development egadng DEA model. Bede the capablt to cove the clac DEA model and podcng complete elt, t alo nclde advanced model that wee not condeed b othe DEA oftwae package (Anglo-Meza et al., 2003a). The cent veon of the oftwae package peented n Potgee langage and called SLAD (Softwae Lve de Apoo à Decão) althogh a fte eleae n Englh alo nde development. The SLAD wa wtten n Delph 7.0 de manl to allow obect Pacal codng fo wtng the Smplex algothm to olve LPP and alo to t capablt to deal wth gaphc. The developed oftwae package wa hown to be ve efl fo tetng new model and ha been ed n man pape wtten b the atho. 2 DATA ENVELOPMENT ANALISYS Data Envelopment Anal (DEA) wa developed b Chane et al. (978) and a methodolog that e lnea pogammng fo the compaatve evalaton of DMU effcence The DEA ppoe to compae a cetan nmbe of DMU pefomng mla tak and that dtnghe themelve n the nmbe of ed npt and the nmbe of podced otpt. Thee ae bacall two clac DEA model: the Contant Retn Scale (CRS) model alo known a CCR (Chane, Coope and Rhode, 978) and the Vaable Retn Scale (VRS) model o BCC (Banke, Chane and Coope, 984). The ft model conde contant cale etn and the econd one vaable cale etn and doe not ame popotonalt among npt and otpt. Each k th DMU, k =,..., n, condeed to be a podcton nt that e n npt x k, =,,, to podce m otpt k, =,,. The CCR model decbed b () maxmze the ato between a lnea combnaton of otpt and a lnea combnaton of npt wth the contant that fo each DMU that ato can not be geate than one. So fo a patcla DMU o, h o t effcenc; x o and o ae t npt and otpt and v and ae the calclated weght fo the npt and otpt. max = = h, v 0 o bect to = k k = =,, o o k =,..., n () Afte ome mathematcal manplaton, the model can be ewtten, eldng n a Lnea Pogammng Poblem (LPP) a hown n (2). = h bect to k = =, v 0 max o o = = =, k o 0, k =,..., n (2) A a LPP olved fo each DMU, fo n DMU n LPP ae olved, wth + decon vaable. The model t peented the ba fo all othe DEA model. Bede the effcenc ndex, DEA model eld fo each DMU the vaable weght, benchmak, and taget fo the neffcent DMU. The lat two element ae detemned fom the vale of the dal vaable.e. b olvng the dal LPP o b the e of the complement lack theoem. The et of all thoe elt defne what we call n th pape complete elt. In ecent ea, oftwae package wee developed de to the geat nteet and the lage nmbe of applcaton ng the DEA appoach. Thoe pogam nclde motl bac model and wee developed to avod the effot of nnng epaatel LPP wthot the ntegaton povded b DEA package oftwae n ode to get the fnal evalaton. On the othe hand, theoetcal development have been made and ae wdel ed. 208

3 FREE SOFTWARE FOR DECISION ANALYSIS: A Softwae Package fo Data Envelopment Model Fo example, weght etcton (Allen et al, 997) allow the nclon of a po nfomaton,.e. bectve apect can be ncopoated wthn DEA model that ae eentall ve obectve. Th the e of ome advanced development have been eental fo DEA anal and ome oftwae package alead nclde ome advanced model. Howeve, n ome cae dffeent oftwae nnng the ame model elded dffeent elt o elt not followng the model contant whch make them nelable. That alo happened even fo the bac model. Mot oftwae package how onl effcenc ndexe and taget leavng ot the vaable weght whch mght be efl n a deep aement of the DMU and fo ad n late theoetcal development (Anglo-Meza e Ln, 2000). Sch poblem motvated the atho to bld a package oftwae n ode to podce complete elt nvolvng the bac model CCR and BCC (npt o otpt oented, Coope et al, 2000), wth open code acce to check evental poblem o dcepance among elt and the capablt to nclde model fo new theoetcal advanced development. 3 THE FSDA FREE SOFTWARE FOR DECISION ANALYSIS A fndamental tep fo the development of a DEA oftwae the etp and choce of the algothm to olve the LPP aocated wth the poblem. The Smplex algothm ve popla fo olvng LPP, o the nteo pont algothm patclal fo lage cale LPP. The FSDA e the Smplex algothm fo the olton of lnea pogammng poblem. The Smplex algothm wa ceated b Dantzg and pblhed n 948. Befl, accodng to Dantzg (963) a lnea pogammng poblem can be edced to a combnato poblem n ch a wa that the method fo eachng the optmm olton pefomed b tetng a eqence of combnaton n whch the vale of the obectve fncton ncemented gadall. An optmm olton condeed to be eached afte a cetan nmbe of teaton not geate than the nmbe of contant o the nmbe of vaable whateve the laget. The FSDA e Kenz et al (Kenz et al, 97) appoach that nclde a botne to avod degeneatng poblem, a common poblem n DEA model de to the tpcal tcte of the nvolved LPP that peent a lage nmbe of edndant contant fo the neffcent DMU. In man cae that lead to mltple optmal olton. Matce and vecto ae ed to epaate the vale of the coeffcent coepondng to the bac vaable (vaable that ae pat of the olton) and to the non bac vaable ( vaable whch ae not pat of the olton and whoe vale ae et to zeo). Moeove, two lt ae kept contanng thoe two vaable whch ae pdated at each algothm teaton. The mentoned pocede ha two phae fo evalatng the olton of a LPP. The ft one eache an ntal bac olton. The econd tat fom the ntal bac olton fond n pat one. Both phae have thee tep. The ft tep detemne the vale of a econda obectve fncton that wll be ed n the othe two tep and alo a vaable that wll ente the bae. The econd tep locate the pvot element takng nto condeaton a poble degeneaton n the coepondng LPP. If the pvot element can not be fond a meage ent and the each end. The lat tep pdate the matce n ode to change the et of bac and non bac vaable. Thee ae thee poble otcome fo a gven LPP: an optmal olton acheved, no olton acheved, n thoe cae the LPP ad to be non lmted o no ntal vecto poble whch mean the LPP not feable. The algothm ed n the FSDA oftwae now peented n detal: Phae : Detemne an ntal feable bac olton and check f that olton the ogn, othewe each one. Step : Seach a vaable to ente the bae of the ntal feable olton and evalate a econda obectve fncton. If the cent olton feable go to phae 2, othewe f thee a vaable to be ent nto the bae go to tep 2, othewe the LPP non feable and the pogam end and a meage ent to the e. Step 2: Locate pvot element f npt go to tep 3, othewe END, LPP not feable. Phae 2: Thee an ntal bac olton go to tep. Step : Seach a vaable to be n the bae and evalate the ecnda obectve fncton. If the cent olton optmm then END, othewe f thee a vaable to be n the bae go to tep 2, othewe LPP non lmted. 209

4 ICEIS ARTIFICIAL INTELLIGENCE AND DECISION SUPPORT SYSTEMS Step 2: Locate pvot element. Step 3: Update the et of bac and non bac vaable and go to tep. It hold be teed that n bac DEA model (CCR o BCC, whateve oentaton) at leat one olton can alwa be fond wth a poblt of an nfnte nmbe of optmm olton whch qte feqent. In that cae, onl the ft optmm olton hown to the e. In the cae of model wth etcton to the weght, thee a poblt of appeang non feable LPP once the addtonal contant can tn the LPP ognall peentng an optmm olton to a non feable LPP. In that cae, a meage ent and the e ha the choce of changng the etcton and epeat the poce. The method fo olvng the LPP nqe, what change the fomat of the LPP, once a dffeent LPP pefomed fo each DEA model. The data npt have to be pt n the pope fomat n a matx tcte dependng on the ed model. The data odeng poce n the efeed matx n the appopate fomat the mot dffclt pat n the oftwae mplementaton. 3. Softwae Decpton The FSDA( SLAD n Potgee veon) openng wndow hown n Fge and wa developed fo Wndow platfom wth Delph 7.0. It capable fo dealng wth 50 DMU and 20 npt o otpt vaable. Althogh fo othe eeach aea 50 DMU mght be nffcent fo DEA applcaton that vale able to deal wth lage cale taton nce n the lteate thee ae few applcaton dealng wth moe than a 00 DMU. In mot applcaton 0 vaable ae ffcent. The oftwae package allow the data npt to be enteed n two wa: dectl nde the pogam ng a table wth the choce of the nmbe of DMU and vaable, and b the e of a txt fle havng the data that ae loaded to the mentoned table hown n fge 2. Fge 2 alo how the poble choce of bac model (CCR o BCC) and oentaton (npt o otpt) coveng the bac and mot ed model. Moeove, advanced opton ae alo nclded n the oftwae a one of the obectve of the FSDA package to allow new DEA development that ma be choen along wth the model and t oentaton. The e can alo the choce of ng weght etcton, o condeng data ncetant. The advanced opton of weght etcton lead the e to an addtonal wndow ndcatng the nmbe of etcton to be nclded n the choen model. The choce of ncetant n ome o all vaable alo lead the e to anothe wndow, howng the data npt. A DEA anal wth ncetante e vaaton nteval fo ome o all vaable of anal. Relt fo an model, advanced o not, ae peented n an addtonal wndow a lltated n fge 3. That wndow how the effcenc ndexe fo all DMU. Bede, addtonal opton ae peented to how othe elt: nveted fonte, that expand the elt wndow to nclde the effcenc ndex n the nveted fonte and the compoed ndex (tandad and nveted effcence); the vaable weght; the benchmak of all DMU (effcent and neffcent) and the taget fo the DMU ncldng the lack and the level that the vaable have to each fo tnng the DMU effcent Fge : FSDA (SLAD) Openng Wndow 20

5 FREE SOFTWARE FOR DECISION ANALYSIS: A Softwae Package fo Data Envelopment Model Fge 2: Opton wndow of FSDA (SLAD). Fge 3: Relt wndow of FSDA (SLAD). It hold be noted that the elt wndow t how the effcence of the DMU wheea the othe elt ae hown onl when aked fo b clckng the appopate con on the ame wndow. That wa done fo the ake of eang the valzaton of the elt once the peentaton of the complete elt n one wndow mght be dffclt to ntepet the elt patclal fo a lage nmbe of vaable and DMU. In the data npt wndow thee anothe opton, not et mentoned, that allow the e of mltctea model. B choong that opton the wndow change colo to ndcate the e the bttton of the DEA appoach fo the mltctea appoach. A th modle nde development, the onl avalable method the Analtc Heaqc Poce (AHP) accodng to Clímaco et al. (996), bt othe method wll be nclde n de tme. 4 CONCLUSIONS The gowng nteet n ecent ea of DEA appoach fo the evalaton of effcenc and the theoetcal development de to eal wold applcaton have ndcated the need of a elable oftwae package that nvolve ontl a fendl e nteface, eldng elable, content and complete elt and havng the capablt to wok wth moe advanced model. Thee ae DEA oftwae package bt the lack of complete and elable elt n thoe oftwae led to the development of a 2

6 ICEIS ARTIFICIAL INTELLIGENCE AND DECISION SUPPORT SYSTEMS oftwae package that met the demand of the atho of th pape. The FSDA (SLAD) wa wtten n Delph 7.0 and e the Smplex algothm to olve the LPP eqed b DEA. The oftwae nclde, bede the clac model, advanced model ch a DEA model wth weght etcton a well a ecent model developed b the atho ch a nveted fonte and data ncetante. The complete elt podced b the oftwae ae table fo a deep anal of the DMU and cold alo eve a a ba fo the development of new theoetcal model. The pefomance of the FSDA n lage cale poblem ha been atfacto, e. g. the tme epone fo poblem nvolvng 80 DMU and 7 vaable wa le than one econd. A geat motvaton of the FSDA fo the atho the poblt of ncldng othe model n the package that ha been ve efl fo the atho n the new development and n the tetng of new model. Fnall, new model developed b the atho ae nde wa to be condeed n the FSDA ch a the DEA-GSZ model (Ln et al., 2003), a well a the expanon of the mltctea modle. Chane, A., Coope, W. W., Rhode, E., 978. Meang the Effcenc of Decon Makng Unt. Eopean Jonal Of Opeatonal Reeach, 2(6), Clmaco, J.,Antne, C.H., Alve, M.J.G., 996. Mltctea Sppot to Decon. Facldade de Economa da Unvedade de Comba e INESC. (n Potgee) Coope, W.W., Sefod, L.M., Tone, K., Data Envelopment Anal: A Compehenve Text wth Model, Applcaton, Refeence and DEA-Solve Softwae. Klwe Academc Pblhe, USA. Dantzg, G.B., 963. Lnea Pogammng and Extenon, Pnceton, N.J.: Pnceton Unvet Pe. Kenz, H.P., Tzchach, H.G., Zehnde, C.A., 97. Nmecal Method of Mathematcal Optmzaton, Academc Pe, New Yok. Ln, M.P.E., Gome, E.G, Soae de Mello, J.C.C.B., Soae de Mello, A.J.R., Olmpc ankng baed on a Zeo Sm Gan DEA model. Eopean Jonal of Opeatonal Reeach, 48 (2), REFERENCES Allen, R., Athanaopol, A., Don, R.G. et al., 997. Weght etcton and Vale dgement n Data Envelopment Anal: Evolton, Development and Fte Decton. Annal of Opeaton Reeach, 73, Anglo-Meza, L, Ln, M.P.E., Data Envelopment Anal (DEA) ng the Fonte Analt. Peqa Opeaconal, 9 (2), (n Potgee) Anglo-Meza, L., Gome, E.G., Soae de Mello, J.C.C.B., Bond Neto, L., 2003b. DEA Bode Havng Doble Envelopment n the Std of the Evolton of the Ro-São Palo Shttle Sevce.In: Ana do XVII Congeo de Peqa e Enno em Tanpote, Ro de Janeo, RJ,Novembo. (n Potgee) Anglo-Meza, L.A., Bond Neto, L., Soae de Mello, J.C.C.B., Gome, E.G., 2003a. SLAD - Integated Stem fo Decon Sppot: A Comptatonal Implementaton of Data Envelopment Anal Model. In I Enconto Regonal da Socedade Balea de Peqa Opeaconal, Cadeno de Remo, 24, Nteó, RJ, Bazl. (abtact n Potgee) Banke, R. D., Chane, A., Coope, W. W., 984. Some Model fo Etmatng Techncal and Scale Ineffcence n Data Envelopment Anal. Management Scence, 30(9),