Technology Selection in the Presence of Imprecise Data, Weight Restrictions, and Nondiscretionary Factors

Transcription

1 Techolog Selecto the Peece of Impece Data Weght Retcto ad Nodcetoa Facto Reza Fazpoo Sae Depatmet of Idutal Maagemet Facult of Maagemet ad Accoutg Ilamc Azad vet-kaa Bach Kaa Ia P. O. Bo: Tel: 98 (26) Fa: 98 (26) Emal: Abtact Techolog electo a mpotat pat of maagemet of techolog. Tadtoall techolog electo model ae baed o cadal data th le empha o odal data. Hoeve th epect to techolog electo complet empha ha hfted to the multaeou codeato of cadal ad odal data techolog electo poce. The applcato of Data Evelopmet Aal (DEA) fo techolog electo poblem baed o total fleblt of the eght. Hoeve the poblem of allog total fleblt of the eght that the value of the eght obtaed b olvg the uetcted DEA pogam ae ofte cotadcto to po ve o addtoal avalable fomato. O the othe had cuet model of techolog electo poblem aume complete dcetoa of deco makg ctea ad do ot aume techolog electo the codto that ome facto ae odcetoa. To elect the bet techologe the peece of cadal data odal data odcetoa facto ad eght etcto the obectve of th pape to popoe a e pa of Auace Rego-Nodcetoa Facto-Impece Data Evelopmet Aal (AR-NF-IDEA) model. A umecal eample demotate the applcato of the popoed method. Keod: Techolog electo Impece data evelopmet aal Nodcetoa facto Auace ego. Itoducto Selectg the ght techolog ala a dffcult tak fo deco make. Techologe have vaed tegth ad eakee hch eque caeful aemet b the puchae. Techolog electo model help deco make chooe betee evolvg techologe. The eao fo a pecal focu o techolog electo due to the complet of the evaluato hch clude tategc ad opeatoal chaactetc. Tool that code a de age of dmeo have bee developed fo evaluatg thee ma chaactetc hch clude cot qualt fleblt tme etc. Oe of the ue of Data Evelopmet Aal (DEA) techolog electo. I ogal DEA fomulato the aeed Deco Makg t (DM) ca feel chooe the eght o value to be

2 aged to each put ad output a a that mamze t effcec ubect to th tem of eght beg feable fo all othe DM. Th feedom of choce ho the DM the bet poble lght ad equvalet to aumg that o put o output moe mpotat tha a othe. The fee mputato of put-output value ca be ee a a advatage epecall a fa a the detfcato f effcec coceed. If a DM (techolog) fee to chooe t o value tem ad ome othe techolog ue th ame value tem to ho that the ft techolog ot effcet the a toge tatemet beg made. The advatage of full fleblt detfg effcec ca be ee a dadvatage the detfcato of effcec. A effcet techolog ma become o b agg a zeo eght to the put ad/o output o hch t pefomace ot. Th mght ot be acceptable b Deco Make (DM) a ell a b the aalt ho afte pedg tme a caeful electo of put ad output ee ome of them beg completel eglected b techolog. DM ma have techolog electo poblem value udgmet that ca be fomalzed a po ad theefoe hould be take to accout techolog electo. Thee value udgmet ca eflect ko fomato about ho the facto ued b the techologe behave ad/o "accepted" belef o pefeece o the elatve oth of put output o eve techologe. Fo eample uppoe e at to bu a dot-mat pte ad e ma gve the pce make tade-off amogt the peed pt qualt ad put buffe (memo) hch ae ome of the mot mpotat featue that dtguh 24-p dot-mat pte. We ma ot code the pte memo featue to be ve vtal becaue dot-mat pte ol ue memo a a buffe pace to doload fot. Thu moe codeato gve to peed ad pt qualt. Pehap the pte mpl ued to pt log pogam code o data-bae ltg o that peed outegh pt qualt. Theefoe techolog electo copoato of value udgmet ve mpotat ad gog th apect ma lead to baed effcec eult. To avod the poblem of fee (ad ofte udeable) pecalzato put ad output eght hould be cotaed DEA. Nevethele techolog electo model ae baed o cadal data th le empha o odal data. Hoeve th epect to techolog electo complete empha ha hfted to the multaeou codeato of cadal ad odal data techolog electo poce. O the othe had dcetoa model fo evaluatg the effcec of techologe aume that all ctea ae dcetoa.e. cotolled b the maagemet of each techolog upple ad vaed at t dceto. Thu falue of a techolog to poduce mamal output level th mmal put coumpto eult a deceaed effcec coe. I a ealtc tuato hoeve thee ma et eogeoul fed o odcetoa ctea that ae beod the cotol of a maagemet. Fo eample f the techolog ude aal ha lmted umbe of upple (olgopoltc evomet) the cot of techolog ll be a odcetoa facto.e. cot educto ll ot be acceptable fom the techolog upple pepectve. Th pape depct the techolog electo poce though a Impece Data Evelopmet Aal (IDEA) model hle allog fo the copoato of odcetoa facto ad eght etcto. 2

3 The obectve of th pape to popoe a e pa of Auace Rego-Nodcetoa Facto- Impece Data Evelopmet Aal (AR-NF-IDEA) model fo electg the bet techologe the peece of eght etcto odcetoa facto ad mpece data. Th pape poceed a follo. I Secto 2 lteatue eve peeted. Secto 3 dcue the popoed method fo techolog electo. Numecal eample ad cocludg emak ae dcued Secto 4 ad 5 epectvel. 2. teatue eve Some mathematcal pogammg appoache have bee ued fo techolog electo the pat. Ra et al. [] addeed applcato of a fuzz Goal Pogammg (GP) cocept to model the poblem of mache-tool electo ad opeato allocato th eplct codeato gve to obectve of mmzg the total cot of machg opeato mateal hadlg ad etup. A geetc algothm baed appoach adopted to optmze the fuzz GP. Cha et al. [2] peeted a fuzz GP appoach to model the mache tool electo ad opeato allocato poblem of Fleble Maufactug Stem (FMS). Hoeve oe of the GP poblem ae fom a pecfc techcal equemet. Afte the DM pecf the goal fo each elected cteo the mut decde o a peemptve pot ode of thee goal.e. detemg hch ode the goal ll be attaed. Fequetl uch a po put mght ot poduce a acceptable oluto ad the pot tuctue ma be alteed to eolve the poblem oce moe. I th faho t ma be poble to geeate a oluto teatvel that fall atfe the DM. fotuatel the umbe of potetal pot eodeg ma be ve lage. A techolog electo poblem th fve facto ha up to 2 pot eodeg. Gog though uch a laboou poce ould be cotl ad effcet. Jagaatha et al. [3] popoed a tegated fuzz Aaltc Heach Poce (AHP) baed appoach to facltate the electo ad evaluato of e maufactug techologe the peece of tagble attbute ad ucetat. Hoeve AHP ha to ma eakee. Ft ubectvt of AHP a eake. Secod AHP could ot clude teelatohp th the ctea the model. Becaue of the complet of the deco makg poce volved techolog electo all the afoemetoed lteatue eled o ome fom of pocedue that ag eght to vaou pefomace meaue. The pma poblem aocated th abta eght that the ae ubectve ad t ofte a dffcult tak fo the DM to accuatel ag umbe to pefeece. It a dautg tak fo the DM to ae eghtg fomato a the umbe of pefomace ctea ceaed. Theefoe a moe obut mathematcal techque that doe ot demad too much ad too pece fomato.e. odal pefeece tead of cadal eght fom the DM ca tegthe the techolog evaluato poce. To th ed Khoua [4] popoed a deco model fo techolog electo poblem ug a to-phae pocedue. I phae DEA ued to detf techologe that povde the bet combato of vedo pecfcato o the pefomace paamete of the techolog. I phae 2 a MADM model ued to 3

4 elect a techolog fom thoe detfed phae. Khoua [4] ued MADM to elect a obot fom the effcet obot. Bake ad Tallu [5] popoed a alteate methodolog fo techolog electo ug DEA. The addeed ome of the hotcomg the methodolog uggeted b Khoua [4] ad peeted a moe obut aal baed o co-effcece DEA. Hoeve a facto hch pobl educe the uefule of co-effcec that the eght that mamze DM mple effcec ma be ot uque. The ame eult ca be acheved va dffeet oluto. Becaue the choce of the eght fluece the co-effcec meauemet fo the othe DM t cauale ma mpl dtoted udgmet. Ramaatha [6] toduced the ue of DEA fo thezg the dvee chaactetc of eeg uppl techologe to a gle obectve effcec coe. It ha bee foud that of the eght techologe codeed uclea ad ola photovoltac techologe ee ated to be the mot elatvel effcet. To elect the bet techologe the etece of both cadal ad odal data Fazpoo Sae [7] popoed a ovatve appoach hch baed o IDEA. Tallu et al. [8] popoed a fameok hch baed o the combed applcato of DEA ad opaametc tattcal pocedue fo the electo of FMS. The tegth of th methodolog ae that t copoate vaablt meaue the pefomace of alteatve tem povde DM th effectve alteatve choce b detfg homogeeou goup of tem ad peet gaphc ad fo bette tepetato of eult. Sefod ad Zhu [9] eteded the cotet-depedet DEA b copoatg value udgmet to the attactvee ad poge meaue. The method a appled to meaug the attactvee of 32 compute pte. The hoed that the attactve meaue help () cutome to elect the bet opto ad () pte maufactue to detf the potetal competto. To elect the bet advaced maufactug techologe Kaak ad Ahka [] toduced a mult-ctea deco methodolog that ca tegate multple output uch a vaou techcal chaactetc ad qualtatve facto th a gle put uch a cot. The model deved fom the co-effcec aal hch oe of the bache of DEA model. Sak ad Tallu [] toduced a applcato of DEA that code both cadal ad odal data fo the evaluato of alteatve FMS. The DEA model popoed tegate both qualtatve ad quattatve data. The tal DEA model baed o the ok of Cook et al. [2]. To mpove the dcmato poe of DEA the etece of both cadal ad odal facto a addtoal DEA model elg o pae compao of FMS a popoed. The eult of the pae compao model ae aggegated though co-effcec meaue. Tallu ad Yoo [3] toduced advaced maufactug techolog electo poce. The popoed a combato of a coe-ato DEA model ad a e methodologcal eteo DEA hle allog fo the copoato of pefeece of deco make. Shag ad Sueoh [4] utlzed a combato of AHP ad DEA fo electo of FMS. The model ued AHP to etct facto eght DEA. Hoeve the could ot olve the dffcult th multple optmum oluto. Bagla ad Peto [5] popoed the ue of DEA fo electo of dutal obot. The methodolog baed o a equetal dual ue of DEA th etcted eght. To etct the eght the uggeted a ule of thumb. 4

5 Hoeve all the afoemetoed efeece ae baed o complete dcetoa of deco makg ctea (facto) ad do ot code techolog electo the peece of eght etcto mpece data ad odcetoa facto. Although [6] ad [7] popoed to emplo DEA fo electg the bet techologe the etece of odcetoa facto but the dd ot toduce a model hch elect the techologe the peece of eght etcto mpece data ad odcetoa facto. I othe od the dd ot code eght etcto ad mpece data. To the bet of autho koledge thee ot a efeece that dcue techolog electo the peece of eght etcto mpece data ad odcetoa facto. The appoach peeted th pape ha ome dtctve featue. The popoed model code cadal ad odal data fo techolog electo. The popoed model code odcetoa facto fo techolog electo. The popoed model code eght etcto fo techolog electo. Techolog electo a taghtfoad poce caed out b the popoed model. Impece data eght etcto ad odcetoa facto ae codeed multaeoul. The popoed model deal th mpece data a dect mae. The eult of th pape ae ot ol valuable to bue but to techolog upple a ell. The bue ll be gve the advce to avod ceta techologe a beg effcet fo oe o moe eao. The techolog upple ll ko f the competto peumptve techolog upeo to t o ad that cae hat ubtatal mpovemet ae equed ode to tu t effcet techolog to a effcet oe. A applcato of the methodolog ha bee pefomed o a et of data eteved fom the fomato of 27 obot. 3. Popoed method fo techolog electo DEA popoed b Chae et al. [8] (CCR model) ad developed b Bake et al. [9] (BCC model) a appoach fo evaluatg the effcece of DM. Th evaluato geeall aumed to be baed o a et of cadal (quattatve) output ad put facto. I ma eal old applcato (epecall techolog electo poblem) hoeve t eetal to take to accout the etece of odal (qualtatve) facto he edeg a deco o the pefomace of a DM. Ve ofte t the cae that fo a facto uch a vedo eputato oe ca at mot povde a akg of the DM fom bet to ot elatve to th attbute. The capablt of povdg a moe pece quattatve meaue eflectg uch a facto geeall beod the ealm of ealt. I ome tuato uch facto ca be legtmatel quatfed but ve ofte; uch quatfcato ma be upefcall foced a a modelg coveece. I tuato uch a that decbed the data fo ceta fluece facto (put ad output) mght bette be epeeted a ak poto a odal athe tha umecal ee. Refe aga to the vedo 5

6 eputato eample. I ceta ccumtace the fomato avalable ma pemt oe to povde a complete ak odeg of the DM o uch a facto. Theefoe the data ma be mpece. O the othe had oe eou daback of DEA applcato techolog electo ha bee the abece of DM udgmet allog total feedom he allocatg eght to put ad output data of techolog ude aal. Th allo techologe to acheve atfcall hgh effcec coe b dulgg appopate put ad output eght. The mot depead method fo codeg udgmet DEA model pehap the eght etcto cluo. Weght etcto allo fo the tegato of maageal pefeece tem of elatve mpotace level of vaou put ad output. The dea of codtog the DEA calculato to allo fo the peece of addtoal fomato aoe ft the cotet of boud o facto eght DEA multple de poblem. Th led to the developmet of the coe-ato (Chae et al. [2]) ad Auace Rego (AR) model (Thompo et al. [2]). Both method cota the doma of feable oluto the pace of the vtual multple. Weght etcto ma be appled dectl to the DEA eght o to the poduct of thee eght th the epectve put o output level efeed to a vtual put o vtual output. Retcto o vtual eght ee popoed ft b Wog ad Beale [22]. Saco ad Do [23] ugget le th Thompo et al. [2] the ue of vtual auace ego cocludg that the ca ovecome poblem of feablt a ell a tepetato of taget ad effcec coe hlt etag the beeft of the atual epeetato of pefeece tuctue. I th pape th cocept ued to etct the fleblt of the techologe (DM) electg the eght. To the bet of autho koledge the ol pape that dcu IDEA the peece of eght etcto ae the ok of Coope et al. [24] Coope et al. [25] ad Coope et al. [26]. I thee pape the AR-IDEA model a developed to deal ot ol th mpece data but alo th eght etcto. Hoeve the method make the DEA model become ve complcated becaue of geat umbe of data tafomato ad vaable alteato. Futhemoe dealg th the bouded data the model eque that bouded output ad put at leat have oe eact (mamum) data. Recetl Wag et al. [27] developed a e pa of teval DEA model fo dealg th mpece data uch a teval data odal pefeece fomato fuzz data ad the mtue. Compaed th the IDEA model developed b Coope et al. [24] Coope et al. [25] ad Coope et al. [26] the teval DEA model ae much eae to udetad ad moe coveet to ue. Alo compaed th the teval DEA model developed b Depot ad Sml [28] the teval DEA model utlze a fed ad ufed poducto fote a a bechmak to meaue the effcece of all DM hch make the model moe atoal ad moe elable. Moeove the mea the teat odal pefeece fomato alo eem moe eaoable tha the a Zhu [29] dd. Hoeve Wag et al. [27] dd ot code eght etcto ad odcetoa facto. I th ecto a e pa of AR-NF-IDEA model popoed that ca ovecome the hotcomg metoed above to code odcetoa facto of the techologe (DM) hle mpece data 6

7 ad eght etcto ae peet. The fal effcec coe fo each DM ll be chaactezed b a teval bouded b the bet loe boud effcec ad the bet uppe boud effcec of each DM. Suppoe that thee ae DM to be evaluated. Each DM coume m put to poduce output. I patcula DM coume amout X { } of put ( m) ad poduce amout Y { } of output ( ). Wthout lo of geealt t aumed that all the put ad output data ad ( m; ; ) caot be eactl obtaed due to the etece of ucetat. The ae ol ko to le th the uppe ad loe boud epeeted b the teval [ ] ad [ ] hee > ad >. I ode to deal th uch a uceta tuato the follog pa of lea pogammg model have bee developed to geeate the uppe ad loe boud of teval effcec fo each DM (Wag et al. [27]): Maθ. t. o m v u u o u v ε o m v. () Maθ. t. o m v u u o u v ε o m v. (2) hee o the DM ude evaluato (uuall deoted b DM o ); u ad v ae the eght aged to the output ad put; θ o tad fo the bet poble elatve effcec acheved b DM o he all the DM ae the tate of bet poducto actvt hle θ o tad fo the loe boud of the bet poble elatve effcec of DM o. The cottute a poble bet elatve effcec teval [ ] ε the o-achmedea ftemal. θ. o θ o 7

8 Note that Model () deteme the poducto fote fo all the DM ad Model (2) ue the poducto fote a a bechmak to meaue the loe boud effcec of each DM. No matte hat value the put ad output take fo each DM ad o matte hat eght the model ue the effcece of DM ae all lmted to le tha o equal to oe. It alo ve clea fom Model () ad (2) that the cotat et ued to meaue the effcece of DM completel the ame hch l u made up of the data et {( ) ( m ) }. Hoeve t mut be poted out that both the bet ad the ot poducto actvte of DM o ae codeed (2) oe the cotat et ad the othe obectve fucto. I ode to udge hethe a DM DEA effcet o ot the follog defto gve. Defto. A DM DM o ad to be DEA effcet f t bet poble uppe boud effcec θ * o ; othee t ad to be DEA effcet f θ * <. o I (3) the vaou tpe of eght etcto that ca be appled to multple model ae ho. Abolute eght etcto δ v τ ( g ) ρ u η ( ) go Auace ego of tpe I (elatve eght etcto) v u α β ( h ) θ ζ ( h ) o v + u+ Auace ego of tpe II (put - output eght etcto) γ v u ( l) (3) The Geek lette ( δ τ ρ η α β θ ζ γ ) ae ue-pecfed cotat to eflect value udgmet the DM he to copoate the aemet. The ma elate to the peceved mpotace o oth of put ad output facto. The etcto (g) ad (h) (3) elate o the left had de to put eght ad o the ght had de to output eght. Cotat (l) lk dectl put ad output eght. Abolute eght etcto ae the mot mmedate fom of placg etcto o the eght a the mpl etct them to va th a pecfc age. Auace ego of tpe I lk ethe ol put eght (h ) o ol output eght (h o ). The elatohp betee put ad output eght ae temed auace ego of tpe II. Retcto o vtual put/vtual output aume the fom (4) hee the popoto of the total vtual output of DM accouted fo b output etcted to le the age [ a b ] ad the 8

9 popoto of the total vtual put of DM accouted fo b put etcted to le the age [ d c ]. a c u u v m v b d m (4) All popoed vtual eght etcto ca be decbed b the geeal et of t eght etcto applg to the DM o : m a v + o b o u k (5) hee a the eght of th put th eght etcto ad b the eght of th output th eght etcto. Th epeo ecapulate the thee dffeet kd of vtual eght etcto of the clafcato peeted belo. 3. Abolute vtual eght etcto Abolute vtual eght etcto volve cotag the vtual of a gle facto. Th appoach equvalet to ug popotoal vtual eght etcto appled to output vtual a output oeted model a o u. If appled alo to put vtual a output oeted model t ll ol be equvalet fo the DM that ae effcet (.e. o v of the fom: m ) ad theefoe defe the fote. The ae a o k a (6) b fo etctg the vtual put ; ad 9

10 b o k b (7) a fo etctg the vtual output. Thee etcto ae ueful he the DM able to pecf patcula boud o at to aue that a ceta facto atta a thehold value fo tace. 3.2 Vtual auace ego of tpe I Auace ego of tpe I vtual etcto lk vtual put o output to talate a odeg of pefeece. The ae m a v o b to lk vtual put ad b u o (8) a to lk vtual output. (9) Thee etcto ae ueful he the DM caot ag patcula boud to the facto but able to decde that a facto moe mpotat tha aothe tce a mpotat etc. 3.3 Vtual auace ego of tpe II Fall auace ego of tpe II vtual etcto lk the put-output dvde. The ca be talated b m a v + b u () o o hee at leat oe a ad oe b. Thee etcto ae ueful he thee a ko elatohp betee a put ad a output. Fo tace t ko that to poduce a ceta output oe eed to have a ceta level of a ceta put. The multple fomulato th the vtual eght etcto applg to all DM a belo

11 Maθ o u o. t. m v o m u v m b u a v + k () u v ε. Maθ o u o. t. m v o m u v m b u a v + k (2) u v ε. The evelopmet fomulato (dual poblem) of Model () ad (2) become

12 Mc o θo t k ρ m ε + ε. t. λ t b ρ + o (3) θ o o λ t a ρ m θo fee ρ λ + m. Mc o θo t k ρ m ε + ε. t. λ t b ρ + o (4) θ o o λ t a ρ m θo fee ρ λ + m. + hee θ o λ ρ ad ae the dual vaable. θ o adal put hkage facto (evetuall to become effcec meaue) ad λ { λ } vecto of DM loadg detemg "bet pactce" fo 2

13 the DM beg evaluated. c o tad fo the bet poble elatve effcec acheved b DM o he all the DM ae the tate of bet poducto actvt hle c o tad fo the loe boud of the bet poble elatve effcec of DM o. The cottute a poble bet elatve effcec teval [ c ] The vaable + hotfall amout of output ad c. ece amout of put. Fom the dualt theo lea pogammg fo a effcet DM o λ * > the optmal dual oluto mple that DM a ut of the pee goup. A pee goup of a effcet DM o defed a the et of DM that each the effcec coe of ug the ame et of eght that eult the effcec coe of DM o. It the etece of th collecto of DM that foce the DM o to be effcet. No uppoe that the put vaable ma be pattoed to ubet of dcetoa (D) ad odcetoa (N) vaable. Thu o o I { 2... m} I I I I Φ (5) D N D N The pa of AR-NF-IDEA model the fall gve b 3

14 4. fee (7)... fee (6).. N D o N t a o D t a o o o t b t m D t k o o Mc N D o N t a o D t a o o o t b t m D t k o o Mc λ ρ θ ρ λ ρ λ θ ρ λ ε ε ρ θ λ ρ θ ρ λ ρ λ θ ρ λ ε ε ρ θ

15 It to be oted that the θ o to be mmzed appea ol the cotat fo hch heea the cotat fo hch D N opeate ol dectl (a the hould) becaue the put level ae ot ubect to maageal cotol. Theefoe th ecogzed b eteg all o o N at the fed (obeved) value. Note that the lack N ae omtted fom the obectve fucto. Hece thee odcetoa put do ot ete dectl to the effcec meaue beg optmzed (6) ad (7). The ca evethele affect the effcec evaluato b vtue of the peece the cotat. Fo model (6) ad (7) t ot elevat to mmze the popotoal deceae the ete put vecto. Such mmzato hould be detemed ol th epect to the ubvecto that compoed of dcetoa put. I ode to udge hethe a DM DEA effcet o ot the follog defto gve. Defto 2. A DM DM o ad to be DEA effcet f t bet poble uppe boud effcec c othee t ad to be DEA effcet f c * <. * ; o o Theefoe oe ufed model that deal th all apect of the eght etcto mpece data ad odcetoa facto a dect mae have bee toducedf. No the method of tafomg odal pefeece fomato to teval data dcued o that the pa of AR-NF-IDEA model peeted th pape ca tll ok popel eve thee tuato. Suppoe ome put ad/o output data fo DM ae gve the fom of odal pefeece fomato. uall thee ma et thee tpe of odal pefeece fomato: () tog odal pefeece fomato uch a > k o > k hch ca be futhe epeed a χ ad k η hee χ > ad η > ae the paamete o the degee of pefeece tet povded b k deco make; (2) eak odal pefeece fomato uch a o ; (3) dffeece p q p q elatohp uch a l t o l t. Sce DEA model ha the popet of ut-vaace the ue of cale tafomato to odal pefeece fomato doe ot chage the ogal odal elatohp ad ha o effect o the effcece of DM. Theefoe t poble to coduct a cale tafomato to eve odal put ad output de o that t bet odal datum le tha o equal to ut ad the gve a teval etmate fo each odal datum. Note that the Model () ad () could be olved b oe of the optmzato techque (e.g. go oftae). Sce Model () ad () ae lea o the computato ll be doe quckl ad global optmum oluto ll be foud. Meahle educg umbe of put ad output ll eue bette dcmato betee the DM beg aalzed. Thee a ule of thumb hee the umbe of DM hould be at leat thee tme the total umbe of put ad output. Theefoe educg the dmeoalt of the poblem ll eult le DM beg effcet ad thu moe koledge gaed. 5

16 No code the tafomato of odal pefeece fomato about the output ( ) fo eample. The odal pefeece fomato about put ad othe output data ca be coveted the ame a. Fo eak odal pefeece fomato e have the follog odal elatohp afte cale tafomato: ˆ ˆ 2 ˆ σ 2 hee σ a mall potve umbe eflectg the ato of the poble mmum of { } to t poble mamum. It ca be appomatel etmated b the deco make. It efeed a the ato (8) paamete fo coveece. The eultat pemble teval fo each ŷ gve b ˆ [ ]. (9) σ Fo tog odal pefeece fomato > > > thee the follog odal elatohp afte cale tafomato: 2 ˆ ˆ χ ˆ ( ) + ad ˆ σ (2) hee χ a pefeece tet paamete atfg χ > povded b the deco make ad σ the ato paamete alo povded b the deco make. The eultat pemble teval fo each ŷ ca be deved a follo: ˆ σ χ χ [ ] th σ χ. (2) Fall fo dffeece elatohp the pemble teval ae the ame a thoe obtaed fo eak odal pefeece fomato. Though the cale tafomato above ad the etmato of pemble teval all the odal pefeece fomato coveted to teval data ad ca thu be copoated to the pa of AR- NF-IDEA model. The follog ubecto lt the omeclatue ued to fomulate the poblem ude codeato. 3.4 Nomeclatue... collecto of techologe (DM) o DM o the DM ude evaluato... the et of output... m the et of put the th output of th DM the th put of th DM k the th output of kth DM elated to tog odal pefeece fomato k the th put of kth DM elated to tog odal pefeece fomato p q the th output of the DM elated to eak odal pefeece fomato p q the th put of the DM elated to eak odal pefeece fomato 6

17 l t dffeece elatohp amog output l t dffeece elatohp amog put loe boud uppe boud θ o the bet poble elatve effcec acheved b DM o θ the loe boud of the bet poble elatve effcec of DM o o θ adal put hkage facto (evetuall to become effcec meaue of DM o ) o χ η the paamete o the degee of pefeece tet povded b deco make σ mall potve umbe eflectg the ato of the poble mmum of { } to t poble mamum ŷ the th output of th DM afte cale tafomato u eght of the th output v eght of the th put λ vecto of DM loadg detemg "bet pactce" fo the DM beg evaluated δ the loe boud of the th put eght τ the uppe boud of the th put eght ρ the loe boud of the th output eght η the uppe boud of the th output eght α the loe boud of elatve eght etcto of the th put β the uppe boud of elatve eght etcto of the th put θ the loe boud of elatve eght etcto of the th output ζ the uppe boud of elatve eght etcto of the th output γ put-output eght etcto of auace ego of tpe II a the loe boud of th vtual output b the uppe boud of th vtual output c the loe boud of th vtual put d the uppe boud of th vtual put t et of vtual eght etcto a the eght of th put th vtual eght etcto b the eght of th output th vtual eght etcto the vtual put the vtual output ρ dual vaable coceed to vtual eght etcto k et of th vtual eght etcto ece amout of put + o hotfall amout of output c the bet poble elatve effcec acheved b DM o 7

18 c o the loe boud of the bet poble elatve effcec of DM o. D ubet of dcetoa vaable N ubet of odcetoa vaable I D the ubet of dcetoa put I N the ubet of odcetoa put I the et ecto a umecal eample peeted. 4. Numecal eample I th ecto the popoed methodolog that ma be appled to a de age of techolog electo poblem ued fo obot electo ad llutated though a pevoul epoted dutal obot electo poblem. Fazpoo Sae [7] appled DEA to detf the optmal obot. I patcula th eample ued to ho ho odal data bouded data ad eght etcto a ell a odcetoa facto ca be combed to the oe ufed appoach povded b AR-NF-IDEA. The obot electo poblem addeed Fazpoo Sae [7] volve the evaluato of elatve effcec of 27 obot th epect to attbute cludg "load capact" ad "veloct" hch ae codeed ome ee a output ad "cot" ad "vedo eputato" hch ae codeed ome ee a put. "Vedo eputato" cluded a a qualtatve put hle "load capact" ll eve a the bouded data output. "Vedo eputato" a tagble facto hch ot uuall eplctl cluded evaluato model fo techolog. Th qualtatve vaable meaued o a odal cale o that fo tace techolog 23 gve the hghet ak ad techolog 7 the loet. Note that thee meaue ae ot ehautve b a mea but fequetl ued obot pefomace evaluato. I a applcato of th methodolog DM mut caefull detf appopate put ad output to be ued the deco makg poce. Aume that "cot" a cadal put ad becaue of lmtato of umbe of upple of th kd of techolog (olgopoltc evomet) th facto codeed a odcetoa facto. Table depct the obot attbute. 8

19 Robot No. (DM) Table. Related attbute fo 27 obot Iput Output oad * Vedo Reputato Capact 2 (kg) Cot ($) Veloct (m/) [5 65] [6 7] [4 5] [ 3] [45 55] [ 2] [4 5] [ 2] [9 2] [5 8] [25 35] [ 5] [8 2] [2 35] [4 55] [75 85] 7 8 [ 8] [9 5] [ 3] [ 4] [25 3] [.8.2] [2 4] [ 5] [8 2] [65 8] [9 22].75 * Rakg uch that 27 hghet ak loet ak ( 2 23 > 2 2 > > 2 7 ) 9

20 Suppoe the pefeece tet paamete ad the ato paamete about the tog odal pefeece fomato ae gve (o etmated) a η.2 ad σ. epectvel. g the tafomato 2 2 techque decbed pevou ecto a teval etmate fo "vedo eputato" of each techolog ca be deved hch ho the Table 2. Table 2. Iteval etmate fo the 27 obot afte the tafomato of odal pefeece fomato Robot No. Vedo Reputato (DM) [ ] 2 [ ] 3 [ ] 4 [ ] 5 [ ] 6 [ ] 7 [ ] 8 [ ] 9 [ ] [ ] [ ] 2 [ ] 3 [ ] 4 [ ] 5 [ ] 6 [ ] 7 [ ] 8 [ ] 9 [ ] 2 [ ] 2 [ ] 22 [ ] 23 [.947 ] 24 [ ] 25 [ ] 26 [ ] 27 [ ] Theefoe all the put ad output data ae o tafomed to teval umbe ad ca be evaluated ug the pa of AR-NF-IDEA model. Accodg to the deco of DM the mpotace of cot mut be geate tha vedo eputato. Aume that cot tce a mpotat a vedo eputato (vtual auace ego of tpe I). 2

21 Applg Model (6) ad (7) the effcec coe of obot (DM) ad pee goup of obot have bee peeted Table 3. The potve o-achmedea ftemal ε ha bee et to.. Table 3. The effcec teval ad pee goup fo the 27 obot Robot No. Effcec Iteval Pee goup (DM) [ ] [ ] [ ] [.29.26] 7 5 [ ] 27 6 [ ] [ ] [ ] [ ] 7 27 [.8977 ] N/A [ ] [ ] [ ] [ ] [ ] [ ] [.896 ] N/A 8 [.27.76] [ ] [.9 ] N/A 2 [ ] [ ] [ ] [ ] [ ] [.723.6] [.7265 ] N/A Baed o the defto 2 obot 7 2 ad 27 have the poblt to be DEA effcet. If the ae able to ue the mmum put to poduce the mamum output the ae DEA effcet (effcet cale); othee the ae ot DEA effcet. The emag 23 obot th elatve effcec coe of 2

22 le tha ae codeed to be effcet. Theefoe DM ca chooe oe o moe of thee effcet obot. Alo the lat colum of Table 3 povde pee goup fo effcet obot. Note that each DEA model eek to deteme hch of the DM defe a evelopmet uface that epeet bet pactce efeed to a the empcal poducto fucto o the effcet fote. DM that le o the uface ae deemed effcet DEA hle thoe DM that do ot ae temed effcet. DEA povde a compeheve aal of elatve effcece fo multple put-multple output tuato b evaluatg each DM ad meaug t pefomace elatve to a evelopmet uface compoed of othe DM. Thoe DM ae the pee goup fo the effcet DM ko a the effcet efeece et. A the effcet DM ae poected oto the evelopmet uface the effcet DM cloet to the poecto ad hoe lea combato compe th vtual DM fom the pee goup fo that patcula DM. The taget defed b the effcet poecto gve a dcato of ho th DM ca mpove to be effcet. The pee goup eve a a bechmak to ue eekg mpovemet fo effcet obot. Ieffcet obot upple ca ue thee eult fom a maketg pepectve. 5. Cocludg emak DEA ha pevoul bee ued fo the electo of techologe. Such a lea pogammg techque eem to be able to uppot maagemet the ctcal ad delcate tak of electg the mot effcet techolog amog a et of competg mult-attbute techologe. Th pape ha toduced a e pa of AR-NF-IDEA model ad emploed t fo techolog electo. Alo th pape popoed a tematc aal to povde pee goup fo effcet techolog upple. The popoed methodolog ca be appled fom both a bue ad techolog upple pepectve. The bue ca ue t a a tool electg the "bet" techolog. The techolog upple ca ue thee eult fom a maketg pepectve. A pecfc techolog upple ho acheve a hgh mea coe he compaed to the othe techolog upple ca ue thee eult fo pomotg the techolog. O the othe had f a patcula techolog pool pefomg the the techolog upple ca ue the aal fo bechmakg pupoe. Th eult ma mea that the techolog upple mut povde bette pefomace level at the ame cot. ltmatel the ablt of a techolog upple to ca the techologcal evomet ma lead to the etablhg of oud acto gudele amed at mpovg a techolog upple log-tem compettve poto. The poblem codeed th tud at tal tage of vetgato ad much futhe eeache ca be doe baed o the eult of th pape. Some of them ae a follo: Smla eeach ca be epeated fo techolog akg the peece of mpece data eght etcto ad odcetoa facto. I th tud the popoed model ha bee appled to a poblem elated to obot electo. Hoeve the ame model could be appled th mo modfcato to othe poblem elated to electo of 22

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