A Mathematical Programming Approach for Strategy Ranking
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1 A Mathematcal Pogammng Appoach fo Stategy Rankng Autho Saen, Reza Fazpoo Publshed 2009 Jounal Ttle Asa Pacfc Management Revew Copyght Statement APMR, Ths s the autho's veson of the Atcle. It s posted hee by pemsson of APMR fo you pesonal use. Not fo edstbuton. The defntve veson was publshed n A Mathematcal Pogammng Appoach fo Stategy Rankng, Asa Pacfc Management Revew, Volume 4, Issue 2, 2009, Downloaded fom nk to publshed veson Gffth Reseach Onlne
2 A Mathematcal Pogammng Appoach fo Stategy Rankng Reza Fazpoo Saen Depatment of Industal Management, Faculty of Management and Accountng, Islamc Azad Unvesty - Kaaj Banch, Kaaj, Ian, P. O. Box: Tel: 0098 (26) Fax: 0098 (26) E-mal: fazpou@yahoo.com
3 A Mathematcal Pogammng Appoach fo Stategy Rankng Abstact Befoe wokng out the fnal stategc plan, manages must consde seveal feasble altenatves and contemplate vaous factos behnd each of them. It s a vey complcated task to ank the stateges. The objectve of ths pape s to popose a method that allows stategy to be evaluated on both odnal and cadnal ctea on the one hand, and on the othe hand s to use a method fo ankng stateges wthout elyng on weght assgnment by decson makes. A numecal example demonstates the applcaton of the poposed method. Keywods: Stategc Management, Stategy ankng, Cadnal and odnal data, Mnmax eget-based appoach. Intoducton Stategc management can be consdeed as a collecton of decsons and actons taken by the decson make n consultaton wth all levels wthn the company to detemne the longtem actvtes of the company. The expeences of many busnesses, ndcate that the hghest poftablty levels ae found n busnesses that possess both types of compettve advantage at the same tme. In othe wods, busnesses that have one o moe value chan actvtes that tuly dffeentate them fom key compettos and also have value chan actvtes that let them opeate at a lowe cost wll consstently outpefom the vals that do not. So, the challenge fo today s decson makes s to evaluate and choose busness stateges based on coe competences and value chan actvtes that sustan both types of compettve advantage smultaneously. Among multple stateges, manages choose one of those stateges. If the analyss dentfed a clealy supeo stategy o f the cuent stategy wll clealy meet futue company objectves, then the decson s elatvely smple. Such claty s the excepton, howeve, and stategc decson makes often ae confonted wth seveal vable altenatves athe than the luxuy of a clea-cut choce. Unde these ccumstances, seveal ctea such as sk, ablty of stategy to satsfy ageed-on objectves wth the least esouces and the fewest negatve sde effects nfluence the stategc choce. Some appoaches have been used fo stategy selecton and ankng n the past. Cone and Kkwood (99) suveyed mult-attbute decson analyss applcatons n opeatons 2
4 eseach lteatue and found many of the applcatons to addess stategc decsons. Wnd and Saaty (980) appled the Analytc Heachy Pocess (AHP) to the potfolo decson of a fm whose management s concened wth the detemnaton of the desed taget potfolo and allocaton of esouces among ts components. Wnd (987) pesented an applcaton fo copoate stategy fo evaluatng stategc optons on multple and ntedependent objectves to ensue effectve utlzaton of esouces. Hastngs (996) povded a method fo ankng stategy on quanttatve, qualtatve and ntangble ctea based on AHP. Chou et al. (2005) poposed a fuzzy AHP to deve the weght of consdeed ctea and the fnal synthetc utlty values, and then anked the mpotance of the ctea as well as the sustanable development stateges. Howeve, AHP has two man weaknesses. Fst subjectvty of AHP s a weakness. Second AHP could not nclude nteelatonshp wthn the ctea n the model. Chen et al. (999) establshed a systematc appoach that ncopoates neual netwoks n conjuncton wth potfolo matces to assst manages n evaluatng and fomng stategc plans. Based on the pncple of dspesng sks, they also povded a lnea ntege pogammng model, whch helps n allocatng the annual budget optmally among poposed stateges. Howeve, the poposed appoach s computatonal buden. Meanwhle, the lnea ntege pogammng model consdes just two factos ncludng cost and poft of the stategy. Kajanus et al. (200) pesented the pncples of even swaps method and ts use was llustated by applyng t to a case of stategy selecton n a ual entepse n Fnland. Nevetheless, n the case of stateges abundance, the pawse compason between stateges s computatonal buden. In addton, the poposed method suffes fom subjectve judgments. Howeve, all of the abovementoned efeences suffe fom subjectve judgments. A technque that can deal wth both odnal and cadnal data and not elyng on weght assgnment by decson makes s needed to bette model such stuaton. A ctcal ssue of tadtonal appoaches ae the coect choce of the weghts. These must be assgned by the decson make o a decson commttee and ae often vey subjectve measues. The basc dea of DEA s that the weghts ae chosen by an optmzaton pocedue and not by the decson make. Weghts ae assgned optmally fo evey nput and output attbute. Ths makes the appoach moe obust aganst human nfeence. To the best of autho s knowledge, thee s not any efeence that deals wth stategy ankng wthout elyng on weght assgnment by decson makes. The objectve of ths pape s to popose a method that allows stategy to be evaluated on both odnal and cadnal ctea on the one hand, and on the othe hand s to use a method fo ankng stateges 3
5 wthout elyng on weght assgnment by decson makes. In summay, the appoach pesented n ths pape has some dstnctve contbutons. The poposed model does not demand weghts fom the decson make. The poposed model consdes cadnal and odnal data fo stategy ankng. The poposed model deals wth mpecse data n a dect manne. Stategy ankng s a staghtfowad pocess caed out by the poposed model. Ths pape poceeds as follows. In Secton 2, the method that anks the stateges s ntoduced. Numecal example and manageal mplcatons ae dscussed n Sectons 3 and 4, espectvely. Secton 5 dscusses concludng emaks. 2. Poposed method fo ankng stateges Data Envelopment Analyss (DEA) poposed by Chanes et al. (978) (CCR model) and developed by Banke et al. (984) (BCC model) s an appoach fo evaluatng the effcences of Decson Makng Unts (DMUs). Ths evaluaton s geneally assumed to be based on a set of cadnal (quanttatve) output and nput factos. In many eal wold applcatons (especally stategy ankng poblems), howeve, t s essental to take nto account the pesence of odnal (qualtatve) factos when endeng a decson on the pefomance of a DMU. Vey often t s the case that fo a facto such as stategy sk, one can, at most, povde a ankng of the DMUs fom best to wost elatve to ths attbute. The capablty of povdng a moe pecse, quanttatve measue eflectng such a facto s geneally beyond the ealm of ealty. In some stuatons such factos can be legtmately quantfed, but vey often such quantfcaton may be supefcally foced as a modelng convenence. In stuatons such as that descbed, the data fo cetan nfluence factos (nputs and outputs) mght bette be epesented as ank postons n an odnal, athe than numecal sense. Refe agan to the stategy sk example. In cetan ccumstances, the nfomaton avalable may pemt one to povde a complete ank odeng of the DMUs on such a facto. Theefoe, the data may be mpecse. Outcome of DEA models s an effcency scoe equal to one to effcent DMUs and less than one to neffcent DMUs. So, fo neffcent DMUs a ankng s gven but effcent DMUs can not be anked. One poblem that has been dscussed fequently n the DMUs ankng lteatue, has been the lack of dscmnaton n DEA applcatons, n patcula when thee ae nsuffcent DMUs o the numbe of nputs and outputs s too hgh elatve to the 4
6 numbe of DMUs. In the stategy selecton poblem a dffculty ases when attemptng to dentfy the best, when multple canddates have an effcency scoe of. If a decson make abtaly selects an effcent stategy, then thee s a possblty that ths system s a nche membe pefomng well on few nputs and outputs, and dong pooly wth a majoty of nput-output measues. Ths pape poposes to use a fomulaton called "Mnmax Regetbased Appoach" (MRA) to ank the stateges. In ths secton, the model that can ank the effcency of stateges n the pesence of both odnal and cadnal data (wthout elyng on weght assgnment by decson makes) s pesented. Suppose that thee ae n stateges (DMUs) to be evaluated. Each DMU consumes m nputs to poduce s outputs. In patcula, DMU j consumes amounts X j ={ x j } of nputs (=,, m) and poduces amounts Y j ={ y j } of outputs (=,, s). Wthout loss of genealty, t s assumed that all the nput and output data x j and y j (=,, m; =,, s; j=,, n) cannot be exactly obtaned due to the exstence of uncetanty. They ae only known to le wthn the U U uppe and lowe bounds epesented by the ntevals [ x, x ] and [ y ] y > 0. j j j y,, whee x > 0 and In ode to deal wth such an uncetan stuaton, the followng pa of lnea pogammng models has been developed to geneate the uppe and lowe bounds of nteval effcency fo each DMU (Wang et al. 2005): j j j 5
7 Maxθ s. t. U jo = m = s = s = v x u u jo y y U j u, v ε U jo =, m = v x j,. 0, j =,, n, () Maxθ s. t. jo = m = s = s = v x u u U jo y y U j u, v ε jo =, m = v x j,. 0, j =,, n, (2) whee j o s the DMU unde evaluaton (usually denoted by DMU o ); u and v ae the weghts assgned to the outputs and nputs; θ U jo stands fo the best possble elatve effcency acheved by DMU o when all the DMUs ae n the state of best poducton actvty, whle stands fo the lowe bound of the best possble elatve effcency of DMU o. They consttute a U possble best elatve effcency nteval [ ] gven. θ,. ε s the non-achmedean nfntesmal. jo θ jo In ode to judge whethe a DMU s DEA effcent o not, the followng defnton s θ jo Defnton. A DMU, DMU o, s sad to be DEA effcent f ts best possble uppe bound effcency θ U* = ; othewse, t s sad to be DEA neffcent f θ U* <. jo jo Now, the method of tansfomng odnal pefeence nfomaton nto nteval data s dscussed, so that the nteval DEA models pesented n ths pape can stll wok popely even n these stuatons. Suppose some nput and/o output data fo DMUs ae gven n the fom of odnal pefeence nfomaton. Usually, thee may exst thee types of odnal pefeence nfomaton: () stong odnal pefeence nfomaton such as y j >y k o x j >x k, whch can be 6
8 futhe expessed as y j χ yk and xj η xk, whee χ > and η > ae the paametes on the degee of pefeence ntensty povded by decson make. Hee, both χ and η ae postve scalas used to dstngush ank postons stctly, wth lage values, tendng to povde geate dscmnatons n the esultng effcency values. To detemne these values, decson make uses fom hs expeences. In addton, thee s a mathematcal model fo detemnng the values of pefeence nfomaton such as p χ η and q (see Cook et al. (996)); (2) weak odnal y y o x ; (3) ndffeence elatonshp such as y l p x q = y t o x l = x t. Snce DEA has the popety of unt-nvaance, the use of scale tansfomaton to odnal pefeence nfomaton does not change the ognal odnal elatonshps and has no effect on the effcences of DMUs. Theefoe, t s possble to conduct a scale tansfomaton to evey odnal nput and output ndex so that ts best odnal datum s less than o equal to unty and then gve an nteval estmate fo each odnal datum. Now, consde the tansfomaton of odnal pefeence nfomaton about the output y j (j=,, n) fo example. The odnal pefeence nfomaton about nput and othe output data can be conveted n the same way. Fo weak odnal pefeence nfomaton y y y, we have the followng odnal elatonshps afte scale tansfomaton: yˆ yˆ yˆ 2 n σ, 2 n whee σ s a small postve numbe eflectng the ato of the possble mnmum of {y j j=,, n} to ts possble maxmum. It can be appoxmately estmated by the decson make. It s efeed as the ato paamete fo convenence. The esultant pemssble nteval fo each ŷ j s gven by yˆ j [,], j =,, n. σ Fo stong odnal pefeence nfomaton y > y > > y, thee s the followng odnal elatonshps afte scale tansfomaton: yˆ, yˆ χ yˆ + ( j =,, n ) 2 n and yˆ σ, j, j n whee χ s a pefeence ntensty paamete satsfyng χ > povded by the decson make and σ s the ato paamete also povded by the decson make. The esultant pemssble nteval fo each ŷ j can be deved as follows: 7
9 yˆ j n j j n [ σ χ, χ ], j =,, n wth σ χ. To tansfom the odnal pefeence nfomaton to nteval data, geometcal spacng s utlzed. Fo moe detals see Wang et al. (2005). Fnally, fo ndffeence elatonshp, the pemssble ntevals ae the same as those obtaned fo weak odnal pefeence nfomaton. Though the scale tansfomaton above and the estmaton of pemssble ntevals, all the odnal pefeence nfomaton s conveted nto nteval data and can thus be ncopoated nto nteval DEA models. In nteval effcency assessment, snce the fnal effcency scoe fo each DMU s chaactezed by an nteval, a smple yet pactcal ankng appoach s thus needed fo ankng the effcences of dffeent DMUs. Hee the MRA developed by Wang et al. (2005) s ntoduced. The appoach s summazed as follows: U et A [ a, a ] m( A ), w( A ) (,, n) = = = be the effcency ntevals of n DMUs, U U whee m( A ) = ( a + a ) and w( A ) = ( a a ) ae the mdponts (centes) 2 2 U and wdths. Wthout loss of genealty, suppose A [ a, a ] = s chosen as the best effcency U nteval. et b = max j { a j }. Obvously, f a < b, the decson make mght suffe the loss of effcency (also called the loss of oppotunty o eget) and feel eget. The maxmum loss of effcency he/she mght suffe s gven by max( ) = b a U = max{ a } a. j j If a b, the decson make wll defntely suffe no loss of effcency and feel no eget. In ths stuaton, hs/he eget s defned to be zeo,.e. = 0. Combnng the above two stuatons, thee s max( ) max = max( a j U j ) a,0. Thus, the mnmax eget cteon wll choose the effcency nteval satsfyng the followng condton as the best (most desable) effcency nteval: mn { max( )} mn max U = max( a ) a,0. j j Based on the above analyss, the followng defnton fo ankng effcency ntevals s gven. 8
10 U Defnton 2. et A [ a, a ] = m( A ), w( A ) ( =,, n) = be a set of effcency ntevals. The maxmum loss of effcency (also called maxmum eget) of each effcency nteval A s defned as = U R( A ) max max ( a ) a,0 = max max m( A ) + w( A ) ( m( A ) w( A )),0, =,, n. j j j j j It s evdent that the effcency nteval wth the smallest maxmum loss of effcency s the most desable effcency nteval. To be able to geneate a ankng fo a set of effcency ntevals usng the maxmum losses of effcency, the followng elmnatng steps ae suggested: Step : Calculate the maxmum loss of effcency of each effcency nteval and choose a most desable effcency nteval that has the smallest maxmum loss of effcency (eget). Suppose A s selected, whee n. Step 2: Elmnate A fom the consdeaton, ecalculate the maxmum loss of effcency of evey effcency nteval and detemne a most desable effcency nteval fom the emanng (n-) effcency ntevals. Suppose A s chosen, whee but. 2 2 n 2 Step 3: Elmnate A fom the futhe consdeaton, e-compute the maxmum loss of 2 effcency of evey effcency nteval and detemne a most desable effcency nteval A 3 fom the emanng (n-2) effcency ntevals. Step 4: Repeat the above elmnatng pocess untl only one effcency nteval The fnal ankng s A A A, whee the symbol " " means s supeo to. 2 n A s left. n The above ankng appoach s efeed to as the MRA. In the next secton, a numecal example s pesented. 9
11 3. Numecal example The data set fo ths example contans specfcatons on 27 stateges. The cadnal nput consdeed s Total Cost of stategy (TC). The nputs and outputs selected n ths pape ae not exhaustve by any means, but ae some geneal measues that can be utlzed to evaluate stateges. In fact, ctea that ae ctcal to stategc choces concenng the futue wll vay fom company to company and ove tme, and wll emege fom dffeent pats of the stategy analyss. In an actual applcaton of ths methodology, decson makes must caefully dentfy appopate nputs and outputs measues to be used n the decson makng pocess. Rsk s ncluded as a qualtatve nput whle Net Pesent Value (NPV) of the stategy wll seve as the bounded data output. Rsk s an ntangble facto that s not usually explctly ncluded n evaluaton model fo stategy. Ths qualtatve vaable s measued on a stong odnal scale. Payback tme fo the stategy s consdeed as cadnal output. Table depcts the stategy's attbutes. "Take n Table " Suppose the paametes of degee of pefeence ntensty about the stong odnal pefeence nfomaton ae gven (o estmated) as η 2 =.2 and σ 2 = Usng the tansfomaton technque descbed n pevous secton, an nteval estmate fo sk of each stategy can be deved, whch s shown n the Table 2. Fo example, the tansfomaton esult fo stategy 23 s as follows: 26 [ 0.0(.2),.2 ] [ , ] 0 x ˆ2,23 = "Take n Table 2" Theefoe, all the nput and output data ae now tansfomed nto nteval numbes and can be evaluated usng nteval DEA models. Table 3 epots the esults of effcency assessments fo the 27 stateges obtaned by usng nteval DEA models () and (2). The non- Achmedean nfntesmal was set to beε = "Take n Table 3" Based on the defnton, stateges 0, 7, 20, and 27 all have the possblty to be DEA effcent. If they ae able to use the mnmum nputs to poduce the maxmum outputs, they 0
12 ae DEA effcent (effcent n scale); othewse, they ae not DEA effcent. Although stateges 0, 7, 20, and 27 all have the possblty to be DEA effcent, due to the dffeences n the lowe bound effcences, the pefomances ae n fact dffeent. In ode to ank the effcences of the 27 stateges (DMUs), the MRA s employed to compute the maxmum loss of effcency fo each stategy (see appendx). As computatons show, stategy 20 s selected as the best stategy. 4. Manageal mplcatons No oganzaton has unlmted esouces. No fm can take on an unlmted amount of debt o ssue an unlmted amount of stock to ase captal. Theefoe, no oganzaton can pusue all the stateges that potentally could beneft the fm. Stategc decsons thus always have to be made to elmnate some couses of acton and to allocate oganzatonal esouces among othes. Most oganzatons can affod to pusue only a few copoate-level stateges at any gven tme. It s a ctcal mstake fo manages to pusue too many stateges at the same tme, theeby speadng the fm s esouces so thn that all stateges ae jeopadzed. The stategc management pocess esults n decsons that can have sgnfcant, longlastng consequences. One majo component of stategc management s stategy selecton. Eoneous stategc decsons can nflct sevee penaltes and can be exceedngly dffcult, f not mpossble, to evese. Most stategsts agee, theefoe, that stategy evaluaton s vtal to an oganzaton s well-beng. Stategy evaluaton s mpotant because oganzatons face dynamc envonments n whch key extenal and ntenal factos often change quckly and damatcally. Stategy analyss and choce seeks to detemne altenatve couses of acton that could best enable the fm to acheve ts msson and objectves. The fm s pesent stateges, objectves, and msson, coupled wth the extenal and ntenal audt nfomaton, povde a bass fo geneatng and evaluatng feasble altenatve stateges. Unless a despeate stuaton faces the fm, altenatve stateges wll lkely epesent ncemental steps to move the fm fom ts pesent poston to a desed futue poston. Stategsts neve consde all feasble altenatves that could beneft the fm, because thee ae an nfnte numbe of possble actons and an nfnte numbe of ways to mplement those actons. Theefoe, a manageable set of the most attactve altenatve stateges must be developed. The advantages, dsadvantages, tade-offs, costs, and benefts of these stateges should be detemned.
13 Stategy selecton has long been ecognzed as a mult-ctea poblem. The jont consdeaton of multple ctea complcates the selecton decson, even n the case of expeenced manages, because competng stateges have dffeent levels of success unde multple ctea. Ths pape ntoduces a technque that can help stategsts evaluate the feasble stateges and choose a specfc stategy. Wthout the technque, pesonal bases, poltcs, emotons, pesonaltes, and halo eo (the tendency to put too much weght on a sngle facto) unfotunately may play a domnant ole n the stategy ankng pocess. Ths pape has followng advantages fo stategsts: Wth espect to dynamc envonments n whch key extenal and ntenal factos often change apdly and consdeably, ths pape helps stategsts to eact quckly and accuately. Snce classcal technques always eque ntutve judgments that have bases, ths pape helps stategsts to select and ank the stateges wthout elyng on ntutve judgments. The nceasng numbe of decson makng ctea, complcates the stategy ankng pocess. Ths pape pesents a obust model to solve the multple-ctea poblem. 5. Concludng emaks Stategc decsons deal wth the long-tem futue of the ente oganzaton. The decsons ae ae and typcally have no pecedent to follow. In addton, stategc decsons usually commt substantal esouces and demand a geat deal of commtment. Moeove, they ae dectve, they set pecedents fo moe detaled (tactcal level) decsons and futue actons thoughout the oganzaton. To ank the stateges a method was ntoduced. The poblem consdeed n ths study s at ntal stage of nvestgaton and much futhe eseaches can be done based on the esults of ths pape. Some of them ae as follows: Smla eseach can be epeated fo the case that some of the stateges ae slghtly nonhomogeneous. One of the assumptons of all the classcal models of stategy evaluaton s based on complete homogenety of stateges, wheeas ths assumpton n many eal applcatons cannot be genealzed. In othe wods, some ctea (nputs and/o outputs) ae not common fo all the stateges occasonally. Theefoe, thee s a need to a model that deals wth these condtons. Compang the esults of pefomance of poposed method wth fuzzy DEA wll be anothe eseach topc. To tansfom the odnal pefeence nfomaton to 2
14 nteval data, geometcal spacng was utlzed. Compang statstcal popetes of lnea spacng and geometcal spacng and the effects on the esult of effcency could be an nteestng topc fo futue study. Appendx R(stategy )= , R(stategy 2 )= , R(stategy 3 )=.82939,, R(stategy 27 )= Obvously, stategy 20 has the smallest maxmum loss of effcency. So, stategy 20 s ated as the best stategy and elmnated fom the futhe consdeaton. Theefoe fo the emanng stateges, maxmum losses of effcency ae ecalculated as follows: R(stategy )= , R(stategy 2 )= , R(stategy 3 )=.82939,, R(stategy 27 )= Among the above egets, the maxmum loss of effcency of stategy 27 s the smallest, so stategy 27 s ated as the second best stategy and elmnated fom the futhe consdeaton. So, fo the emanng stateges, maxmum losses of effcency ae ecalculated and shown below: R(stategy )= , R(stategy 2 )= , R(stategy 3 )=.82939,, R(stategy 26 )= Snce stategy 7 has the smallest maxmum loss of effcency. So, t s ated as the thd best stategy and elmnated fom the futhe consdeaton. Repeatng the above pocess, the ankng ode of 27 stateges s obtaned as follows: stategy 20 stategy 27 stategy 7 stategy 0 stategy 25 stategy 2 stategy 7 stategy 5 stategy 26 stategy 2 stategy 9 stategy 6 stategy stategy 9 stategy stategy 3 stategy 4 stategy 22 stategy 6 stategy 8 stategy 24 stategy 3 stategy 5 stategy 23 stategy 8 stategy 4 stategy 2. Theefoe, stategy 20 s selected as the best stategy. 3
15 Acknowledgements The autho wshes to thank the thee anonymous evewes fo the valuable suggestons and comments. Refeences Banke, R. D., Chanes, A., Coope, W. W. (984) Some Methods fo Estmatng Techncal and Scale Ineffcences n Data Envelopment Analyss. Management Scence, 30(9), Chanes, A., Coope, W. W., Rhodes, E. (978) Measung the Effcency of Decson Makng Unts. Euopean Jounal of Opeatonal Reseach, 2(6), Chen, T. W., n, C., Tan, B., ee, W. C. (999) A Neual Netwoks-Based Appoach fo Stategc Plannng. Infomaton & Management, 35(6), Chou, H. K., Tzeng, G. H., Cheng, D. C. (2005) Evaluatng Sustanable Fshng Development Stateges usng Fuzzy MCDM Appoach. Omega, 33(3), Cook, W. D., Kess, M., Sefod,. M. (996) Data Envelopment Analyss n the Pesence of Both Quanttatve and Qualtatve Factos. Jounal of the Opeatonal Reseach Socety, 47(7), Cone, J., Kkwood, C. (99) Decson Analyss Applcatons n the Opeatons Reseach teatue Opeatons Reseach, 39(2), Hastngs, S. (996) A Stategy Evaluaton Model fo Management. Management Decson, 34(), Kajanus, M., Ahola, J., Kuttla, M., Pesonen, M. (200) Applcaton of Even Swaps fo Stategy Selecton n a Rual Entepse. Management Decson, 39(5),
16 Wang, Y. M., Geatbanks, R., Yang, J. B. (2005) Inteval Effcency Assessment Usng Data Envelopment Analyss. Fuzzy Sets and Systems, 53(3), Wnd, Y. (987) An Analytc Heachy Pocess based Appoach to the Desgn and Evaluaton of a Maketng Dven Busness and Copoate Stategy. Mathematcal Modelng, 9(3-5), Wnd, Y., Saaty, T. (980) Maketng Applcatons of the Analytc Heachy Pocess. Management Scence, 26(7)
17 Stategy No. (DMU) Table Related attbutes fo 27 stateges Inputs Outputs TC NPV (0000$) (0000$) x j Rsk * x 2j y j Payback tme (yea) y 2j [50, 65] [60, 70] [40, 50] [, 3] [45, 55] [, 2] [4, 5] [0, 20] [9, 2] [5, 8] [25, 35] [0, 5] [8, 2] [20, 35] [40, 55] [75, 85] 7 8 [0, 8] [9, 5] [0, 3] [, 4] [25, 30] [0.8,.2] [2, 4] [, 5] [8, 2] [65, 80] [90, 220].75 * Rankng such that 27 hghest ank,, lowest ank (x 2, 23 >x 2, 2 > >x 2, 7 ) 6
18 Table 2 Inteval estmate fo the 27 stateges afte the tansfomaton of odnal pefeence nfomaton Stategy No. Rsk (DMU) [.04887, ] 2 [ , ] 3 [.2003,.63558] 4 [ , ] 5 [ ,.77802] 6 [.02544, ] 7 [ ,.6068] 8 [ , ] 9 [ , ] 0 [.02, ] [ ,.3606] 2 [ , ] 3 [.57863, ] 4 [ , ] 5 [ ,.6327] 6 [ , ] 7 [.0, ] 8 [ ,.50663] 9 [ , ] 20 [ , ] 2 [ , ] 22 [ , ] 23 [ , ] 24 [ , ] 25 [ , ] 26 [ , ] 27 [ , ] 7
19 Table 3 The effcency nteval fo the 27 stateges Stategy No. Effcency Inteval (DMU) [.44443,.49936] 2 [ , ] 3 [.70609,.20524] 4 [ ,.6333] 5 [.08522,.0452] 6 [ , ] 7 [.6622,.70772] 8 [.09037, ] 9 [.45532, ] 0 [.3006, ] [.8922,.2693] 2 [ , ] 3 [ ,.5235] 4 [.223, ] 5 [ ,.54024] 6 [.20202, ] 7 [ , ] 8 [ ,.75404] 9 [.22485,.28638] 20 [ , ] 2 [.22552,.25724] 22 [ , ] 23 [ ,.0363] 24 [ ,.22788] 25 [ , ] 26 [ , ] 27 [ , ] 8
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