MULTI-CRITERIA DECISION AIDING IN PROJECT MANAGEMENT OUTRANKING APPROACH AND VERBAL DECISION ANALYSIS

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1 Dorot Górec Deprtment of Econometrcs nd Sttstcs Ncolus Coperncus Unversty n Toruń MULTI-CRITERIA DECISION AIDING IN PROJECT MANAGEMENT OUTRANKING APPROACH AND VERBAL DECISION ANALYSIS Introducton A proect s temporry endevour underten to delver unque product or servce. Proect mngement, then, s the pplcton of nowledge, slls, tools nd technques to proect ctvtes to meet proect requrements. Ths pplcton of nowledge requres the effectve mngement of pproprte processes PMBOK Gude Ech proect s orgnl nd exceptonl becuse t lest one of the followng prmeters lwys chnges: gols, resources nd/or envronment. Ths mes proect mngement complex undertng Vdl et l. 2011, wth mny stges nd processes, unvodbly connected wth multcrter decson mng. Vrous stutons nd ssues durng the course of the proect requre from proect mnger or other person responsble for the prtculr mtter to choose the best vrnt from set of vlble decson-mng vrnts tng nto ccount number of mportnt spects crter whle comprng them. Acqurng fxed ssets, selectng tender, choosng nvestment opton re merely the exmples of such ssues. Exemplry crter for these problems re presented n the tble below.

2 12 Dorot Górec Exmples of decson-mng problems nd evluton crter Tble 1 No. Decson-mng problem Exemplry crter 1 Acqurng fxed ssets 2 Selectng tender prce, producton cpcty, energy ntensty, nose emsson, vlblty nd cost of servce prce, expected executon tme, contrctor s experence, resources, fnncl stblty s well s mngement nd techncl blty 3 Choosng proect concept soluton prce, usble propertes, durblty nd esthetcs of performnce, sfety of the utlzton, mpct on the envronment, nfluence on the employment, n fluence on the nhbtnts helth, mpct on the nvestment ttrctveness, mpct on the tourst ttrctveness Besdes bove mentoned decson-mng problems MCDA n proect mngement cn be used n: proect selecton whch s crucl ssue for every orgnzton, selecton of worers, selecton of softwre proect mngement tool, mesurng proect complexty, controllng proect performnce, ssgnng prortes to ctvtes. Exmples of suggested pplctons re brefly descrbed n the tble below. Exmples of MCDA pplctons n proect mngement Tble 2 No. Applcton re Ctton Descrpton 1 Proect selecton [Prdsht et l., 2009] Artcle s connected wth Reserch nd Development R&D proect selecton n chemcl ndustry. It presents severl dfferent methods of MCDM for use n cnddte proect evluton nd prortzton. 2 Selecton of worers [Lng, 2003] Artcle presents conceptul model for the selecton of rchtects by proect mngers. The model ws developed from four theores: Theory of Job Performnce, Theory of Contextul Performnce, Networ Theory of Embeddedness nd Theory of the Frm. It ws tested by postl survey of proect mngers who wor for property developers.

3 MULTI-CRITERIA DECISION AIDING IN PROJECT MANAGEMENT The prncpl fndng s tht 34 of the 40 ttrbutes dentfed re mportnt, nd these were used to construct the Archtect Selecton Model. It s bsed on MAUT nd uses weghted sum method to determne overll score of the rchtects who re beng evluted. In the pper model for selectng softwre proect mngement tool usng the AHP s presented. 3 Selecton of softwre tool [Ahmd, Lplnte, 2006] Severl relevnt fctors bsed on the most common fetures offered by commercl off-the-shelf solutons COTS re used s the selecton crter n rnng the softwre tools. The contrbuton of the wor s to pply well-nown decson-mng method n novel wy to help decson-mers better dentfy n pproprte softwre proect mngement tool wthout hvng to go through more extensve evluton process. Moreover, the wor estblshes frmewor for comprng ndvdul product decsons cross proects, proect mngers, orgnztonl groups nd orgnztons. 4 Mesurng proect complexty [Vdl et l., 2011] The m of the pper s to defne mesure of proect complexty n order to ssst decson-mng. A syntheszed lterture revew on exstng complexty mesures s proposed n order to hghlght ther lmttons. Then, mult-crter pproch to proect complexty evluton, through the use of the AHP, s proposed. A cse study wthn strt-up frm n the entertnment ndustry the mn ctvty of whchs the producton of stge muscls n Frnce s performed. Study s focused on decson support n the context of product nd servce development proects. In the pper new mult-dmensonl Proect Performnce Mesurement System to enble mngers to del wth the volume of dt s proposed. 5 Controllng proect performnce [Mrques et l., 2010] The proposton ntegrtes the unque chrcter of ech proect tss, obectves, decson-mers personlty nd competences, severl good prctces n terms of unversl proect mngement dmensons on the one hnd, nd n terms of performnce nlyss on the other hnd. As n ggregton tool MACBETH method s used to nlyze the performnce mesures ccordng to proect mngers own performnce nterests. A cse study connected wth the lndng ger door proect llustrtes the proposed system.

4 14 Dorot Górec 6 Assgnng prortes to ctvtes [Mot et l., 2009] Artcle presents model for supportng proect mngers to focus on the mn tss of proect networ usng MCDA pproch. As result, mngers cn ncrese ther performnce n controllng proect ctvtes, prtculrly n dynmc nd chngng envronment. A cse study on the constructon of n electrcty sub-stton s used to demonstrte the model proposed. In the study, the ELECTRE TRI method s used n order to clssfy ctvtes nto set of dfferent mngerl clsses ccordng to some norms. Source: Ahmd, Lplnte, 2006; Lng, 2003; Mrques et l. 2010; Mot et l. 2009; Prdsht et l. 2009; Vdl et l., Presentton of MCDA pproches Accordng to the results of descrptve studes see Russo nd Rosen, 1975; Montgomery nd Svenson, 1989; Pyne et l. 1993; Lrchev 1992; Korhonen et l. 1997, the mult-crter decson-mng problems consttute gret chllenge for people, nd the more crter the problems nvolve, the more complcted they re Ashhmn, Furems, There re severl pproches whch my be mplemented to solve ths nd of problems, for nstnce: mult-ttrbute utlty theory MAUT see Keeney, Rff 1976, pproch bsed on the outrnng relton see Roy 1990, verbl decson nlyss VDA see Lrchev, Moshovch 1995, Methods bsed on the mult-ttrbute utlty theory see Keeney, Rff 1976 ssume tht there exst globl utlty functon to represent the decson-mer s preferences nd t cn be bult through ggregtng vrnts prtl utltes ccordng to ech crteron. But the reducton of multdmensonl evluton to onedmensonl one v the formulton of globl utlty functon s possble only when certn rgorous condtons 1 re met. Besdes, t my led to the complete compenston between crter the stuton n whch vrnt evluted low gnst one or even more crter s rned hghly becuse t hs cheved hgh grdes gnst remnng crter. In ths pproch not very relstc ssumpton s ccepted tht decson-mer s preferences re gven nd fxed,.e. they re expressed clerly nd result n good orderng vrnts gnst crter the decson-mer s ble 1 For nstnce, the necessry nd suffcent condton of pplyng n ddtve form of the utlty functon n the stuton when the evlutons re determnstc s mutul preferentl ndependence of the crter. If the evlutons hve the form of probblty dstrbutons the bove mentoned condton s not suffcent n tht cse the utlty ndependence condton must be stsfed Trzsl et l

5 MULTI-CRITERIA DECISION AIDING IN PROJECT MANAGEMENT to ndcte, wthout ny hestton, even the smllest dfferences n utltes nd confdently, consequently nd precsely ssgn the scores to vrnts consdered. In ddton, determnng n nlytcl form of the globl utlty functon s usully very dffcult nd sometmes even unfesble t hppens frequently tht the decson-mer s not ble to provde nformton essentl to buld ths functon Trzsl et l An nterestng lterntve s the pproch bsed on the outrnng relton nd on the fundmentl prtl comprblty xom see Roy 1990, n whch ncomprblty plys ey role Mrtel The bsc de of ths pproch s s follows: vrnt outrns vrnt f on gret prt of the crter performs t lest s good s concordnce condton, whle ts worse performnce s stll cceptble on the other crter non-dscordnce condton. Indfference thresholds nd preference thresholds re ntroduced n order to buld outrnng reltons tht represent decson-mers preferences nd consttute prtl reltons of the globl preferences. In ths nd of pproch there s plce for ncomprblty, explned e.g. by the lc of suffcent nformton to defne preferentl stuton Trzsl et l The procedures exploted ccordng to ths pproch mong whch the ELECTRE see Roy, Bouyssou 1993; Vnce 1992 nd PROMETHEE see Brns, Vnce 1985; Brns et l methods stnd out re usully less demndng for ther users t the nformtonl level nd result n more blnced recommendtons thn those belongng to the frst pproch of sngle crteron synthess Mrtel, Snce ther ssumptons re n ccordnce wth the relty they cn defntely be recommended for pplyng n proect mngement Górec Although outrnng pproch hs mny dvntges, t hs lso one mor weness: wthn respectve technques bsed on ths pproch t s essentl to elct nformton bout prmeters utlzed n them from decson-mers nd they my encounter problems n revelng preferences nd fxng them. In fct number of psychologcl experments confrm see Korhonen et l tht people me sgnfcnt errors n quntttve mesurement of subectve fctors Ashhmn, Furems As fr s VDA-bsed methods re consdered the stuton s dfferent: preferentl nformton n the ordnl form for nstnce more preferble, less preferble or eqully preferble, whch s requred from the decson-mers wthn these methods, seems to be stble nd relble ccordng to the results of psychologcl experments. Moreover, t s checed n order to ensure ts consstency. Technques bsed on VDA do not use quntttve nformton on crter mportnce, but only verbl estmtes nd no quntttve opertons re mde on them. Hence, ll opertons re cler nd understndble to decson-mers Ashhmn, Furems 2005.

6 16 Dorot Górec In the frmewor of VDA prdgm methods belongng to the ZAPROS fmly see Lrchev, Moshovch 1995, 1997; Lrchev 2001b re very well nown. In these technques preference elctton bols down to comprsons of prs of hypothetcl vrnts ech wth the best evlutons on ll crter but one dfferng n performnces of two crter only. Results of these comprsons re trnsformed nto the so-clled Jont Ordnl Scle JOS, whch s subsequently used to compre rel decson-mng vrnts Ashhmn, Furems In the method of dyd comprson of crter estmtes see Moshovch et l vrnts wth dfferent ttnments upon only two crter re compred s well, but contrry to ZAPROS method they do not necessrly nclude the best levels of performnce. Then, n ddton to JOS, pred JOS PJOS s constructed n order to compre decson-mng vrnts ncomprble upon JOS Ashhmn, Furems Both the forementoned methods meet the frst two requrements of VDA, nmely: psychologcl relblty of nformton on the decson-mer s preferences nd the possblty to chec the consstency of ths nformton. Both JOS nd PJOS re formed wthout ny quntttve opertons, nd ther correctness s proven wthn the frmewor of ddtve vlue model. Nevertheless, ther mplementton to the comprson of rel decson-mng vrnts, however rtonl, does not seem to be esly explnble to the prtcpnts of the decson-mng process. Furthermore, psychologcl lmttons ssumed n these methods re rther restrctve. They re bsed on the results of psychologcl experments, ccordng to whch the pr-wse qulttve comprsons of hypothetcl vrnts vryng n estmtes of not more thn two crter re reltvely esy for humn bengs see Lrchev As mtter of fct experments crred out wthn the cooperton between the Acdemy of Fnlnd nd the Russn Acdemy of Scences hve shown see Furems et l tht people re ble to me relble pr-wse comprsons usng specl grphcl ds such s color dfferentton of preferences of vrnts tht dffer n estmtes on three or even on four crter Ashhmn, Furems Tng tht nto ccount Intellectul Decson Support System IDSS UnComBOS Unt Comprson for the Best Obectve Selecton hve been proposed see Furems, Ashhmn It s bsed on the VDA prncples but mplements new pproch to mult-crter comprson nd choce tryng to overcome the lmttons mentoned bove s well s to dust decson-mng procedure,.e. the complexty of questons, to the ndvdul cpbltes of decson-mers. One of ts ey orgnl fetures s usng specl vsulzton technques n order to gther preference nformton from the decson-mers nd the other one s n on-lne preference consstency control system llowng to revel mong other thngs errors n the nswers of decson-mers Furems, Ashhmn 2004.

7 MULTI-CRITERIA DECISION AIDING IN PROJECT MANAGEMENT The rtcle s med t bref descrpton of chosen mult-crter decson dng methods bsed on the outrnng relton from the ELECTRE nd PROMETHEE fmles s well s procedure belongng to the verbl decson nlyss frmewor, nmely UnComBOS. Addtonlly, t wll provde short comprson of these two pproches focusng on types of decson-mng problems on whch they re orented. Furthermore, n llustrtng exmple of ther pplcton connected wth proect mngement wll be presented. 2. Descrpton of mult-crter methods Below chosen mult-crter decson-dng procedures wll be concsely presented, nmely: ELECTRE I wth veto threshold ELECTRE Iv, PROMETHEE I nd PROMETHEE II s well s IDSS UnComBOS. ELECTRE Iv ELECTRE Iv procedure conssts of the followng steps Fguer et l. 2005; Metody weloryterlne n polsm rynu fnnsowym 2006: 1. Clculton of concordnce ndces c, : n = 1 c, = w ϕ,, where: w coeffcent of mportnce for crteron f, n = 1 w = 1, f evluton of vrnt wth respect to crteron f, ϕ, 1, = 0 f otherwse. f f, 2. Constructon of concordnce set C s : C = {, A A: c, s s [0,5;1]} s.

8 18 Dorot Górec 3. Determnton of dscordnce ndces d, : d, 1, = 0, f f : d : d,, = 1, = 0, where: d, 1, f f + v[ f ] < = 0 otherwse. f, 4. Constructon of dscordnce set D v : D {, A A: d, = 1}. v = 5. Determnton of outrnng relton: S s, v = C s Dv, where D = A A \ D. v v 6. Defnng grphs wth the help of outrnng relton showng reltonshps between vrnts. 7. Select the best vrnt or subset of vrnts the decson-mer should focus hs ttenton on. PROMETHEE I nd PROMETHEE II Both PROMETHEE methods nclude Brns, Mreschl 2005: 1. Defnng generlzed crteron { f P, } s crteron nd, for ech crteron ; f P, represents preference functon showng the strength of preference of vrnt over vrnt under the crteron : P, = F [ d, ],, where d, = f f nd for whch P, [ 0;1 ]. In order to fcltte the determnton sx types of generlzed crter hve been proposed: usul, u-shpe, v-shpe, level, v-shpe wth ndfference nd Gussn crteron.

9 MULTI-CRITERIA DECISION AIDING IN PROJECT MANAGEMENT Types of generlzed crter Tble 3 Generlzed crteron Preference functon Prmeters Type 1: usul crteron 0, f d 0 d = 1, f d > 0 P none Type 2: qus-crteron u-shpe crteron 0, f d q P d = 1, f d > q Type 3: v-shpe crteron Type 4: level crteron Type 5: pseudo-crteron v-shpe wth ndfference crteron 0, f d 0 d P d =, f 0 < d p p 1, f d > p 0, f d q 1 P d =, f q < d p 2 1, f d > p 0, d P d = p 1, f q q f, d d q f q > p < d p ndfference threshold q preference threshold p ndfference threshold q preference threshold p ndfference threshold q preference threshold p Type 6: Gussn crteron P d 0, f d 0 = 2 d 1 exp, 2 2s f d > 0 s t defnes the nflecton pont of the preference functon Source: Brns et l Clculton for ech pr of vrnts, ggregted preference ndces n π, : π, = w P,, where π, shows wth whch = 1 degree s preferred to over ll the crter.

10 Dorot Górec Defnng two outrnng flows for ech vrnt : the postve outrnng flow: = + = m m 1, 1 1 π, the negtve outrnng flow: = = m m 1, 1 1 π. The PROMETHEE I prtl rnng s obtned on the bss of the postve nd the negtve outrnng flows. Both flows do not usully nduce the sme rnngs. Fnl rnng n PROMETHEE I s ther ntersecton: < < > > = = = > < = < > ;, ;, ;, nd or nd f R nd f I nd or nd or nd f P where P, I nd R represent preference, ndfference nd ncomprblty respectvely. In PROMETHEE II on the bss of the postve nd the negtve outrnng flows the net outrnng flow s clculted for ech vrnt : + =. A fnl complete rnng s constructed ccordng to the descendng order of the net flows. IDSS UnComBOS The procedure mplemented n IDSS UnComBOS conssts of the followng steps Furems, Ashhmn 2004; Ashhmn, Furems 2005: 1. Problem structurng Decson-mer hs to defne decson-mng vrnts, specfy lst of evluton crter nd gve verbl estmtes of ll vrnts upon ll crter. Such estmtes exst n orgnl descrptons of vrnts, my be determned by the decson-mer or obtned from experts, ctlogues, etc.

11 MULTI-CRITERIA DECISION AIDING IN PROJECT MANAGEMENT Procedure of unt comprson Let us ntroduce D-unt s prtl descrpton of vrnt upon D K crter, where K = { 1,2,...,n} s the set of crter numbers. D-unt for vrnt A f, f,..., f s s follows: wth estmtes 1 2 n f α,..., α, D f = f K 1 f α, D f α = f ω \ where f ω stnds for crteron f, n estmte of whch s not present n such prtl descrpton. Let us ssume tht crter from F re mutully preference-ndependent see Fshburn, 1979 nd preferences between D-unts re trnstve for ny D. Then the followng rule of unt-wse domnnce U-Domnnce tes plce: vrnt s preferble to vrnt, f there exsts such prtton of the crter set K on subsets D 1 D,..., D, m D = K,,,, D D = Ø, tht D D., 2 m =1 Preferences of the decson-mer re elcted step-by-step through pr-wse comprsons between unts wthn the sme crter subsets. The procedure begns wth pr-wse comprsons of one-crteron unts to convert nomnl estmte scles of crter to ordnl ones n ccordnce wth the preferences of decson-mer. Hrdly ever would such type of comprsons be suffcent for the best vrnt choce on the bss of U-Domnnce rule. If there s no vrnt chosen s the best one, IDSS UnComBOS proceeds to pr-wse comprsons of two-crter unts 2. After ech comprson mde by decsonmer UnComBOS lgorthm s ppled to chec preference consstency nd to try to fnd the best vrnts. If set of decson-mer s nswers enbles t to do tht, the problem deems to be solved. Otherwse, IDSS UnComBOS proceeds to three-crter unts comprsons. And once gn, fter ech comprson mde by decson-mer lgorthm verfes preference consstency nd ttempts to select the best vrnt usng the preference nformton obtned. IDSS UnComBOS determnes mxml complexty of comprsons.e., the number of crter n unts to decson-mer ndvdully. A decsonmers cpbltes to compre mult-crter unts re represented by the frequency of ther errors. If decson-mer encounters dffcultes 2 IDSS UnComBOS fclttes comprsons of two- nd more crter dmenson unts through color dfferentton of preferences. For nstnce, when pr of two-crter unts s dsplyed to the decson-mer for comprson, the better estmtes of ech unt re hghlghted wth one color e.g. green nd the worse estmtes wth nother one e.g. blue. If two unts re eqully preferble to the decson-mer, they re dsplyed wth the sme color e.g. yellow. Hence, decson-mer clerly sees dvntges nd dsdvntges of ech unt n the pr Ashhmn, Furems 2005.

12 22 Dorot Górec n comprng unts of the current dmenson, dlogue s nterrupted nd nformton obtned from comprsons of unts of the prevous dmenson s used to compre vrnts. As consequence system mght not be ble to fnd the sngle best vrnt, but n such cse t wll ndcte the set of ncomprble vrnts preferble for decson-mer n comprson to ny vrnt not ncluded n ths set. 3. Anlyss nd correctons of nconsstency Inconsstences reveled re presented to decson-mer for nlyss nd correcton. Decson-mers hve opportunty to ndcte nd correct the errors n ther prevous nswers s well s to dsgree wth the results of the conducted opertons. In the ltter cse t mens crter preference-dependence nd/or ntrnstvty of preferences nd the consdered decson-mng problem my need restructurng. 4. Dsply of results nd explnton Results of comprsons re presented n the form of orented grph, n whch nodes correspond to vrnts nd rcs go from better vrnt to the worse one. Decsonmers my prompt explnton dlogue for ny rc of the grph nd see how ths prtculr relton hs been obtned. Moreover, t s possble to return to the stge of unt comprsons f decson-mers decde to revse ther prevous nswers. 3. Outrnng pproch versus verbl decson nlyss Outrnng methods hve become very populr over the lst three decdes. They hve lredy been ppled n vrous felds such s bnng, med plnnng, trnsport, ndustrl locton, wter resources, wste mngement, nvestments, mnpower plnnng, medcne, chemstry, helth cre, toursm, ethcs nd mny more. Verbl decson nlyss s new methodologcl pproch, bsed on cogntve psychology, ppled mthemtcs nd computer scence, whch ws proposed s frmewor for the unstructured decson-mng problems, whch re the problems wth mostly qulttve prmeters wth no obectve model for ther ggregton. Exmples of such tss cn be found n polcy mng nd strtegc plnnng n dfferent felds, s well s n personl decsons. For nstnce VDA-bsed ZAPROS method nd ts vrtons hs been used n R&D plnnng, pplcnts selecton, ob selecton nd ppelne selecton Moshovch et l Generl fetures for the unstructured problems re s follows Lrchev, 2001; Moshovch et l. 2005: they re unque n the sense tht ech problem s new to the decson-mer nd hs chrcterstcs not prevously experenced; crter n these problems re mostly qulttve n nture, most often formulted n nturl lnguge;

13 MULTI-CRITERIA DECISION AIDING IN PROJECT MANAGEMENT n mny cses evlutons of vrnts gnst the crter my be obtned only from humn bengs experts or the decson-mers; the qulty grdes on crter scles re verbl defntons presentng subectve vlues of the decson-mer. Both outrnng methods nd verbl decson nlyss provde outrnng reltonshps mong mult-crter decson-mng vrnts. However, there re some mportnt dfferences between these pproches. They re summrzed n the tble below. Dfferences between outrnng nd VDA pproches Outrnng methods Verbl decson nlyss Tble 4 Applcton Outrnng methods re ntended to compre VDA s desgned to elct sound preference gven set of decson-mng vrnts. reltonshp tht cn be ppled to future cses. Decson-mng problem Outrnng methods del mostly wth cses VDA s more orented on tss wth rther n whch number of crter s rther lrge lrge number of vrnts whle number up to twelve or thrteen nd number of vrnts of crter s usully reltvely smll. reltvely smll. Methodology Outrnng methods use crter weghts s well VDA bses ts outrnng on xomtc reltonshps, to nclude drect ssessment, dom- s other prmeters, whch serve n opertonl purpose but lso ntroduce heurstcs nd possble nnce, trnstvty nd preferentl ndependence. ntrnstvty of preferences. Decson-mers Snce some of the outrnng methods re qute VDA methods do not requre ny specl complex nd mthemtclly complcted ntellectul bltes nd trnng help decson-mers to nowledge n decson nlyss on the prt of the decson-mers. understnd nd ccept ths pproch. Source: Moshovch et l

14 24 Dorot Górec 4. Illustrtng exmple Usefulness of the bove-mentoned methods for decson dng processes connected wth proect mngement wll be llustrted by n exmple whch concerns the problem of choosng the best vrnt of the rod constructon out of fve tht hve been dentfed t the stge of drwng up the proect concept. Rod constructon s complex proect whch conssts of mny stges nd the mngement n ths cse requres deep nowledge regrdng rod buldng. A lot of wor hs to be done before the frst lyer of concrete s ever poured. Rod constructon requres the creton of rght-of-wy, overcomng geogrphc obstcles nd hvng grdes low enough to llow vehcle to trvel. Besdes, vrety of equpment s engged n rod buldng, whch depends strongly on the wether condtons, resultng n the rndom executon tme of proect tss Bru et l Before ny constructon cn begn the courses of the proposed route solutons hve to be dentfed nd evluted tng nto ccount functonl, techncl, economc, envronmentl nd socl spects. Ctzens re encourged to prtcpte n ths process. In mny nstnces, severl lterntves re nlyzed sometmes even over dozen or tens. Informton gthered durng ths stge s used to determne the locton nd type of the rod to be constructed. In mny cses certn mount of prvte property must be cqured. Once the rod desgn defnng for exmple the type of ntersectons, nterchnges, brdges, culverts nd other drnge fetures s well s specfyng the type nd pproxmte quntty of mterls to be used to construct the rod s complete, bds re receved for constructon. The bdder who hs been wrded the contrct s oblged to construct the rod n ccordnce wth pln requrements nd specfctons upon whch the bd ws receved. Rod cn be opened to trffc only fter the fnl nspecton conducted by n engneer not nvolved n ts constructon. Exmple consdered n ths pper s connected wth the nlyss regrdng drftng of rod route. It s not expnded s ts mn m s to llustrte the pplcton of vrous MCDA methods. Input dt,.e. evlutons of decson-mng vrnts nd weghts of crter, comes from Bru et l In the ssessment of the route solutons the followng four crter re ten nto consderton: f 1 cost of relzton n mllon PLN, f 2 vehcle s verge trvel tme n mnutes, f 3 the mpct on the envronment on scle from 0 to 10, f 4 the sfety of the trvelers on scle from 0 to 10. Tble 5 provdes the performnce mtrx for fve vrnts of rod constructon nd four crter used to evlute them. It ncludes lso type of preference functon defned for ech crteron s well s thresholds nd weghtng coeffcents. Both type of preference functon nd thresholds were determned by the uthor of ths rtcle.

15 MULTI-CRITERIA DECISION AIDING IN PROJECT MANAGEMENT Input dt for the llustrtng exmple Tble 5 f 1 f 2 f 3 f 4 Sfety Cost of relzton trvel tme envronment Vehcle s verge Impct on the Crter of the trvelers [mllon PLN] [mnutes] [0-10] [0-10] Mx/mn mn mn mx mx Crter weghts 0,4 0,1 0,2 0,3 Type of preference functon V V IV IV q p v Decson vrnts Applcton of ELECTRE I At the begnnng, the ELECTRE Iv method ws used for selectng the best vrnt of rod constructon. Tbles 6 nd 7 present the concordnce mtrx nd the dscordnce set. Tble 6 Mtrx of concordnce ndces

16 26 Dorot Górec Dscordnce set Tble An outrnng relton exsts f the concordnce nd non-dscordnce condtons re fulflled smultneously. The tble below presents the outrnng relton for the concordnce level equl to 0,6. Outrnng relton for concordnce level s = 0,6 Tble Fgure 1. Outrnng relton for s = 0,6 grph constructed from the best to the worst vrnt

17 MULTI-CRITERIA DECISION AIDING IN PROJECT MANAGEMENT Fgure 2. Outrnng relton for s = 0,6 grph constructed from the worst to the best vrnt The results of grphs nlyss Tble 9 Level s = 0,6 from the best vrnt to the weest one from the weest vrnt to the best one , , 5 In both cses vrnt 1 of rod constructon turned out to be the best nd should be recommended for relzton. On the second plce vrnt 2 ws clssfed. In turn, on the lowest level vrnt 5 ws plced, whch leds to the concluson tht ths s the worst soluton. Another vrnt tht cn be defntely excluded from further nlyss s vrnt 3 s t occurred on the lowest level n the cse of grph constructed from the weest to the strongest vrnt. Applcton of PROMETHEE I nd PROMETHEE II Tble 10 contns ggregted preference ndces for ech pr of vrnts s well s the postve nd the negtve outrnng flows for ech vrnt.

18 28 Dorot Górec Tble 10 Aggregted preference ndces nd outrnng flows postve nd negtve postve outrnng flow 1 0 0,4 0,4 0,5 0,5 0,45 2 0,4 0 0,35 0,4 0,225 0, ,25 0, ,4 0,4 0, ,4 0,1 0, ,25 0, , ,1 0,4 0 0,16875 negtve outrnng flow 0, , , ,425 0,34375 On the bss of the postve nd the negtve outrnng flows the prtl rnng n PROMETHEE I nd the complete rnng n PROMETHEE II were bult. Tble 11 Reltons between vrnts determned wth the help of PROMETHEE I I R P P P 2 I P P P 3 I P P 4 I R 5 I Fgure 3. Prtl vrnts rnng produced usng PROMETHEE I

19 MULTI-CRITERIA DECISION AIDING IN PROJECT MANAGEMENT Complete vrnts rnng obtned wth the d of PROMETHEE II Tble 12 Plce Vrnt Net outrnng flow 1 2 0, , , , ,175 It cn be esly notced tht ccordng to the results obtned wth the help of methods belongng to the PROMETHEE fmly vrnts 1 nd 2 turned out to be the best. As PROMETHEE I method s consdered they re ncomprble, but they re both on the hghest level of the grph. In the cse of PROMETHEE II they were clssfed on two frst plces wth postve net outrnng flows. On the opposte ste we hve vrnts 4 nd 5 whch were clssfed on two lst plces nd on the lowest level of the grph ccordng to PROMETHEE II nd PROMETHEE I respectvely. Applcton of UnComBOS Pr-wse comprsons of one-crteron unts resulted n the grph tht s plced below. The wndow on the fgure shows how the relton between vrnts nd 5 ws obtned. 2 Fgure 4. Result grph bsed on the comprsons of one-crteron unts

20 30 Dorot Górec Becuse comprsons of one-crteron unts were not suffcent for the best vrnt choce, IDSS UnComBOS proceeds to pr-wse comprsons of two-crter unts. They re presented on the Fgures 5-8. Dgrms bove show tht: on Cost of relzton, 30 on Vehcle s verge trvel tme s less preferble thn 300 on Cost of relzton, 40 on Vehcle s verge trvel tme 2. 7 on "Impct on the envronment", 6 on Sfety of the trvelers s less preferble thn 6 on Impct on the envronment, 7 on Sfety of the trvelers on Cost of relzton, 7 on Sfety of the trvelers s less preferble thn 300 on Cost of relzton, 6 on Sfety of the trvelers on Cost of relzton, 7 on Sfety of the trvelers s s preferble s 250 on Cost of relzton, 2 on Sfety of the trvelers on Vehcle s verge trvel tme, 6 on Impct on the envronment s more preferble thn 50 on Vehcle s verge trvel tme, 8 on Impct on the envronment Fgure 5. Comprsons of two-crter unts prt I

21 MULTI-CRITERIA DECISION AIDING IN PROJECT MANAGEMENT Dgrms bove show tht: on Cost of relzton, 7 on Sfety of the trvelers s s preferble s 280 on Cost of relzton, 4 on Sfety of the trvelers on Cost of relzton, 30 on Vehcle s verge trvel tme s s preferble s 320 on Cost of relzton, 45 on Vehcle s verge trvel tme on Cost of relzton, 6 on Sfety of the trvelers s more preferble thn 250 on Cost of relzton, 2 on Sfety of the trvelers on Vehcle s verge trvel tme, 7 on Impct on the envronment s more preferble thn 50 on Vehcle s verge trvel tme, 8 on Impct on the envronment on Cost of relzton, 7 on Impct on the envronment s more preferble thn 280 on Cost of relzton, 2 on Impct on the envronment Fgure 6. Comprsons of two-crter unts prt II

22 32 Dorot Górec Dgrms bove show tht: on Vehcle s verge trvel tme, 6 on Sfety of the trvelers s more preferble thn 35 on Vehcle s verge trvel tme, 4 on Sfety of the trvelers on Cost of relzton, 2 on Sfety of the trvelers s s preferble s 280 on Cost of relzton, 4 on Sfety of the trvelers on Vehcle s verge trvel tme, 8 on Impct on the envronment s s preferble s 35 on Vehcle s verge trvel tme, 2 on Impct on the envronment on Cost of relzton, 2 on Impct on the envronment s s preferble s 320 on Cost of relzton, 5 on Impct on the envronment on Vehcle s verge trvel tme, 4 on Sfety of the trvelers s more preferble thn 45 on Vehcle s verge trvel tme, 5 on Sfety of the trvelers Fgure 7. Comprsons of two-crter unts prt III

23 MULTI-CRITERIA DECISION AIDING IN PROJECT MANAGEMENT Dgrms bove show tht: on Cost of relzton, 50 on Vehcle s verge trvel tme s more preferble thn 320 on Cost of relzton, 45 on Vehcle s verge trvel tme 2. 8 on Impct on the envronment, 2 on Sfety of the trvelers s less preferble thn 5 on Impct on the envronment, 5 on Sfety of the trvelers on Cost of relzton, 2 on Sfety of the trvelers s s preferble s 320 on Cost of relzton, 5 on Sfety of the trvelers on Vehcle s verge trvel tme, 8 on Impct on the envronment s more preferble thn 45 on Vehcle s verge trvel tme, 5 on Impct on the envronment Fgure 8. Comprsons of two-crter unts prt IV On the bss of the conducted comprsons the followng grph hs been constructed.

24 34 Dorot Górec Fgure 9. Fnl grph Accordng to the grph the set of best vrnts ncludes vrnts 2 nd 4. They re mutully ncomprble but preferble to other decson-mng vrnts. The worst soluton s vrnt 5. Addtonlly, t s worth mentonng tht vrnts 1 nd 3 turned out to be eqully preferble to the decson-mer.

25 MULTI-CRITERIA DECISION AIDING IN PROJECT MANAGEMENT Conclusons Two dfferent pproches were mplemented to d the process of selectng the best vrnt of rod constructon, nmely pproch bsed on the outrnng relton nd verbl decson nlyss. Out of wde rnge of outrnng methods three very well nown were ppled: ELECTRE Iv, PROMETHEE I nd PROMETHEE II. In the cse of VDA UnComBOS ws used. The results obtned wth dfferent methods were not dentcl, nevertheless t ws possble to dentfy vrnt worth recommendton,.e. vrnt 2, whch ws lwys on one of two frst plces n rnngs, regrdless of the method tht ws used. On the other hnd, vrnt 5 ws found to be the worst soluton ts weness ws confrmed by ll methods. The nlyss conducted n the rtcle proved tht both descrbed pproches cn be used for solvng the decson-mng problems connected wth proect mngement. Although both of them hve some dsdvntges, s for exmple necessty to nterct wth decson-mer n order to determne vlues of prmeters n the cse of outrnng methods nd tme-consumng s well s trng comprsons n the cse of VDA, they cn mprove the decson-mng processes nd help proect mngers to me more resonble decsons. As mtter of fct, becuse of the dfferences between them, they cn complement ech other. Therefore t would be prctcl nd benefcl to employ them smultneously n ll cses when t s merely possble nd fesble. References Ahmd N., Lplnte P.A. 2006, Softwre Proect Mngement Tools: Mng Prctcl Decson Usng AHP, Proceedngs of the 30 th Annul IEEE/NASA Softwre Engneerng Worshop, Ashhmn I., Furems E. 2005, UnComBOS Intellgent Decson Support System for Mult-crter Comprson nd Choce. Journl of Mult-crter Decson Anlyss, 13, Bru S., Jwors K.M., Tors Z. 2007, Podstwy orgnzc robót drogowych. Wydwnctwo Nuowe PWN, Wrszw, 11-12, Brns J.P., Mreschl B. 2005, PROMETHEE Methods, n: Multple Crter Decson Anlyss: Stte of the Art Surveys. Eds. J. Fguer, S. Greco, M. Ehrgott. Sprnger, New Yor. Brns J.P., Vnce Ph. 1985, A Preference Rnng Orgnzton Method: The PROMETHEE Method for Multple Crter Decson-Mng. Mngement Scence, 31,

26 36 Dorot Górec Brns J.P., Vnce Ph., Mreschl B. 1986, How to select nd how to rn proects: The PROMETHEE method. Europen Journl of Opertonl Reserch, 24, Fguer J., Mousseu V., Roy B ELECTRE Methods, n: Multple Crter Decson Anlyss: Stte of the Art Surveys. Eds. J. Fguer, S. Greco, M. Ehrgott. Sprnger, New Yor. Fshburn P.C. 1979, Utlty Theory for Decson Mng. Kreger Publshng Compny, New Yor. Furems E., Ashhmn I. 2004, UnComBOS Intellectul Decson Support System for Mult-crter Comprson nd Choce. MCDM, Whstler, Brtsh Columb, Cnd. Furems E.M., Lrchev O.I., Rozenson G.V., Lotov A.V., Mettnen K. 2003, Humn behvor n mult-crter choce problem wth ndvdul tss of dfferent dffcultes. Interntonl Journl of Informton Technology & Decson Mng, 21, Górec D. 2011, On the choce of method n mult-crter decson dng process concernng Europen proects, n: Multple Crter Decson Mng 10-11, Eds. T. Trzsl, T. Wchowcz. Publsher of The Krol Admec Unversty of Economcs n Ktowce, Ktowce, Keeney R.L., Rff H. 1976, Decsons wth Multple Obectves: Preferences nd Vlue Trdeoffs. Wley, New Yor. Korhonen P., Lrchev O., Moshovch H., Mechtov A., Wllenus J. 1997, Choce behvor n computer-ded multttrbute decson ts. Journl of Mult-Crter Decson Anlyss, 6, Lrchev O.I. 1992, Cogntve vldty n desgn of decson-dng technque. Journl of Mult-Crter Decson Anlyss, 13, Lrchev O.I. 2001, Method ZAPROS for Multcrter Alterntves Rnng nd the Problem of Incomprblty. Informtc, 12, Lrchev O.I. 2001b, Rnng multcrter lterntves: the method ZAPROS III. Europen Journl of Opertonl Reserch, 131, Lrchev O.I., Moshovch H.M. 1995, ZAPROS-LM A method nd system for orderng multttrbute lterntves. Europen Journl of Opertonl Reserch, 82, Lrchev O.I., Moshovch H.M. 1997, Verbl Decson Anlyss for Unstructured Problems. Kluwer Acdemc Publshers, Berln. Lng Y.Y. 2003, A conceptul model for selecton of rchtects by proect mngers n Sngpore. Interntonl Journl of Proect Mngement, 21, Mrques G., Gourc D., Lurs M. 2010, Mult-crter performnce nlyss for decson mng n proect mngement. Interntonl Journl of Proect Mngement, 29,

27 MULTI-CRITERIA DECISION AIDING IN PROJECT MANAGEMENT Mrtel J.M. 1998, Multcrteron Anlyss under Uncertnty: the Approch of Outrnng Synthess, n: Modelowne preferenc ryzyo 98. Ed. T. Trzsl. Adem Eonomczn w Ktowcch, Ktowce. Metody weloryterlne n polsm rynu fnnsowym. 2006, Ed. T. Trzsl. PWE, Wrszw. Montgomery H.,. Svenson O. 1989, A thn-loud study of domnnce structurng n decson processes, n: Process nd Structure on Humn Decson Mng. Eds. H. Montgomery, O. Svenson. Wley, Chchester, Moshovch H.M., Mechtov A.I., Olson D.L. 2002, Ordnl udgments n multttrbute decson nlyss. Europen Journl of Opertonl Reserch, 137, Moshovch H.M., Mechtov A.I., Olson D.L. 2005, Verbl Decson Anlyss, n: Multple Crter Decson Anlyss: Stte of the Art Surveys. Eds. J. Fguer, S. Greco, M. Ehrgott. Sprnger, New Yor. Moshovch H.M., Schellenberger R., Olson D.L. 1998, Dt nfluences the result more thn preferences: Some lessons from mplementton of multttrbute technques n rel decson ts. Decson Support Systems, 22, Mot C.M.M., De Almed A.T., Alencr L.H. 2009, A multple crter decson model for ssgnng prortes to ctvtes n proect mngement. Interntonl Journl of Proect Mngement, 27, Pyne J.W., Bettmn J.R., Coupey E., Johnson E.J. 1993, A constructve process vew of decson mng: multple strteges n udgment nd choce, n: Current Themes n Psychologcl Decson Reserch. Eds. O. Huber, J. Mumpower, J. vn der Plgt, P. Koele. North Hollnd, Amsterdm, Prdsht M., Ghd A., Mohmmd M., Shotlb G. 2009, Mult-Crter Decson-Mng Selecton Model wth Applcton to Chemcl Engneerng Mngement Decsons. Interntonl Journl of Humn nd Socl Scences, 4:15, PMBOK Gude A Gude to the Proect Mngement Body of Knowledge. Proect Mngement Insttute, Roy B. 1990, Weloryterlne wspomgne decyz. Wydwnctw Nuowo- Technczne, Wrszw. Roy B., Bouyssou D. 1993, Ade Multcrtere l Decson: Methodes et Cs. Economc, Prs. Russo J.E., Rosen L.D. 1975, An eye fxton nlyss of multttrbute choce. Memory nd Cognton, 3, Trzsl T., Trzpot G., Zrś K. 1998, Modelowne preferenc z wyorzystnem domnc stochstycznych. Adem Eonomczn w Ktowcch, Ktowce.

28 38 Dorot Górec Vdl L-A., Mrle F., Bocquet J-C 2011, Mesurng proect complexty usng the Anlytc Herrchy Process. Interntonl Journl of Proect Mngement, 29, Vnce Ph. 1992, Multcrter Decson-Ad. John Wley & Sons, New Yor.

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