Multiple Criteria Decision Making in Application Layer Networks

Bay eu he A bei spapie e zu Wi scha sin o ma ik Leh s uhl ü Wi scha sin o ma ik In o ma ion Sys ems Managemen Bay eu h Repo s on In o ma ion Sys ems Managemen No. 36 July 2008 F ank Schneide Mul iple C i e ia Decision Making in Applica ion Laye Ne wo ks ISSN 1864-9300 Die A bei spapie e des Leh s uhls ü Wi scha sin o ma ik dienen de Da s ellung o läu ige E gebnisse, die i. d. R. noch ü spä e e Ve ö en lichungen übe a bei e we den. Die Au o en sind deshalb ü k i ische Hinweise dankba . The Bay eu h Repo s on In o ma ion Sys ems Managemen comp ise p elimina y esul s which will usually be e ised o subsequen publica ions. C i ical commen s would be app ecia ed by he au ho s. Alle Rech e o behal en. Insbesonde e die de Übe se zung, des Nachd uckes, des Vo ags, de En nahme on Abbildungen und Tabellen – auch bei nu auszugsweise Ve we ung. All igh s ese ed. No pa o his epo may be ep oduced by any means, o ansla ed. Au ho s: In o ma ion Sys ems and Managemen Wo king Pape Se ies Edi ed by: P o . D . To s en Eymann Managing Assis an and Con ac : Raimund Ma os Uni e si ä Bay eu h Leh s uhl ü Wi scha sin o ma ik (BWL VII) P o . D . To s en Eymann Uni e si ä ss asse 30 95447 Bay eu h Ge many Email: aimund.ma os@uni-bay eu h.de ISSN F ank Schneide (Uni e si y o Bay eu h) 1864-9300 i Con en s Con en s............................................................................................. i Lis o Figu es ...................................................................................i Lis o Tables..................................................................................... i Lis o Abb e ia ions ........................................................................ ii Lis o Symbols..................................................................................ix 1 In oduc ion ................................................................................ 1 1.1 S a ing Posi ion: T us in eComme ce ............................................. 1 1.2 Objec i es o his S udy......................................................................2 1.3 Conduc o his S udy .........................................................................3 2 In e ac ions in Applica ion Laye Ne wo ks .................................5 2.1 Depic ing he En i onmen ................................................................5 2.2 Coo dina ion in Applica ion Laye Ne wo ks....................................5 2.2.1 Applica ion Laye Ne wo ks...............................................................5 2.2.2 Ca allac ic In o ma ion Sys ems........................................................6 2.3 So wa e Agen s in Mul i Agen Sys ems...........................................7 2.3.1 So wa e Agen s..................................................................................7 2.3.2 Mul i Agen Sys ems.........................................................................10 2.3.3 Dissemina ing and Ga he ing In o ma ion ......................................11 2.4 The Objec o In e ac ion: T ading Goods....................................... 12 2.4.1 Homogeneous and He e ogeneous Goods and Se ices .................12 2.4.2 P ice Fo ma ion Mechanisms .......................................................... 13 2.5 Di e en ia ion h ough Repu a ion................................................. 17 2.5.1 Repu a ion and Image...................................................................... 17 2.5.2 Repu a ion Sys ems..........................................................................18 ii 2.6 Decision Making...............................................................................23 2.6.1 Theo y o Decision............................................................................23 2.6.2 The Classical Model o Decision Making........................................25 2.6.3 Mul iple C i e ia Decision Making.................................................. 28 2.6.4 P e e ence Modeling h ough U ili y and Values ............................29 3 Mul iple C i e ia Decision Making ............................................. 31 3.1 Classi ica ion o MCDM Me hods .................................................... 31 3.2 On Da a and Weigh s .......................................................................32 3.2.1 Scales o Da a....................................................................................32 3.2.2 No maliza ion Techniques o Equalizing Di e se Scales...............34 3.2.3 Weigh s as Means o Rela i e Impo ance o C i e ia ...................35 3.3 Mul iple A ibu e Decision Making ............................................... 38 3.3.1 A Taxonomy o MADM Me hods .................................................... 38 3.3.2 Deciding wi hou P e e ence In o ma ion.......................................39 3.3.3 Sa is icing (Conjunc i e and Disjunc i e App oaches) ...................41 3.3.4 Sequen ial Elimina ion.....................................................................42 3.3.5 Value Func ion Me hods ..................................................................44 3.4 Mul iple Objec i e Decision Making................................................55 3.4.1 O e iew o MODM Me hods ..........................................................55 3.4.2 Goal P og amming ...........................................................................56 3.5 Decision Aids....................................................................................59 3.5.1 Ou anking Rela ions .......................................................................59 3.5.2 The ELECTRE App oach................................................................. 60 4 Applica ion o he Ex ended TOPSIS o he Scena io ..................64 4.1 S uc u e...........................................................................................64 iii 4.2 A Syn hesis o ALN and MCDM.......................................................64 4.2.1 Summa y o En i onmen Cha ac e is ics ......................................64 4.2.2 Compa ison o MCDM Me hods ......................................................67 4.2.3 Conclusion o Me hod Applica ion................................................. 71 4.3 Scena io Speci ica ions.....................................................................72 4.3.1 En i onmen and Ac o s ..................................................................72 4.3.2 In e ac ion be ween Ac o s ..............................................................73 4.3.3 O e A ibu es.................................................................................75 4.3.4 P incipal’s P e e ence In o ma ion..................................................76 4.4 The Ex ended TOPSIS......................................................................77 4.4.1 Desc ip ion o he Technique...........................................................77 4.4.2 Applica ion o he xTOPSIS: A Nume ical Example........................78 4.5 Findings om he Scena io Applica ion ......................................... 83 4.5.1 In e empo al Compa ison o Reached Ag eemen s...................... 83 4.5.2 Selle E alua ion ............................................................................. 84 4.5.3 Summa y ......................................................................................... 84 5 Conclusion .................................................................................85 5.1 Resul s ..............................................................................................85 5.2 Sugges ions o Resea ch and some C i ical Anno a ions.............. 88 Re e ences ...................................................................................... 90 Appendix........................................................................................ 105 Appendix A........................................................................................................105 Appendix B: Case S udy....................................................................................108 i Lis o Figu es Figu e 1: Pe cen age o EU en e p ises' o al u no e om eComme ce ia In e ne ....1 Figu e 2: Gene al app oach o his wo k........................................................................ 4 Figu e 3: Ou line o he 2nd Sec ion................................................................................ 5 Figu e 4: The ALN as a i ual ha d disk ....................................................................... 6 Figu e 5: The P ocedu al Reasoning Sys em ................................................................. 9 Figu e 6: Typology o goods ..........................................................................................13 Figu e 7: P ice o ma ion mechanisms .........................................................................14 Figu e 8: Well-known auc ion ypes .............................................................................16 Figu e 9: Building blocks o epu a ion ....................................................................... 18 Figu e 10: Calcula ion o us in ReG eT.................................................................... 22 Figu e 11: Decision-making p ocess............................................................................. 24 Figu e 12: Non-sequen ial decision-making p ocess................................................... 25 Figu e 13: Subp ocess o de ining a decision ma ix ................................................... 26 Figu e 14: Classical model o decision-making............................................................28 Figu e 15: MCDM me hodology ....................................................................................31 Figu e 16: Ou line o he 3 d Sec ion............................................................................. 32 Figu e 17: Rela i e and cumula i e weigh s in alue ees .......................................... 37 Figu e 18: The subp ocess o de ining weigh s ............................................................38 Figu e 19: O e iew o MADM me hods...................................................................... 39 Figu e 20: E icien on ie .........................................................................................40 Figu e 21: P ocess o he Simple Addi i e Weigh ing me hod ....................................46 Figu e 22: P ocess o he Weigh ed P oduc Me hod ..................................................48 Figu e 23: Gene ic ou - and i e-le el hie a chies .....................................................49 Figu e 24: Simpli ied p ocess o he Analy ic Hie a chy P ocess................................50 Figu e 25: A h ee-le el hie a chy o means o a el .................................................51 Figu e 26: Euclidean dis ances o he ideal solu ions in wo-dimensional space....... 52 Figu e 27: P ocess o he Technique o O de P e e ence by Simila i y o Ideal Solu ion . 53 Figu e 28: A axonomy o me hods o Mul iple Objec i e Decision Making............. 56 Figu e 29: Po ay o easible solu ions in a GP example............................................ 57 Figu e 31: Ou line o he 4 h Sec ion............................................................................. 64 Figu e 32: The main p ocess o buying s o age capaci y and he MCDM blackbox ...66 Figu e 33: P e equisi es o he app op ia e MCDM me hod .....................................68 Figu e 34: Classi ica ion o MCDM me hods in he ligh o he scena io ....................71 Figu e 35: Scheme o he scena io ............................................................................... 73 Figu e 36: In e ac ion wi hin he ALN......................................................................... 74 Figu e 37: P ocess o he ex ended TOPSIS..................................................................77 i Lis o Tables Table 1: S anda d cases o he employmen o DBAs ................................................. 10 Table 2: Dis inc ion be ween DPS and MAS.................................................................11 Table 3: Example o a decision ma ix .........................................................................26 Table 4: Te minology in decision-making ................................................................... 27 Table 5: Example o a mul iple c i e ia decision p oblem...........................................28 Table 6: Scale le els and hei p ope ies..................................................................... 33 Table 7: No maliza ion wi h linea scale ans o ma ion............................................ 34 Table 8: Vec o no maliza ion...................................................................................... 35 Table 9: Maximin and Maximax decision ules............................................................41 Table 10: Sa is icing app oaches ..................................................................................42 Table 11: Addi i e and mul iplica i e weigh ing app oaches ...................................... 47 Table 12: Assembling posi i e and nega i e ideal solu ions........................................ 53 Table 13: Ou anking ela ions..................................................................................... 59 Table 14: Summa y o scena io cha ac e is ics............................................................ 65 Table 15: Dimensions o he compa ison able ............................................................69 Table 16: Compa ison o MCDM me hods................................................................... 70 Table 17: O e a ibu es.............................................................................................. 75 Table 18: Weigh ec o ................................................................................................ 76 Table 19: Decision ma ix o he 1s ound ................................................................... 79 Table 20: Weigh ed no malized decision ma ix o he 1s ound ............................... 79 Table 21: Closeness alues and anking o he 1s ound ............................................80 Table 22: Decision ma ix o he 2nd ound.................................................................. 81 Table 23: Weigh ed no malized ma ix, closeness alues and anks o he 2nd ound... 82 Table 24: Weigh ed no malized ma ix, closeness alues and anks o he 3 d ound... 82 ii Lis o Abb e ia ions AHP.................................................................................... Analy ical Hie a chy P ocess ALN ....................................................................................... Applica ion Laye Ne wo k BDI.............................................................................................. Belie -Desi e-In en ion CAGR ............................................................................Compound Annual G ow h Ra e CIS...................................................................................Ca allac ic In o ma ion Sys em DBA...............................................................................................Digi al Business Agen DM ...........................................................................................................decision-make DPS......................................................................................Dis ibu ed P oblem Sol ing EbA...............................................................................................Elimina ion by Aspec s ELECTRE................................................... ELimina ion E Choix T aduisan la REali é eRep ..........................................Social Knowledge o e-Go e nance (p ojec ac onym) EU .......................................................................................................... Eu opean Union EUR........................................................................................................................... Eu o Eu o NCAP................................................. Eu opean New Ca Assessmen P og amme FPSB................................................................................................ i s -p ice sealed-bid g............................................................................................................................ g am(s) GB.........................................................................................................................gigaby e ICT............................................................. in o ma ion and communica ion echnology IDB................................................................................................ Imp essions Da abase IVD................................................................................................ Ideal Vec o Da abase km ......................................................................................................................kilome e kmph ...................................................................................................kilome e pe hou LM.................................................................................................Lexicog aphic Me hod LS ............................................................................................. Lexicog aphic Semio de L ................................................................................................................................li e MAS................................................................................................... Mul i Agen Sys em MADM .................................................................... Mul iple A ibu e Decision Making MCDM........................................................................Mul iple C i e ia Decision Making MODM ....................................................................Mul iple Objec i e Decision Making ODB...................................................................................................Ou comes Da abase PD..........................................................................................................Pa ne Da abase 4 Sec ion Sec ion T us in eComme ce Goals o his s udy The app oach In oduc ion 1. 1. Applica ion Laye Ne wo ks So wa e agen s and Mul i Agen Sys ems T ading goods and o ming p ices Repu a ion and epu a ion sys ems Decision-making – Theo y and classical model In e ac ions in Applica ion Laye Ne wo ks 2. 2. Da a and weigh s Mul iple A ibu e Decision Making Mul iple Objec i e Decision Making Decision Aids Mul iple C i e ia Decision Making 3. 3. Syn hesis o MCDM and ALN Scena io Speci ica ions The TOPSIS ex ension Findings om he applica ion Applying he MCDM Me hod 4. 4. Resul s Sugges ions o esea ch and some C i ical Wo ds Resul s & Ou look 5. 5. Figu e 2: Gene al app oach o his wo k The Appendix a he end includes he example o a mul iple c i e ia decision p oblem conce ning he pu chase o a ca . The case s udy complemen s he wo k in e ms o illus a ing he calcula ion s eps o almos all p esen ed decision-making me hods. 5 2 In e ac ions in Applica ion Laye Ne wo ks 2.1 Depic ing he En i onmen This Sec ion cla i ies he used e minology and desc ibes he economic en i onmen in which he decision-making scena io is loca ed (Figu e 3). To achie e ha , we ex- plain he coo dina ion p inciple (Subsec ion 2.2) and p esen he ac o s (Subsec ion 2.3). The ea e , we cla i y he a ionale o and he conduc o in e ac ion (Subsec- ion 2.4) be o e we a end o he unc ion o epu a ion in gene al and as an inhe en ins i u ion o he en i onmen (Subsec ion 2.5). Finally, we explica e decision- making and glance a p e e ence modeling (Subsec ion 2.6). ALN ALN Applica ion Laye Ne wo ks Ca allac ic In o ma ion Sys em Applica ion Laye Ne wo ks Ca allac ic In o ma ion Sys em 2.2 MAS MAS So wa e agen s Mul i Agen Sys ems In o ma ion ansmission So wa e agen s Mul i Agen Sys ems In o ma ion ansmission 2.3 Repu a ion and image Repu a ion sys ems Repu a ion and image Repu a ion sys ems Repu a ion Repu a ion 2.5 Goods and Se ices P ice Fo ma ion Mechanisms Goods and Se ices P ice Fo ma ion Mechanisms T ading T ading 2.4 Theo y o decision Classical model o decision- making P e e ence modeling Theo y o decision Classical model o decision- making P e e ence modeling Decision Making Decision Making 2.6 Te minology Te minology Subsec ion ALN ALN Applica ion Laye Ne wo ks Ca allac ic In o ma ion Sys em Applica ion Laye Ne wo ks Ca allac ic In o ma ion Sys em ALN ALN Applica ion Laye Ne wo ks Ca allac ic In o ma ion Sys em Applica ion Laye Ne wo ks Ca allac ic In o ma ion Sys em 2.2 MAS MAS So wa e agen s Mul i Agen Sys ems In o ma ion ansmission So wa e agen s Mul i Agen Sys ems In o ma ion ansmission MAS MAS So wa e agen s Mul i Agen Sys ems In o ma ion ansmission So wa e agen s Mul i Agen Sys ems In o ma ion ansmission 2.3 Repu a ion and image Repu a ion sys ems Repu a ion and image Repu a ion sys ems Repu a ion Repu a ion 2.5 Goods and Se ices P ice Fo ma ion Mechanisms Goods and Se ices P ice Fo ma ion Mechanisms T ading T ading Goods and Se ices P ice Fo ma ion Mechanisms Goods and Se ices P ice Fo ma ion Mechanisms T ading T ading 2.4 Theo y o decision Classical model o decision- making P e e ence modeling Theo y o decision Classical model o decision- making P e e ence modeling Decision Making Decision Making 2.6 Te minology Te minology Subsec ion Figu e 3: Ou line o he 2nd Sec ion 2.2 Coo dina ion in Applica ion Laye Ne wo ks 2.2.1 Applica ion Laye Ne wo ks An ex ensi e compu e ne wo k which p o ides se ices equi ing a conside able amoun o esou ces is called Applica ion Laye Ne wo k (ALN). In o de o acqui e hese esou ces, ALNs use communica ion in as uc u es such as he In e ne in o - de o in e connec nume ous indi idual compu e s [ESR+05, 7]. Resou ce alloca ion by means o cen alized mechanisms p o es o be ine icien o wo easons: Fi s , he coo dina ing ins i u ion is supposed o ans e ins an ly a huge numbe o eques s om connec ed pee s. Second, apidly changing membe 6 s uc u es in dynamic ne wo ks and mul iple a ying en i onmen al s a es place g ea demand on he p ocessing capaci ies o he coo dina o . Especially la ge-scale ne wo ks call o coo dina ion mechanisms which a e capable o alloca ing esou ces and se ices in eal ime o ul ill speci ied se ice-le els [ERA+04, 10], [Eyma03, 53–54]. Hence, we explain a decen alized philosophy in he nex Subsec- ion. A p ominen example o an ALN is he Pee - o-Pee sys em Bi To en which en- ables membe s o sha e esou ces and ans e iles o each o he [SNV+07, 91–92], [Cohe03, 1]. Fo he applica ion o ALNs in academics, p ime examples a e he S an- o d Uni e si y’s Folding@home p ojec o he dis ibu ed sea ch o ex a- e es ial in elligence, SETI@home, un by he Space Science Labo a o y a he Uni e si y o Cali o nia, Be keley [Pand08, 1-2], [Uni 08]. In he scena io o his wo k, he ALN is a i ual ha d disk composed o space p o- ided by linked up compu e sys ems (Figu e 4). ALN: i ual ha d disk ALN: i ual ha d disk Compu e sys em wi h ha d disk Compu e sys em wi h ha d disk Figu e 4: The ALN as a i ual ha d disk 2.2.2 Ca allac ic In o ma ion Sys ems Wi h ega d o he economic p inciples o F ied ich Augus on Hayek’s Ca allaxy, he Ca allac ic In o ma ion Sys em (CIS) p oposes a decen alized coo dina ion mechanism as a new pa adigm o he design o in o ma ion sys ems [EPSc00, 349– 350]. Hayek’s Ca allaxy can be unde s ood as a synonym o ee-ma ke economy, using p ices as coo dina ion mechanisms and, wi hou knowledge o he indi idual ac o s’ 7 beha io s, leading o a “spon aneous o de ” [Eyma03, 157]. The concep assumes membe s in he sys em a e sel -in e es ed and s i e o maximize hei u ili y. As pa - icipan s can nei he o esee u u e ma ke s a es no p edic o he agen s’ beha io s (cons i u ional igno ance), hey a e o ced o make decisions unde bounded a ion- ali y [ESR+05, 13]. The CIS molds he concep o Ca allaxy using he echnology o Mul i Agen Sys ems (MAS), which consis o so wa e agen s ep esen ing he ac o s in he Ca allaxy (c . Subsec ion 2.3.2). The e alua ion o a Ca allaxy-based coo dina ion mechanism has been subjec o e- sea ch in he CATNETS p ojec . The au ho s deduced se e al ields o u he e- sea ch, including, bu no limi ed o, he necessi y o implemen elec onic ins i u- ions and social con ol mechanisms o cope wi h ola ile se ice quali ies and ma- le olen so wa e agen s [S Ey07, 27–30]. Wi h espec o hese indings we imple- men a go e nance mechanism in ou u u e scena io. 2.3 So wa e Agen s in Mul i Agen Sys ems 2.3.1 So wa e Agen s 2.3.1.1 Agen s in Compu e Science The Me iam-Webs e explains he e m agen as “one who is au ho ized o ac o o in he place o ano he ”, i.e. a ep esen a i e o someone o some hing [Me 08a, § 4]. The ansla ion o he adi ional meaning in he con ex o compu e science is called so wa e agen o in elligen agen . Due o he e sa ili y o agen s in applica- ions, a de ini e and o e a ching explica ion is s ill open [Bu k03, 1014–1015], [Nwan96, 208]. Re e ing o Woold idge, we unde s and so wa e agen s as au onomous en i ies in- e ac ing wi h hei en i onmen in a bidi ec ional way: Agen s ecei e inpu h ough senso s and use e ec o s o eac wi h ou pu ac ions [Wool00, 29]. In addi ion o au onomy, ou agen s a e in elligen in he sense ha hey a e lexible in conduc ing ac ions o achie e hei goals. Flexibili y in u n comp ises he ollow- ing h ee ea u es:  eac i i y e e s o immedia e esponse o en i onmen al changes, 8  p o-ac i eness is he abili y o ake he ini ia i e, and  social abili y means in e ac ing wi h o he agen s. Each ea u e has implica ions o he emainde o his wo k: Social abili y equi es he p esence o addi ional agen s o coope a e wi h as well as he implemen a ion o a common communica ion language. P o-ac i eness and eac i i y seem con adic o y, and eac i i y e en pu s au onomy in o ques ion – in o de o balance hese ea u es, an in e nal model is equi ed ha allows elabo a ing and adjus ing plans o ac ion [Wool00, 32–33]. Supplemen a y o Woold idge’s de ini ion o eac i i y, sugges ions o u he po en- ial dimensions a e lis ed in [Bu k03, 951–953]. Nwana akes up lea ning which e ol es om pas in e ac ions wi h he en i onmen , and a gues o i s explici con- side a ion [Nwan96, 210]. Lea ning is “any ins ance o imp o emen o beha io h ough inc eased in o ma ion abou he en i onmen ” [Kael93, 4]. Though lea ning seems implici when a ibu ing eac i i y o agen s, i can ake a ious o ms in MAS; a gene al cha ac e iza ion can be ound in [SeWe00, 260–264]. In ou con ex , he agen lea ns om encoun e s wi h o he s in he way ha he ad- jus s his belie s abou he en i onmen . 2.3.1.2 P ac ical Reasoning in he In e nal Model Be ween pe cep ion and ac ion, he in e nal model p o ides he basis on which agen s make decisions and ul ill hei assigned unc ion. P ac ical easoning is he wo-phase p ocess o delibe a ion and means-end easoning. A i s , delibe a ion e e s o deciding wha s a e o achie e, whe eas means-end easoning a e wa ds e e s o deciding how o achie e he pa icula s a e. S a es an agen has commi ed o a e called in en ions: hey d i e means-end easoning, cons ain u u e delibe a- ion, and exe in luence on belie s [Wool05, 66–69]. Among he a ailable models, we will ou line he P ocedu al Reasoning Sys em (PRS) in he ollowing pa ag aphs, since i is an app o ed implemen a ion o delibe a e agen s and embodies he Belie -Desi e-In en ion (BDI) pa adigm [Wool05, 82]. Fa - he , he PRS co esponds o he amewo k used in he eRep p ojec [SPV+07, 13]. In he PRS a chi ec u e, ou a i udes de e mine he beha io o he agen , i.e. how p ac ical easoning is conduc ed. Ou agen is in possession o he key da a s uc u es 9 belie s, desi es, in en ions and plans (Figu e 5) [Wool96, 663–664]:  Belie : knowledge eme ging om in o ma ion abou en i onmen al s a es e- cei ed and upda ed h ough he agen ’s senso . Belie is subjec i e and no necessa ily co ec o comple e.  Desi e: objec i es o asks, he agen is supposed o accomplish, and p io i ies associa ed wi h hem. Desi e ep esen s he mo i a ional s a e o an agen .  In en ions: delibe a i e s a e. In en ions a e he cu en ly chosen cou se o ac- ion, i.e. he objec i e he agen has commi ed o pu sue a he momen .  Plans: pa icula pa e ns o ins uc ions o achie e an objec i e. Plans a e made up o a goal, a con ex (p econdi ions) and a body ( he sequence o ac- ions o ca y ou ). Da a Inpu Da a Inpu Ac ion Ou pu Ac ion Ou pu En i onmen Desi es In en ions In e p e e PlansBelie s Senso Agen Agen Figu e 5: The P ocedu al Reasoning Sys em [Wool05, 83] The p ocess o p ocedu al easoning wo ks as ollows: A he beginning, he in e - p e e (planne ) has belie s abou he wo ld, a collec ion o plans and a op-le el goal. He b owses his lib a y o plans o ex ac hose ones ha ma ch bo h goal and p e- condi ion o he cu en s a e. A e wa ds, in he p ocess o delibe a ion he agen selec s a plan om he esul ing se o op ions. A p ac ical means o allow a ional jus i ied selec ions is he implemen a ion o a u ili y alue o op ions: hen he plan 10 wi h he highes alue is selec ed ( o an explica ion o u ili y c . Subsec ion 2.6.4). A e execu ion o he chosen plan, new goals a ise and equi e delibe a ion and so on. [Wool05, 83–84]. 2.3.1.3 Digi al Business Agen s So wa e agen s ac ing on behal o a legal en i y in comme cial en i onmen s a e called digi al business agen s (DBA). They a e obedien , u ili a ian en i ies whose comme cial unc ion (goal) is de ined by a p incipal (human being o o ganiza ion). Obedience implies ha he DBA’s pa amoun goal is always aligned wi h he p inci- pal’s one: o ac in he owne ’s in e es . This in u n jus i ies he u ili a ian a i ude o he agen , exp essed by a ional conduc in o de o con ibu e o he p incipal’s u il- i y [Eyma03, 24–26]. Roughly, one may dis inguish be ween wo di e en cases in which DBAs a e used: he coope a i e and he compe i i e en i onmen (Table 1). Table 1: S anda d cases o he employmen o DBAs (based on [Eyma03, 27]) Pa adigm Coope a ion Compe i ion Pu sued Goals Common Collec i e u ili y maximiza ion (e.g. low cycle ime) Con lic ing Indi idual u ili y maximiza ion (e.g. high p o i ) En i onmen Closed sys em Numbe o pa icipan s is cons an Open sys em Agen s en e and lea e he sys em du ing un ime Numbe o agen s pe p incipal Mul iple One Example P oduc design P ocu emen This wo k assumes a compe i i e en i onmen , since his co esponds wi h he CIS unde lying he ALN and he esea ch subjec o he eRep p ojec . A p esen , possible pu poses o DBAs include capaci y managemen , supply chain coo dina ion, p oduc design, and ade on elec onic ma ke places [Eyma03, 99–107]. This wo k will ocus on he decision-making p ocess o DBAs ading on an elec onic ma ke place. 2.3.2 Mul i Agen Sys ems Discussing how a ious agen s in e ac wi h each o he in ol es explaining how coo - dina ion is ealized be ween hem. On he one hand we ha e coope a ion h ough 11 Dis ibu ed P oblem Sol ing (DPS), on he o he hand compe i ion is sol ed h ough nego ia ion p ocesses (Table 2) [HuS 00, 83]. While in DPS a common goal is ac- u ed op-down and sol ed bo om-up, MAS ha e he op goal eme ging om he bo om as a esul o he a ious agen s’ compe ing goals [Eyma03, 49–51]. Table 2: Dis inc ion be ween DPS and MAS [RoZl98, 15–16] DPS MAS Sys em designing Cen alized Decen alized Coo dina ion Pa adigm Coope a ion: Agen s coope a e o achie e he common goals Compe i ion: Agen s nego ia e wi h each o he Pu sued Goals Common Con lic ing In acco dance wi h he concep o DBAs, pa icipa ing agen s in MAS a e a ional, sel -in e es ed and u ili y-maximizing; hey s i e o ealize he in e es o hei e- spec i e owne [RoZl94, 31]. Thus, DBAs nego ia e wi h each o he in o de o achie e hei goals. As men ioned be o e (c . Sec ion 2.2.2), he implemen a ion o he CIS cons i u es a p ice mechanism o encou age coo dina ion be ween he i al agen s. Assuming ha we apply he MAS idea o an elec onic ma ke place, we p edic he o e a ching goal is sys em e iciency in e ms o a Pa e o e icien alloca ion o aded goods wi h hei espec i e u ili y (wel a e maximiza ion) [Va i06, 618–620], [RoZl94, 31]. 2.3.3 Dissemina ing and Ga he ing In o ma ion Wi h he implemen a ion o epu a ion (c . Subsec ion 2.5.1.2), i becomes necessa y o compu e an agg ega e which e lec s he common image o he a ge agen . We assume agen s dissemina e hei expe iences on a olun a y basis, hough his con- adic s wi h he de ini ion o he sel -cen e ed, u ili a ian agen (c . Subsec ion 2.3.1.3). Mille e al. sugges a complex ewa d sys em based on sco ing ules o elici hones eedback om o he pa icipan s [MRZe05]. Fo he sake o simplici y, we suppose agen s sp ead in o ma ion on a olun a y basis. In o de o allow dissemina ion and accumula ion o in o ma ion in he ALN, a o - mal communica ion mechanism has o be implemen ed. Possible o ms ange om b oadcas ing mechanisms o e blackboa d sys ems o di ec communica ion 12 [Eyma03, 56–58]. Whe eas b oadcas ing means ansmi ing in o ma ion o all pa - icipan s (“one- o-many”), di ec communica ion ela es o he opposi e channel-wise messaging (“one- o-one”). Blackboa d sys ems s o e news ( eedback) in eposi o ies and dissemina e in o ma ion upon eques ; well-known eComme ce examples in- clude online epu a ion sys ems such as he ones o Amazon Ma ke place, Ebay, o Yahoo!Shopping [Amaz08], [Ebay08a], [Yaho08]. Resea che s o he eRep p ojec ha e also examined possible means o communica ion and hei e ec s on epu a ion [CoPa07, 9–13]. Despi e he high deg ee o decen aliza ion o ou e e ence sys em, we p esume agen s s o e da a pa ially in public local eposi o ies which a e accessi- ble o all connec ed membe s when eques ing in o ma ion (Subsec ion 2.5.2.3). 2.4 The Objec o In e ac ion: T ading Goods 2.4.1 Homogeneous and He e ogeneous Goods and Se ices In o dina y language, goods a e “some hing ha has economic u ili y o sa is ies an economic wan “ [Me 08b]. Mo eo e , we need o di e en ia e goods wi h espec o hei impac on ma ke ing: While some goods do no allow di e en ia ion and u he ma ke segmen a ion, some goods pe mi mul i-dimensional cus omiza ion. Thus, he ollowing e minology is being used om now on: When we alk abou goods, we mean goods and se ices. Ve y complex, mul i- ace ed goods which can ha dly be compa ed a e named he e ogeneous goods (e.g. ca s, ad iso y, holiday ips), while e y simple goods, which only di e in hei p ice, a e called homogeneous goods (e.g. powe , coal o s o age capaci y in megaby es) [WRSc05, 69], [GLFo04, 257]. These wo ypes o goods can be unde s ood as ex eme alues on a con inuum – many goods a e posi ioned in be ween. To de e mine he g ade o complexi y, we use he ypology o Wo a schek and classi y goods on h ee dimensions: beha io al un- ce ain y associa ed wi h he ansac ion, he deg ee o cus ome in eg a ion and he deg ee o cus omiza ion [WRSc05, 69], [Wo a96, 69]. We can illus a e he con in- uum be ween homogenei y and he e ogenei y using a sliced cube (Figu e 6). A dis inc ion be ween homogeneous and he e ogeneous goods is applicable in ALNs as well: he o me a e e med esou ces, he la e se ices. Mo eo e we assume applica ion se ices (e.g. con e ing a Po able Documen Fo ma ile [PDF]) can be b oken down in o esou ces needed o p o ide he se ice (like ha d disk capaci y and 13 p ocessing powe ) [S Ey07, 7–8]. We hold on o a commodi y o plain esou ce (such as a coal o whea ) and assume selle s canno modi y he good in a way ha allows hem o di e en ia e om com- pe ing supplie s. F om a cus ome ’s pe spec i e, all o e s a e equal excep o he p ice and he po en ial supplie (unce ain y abou he supplie s’ us wo hiness is a dis inguishing ea u e). low high Beha io al unce ain y lowhigh Cus ome in eg a ion low high Cus omiza ion He e ogeneous goods Homogeneous goods Ad iso y Ca (mass-cus omized) S o age capaci y low high Beha io al unce ain y low high low high Beha io al unce ain y lowhigh lowhigh Cus ome in eg a ion low high Cus omiza ion low high low high Cus omiza ion He e ogeneous goods Homogeneous goods Ad iso y Ca (mass-cus omized) S o age capaci y Figu e 6: Typology o goods (based on [Wo a96, 69]) The pa icula objec o ade in he scena io o his wo k is s o age capaci y in uni s o one gigaby e pe mon h (GB/mon h). 2.4.2 P ice Fo ma ion Mechanisms 2.4.2.1 How P ices Eme ge The p ice demanded by p oduce s ep esen s he e alua ion o a p oduc in mone a y uni s. F om a cus ome ’s poin o iew, he p ice is a sac i ice made o bene i om he possession o some hing, i.e. his willingness- o-pay depends on his associa ed u ili y wi h he pa icula good [Simo92, 3–4]. F om he p oduce ’s posi ion, he p ice has o compensa e o cos s incu ed in he manu ac u ing p ocess and has o 20 As in ui i ely assumed and suppo ed by he indings o a lab expe imen in 2004, he gain om one’s own expe ience is likely o exceed a cumula i e public epu a ion alue [BKOc04, 1595]. These indings a e unde pinned by ecen su ey esul s show- ing 60 pe cen o p i a e online shoppe s emain loyal o endo s hey had a posi i e shopping expe ience wi h [Niel08, 5]. Since he e ec s o locally managed epu a ion a e in es iga ed in he eRep p ojec , he ollowing pa ag aphs ocus on such epu a ion sys ems. 2.5.2.2 A Pano amic View on Cu en Sys ems I is bene icial o he de elopmen o an app op ia e epu a ion amewo k o con- as ou comes om empi ical esea ch wi h heo e ical indings [Dell03]. A aluable oundup o epu a ion sys ems se es h ee pu poses: i lis s exis en amewo ks, desc ibes he designs, and ex ac s pa icula con ibu ions om each sys em. Saba e and Sie a p o ide such a summa y: hey e iewed hi een di e en con- cep s and classi ied hem on se en dimensions (c . Appendix A 2, p. 106, and o he abb e ia ions Appendix A 1, p. 105) [SaSi05, 55–56]. We explain wo o hese dimen- sions, since hey exe di ec in luence on he selec ion o decision-making ools. Fi s , in o ma ion sou ces comp ise he ypes o sou ces aken in o accoun when de e mining he epu a ion alue o ano he en i y. The pe cei ed epu a ion o a ade depends on he subjec i e image o he cus ome buil om imp essions and he ade ’s ci cula ing social epu a ion. The subjec i e imp essions s em om ex- pe iences made in di ec in e ac ions o obse a ions wi h he ade . Following he na ow de ini ion abo e, wi nesses’ expe iences a e agg ega ed and esul in social epu a ion. Beyond hese expe iences, in o ma ion based on he ade ’s socie al a - ilia ions and social ela ions is likely o in luence his pic u e. Hence, hose po en ial sou ces a e as well subsumed unde social epu a ion [SaSi05, 35–37]. Second, an associa ed eliabili y measu e helps o unde s and how s able each im- p ession is. Thus, ou cus ome can use he measu e o weigh he in o ma ion alue. In communi ies wi h a emendous numbe o en i ies, he eliabili y measu e se es as a h eshold and il e s less c edible imp essions. Bu e en he subjec i e image a cus ome has is ins able: Memo ies a e ugacious, and in he cou se o ime expe i- ences blu o disappea comple ely. By assigning a eliabili y measu e o each imp es- 21 sion, he indi idual compu a ion o an agg ega e epu a ion sco e becomes mo e p e- cise and comp ehensible [SaSi05, 40–41]. Ou scena io wi h au onomous and delibe a e agen s encou ages local decision- making. Hence, a epu a ion sys em ha makes use o di ec expe ience as well as wi ness in o ma ion has o be implemen ed. Though no c i ical, a measu e o eli- abili y is use ul when dealing wi h la ge-scale MAS. Wi h he aid o Saba e and Si- e a’s compa ison, wo possible sys ems a e iden i ied: AFRAS and ReG eT. Since ReG eT includes a comp ehensi e amewo k o e alua ing sociological in o - ma ion, we p e e i o AFRAS and p esen i in he ollowing chap e . 2.5.2.3 ReG eT The ReG eT sys em consis s o a di ec us and a epu a ion module o assess he us wo hiness ( us ) o a p ospec i e, so called a ge agen . T us owa ds a a ge agen is he weigh ed sum o social epu a ion and di ec us (i.e. image). The com- pu a ion o each componen is de e mined by he sys em’s a chi ec u e: i dis in- guishes be ween h ee epu a ion dimensions, he indi idual dimension, he social dimension and he on ological dimension (Figu e 2 1) [SaSi01, 194]. In he nex pa ag aphs, each dimension wi h i s componen s will be p esen ed in a nu shell; o a de ailed explica ion see [Saba03, 44–62]. On he indi idual le el, ou comes o dialogues be ween agen s a e used o compu e a di ec us alue. An ou come is ep esen ed by a subjec i e a ing and a uple o in- o ma ion; i is s o ed in he ou comes da abase (ODB). The uple o in o ma ion cha ac e izes he ou come (e.g. p ice o expec ed quali y) and he a ing e lec s he pe cei ed e alua ion. Di ec us is usually he mos s able sou ce o p edic he sin- ce eness o a pa ne ; on he downside, i is una ailable o new en an s and expen- si e o build [Saba03, 44–46]. In he social dimension, he epu a ion measu e is compu ed by he weigh ed esul s o h ee sou ces: wi ness, neighbo hood, and sys em epu a ion. The weigh s a e ob- ained om he c edibili y o each sou ce, which is in u n calcula ed om he num- be s o imp essions and he s anda d de ia ions [SaSi01, 195]. We alk abou wi ness epu a ion when in o ma ion is collec ed om o he agen s who ansmi hei di ec expe iences o eedback ob ained om pee s. E alua ed 22 imp essions o wi nessed ou comes a e eco ded in a second s o age, he imp ession da abase (IDB). Neighbo hood epu a ion is de e mined by he a ge ’s social en i- onmen and he ela ions he a ge has es ablished wi h his en i onmen . I is com- pa able o p ejudice, bu no necessa ily disc imina ing. Sys em epu a ion is based on he a ge ’s ole in a g oup. I assumes ha oles adhe e o ce ain obse able ea- u es o beha io s which may be assigned o he a ge agen [Saba03, 47–48]. T us o Agen A In e ac ion AB Imp ession Imp ession Social Repu a ion SDB SDB ODB ODB IDB IDB Social Rela ion G oup Ou come Di ec us ! ! Social Dimension Indi idual Dimension Neighbou hood epu a ion Sys em epu a ion Wi ness epu a ion T us o Agen A In e ac ion AB In e ac ion AB Imp ession Imp ession Social Repu a ion SDB SDB ODB ODB IDB IDB Social Rela ion G oupG oup Ou come Di ec us ! ! Di ec us ! !! ! Social Dimension Indi idual Dimension Neighbou hood epu a ion Sys em epu a ion Wi ness epu a ion Figu e 10: Calcula ion o us in ReG eT (based on [Saba03, 92]) The compu a ion o neighbo hood and sys em epu a ion depends on he g oup he indi idual belongs o; hus, bo h can be unde s ood as g oup knowledge, and bo h a e in luenced by he social s uc u es. Those s uc u es, mapped as sociog ams, a e s o ed in a hi d con aine , he sociog am da abase (SDB). Though no ully speci ied ye , sociog ams will suppo each es ima e o c edibili y o all conside ed imp es- sions by p o iding aid o p ope weigh assessmen (e.g. wi ness epu a ion issued 23 by a node ela ed o he a ge agen may be biased and hus less aluable han o he s’ eedback) [Saba03, 51], [Saba03, 41]. Finally, he on ological dimension desc ibes he con ex o in o ma ion on which he a ge agen is a ed. The ODB does no me ely p o ide an agg ega ed alue on each ou come bu also de ailed in o ma ion on a ibu es such as p ice o deli e y da e; ou subjec can e alua e he o e all imp ession by combining di e en aspec s ac- co ding o his p e e en ial s uc u e. This e lec s di e en pe cep ions in eal li e, in which he selle ’s epu a ion s ongly depends on he a ing cus ome [Saba03, 61]. König e al. p opose a comple ely decen alized implemen a ion o he ReG eT sys- em using pee - o-pee echnology o in o ma ion exchange [KKWi07]. Due o i s complexi y, we ejec hei sugges ion and p esume he IDB is cen ally implemen ed and social epu a ion o an agen is iden ically pe cei ed by all pa icipan s. O cou se, his does no a ec he decen ally calcula ed image es ima e. We assume ou pa icipan s will conside po en ial pa ne s’ social epu a ion as well as di ec us om p e ious encoun e s. Consequen ly, social epu a ion and image a e di e en ia ing ea u es o agen s in MAS. 2.6 Decision Making 2.6.1 Theo y o Decision Decision heo y is conce ned wi h a decision-make ’s (DM) goal-di ec ed a ional beha io o coming o a decision in p esence o possible op ions. Ra ionali y implies delibe a ing abou he ac ion be o e and du ing decision-making, as well as commi - men o he selec ion [SzWi74, 3–5]. In his wo k agen s unde ake decision-making and se e as p oxies o hei p incipal, he DM. A dis inc ion is made be ween no ma i e and desc ip i e decision heo y: No ma i e decision heo y p esc ibes how p oblems can be sol ed. I p o ides ad ice on p ob- lem sol ing by o mal means o depic ing ini ial si ua ions and solu ions. In con as , desc ip i e decision heo y esea ches empi ical indings and deals wi h he ex pos analysis o decisions made [Laux07, 2], [SzWi74, 18–21]. Decision-making is a mul i-s age p ocess ha “begins wi h he iden i ica ion o a s imulus o ac ion and ends wi h a speci ic commi men o ac ion” [MRTh76, 246]. 24 The amous economis and Nobel p ize winne He be A. Simon (1960) p oposed a sequen ial model wi h he h ee p incipal phases in elligence, design, and choice – simila in s uc u e and con en o he models la e de eloped by I le (1971) o Szype ski (1974) (Figu e 11) [Simo77, 40], [SzWi74, 7–10]. The i s phase, in elligence, co e s he sea ch o decision p edica es in he en i on- men ; Simon has bap ized his phase in analogy o he mili a y meaning. The ollow- ing s ep, design, in ol es o ging, de eloping, and s udying possible conduc . Finally, he choice ac i i y deals wi h selec ing a pa icula conduc om he a ailable ones [Simo77, 40–41]. In elligence Design Choice Re iew Simon P oblem de ec ion In o sea ch Op ion c ea ion E alua ion Ranking Decision CheckupI le Szype ski Cogni ion Concep ion Realiza ion De elop- men Min zbe g e al. Iden i ica ion Selec ion CyclesSequence In elligence Design Choice Re iew Simon P oblem de ec ion In o sea ch Op ion c ea ion E alua ion Ranking Decision CheckupI le Szype ski Cogni ion Concep ion Realiza ion De elop- men Min zbe g e al. Iden i ica ion Selec ion CyclesCyclesSequence Sequence Figu e 11: Decision-making p ocess (c . [SzWi74, 7–10], [Simo77, 40–41]) La e on, Min zbe g e al. (1976) ecommend a non-sequen ial, i e a i e model wi h h ee in e wined phases comp ising o se en cen al ou ines (Figu e 12) [MRTh76, 252]. In con as o he sequen ial models, hei p oposal assumes a he an i e a i e p ocess o ou ines han he linea succession o ac ions. I e a ions in- clude cycles be ween ou ines wi hin a phase as well as cycles be ween phases. The ini ial phase is e med iden i ica ion and comp ises wo ou ines. The i s , deci- sion ecogni ion, is conce ned wi h he iden i ica ion o p oblems, c ises, and oppo - uni ies. The second ou ine, diagnosis, deals wi h accumula ion and assessmen o ela ed in o ma ion, and de e mina ion o cause-e ec ela ionships [MRTh76, 253– 254]. The de elopmen s age is composed o he sea ch and he design ou ine. While he sea ch aims a inding exis ing solu ions, design is abou he de elopmen o cus om- made solu ions as well as he modi ica ion o eady-made ones. The pu pose o bo h 25 ou ines is de ining op ions o la e decision [MRTh76, 255–256]. 6 E alua ion- choice E alua ion- choice Sc een Sc een Au ho iza ion Au ho iza ion Design Design Sea ch Sea ch Diagnosis Diagnosis Decision ecogni ion Decision ecogni ion Selec ionDe elopmen Iden i ica ion 12 3 4 5 7 6 E alua ion- choice E alua ion- choice Sc een Sc een Au ho iza ion Au ho iza ion Design Design Sea ch Sea ch Diagnosis Diagnosis Decision ecogni ion Decision ecogni ion Selec ionSelec ionDe elopmen De elopmen Iden i ica ion Iden i ica ion 12 33 44 55 7 Figu e 12: Non-sequen ial decision-making p ocess [MRTh76, 266] Finally, du ing he selec ion s age, h ee ou ines ake place: The sc een ou ine is conce ned wi h he elimina ion o in easible al e na i es. In he e alua ion-choice ou ine possible cou ses o ac ion a e e alua ed and a choice is made. The las ou- ine, au ho iza ion, deals wi h he submission o he decision o supe io ins ances o app o al [MRTh76, 257–260]. Depending on he model, he ocus o his wo k lies on he choice s age (Figu e 11) o he selec ion s age (Figu e 12), bo h dealing wi h o mal models o compa ing and anking conside ed al e na i es. 2.6.2 The Classical Model o Decision Making Whe he we app o e o Simon’s sequen ial decision p ocess o he cycling phases o Min zbe g e al., decision-making is conce ned wi h selec ing one o mo e op ions om a numbe o al e na i es. In o de o suppo DMs, decision ma ices a e com- monly used o isualize and o mula e decision si ua ions [Laux07, 36–37], [YoHw95, 3]: The columns in he ma ix ep esen he c i e ia and he ows he al- e na i es wi h hei speci ic ou come ec o . 26 We show an example si ua ion below: A passenge who is eques ed o jou ney low- budge om F ank u o Munich is con on ed wi h h ee a el op ions (Table 3). Table 3: Example o a decision ma ix C i e ion Al e na i e C1: Cos s incu ed A1: Take he ain EUR 70 A2: Take he ca EUR 120 A3: T a el by ai plane EUR 150 A decision ma ix is cons uc ed by ga he ing and a ibu ing in o ma ion o al e na- i es and c i e ia (Figu e 13; p ocesses in his wo k a e illus a ed using ac i i y dia- g ams o he UML no a ion, see [OMG08]). De e mine ou comes aij De e mine ou comes aij Iden i y n al e na i es Iden i y n al e na i es Iden i y m a ibu es Iden i y m a ibu es Decision ma ix Decision ma ix De ine decision ma ix De ine decision ma ix De ine decision ma ix Da a Da a De e mine ou comes aij De e mine ou comes aij Iden i y n al e na i es Iden i y n al e na i es Iden i y m a ibu es Iden i y m a ibu es Iden i y n al e na i es Iden i y n al e na i es Iden i y m a ibu es Iden i y m a ibu es Decision ma ix Decision ma ix De ine decision ma ix De ine decision ma ix De ine decision ma ix De ine decision ma ix De ine decision ma ix De ine decision ma ix De ine decision ma ix Da a Da a Figu e 13: Subp ocess o de ining a decision ma ix A decision ma ix is a pa icula decision model wi h some building blocks which a e always appa en (Table 4) [Laux07, 19–26]. We deno e by he decision ma ix A on he whole × nm , he se o n al e na i es {} =!, 1, , i AAi n, he se o m c i e ia {} , 1, , j CC j m=…. Upon deciding, ou passenge picks A1 and aces he sa e ou - come a11= 70, i.e. paying 70 Eu os o he ain icke . 27 Table 4: Te minology in decision-making [Laux07, 19–26] Te m Desc ip ion Symbol Example A goal desc ibes an aspi ed si ua ion o change o p esen s a e. I is o mula ed using a p e e ence unc ion and he c i e ion o op i- mize. Goal The p e e ence unc ion (which ep esen s he DM’s p e e ence s uc u e) e alua es ou comes. = (Ai) T a el cheaply om F ank- u o Munich (one-way) Al e na i e An al e na i e is a unique op ion cha ac e ized by a speci ic ou come. A leas wo al e na i es a e necessa y o equi e decision-making. Ai A1: Take he ain A2: Take he ca A3: T a el by ai plane Ou come An ou come is a ec o o alues ep- esen ing a unique combina ion o goal- ele an c i e ia o an al e na- i e. The ec o has o be unique o dis in- guish his espec i e al e na i e om o he s. aij a 1j: (Cos s: EUR 70) a2j: (Cos s: EUR 120) a3j: (Cos s: EUR 150) C i e ia C i e ia a e pa ame e alues o goals (e.g. cos s, du a ion). Cj C 1: Cos C2: Du a ion S a e (en i on- men al) En i onmen al s a es depend on exogenous pa ame e s which in luence decision-making. A s a e consis s o in luence s, i.e. da a ha changes he pa ame e al- ues o ou comes and he eby he e alua ion o al e na i es. S a es can ei he be unce ain o de ini e; whe eas he la e simpli ies decision-making ( alues o ou comes a e scala and no inhe en ec o s), unce ain y in ol es isk es ima ion. Ins able gas p ice, new ou - come ec o o al e na i e wo: a2j(low gas p ice): (Cos s: EUR 95) a2j (no mal gas p ice): (Cos s: EUR 120) a2j (high gas p ice): (Cos s: EUR 140) The ela ionship be ween hese building blocks in he classical model o decision- making is depic ed below (Figu e 14): We see he ou come depends on he in e play o decision and cu en s a e. Wi h espec o b e i y, we dis ega d unce ain y and en i onmen al s a es he e. This in u n leads o he ollowing simpli ica ion: () () () () ( ) () () () i i ii ii AauauA AuA  = The calcula ed p e e ence alue  o an al e na i e Ai is equal o he u ili y ui o he ou come ai [Laux07, 27]. 28 P e e ence unc ion P e e ence unc ion Goals Goals Ou comes Ou comes S a es S a es Speci c S a e Speci c S a e ? ? ? ? ? ? Decision Decision Al e na i es Al e na i es P e e ence unc ion P e e ence unc ion Goals Goals Ou comes Ou comes S a es S a es Speci c S a e Speci c S a e ? ? ? ? ? ? Decision Decision Al e na i es Al e na i es Decision Decision Al e na i es Al e na i es Figu e 14: Classical model o decision-making (based on [ZiGu91, 3]) Thus, when we know he p e e ence alue o all al e na i es, an u ili y-maximizing decision can be made wi hou explici ly de i ing u ili y om each pa ame e alue. The ques ion is whe he all al e na i es wi h hei espec i e ou comes a e a ailable o no . Re u ning o he example (c . Table 3), we ecommend aking he ain, which domina es he o he al e na i es in minimizing cos s. 2.6.3 Mul iple C i e ia Decision Making Unde ce ain y, classical models can cope wi h decision-making as long as he p e - e ence unc ion d aws a compa able alue ou o each al e na i e. E e yday p oblems a e usually mo e demanding: A comp ehensi e judgmen in ol es balancing mul iple goal- ela ed c i e ia which a e o en compe ing [BeS 02, 1]. This challenge is called agg ega ion p oblem [Roy05, 14]. The modi ied decision ma ix (Table 5) om he p e ious Subsec ion adds he c i e ion “ a el ime” o he p oblem. Table 5: Example o a mul iple c i e ia decision p oblem C i e ia Al e na i e x1: Cos s incu ed x2: T a el ime A1: Take he ain EUR 70 4 h s. A2: Take he ca EUR 120 3.5 h s. A3: T a el by ai plane EUR 150 2.5 h s. 29 Al hough his p oblem seems simple, he challenge lies in managing he ade-o be- ween a el ime and cos s (assuming less a el ime is associa ed wi h a highe u il- i y). Time and cos s a e incommensu able uni s (Wha is he alue o an hou in Eu- os? How much ime can I buy o a ce ain amoun o money?) and no al e na i e domina es he o he s on bo h dimension ( he ain is now less a ac i e due o he long a el ime). We a e conce ned wi h Mul iple C i e ia Decision Making (MCDM) when we ake accoun o mul iple con lic ing c i e ia which need o be balanced [BeS 02, 5]. In ou la e scena io, he buying agen is choosing be ween se e al selle s, which di - e in social epu a ion, image and he demanded p ice. While shoppe s seek concu - en ly a high epu a ion and a low p ice, well- epu ed selle s will likely seize hei good name and ask o a p emium (c . he esul s o he expe imen in [RZSL06, 21]). 2.6.4 P e e ence Modeling h ough U ili y and Values The p edic abili y o he en i onmen al s a es in luences he means o p e e ence modeling and dis inguishes be ween p e e ence ep esen a ions unde ce ain y and unde isk. When we deal wi h unce ain y o isk, we e e o a p e e ence ep esen- a ion unc ion as a u ili y unc ion, and when all s a es a e ce ain, we e e o a p e - e ence ep esen a ion unc ion as a alue unc ion [Dye 05, 267–268], [BeS 02, 95], [KeRa93, 15–16]. In sympa hy wi h Dye e al. we exclude he ield o Mul ia ibu e U ili y Theo y he e and assume alue unc ions a e ei he implici o no such unc ion exis s a all [DFS+92, 647]. And since we also omi ed cases o unce ain y and isk, we do no need o pay a en ion o u ili y unc ions om now on ( o de ails on u ili y see [Va i06, 54–56]). Ins ead, we de ine alue as being p opo ional o u ili y, i.e. a highe alue implies always a highe u ili y (i.e. mono onically inc easing). In case ou come and e alua ion a e posi i ely co ela ed, we deal wi h a bene i a - ibu e (i.e. maximiza ion goal), in case hey co ela e nega i ely, a cos a ibu e is conside ed (i.e. minimiza ion goal) [YoHw95, 15]. A his poin , we deno e he dependency o he alue ij o an a ibu e’s ou come aij as a alue unc ion () ij ij a=, o ( ) ij a ( echniques o he a ibu e-wise a ing o ou comes a e p esen ed in Subsec ion 3.2.2). We assume u he mo e he ollowing 36 We de i e he alue o he assigned weigh wj om he equency he j- h c i e ion is p e e ed. This me hod is all bu unambiguous because he applica ion o weigh calcula ion o mulas usually esul s in di e en , inconsis en alues [YoHw95, 12–13]. We de- no e he c i e ia compa ison ma ix () {} {} × = = = ! ! 1, , , 1, , , mm im ij jm cCC wi h he cij as he ela i e impo ance o he j- h c i e ion owa ds he i- h one. Then inconsis ency e e s o p e e ence s a emen s which a e in ansi i e and o which he consis ency condi ion {} = ! i, j ,k 1, , ij ik kj ccc m wi h {}  = ! 1 i, j 1, , ij i j cww m does no hold [ZiGu91, 54–55], [YoHw95, 13]. Fo his eason we wi hd aw his ap- p oach and u n o he second one, a g oup o echniques called a io weigh ing. These me hods make use o a ios o display he ade-o be ween wo a ibu es [T ia00, 57]. To be p ecise, we un again () 12mm×÷ pai wise compa isons o c i- e ia, bu in con as o o me echniques, we eques a io alues om he DM which ep esen he p e e ence a io cij o one c i e ion o e ano he , i.e. how many imes is c i e ion i mo e impo an han c i e ion j [T ia00, 58–59]. As consis ency implies ecip oci y, we know ha {}  =… 1 ,1,, ij ji cc i j m. We deno e he weigh ec o () =! 1 Tm m www wi h {} > …0 1, , j w j m and de ine no malized weigh s, so ha = =  1 1 m j j w. Then, weigh s a e compu ed as ollows [ZiGu91, 55–56]: {} = == =…   1 11 ,1,, m ij j jmm ij ij c wi j m c To assu e consis ency, he DM can ei he epea he pai wise assessmen s and adjus he alues o accep a ce ain e o measu e [EdNe90, 56–58]. ` Sophis ica ed echniques like Saa y’s eigen alue app oach o he modi ied leas 37 squa e app oach minimize his e o alue while de e mining op imal weigh s [BeS 02, 154–156], [T ia00, 57–60], [Saa 80, 51]. When p oblems and c i e ia a e complex, alue ees acili a e de ining c i e ia and assigning weigh s (Figu e 17). Value ees make use o he hie a chical ela ion be- ween c i e ia: Ei he an o e all objec i e is decomposed op-down in o se e al sub- o dina e le els wi h amilies o c i e ia and child c i e ia, o in e sely, c i e ia a e composed o de i e he pa amoun objec i e bo om-up. Then he DM compa es each c i e ion wi h i s siblings, and o each le el compa ison ma ices a e cons uc ed and ela i e weigh s a e de i ed [BeS 02, 140], [EdNe90, 62]. Con enien a el y Rela i e weigh Cumula i e weigh Se ice 0,04 0,2 x Size 0,018 0,45 Uphols e y 0,008 0,2 Foo space 0,014 0,35 Sea 0,12 0,6 Noise 0,04 0,2 Com o 0,2 0,2 Cos 0,4 0,4 Du a ion 0,4 0,4 Top-down Bo om-up Con enien a el y Rela i e weigh Cumula i e weigh Se ice 0,04 0,2 Se ice 0,04 0,2 0,04 0,2 x Size 0,018 0,45 Uphols e y 0,008 0,2 Foo space 0,014 0,35 Size 0,018 0,45 Size 0,018 0,45 Size 0,018 0,45 0,018 0,45 Uphols e y 0,008 0,2 Uphols e y 0,008 0,2 Uphols e y 0,008 0,2 0,008 0,2 Foo space 0,014 0,35 Foo space 0,014 0,35 Foo space 0,014 0,35 0,014 0,35 Sea 0,12 0,6 Noise 0,04 0,2 Sea 0,12 0,6 Sea 0,12 0,6 Sea 0,12 0,6 0,12 0,6 Noise 0,04 0,2 Noise 0,04 0,2 Noise 0,04 0,2 Com o 0,2 0,2 Com o 0,2 0,2 Com o 0,2 0,2 0,2 0,2 Cos 0,4 0,4 Cos 0,4 0,4 Cos 0,4 0,4 Du a ion 0,4 0,4 Du a ion 0,4 0,4 Du a ion 0,4 0,4 Top-down Bo om-upTop-down Bo om-up Figu e 17: Rela i e and cumula i e weigh s in alue ees (based on [BeS 02, 140]) The ele ance o a c i e ion is e en ually compu ed om he p oduc o i s ela i e weigh and he ela i e weigh o i s pa en and he pa en ’s pa en and so o h. Re- lec ing he ue ela i e impo ance o all gi en c i e ia, his alue is called cumula- i e weigh . We no e ha consis ency has o be aken ca e o a e e y s age o assess- men [BeS 02, 139], [Saa 80, 78]. Rega ding he sample scena io, we assume ca dinal alues o weigh s a e gi en a p io i and a e subjec o change as a measu e aken by he ading en i y. Fu he - mo e, we will always elici weigh s om he ela i e alue o unde lying p e e ences and implici ly include a consis ency check (Figu e 18). 38 De ine weigh s Wo k ou mweigh s w j Wo k ou mweigh s w j Check consis ency o weigh s Check consis ency o weigh s [weigh s a e consis en ] [weigh s a e inconsis en ] Weigh s ec o w m Weigh s ec o w m Adjus weigh s ec o Adjus weigh s ec o De ine weigh s De ine weigh s De ine weigh s De ine weigh s P e e ence in o ma ion P e e ence in o ma ion De ine weigh s Wo k ou mweigh s w j Wo k ou mweigh s w j Check consis ency o weigh s Check consis ency o weigh s [weigh s a e consis en ] [weigh s a e inconsis en ] Weigh s ec o w m Weigh s ec o w m Adjus weigh s ec o Adjus weigh s ec o De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s P e e ence in o ma ion P e e ence in o ma ion Figu e 18: The subp ocess o de ining weigh s 3.3 Mul iple A ibu e Decision Making 3.3.1 A Taxonomy o MADM Me hods MADM me hods a e used when a ini e (and coun ably small) numbe o al e na i es wi h associa ed in o ma ion on ega ded c i e ia is gi en. The ype o in o ma ion p o ided by he DM in luences he choice o me hod: Is p e e ence in o ma ion a ail- able o no and i so, wha cha ac e izes he salien ea u e o in o ma ion (Figu e 19) [ZiGu91, 29], [HwYo81, 8]? We s a wi h a desc ip ion o me hods which do no need explici p e e ence in o - ma ion (Subsec ion 3.3.2) o me ely ask o aspi a ion le els (Subsec ion 3.3.3), be- o e we u n o app oaches which equi e o dinal p e e ence in o ma ion (Subsec ion 3.3.4) o ca dinal p e e ence in o ma ion (Subsec ion 3.3.5). 39 Type o in o ma ion om DM Subsec ion MADM me hod/ class o me hods Salien ea u e o in o ma ion No in o ma ion No in o ma ion 3.3.2 Dominance Maximin Maximax Dominance Maximin Maximax 3.3.3 Conjunc i e Me hod Disjunc i e Me hod Conjunc i e Me hod Disjunc i e Me hod S anda d le el S anda d le el A ibu e in o ma ion A ibu e in o ma ion 3.3.4 Lexicog aphic Me hods Elimina ion by Aspec s Lexicog aphic Me hods Elimina ion by Aspec s O dinal in o ma ion O dinal in o ma ion 3.3.5 Simple Addi i e Weigh ing Weigh ed P oduc Me hod AHP TOPSIS Simple Addi i e Weigh ing Weigh ed P oduc Me hod AHP TOPSIS Ca dinal in o ma ion Ca dinal in o ma ion Type o in o ma ion om DM Subsec ion MADM me hod/ class o me hods Salien ea u e o in o ma ion No in o ma ion No in o ma ion 3.3.23.3.2 Dominance Maximin Maximax Dominance Maximin Maximax 3.3.3 Conjunc i e Me hod Disjunc i e Me hod Conjunc i e Me hod Disjunc i e Me hod S anda d le el S anda d le el 3.3.33.3.3 Conjunc i e Me hod Disjunc i e Me hod Conjunc i e Me hod Disjunc i e Me hod S anda d le el S anda d le el A ibu e in o ma ion A ibu e in o ma ion 3.3.43.3.4 Lexicog aphic Me hods Elimina ion by Aspec s Lexicog aphic Me hods Elimina ion by Aspec s O dinal in o ma ion O dinal in o ma ion 3.3.5 Simple Addi i e Weigh ing Weigh ed P oduc Me hod AHP TOPSIS Simple Addi i e Weigh ing Weigh ed P oduc Me hod AHP TOPSIS Ca dinal in o ma ion Ca dinal in o ma ion 3.3.5 Simple Addi i e Weigh ing Weigh ed P oduc Me hod AHP TOPSIS Simple Addi i e Weigh ing Weigh ed P oduc Me hod AHP TOPSIS Ca dinal in o ma ion Ca dinal in o ma ion Figu e 19: O e iew o MADM me hods (based on [HwYo81, 6]) 3.3.2 Deciding wi hou P e e ence In o ma ion 3.3.2.1 Absence o A ibu e Rele ance When no in o ma ion on he DM’s p e e ence s uc u e is gi en, a dis inc ion be- ween he ele ance o all a ibu es is no possible. Fo all he me hods ollowing, ad an ages o one a ibu e canno be aded o disad an ages o ano he ; hus, ade-o s a e no pe mi ed. These me hods a e called non-compensa o y, con a y o compensa o y ones which allow o se ing supe io wi h in e io alues [YoHw95, 17]. 3.3.2.2 Dominance P inciple The Dominance p inciple educes he numbe o al e na i es in a gi en se [Macc73, 31]. An al e na i e is nondomina ed i he e is no o he one in he se which excels i in a leas one a ibu e while being equal in all o he ones. All nondomina ed al e na i es cons i u e he e icien on ie , he subse o Pa e o e icien al e na i es which should be aken in o u he conside a ion [KeRa93, 70]. In con as , an al e na i e is called domina ed when in compa ison o ano he one i is de ea ed in a leas one a ibu e while no excelling in ano he one. Domina ed 40 al e na i es play no ole o u he decision-making and can be elimina ed om he se o al e na i es [BeS 02, 83], [YoHw95, 18]. The g aph below depic s a cons ella ion wi h wo a ibu es, whe e al e na i es A and C a e nondomina ed ( hey lie on he e icien on ie ), and al e na i e B is de ea ed in bo h a ibu es by al e na i e C. The ic i ious al e na i e D lies beyond he e i- cien on ie and is called un easible (Figu e 20). Al e na i e D Al e na i e C Al e na i e A A ibu e 1 A ibu e 2 Al e na i e B E icien on ie E icien on ie Al e na i e D Al e na i e C Al e na i e A A ibu e 1 A ibu e 2 Al e na i e B E icien on ie E icien on ie Figu e 20: E icien on ie (based on [KeRa93, 71]) The Dominance p inciple can be used as a i s -s age il e o isola e a subse o al e - na i es; wi h an inc ease in al e na i es and a ibu es, i will less likely de e mine only one e icien op ion. 3.3.2.3 Maximin and Maximax When he decision-making con ex p o ides a endency o p e e ence, ei he in e ms o a pessimis ic o op imis ic a i ude owa ds he al e na i es, we can make use o he Maximin o he Maximax me hod. Bo h me hods do no equi e addi ional in- o ma ion abou he DM’s p e e ences, bu demand compa able a ibu e alues, i.e. no malizing he a ibu e ec o s in ad ance [ZiGu91, 43–44]. The Maximin me hod es ima es he lowes alue o each al e na i e and anks all al e na i es in descending o de by hei lowes alue. The DM is ad ised o selec he highes anked al e na i e. This p ocedu e is also called pessimis ic, since only he 41 lowes alue is aken in o accoun and (possibly) supe io alues o o he a ibu es canno balance he one weakness [YoHw95, 28]. The Maximax me hod wo ks a he simila ; ins ead o he lowes , i iden i ies he highes alue o each al e na i e which se es as a anking c i e ion. Again, he DM is supposed o selec he highes anked op ion. This me hod is called op imis ic, as i ocuses me ely on he highes alue and dis ega ds o he in e io a ibu es [YoHw95, 30]. Table 9: Maximin and Maximax decision ules [YoHw95, 28–30] Me hod Selec ion ule P io i y P econdi ion Maximin () {} *max min iij j i A A = Lowes alue (pessimis ic a i ude) Maximax () *max max iij ij A A    =    Highes alue (op imis ic a i ude) Fo nm× A wi h {} 1,...,in=; {} 1,...,jm= and () [] {} 0;1 ij ij ij a =  . Bo h p ocedu es assign ex eme weigh s o one hund ed pe cen o one a ibu e ( he lowes o highes ) and o null pe cen o he emaining ones o de e mine he bes al e na i e A* (Table 9) [ZiGu91, 44–45]. The wo me hods do no by all means lead o an ad ice o a single al e na i e, and hey a e due o hei na ow ocus dispu able when i comes o wi hd awing all bu one c i e ion ( he weakes one in he Maximin and he s onges one in he Maximax me hod) o jus i y he made decision [Macc73, 29]. Thus, we emo e hem om ou u u e scope. 3.3.3 Sa is icing (Conjunc i e and Disjunc i e App oaches) The idea o sa is icing ela es back o he wo k o Simon, who wo ked ou he human inabili y o conduc ing a ional beha io in decision-making. A DM a he concen- a es on selec ing an al e na i e which sa is ies ce ain aspi a ion le els ins ead o seeking a global op imum [BeS 02, 104], [Simo66, 204–205]. The wo ypes o heu is ics based on sa is icing a e he Conjunc i e and he Disjunc- i e app oach. Whe eas he o me me hod is absolu ely non-compensa o y, he la - e is diame ically opposi e and pe ec ly compensa o y. Ins ead o de e mining a single op imal solu ion, he wo sa is icing app oaches di ide he se o al e na i es in o wo subse s o accep able and unaccep able al e na i es. While he la e a e dis- 42 ega ded om u he conside a ion, he o me comp ise he numbe o ele an solu ions [YoHw95, 20]. Sa is icing equi es aspi a ion le els which ha e o be se ca e ully because he h esholds de e mine he size o he esul ing subse s: I he cu o alues a e se high (low), he numbe o accep able al e na i es diminishes (soa s), and i he DM ails o e ie e a easible solu ion, he mos likely will lowe he aspi a ion le els [YoHw95, 20–21], [Simo55, 111]. When al e na i es ha e o exceed he h esholds o all a ibu es o be conside ed as accep able solu ions, we use he Conjunc i e app oach. In his case an al e na i e is unaccep able, i a leas one o he co esponding alues ails o mee he minimum equi emen s [ZiGu91, 47]. The Disjunc i e app oach is less demanding han he Conjunc i e one; he se o ac- cep able al e na i es is de ined by all al e na i es which mee o exceed a leas one h eshold. Hence, he size o he subse o accep able al e na i es is much la ge han he one in he Conjunc i e app oach [YoHw95, 21–22]. An o e iew o bo h heu is- ics and he o mal ela ion o he gi en cu o alues aj0 is gi en below (Table 10). Table 10: Sa is icing app oaches [ZiGu91, 47–48] Me hod Accep ance ule Main implica ion P econdi ion Conjunc i e  0 ij j aaj Non-compensa o y Disjunc i e {} 0 ij ij j aaa  Compensa o y Fo nm× A wi h {} 1, ,in=!; {} 1, ,jm=! and 0 j a . Sa is icing me hods can be help ul o educe he se o al e na i e and se e as a i s - s age il e o he DM [ZiGu91, 48]. The combina ion o bo h me hods may also wo k well as a comp ehensi e il e o c ea ing ules in epe i i e decision-making [BeS 02, 105], [YoHw95, 22]. 3.3.4 Sequen ial Elimina ion 3.3.4.1 Gene al Cou se o Ac ion The idea o de e mining he op imal solu ion by sequen ially elimina ing al e na i es names he nex wo MADM me hods. I o dinally anked a ibu es a e gi en, he 43 Lexicog aphic Me hods (LM) compa e al e na i es a ibu e-wise and wi hd aw domina ed op ions un il a single one emains. Simila , when no o de o a ibu es is p o ided, Elimina ion by Aspec s (EbA) emo es all al e na i es which do no sa is y a ibu e-wise s anda ds un il all bu one a e disca ded. 3.3.4.2 Lexicog aphic Me hods The name e lec s he way his app oach wo ks: like wo ds in a dic iona y, al e na- i es a e anked s ep-wise (whe e wo ds consis o le e s, al e na i es ha e a ib- u es). In case speci ic a ibu es p edomina e o he s by impo ance, he DM can quickly es ima e an op imal solu ion: Beginning wi h he mos impo an a ibu e, we ank he al e na i es and elimina e all bu he bes one. I mo e han a single al- e na i e p e ails, we epea anking and elimina ing wi h he nex mos impo an a ibu e. The i e a ion s ops when only one op ion emains [ZiGu91, 49–50]. Fo mal: Le n be he numbe o al e na i es A, and m be he numbe o a ibu es o be maximized. Le k be he i e a ion s ep and {} {} 0 j AA=, {} 1, , j m!, we deno e he ule {} {} 1max kk k j j AA x  = , which is epea ed un il {} 1 k A= o kn=, when all a ibu es ha e been used in he p ocess and he inal se o al e na i es {} 1 n A is conside ed as equi alen [Webe93, 68]. A u he explica ion o he o mal backg ound o LMs is gi en in [Fish74]. The imp o ed Lexicog aphic Semio de (LS) has i s ounda ions in he wo k o T e - sky and Luce [T e 69, 32], [Luce56, 181–182]. I uses he same p ocedu e as he LM bu equi es signi ican di e ences be ween compa ed a ibu es be o e judging an al e na i e as domina ing. In addi ion o he anking o a ibu es, h eshold le els a e needed o a ibu e-wise compa isons [ZiGu91, 50–51]. LMs a e in ui i e, easily unde s andable, and do no equi e no maliza ion o a ib- u e a ings; hei disad an age is he neglec o lowe anked a ibu es, which canno compensa e o low alues on highe anked a ibu es [ZiGu91, 50], [T e 69, 46]. 44 3.3.4.3 Elimina ion by Aspec s The EbA me hod has been ini ially p oposed by T e sky and is simila o LMs, bu he basic p e equisi es di e in e ms o in o ma ion on a ibu es [T e 72, 285–287]: Ins ead o a anking o de , so-called s anda ds o sa is ac ion ha e o be gi en. To a ain he o de o he aspec -wise elimina ion o al e na i es, we in es iga e he abili y o disc imina ion o each s anda d. This abili y is de e mined by he numbe o al e na i es elimina ed by applying he s anda d o an aspec on he p esen se o al e na i es. Thus, we begin elimina ing wi h he aspec ha disca ds he mos al e - na i es and con inue un il one elemen emains [ZiGu91, 51–52]. Fo mal: Le n be he numbe o al e na i es A, and m be he numbe o a ibu es o sa is y a speci ied s anda d. Le k be he i e a ion s ep wi h descending abili y o dis- c imina ion so ha {}{ } 1kk AA  , and wi h {} {} 0 j AA=, {} 1, , j m!, we deno e he ule {} {} 1sa is ies kk kj AA x  = , which is epea ed un il {} 1 k A= o kn=, when all a ibu es ha e been used in he p ocess and he inal se o al e na i es {} 1 n A is again ega ded as equi alen [YoHw95, 26]. The EbA app oach combines ideas o he Conjunc i e me hod and he LM: The p ac- ical applica ion is lexicog aphically mo i a ed and he elimina ion decision is based on he sa is ac ion o speci ied s anda ds. Bu he ele ance o a ibu es is comple ely igno ed, and elimina ion happens a he a bi a ily han in a a ional way [Webe93, 72], [ZiGu91, 52]. T e sky admi s he inapp op ia eness o his me hod o many cases in he o iginal wo k as well [T e 72, 298]. 3.3.5 Value Func ion Me hods 3.3.5.1 Syn hesizing Pa ial Values A well-known amily o me hods syn hesizes pa ial alue unc ions in o de o de- e mine a comple e p eo de o al e na i es [Roy05, 15]. The calcula ion o an agg e- ga e measu e expec s ca dinal scaled in o ma ion on he a ibu e ou comes as well as 45 weigh s o each a ibu e; how his ec o o in o ma ion is inally summa ized in o a scala depends on he speci ic app oach used [T ia00, 5]. This Subsec ion ou lines he ollowing ou p ominen me hods: he Simple Addi i e Weigh ing (SAW), he Weigh ed P oduc Me hod (WPM), he Analy ical Hie a chy P ocess (AHP), and he Technique o O de P e e ence by Simila i y o Ideal Solu ion (TOPSIS). 3.3.5.2 Simple Addi i e Weigh ing and Weigh ed P oduc Me hod The SAW app oach, some imes also e e ed o as he Weigh ed Sum Me hod, is pa - icula ly appealing due o i s simple applica ion [BeS 02, 87], [YoHw95, 32]. The s ep-by-s ep cou se o ac ion is illus a ed below (Figu e 21). The SAW me hod as- sumes unde lying addi i e alue unc ions and compu es an al e na i e’s sco e () ii VVA= by adding weigh ed no malized alues {} = ! 1, , jij w j m be o e e en- ually anking al e na i es on his agg ega e (Table 11, p. 47). Two addi ional p econdi ions a e undamen al o his echnique, he p e e en ial independence o pa ial alues and he assessmen o weigh s in p opo ion o he ela i e alue o he c i e ion [YoHw95, 33], [Wins94, 773–774]. As we only de e - mine weigh s om agg ega ing con e sion a ios, he second p econdi ion is o less impo ance he e. Apa om ha , p e e en ial independence ela es o he absence o in e dependen- cies be ween he pa ial alue unc ions: This means he con ibu ion o an indi idual a ibu e alue o he agg ega e is no a ec ed by any o he a ibu e [Dye 05, 274– 275], [KeRa93, 129]. P oo o his necessa y condi ion is gi en in [Fish76, 248]. 52 The name o he app oach does no ully e lec he p ocess: I de e mines he p e e - ence o de on he g ounds o he simila i y o a posi i e ideal solu ion and he dis- simila i y o a nega i e solu ion. Compu ing he dis ance o each conside ed al e na- i e o hose ideal solu ions makes use o he Euclidean dis ance ec o ; o he wo- a ibu e case his is depic ed below using a wo-dimensional coo dina e sys em (Figu e 26) [HwYo81, 128]. Though al e na i e one is close o he posi i e ideal solu ion han al e na i e wo, he app oach may s ill a o he la e due o he g ea e dis ance o he nega i e ideal solu ion compa ed o al e na i e one. A ibu e 2 (inc easing p e e ence) A ibu e 1 (inc easing p e e ence) Al e na i e 2 Al e na i e 1 A + (posi i e ideal solu ion) A - (nega i e ideal solu ion) A ibu e 2 (inc easing p e e ence) A ibu e 1 (inc easing p e e ence) Al e na i e 2 Al e na i e 1Al e na i e 1 A + (posi i e ideal solu ion) A - (nega i e ideal solu ion) Figu e 26: Euclidean dis ances o he ideal solu ions in wo-dimensional space [HwYo81, 129] The e o e, i we wan o ank al e na i es wi h espec o wo e e ence poin s, we ha e o cons uc hese bounda ies in ad ance. The s ep-by-s ep p ocedu e is ou - lined below (Figu e 27). Fi s , s a ing wi h a gi en decision ma ix, we need o ge compa able alues ij in each ma ix en y. This is achie ed wi h a modi ied ec o no maliza ion and mul i- plica ion wi h he co esponding weigh s wj [FeWa01, 465], [HwYo81, 131]. 53 Technique o O de P e e ence by Simila i y o Ideal Solu ion De ine decision ma ix De ine decision ma ix Decision ma ix Decision ma ix So al e na i es by simila i y Ri So al e na i es by simila i y Ri De ine weigh s De ine weigh s De ine weigh s De ine weigh s De i e pa ial alues wi h ec o no maliza ion De i e pa ial alues wi h ec o no maliza ion Weigh s ec o wm Weigh s ec o wm Decision ma ix wi h alues Vnxm Decision ma ix wi h alues Vnxm Posi i e ideal solu ion A+ Posi i e ideal solu ion A+ Nega i e ideal solu ion A- Nega i e ideal solu ion A- De e mine sepa a ion measu es S+ De e mine sepa a ion measu es S+ De e mine sepa a ion measu es S- De e mine sepa a ion measu es S- Cons uc posi i e ideal solu ion A+ Cons uc posi i e ideal solu ion A+ Cons uc nega i e ideal solu ion A- Cons uc nega i e ideal solu ion A- Compu e weigh ed alues wj × ij Compu e weigh ed alues wj × ij Calcula e simila i y o ideal solu ion Calcula e simila i y o ideal solu ion Simila i y R o all al e na i es Simila i y R o all al e na i es Ranking Ranking Da a Da a Technique o O de P e e ence by Simila i y o Ideal Solu ion De ine decision ma ix De ine decision ma ix De ine decision ma ix De ine decision ma ix Decision ma ix Decision ma ix So al e na i es by simila i y Ri So al e na i es by simila i y Ri De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De i e pa ial alues wi h ec o no maliza ion De i e pa ial alues wi h ec o no maliza ion Weigh s ec o wm Weigh s ec o wm Decision ma ix wi h alues Vnxm Decision ma ix wi h alues Vnxm Posi i e ideal solu ion A+ Posi i e ideal solu ion A+ Nega i e ideal solu ion A- Nega i e ideal solu ion A- Posi i e ideal solu ion A+ Posi i e ideal solu ion A+ Nega i e ideal solu ion A- Nega i e ideal solu ion A- De e mine sepa a ion measu es S+ De e mine sepa a ion measu es S+ De e mine sepa a ion measu es S- De e mine sepa a ion measu es S- De e mine sepa a ion measu es S+ De e mine sepa a ion measu es S+ De e mine sepa a ion measu es S- De e mine sepa a ion measu es S- Cons uc posi i e ideal solu ion A+ Cons uc posi i e ideal solu ion A+ Cons uc nega i e ideal solu ion A- Cons uc nega i e ideal solu ion A- Cons uc posi i e ideal solu ion A+ Cons uc posi i e ideal solu ion A+ Cons uc nega i e ideal solu ion A- Cons uc nega i e ideal solu ion A- Compu e weigh ed alues wj × ij Compu e weigh ed alues wj × ij Calcula e simila i y o ideal solu ion Calcula e simila i y o ideal solu ion Simila i y R o all al e na i es Simila i y R o all al e na i es Ranking Ranking Da a Da a Figu e 27: P ocess o he Technique o O de P e e ence by Simila i y o Ideal Solu ion In he second s ep, we cons uc wo i ual ideal al e na i es, A+ consis ing o all bes c i e ia alues j+ ( he posi i e ideal solu ion), and he nega i e ideal solu ion A- wi h all he poo es alues j- (Table 12) [HwYo81, 131]. Table 12: Assembling posi i e and nega i e ideal solu ions [HwYo81, 131] Values P econdi ion Posi i e ideal solu ion {} {} :max jijj i A w ++ = Nega i e ideal solu ion {} {} :min jijj i A w  = Fo ×  nm Vwi h {} =…1, ,in; {} =! 1, , j m and [ ] ,0;1 ij j w 54 These wo ec o s ep esen ex eme poin s in a Ca esian coo dina e sys em, and all gi en al e na i es a e loca ed be ween hem, i.e. all al e na i es can be cons uc ed om linea combina ions o hese poin s (Figu e 26). The me hod makes use o his pa icula ea u e: in he hi d s ep, we compu e sepa a ion measu es S+i (S-i) as indi- ca o s o he dis ance o each al e na i e om he posi i e (nega i e) e e ence poin [HwYo81, 132]. () {} ++ = == ! 2 1 1, , m ijijjj j Sw w in () {}  = == ! 2 1 1, , m ijijjj j Sw w in We do no ely me ely on he closeness o he posi i e ideal solu ion bu a he on bo h dis ances, since he sho es posi i e di e ence does no necessa ily mean i is also leas close o he nega i e ideal one; he dis ance ec o s depic ed abo e (Figu e 26) illus a e a case in which one al e na i e (numbe one) is close o he posi i e ideal and o he nega i e ideal solu ion hen ano he one (numbe wo). The ou h s ep is conce ned wi h compu ing he simila i y o ideal solu ion measu e and anking he al e na i es. Gi en he wo dis ance indices o each al e na i e, we calcula e he simila i y measu e Ri as ollows [HwYo81, 132]: {} 1, , i i ii S Rim SS  + == +! wi h [] 0;1 i R The close he simila i y measu e Ri is o one, he mo e p e e able is he al e na i e; wi h a dec easing (inc easing) di e ence o he nega i e (posi i e) ideal solu ion, he al e na i e becomes he less in e es ing [HwYo81, 132]. Fi h and inally, we can so ou al e na i es in ascending o de by he simila i y measu e and ecommend he op- anked op ion [HwYo81, 132]. Ad ising DMs wi h he help o a TOPSIS e alua ion seems e y appealing and appli- cable in conc e e si ua ions; eason is he simila i y o he SAW me hod [HwYo81, 135–136]. Meanwhile, he me hod has been ex ended o si ua ions wi h con inuous solu ion se s, which usually equi e ex ensi e linea p og amming [HLLi93, 890]. Bu a p oblem a ises when ca dinal alues a e no gi en o when he unde lying u il- i y is no subjec o mono onici y [HwYo81, 137]. As we al eady uled ou he la e in ou de ini ions (c . Subsec ion 2.6.4), one may eel emp ed o sol e he o me by 55 ans o ming o dinal o nominal in o ma ion. Un o una ely, his may lead o dis o - ion (e.g. when in e als be ween alues a e no cons an ); in his case he echnique may become a me ely supe icial ecommenda ion (c . also Subsec ion 3.2.1). On op o ha , Wang and T ian aphyllou claim o ha e ound e idence ha he TOPSIS me hod also su e s om anking i egula i ies (c . AHP, Subsec ion 3.3.5.3) [WaT 08, 46]. 3.4 Mul iple Objec i e Decision Making 3.4.1 O e iew o MODM Me hods In con as o MADM me hods, he se o al e na i es in Mul iple Objec i e Decision Making is no p e-de ined: To cope wi h an in ini e o con inuous space o op ions, speci ied cons ain s and objec i e unc ions de ine he domain om which an op i- mal solu ion is o be “designed”. [ZiGu91, 25], [HwMa79, 6–7]. Such decision p oblems, in which mul iple objec i es a e o be op imized, ha e been ini ially e e ed o as ec o maximum p oblems [KuTu51, 488]. In MODM, he DM’s p e e ence in o ma ion is implemen ed in e ms o aspi a ion o sa is ac ion le els o c i e ia. These le els may ei he be minimum (maximum) p e- equisi es when he co esponding objec i e is o be maximized (minimized), o an exac alue which should be hi as close as possible [BeS 02, 210]. Hwang and Masud classi y MODM me hods on he ype o in o ma ion needed (Figu e 28). A ull in oduc ion in o he ounda ions o MODM and he classi ied me hods can be ound in hei monog aph [HwMa79]. O hese classes o me hods, we will ske ch he idea o Goal P og amming in he ol- lowing Subsec ion. 56 S age a which in o ma ion is needed Majo classes o me hodsType o in o ma ion • Global C i e ion Me hod • Global C i e ion Me hod • Lexicog aphic Me hod •Goal P og amming Me hod • Goal A ainmen Me hod • Lexicog aphic Me hod •Goal P og amming Me hod • Goal A ainmen Me hod • Me hod o Geo ion and In e ac i e Goal P og amming • Su oga e Wo h T ade-o Me hod • Me hod o Sa is ac o y Goals • Me hod o Zion s-Wallenius • Me hod o Geo ion and In e ac i e Goal P og amming • Su oga e Wo h T ade-o Me hod • Me hod o Sa is ac o y Goals • Me hod o Zion s-Wallenius • Pa ame ic Me hod ವˢ-cons ain Me hod • MOLP Me hods • Adap i e Sea ch Me hod • Pa ame ic Me hod ವˢ-cons ain Me hod • MOLP Me hods • Adap i e Sea ch Me hod No a icula ion o p e e ence in o ma ion No a icula ion o p e e ence in o ma ion P og essi e a icula ion o p e e ence in o ma ion (In e ac i e me hods) P og essi e a icula ion o p e e ence in o ma ion (In e ac i e me hods) A p io i a icula ion o p e e ence in o ma ion A p io i a icula ion o p e e ence in o ma ion A pos e io i a icula ion o p e e ence in o ma ion (Nondomina ed solu ions gene a ion me hod) A pos e io i a icula ion o p e e ence in o ma ion (Nondomina ed solu ions gene a ion me hod) • U ili y Me hod • Bounded Objec i e Me hod • U ili y Me hod • Bounded Objec i e Me hod Explici ade-o Explici ade-o Implici ade-o Implici ade-o Implici ade-o Implici ade-o Ca dinal in o ma ion Ca dinal in o ma ion O dinal and ca dinal in o ma ion O dinal and ca dinal in o ma ion • STEM and ela ed me hods • SEMOPS and SIGMOP me hods • Me hod o Displaced Ideal • GPSTEM me hod • Me hod o S eue (In e ac i e MOLP me hod) • STEM and ela ed me hods • SEMOPS and SIGMOP me hods • Me hod o Displaced Ideal • GPSTEM me hod • Me hod o S eue (In e ac i e MOLP me hod) S age a which in o ma ion is needed S age a which in o ma ion is needed Majo classes o me hodsMajo classes o me hodsType o in o ma ionType o in o ma ion • Global C i e ion Me hod • Global C i e ion Me hod • Lexicog aphic Me hod •Goal P og amming Me hod • Goal A ainmen Me hod • Lexicog aphic Me hod •Goal P og amming Me hod • Goal A ainmen Me hod • Me hod o Geo ion and In e ac i e Goal P og amming • Su oga e Wo h T ade-o Me hod • Me hod o Sa is ac o y Goals • Me hod o Zion s-Wallenius • Me hod o Geo ion and In e ac i e Goal P og amming • Su oga e Wo h T ade-o Me hod • Me hod o Sa is ac o y Goals • Me hod o Zion s-Wallenius • Pa ame ic Me hod ವˢ-cons ain Me hod • MOLP Me hods • Adap i e Sea ch Me hod • Pa ame ic Me hod ವˢ-cons ain Me hod • MOLP Me hods • Adap i e Sea ch Me hod No a icula ion o p e e ence in o ma ion No a icula ion o p e e ence in o ma ion P og essi e a icula ion o p e e ence in o ma ion (In e ac i e me hods) P og essi e a icula ion o p e e ence in o ma ion (In e ac i e me hods) A p io i a icula ion o p e e ence in o ma ion A p io i a icula ion o p e e ence in o ma ion A pos e io i a icula ion o p e e ence in o ma ion (Nondomina ed solu ions gene a ion me hod) A pos e io i a icula ion o p e e ence in o ma ion (Nondomina ed solu ions gene a ion me hod) • U ili y Me hod • Bounded Objec i e Me hod • U ili y Me hod • Bounded Objec i e Me hod Explici ade-o Explici ade-o Implici ade-o Implici ade-o Implici ade-o Implici ade-o Ca dinal in o ma ion Ca dinal in o ma ion O dinal and ca dinal in o ma ion O dinal and ca dinal in o ma ion Explici ade-o Explici ade-o Implici ade-o Implici ade-o Implici ade-o Implici ade-o Ca dinal in o ma ion Ca dinal in o ma ion O dinal and ca dinal in o ma ion O dinal and ca dinal in o ma ion • STEM and ela ed me hods • SEMOPS and SIGMOP me hods • Me hod o Displaced Ideal • GPSTEM me hod • Me hod o S eue (In e ac i e MOLP me hod) • STEM and ela ed me hods • SEMOPS and SIGMOP me hods • Me hod o Displaced Ideal • GPSTEM me hod • Me hod o S eue (In e ac i e MOLP me hod) Figu e 28: A axonomy o me hods o Mul iple Objec i e Decision Making [HwMa79, 8] 3.4.2 Goal P og amming The i s Goal P og amming (GP) p ac ice can be aced back o Cha nes e al. who es ima ed a ai compensa ion o company execu i es [CCFe55]. La e , Cha nes and Coope de eloped he basic concep o GP as means o “goals, e en when hey a e una ainable wi hin he limi s o a ailable esou ces” [ChCo67, 215]. The GP echnique has since hen ecei ed wide accep ance in a ious ields, e.g. 265 e e ence cases can be ound in [JoTa02, 134–136] and a bibliog aphy o 443 classed en ies is p o ided by [Rome91, 100–105]. 57 The basis o GP is a linea p og amming p oblem wi h he ollowing cons ain s p e- sen ed in [ChCo67, 216]: 12 1 12 12 12 32 12 510 8 4 ,0 xx x xx xx xx +  + +   Depic ing he p oblem wi h i s cons ain s e eals wo (o ange and blue) shaded a - eas wi h pa ly easible solu ions, bu since bo h subse s do no o e lap, no se o ea- sible solu ions exis s which sa is ies all cons ain s (Figu e 29) [ChCo67, 217]. x1 x2 10 5 0510 5x 1 10 -x 1 + x 2 4 x 1 + x 2 8 3x 1 + 2x 2 12 x1 x2 10 5 0510 5x 1 10 -x 1 + x 2 4 x 1 + x 2 8 3x 1 + 2x 2 12 Figu e 29: Po ay o easible solu ions in a GP example [ChCo67, 216] Now, he GP idea is o in oduce wo de ia ion a iables di- ( o unde achie emen ) and di+ ( o o e achie emen ) when measu ing he a ainmen o a a ge i by an ob- jec i e i [Lee99, 8-2–8-3]. Then we seek o minimize an achie emen unc ion z ha consis s o he weigh ed de ia ions o all q objec i es. We can deno e he linea GP p oblem as () () 1 min subjec o ,,, 0 0 q ii ii i iii i iiii ii znwdpwd x d d nw pw d d nw pw + = + + =+ + =  =  {} 1, ,i q = !, 58 unde he assump ion all objec i es a e no malized [JoTa02, 130–131]. Since we model ela i e impo ance be ween objec i es by applying weigh s (nwi, pwi), his pa icula ype o GP p oblem is called weigh ed GP o A chimedean GP [JoTa02, 130], [ZiGu91, 122]. The modi ied simplex me hod sol es his p oblem [Lee72, 105–106]. In he wide a ay o GP ex ensions, wo o he majo a ian s s and ou no ably o en: Lexicog aphic (o p eemp i e) GP and Chebyshe (o minmax) GP [Lee99, 8-4–8- 6], [Igni85, 12–13]. P eemp i e GP s i es o a ain objec i es in a p ede ined p io i y o de and is help ul when he DM canno quan i y he ela i e impo ance o goals. As he app oach does no allow ade-o s be ween p io i y le els, he DM should ha e a na u al o de o objec i es in mind [JoTa02, 132]. P eemp i e GP is sol ed by a sequence o linea p og ams; a o mal ou line is gi en in [Lee99, 8-5–8-6]. Chebyshe GP aims a a sho coming o A chimedean GP: i a la ge numbe o de ia- ions a e e y small, ew e y la ge de ia ions do no p eponde a e in he a ainmen unc ion. In o de o amelio a e his incon enience, he Chebyshe GP app oach minimizes he maximum weigh ed de ia ion [JoTa02, 132–133], [ZiGu91, 124]. () min subjec o ,,, 0 0 ii ii iii i iiii ii zMax nw d p wd Max x d d nw pw d d nw pw + + + = + + =  = {} 1, ,i q = ! In esul , he heu is ic balances he le els o objec i es ins ead o s icking o a s ic minimisa ion o hei sum. This e lec s he a i ude o a ca e ul DM, simila o he Maximin app oach in MADM (Table 9). Cu en ly, esea ch on he issue o GP includes non-linea GP, ac ional GP, in ege GP and in e ac i e GP. The in eg a ion and combina ion wi h o he echniques such as he AHP o he Da a En elopmen Analysis (DEA) plays also an impo an ole [JoTa02], [Lee99]. In e ms o he DEA, which de e mines an e icien on ie om a domain o al e na i es, de ining uppe and lowe bounds o weigh s and conduc ing sensi i i y analysis a e o in e es ( o an explica ion o he DEA me hod see he o iginal wo k o [CCRh78] ) [BeS 02, 303], [JKWa98], [S ew96]. 59 GP ope a ionalizes Simon’s concep o sa is icing inso a as unc ions o objec i es a e gi en and he DM speci ies his aspi a ion le els (goals) (c . p. 41). Though he echnique is widely ega ded as an “in ui i e and com o able app oach“, i is no lawless [BeS 02, 231]: se ing ealis ic goals in ad ance can cons i u e a majo pi all and may lead ei he o “no al e na i e, o e y la ge numbe s o al e na i es, which sa is y he goals” [S ew92, 576]. Especially when complex o un amilia p oblems a e conce ned, he DM will ha dly be awa e o speci ic a ge le els. Thus he use o GP is ecommended o sc eening pu poses i.e. o p oducing a subse o easible al e na- i es [EhWi05], [S ew92, 578]. 3.5 Decision Aids 3.5.1 Ou anking Rela ions The me hods in his Sec ion di e om he p e ious ones inso a , as hey explici ly pe mi incompa able al e na i es and c i e ia, and do no equi e ansi i i y o com- ple eness in he a angemen o al e na i es [BeS 02, 104–105], [Roy73, 181–183]. The in en o ou anking is no so much e ie ing an op imal solu ion bu a he e- ducing he numbe o gi en al e na i es o a non-domina ed se om which he DM is supposed o selec a e wa ds; o his eason hese me hods a e called aids [ZiGu91, 202]. The ela ion be ween wo al e na i es A1 and A2 is assessed wi h he help o a bina y ou anking ela ion S, in compa ing pai s o al e na i es, which leads o h ee possible ela ions (Table 13) [Roy73, 181–182]. Table 13: Ou anking ela ions [Roy73, 181–182] S ic p e e ence1 Indi e ence Incompa abili y A1SA2 and no A2SA1 A1SA2 and A2SA1 No A1SA2 and no A2SA1 12 AA; 12 AA 12 AA/ A1 is s ic ly p e e ed o A2 A1 is indi e en o A2 A1 is incompa able o A2 1) applies o he in e se ela ion as well The inclusion o incompa able ela ions is use ul o modeling a p e e ence o de when he DM is incapable o unwilling o dis inguish [Roy73, 182–183]. We ou line he oldes amily o me hods, called ELECTRE, in he ollowing Subsec ion [ZiGu91, 207]. 60 Apa om ELECTRE, ano he class o me hods named PROMETHEE (ac onym o P e e ence Ranking O ganiza ion METhod o En ichmen E alua ions) is wide- sp ead in ou anking esea ch [BeS 02, 233]. Fo an in oduc ion wi h la es de el- opmen s we e e o [B Ma05] o he o iginal publica ion [BVMa86]. 3.5.2 The ELECTRE App oach The amily o ELECTRE me hods was ini ially de eloped in 1965, and he i s ELECTRE me hod was o icially published h ee yea s la e [Roy68]. The ac onym ELECTRE is deduced om ELimina ion E Choix T aduisan la REali é (ELimina- ion and Choice Exp essing he REali y) [T ia00, 13], [Roy68]. Fo a summa y o six ELECTRE me hods, namely ELECTRE I, II, III, IV, IS, and TRI, we e e o [Vinc99, 11-5–11-10]. The oldes and simples o hese, ELECTRE I, is p esen ed in his Subsec ion. ELECTRE me hods ha e been applied o a wide ield o conc e e decision p oblems, including en i onmen al planning ([GSM+03], [SHLa98], [TeTz94]), employee e- c ui men ([SGKM07]), loca ion planning ([No e06], [BDLe90]), anspo a ion managemen ([RoHu82]) and inancial issues ([MKBe88]). The unde lying p inciple o ELECTRE is he ollowing: We compa e al e na i es pai wise and assess he ex en o which an al e na i e is ou anking ano he and up o which ex en his is no he case. In o de o ou ank an al e na i e, su icien e i- dence o he assump ion (conco dance) and insu icien e idence agains he as- sump ion (disco dance) a e needed. The s eng h o an e idence is de e mined by he e alua ion o cons uc ed conco dance and disco dance measu es o each compa i- son [ZiGu91, 207]. The cou se o ac ion is illus a ed below (Figu e 30) and he i e s eps o he ELECTRE I me hod a e desc ibed in he nex pa ag aphs. Fi s , we need a no malized and weigh ed decision ma ix, al hough incompa abili y is allowed; o ELECTRE me hods, i is common p ac ice o apply he ec o no mali- za ion [T ia00, 13]. 61 ELECTRE De ine decision ma ix De ine decision ma ix Decision ma ix Decision ma ix De ine weigh s De ine weigh s De ine weigh s De ine weigh s De i e pa ial alues wi h ec o no maliza ion De i e pa ial alues wi h ec o no maliza ion Weigh s ec o wm Weigh s ec o wm Decision ma ix wi h alues Vnxm Decision ma ix wi h alues Vnxm Compu e weigh ed alues wj × ij Compu e weigh ed alues wj × ij Da a Da a <<localP econdi ion>> Couples o al e na i es le , which a e no compa ed ye <<localP econdi ion>> All al e na i es compa ed De e mine se o conco dance indices De e mine se o conco dance indices De e mine se o disco dance indices De e mine se o disco dance indices Compa e al e na i es pai wise on each c i e ion Compa e al e na i es pai wise on each c i e ion Quan i y s eng h o conco dance indices conkl Quan i y s eng h o conco dance indices conkl Quan i y s eng h o disco dance indices disckl Quan i y s eng h o disco dance indices disckl Selec pai o al e na i es Selec pai o al e na i es B Calcula e mean s eng h o disco dance Calcula e mean s eng h o disco dance Disco dance h eshold alue Disco dance h eshold alue Build disco dance dominance ma ix G Build disco dance dominance ma ix G Disco dance dominance ma ix G Disco dance dominance ma ix G Conco dance dominance ma ix F Conco dance dominance ma ix F Calcula e mean s eng h o conco dance Calcula e mean s eng h o conco dance Conco dance h eshold alue Conco dance h eshold alue Build conco dance dominance ma ix F Build conco dance dominance ma ix F Ke nel o leading al e na i es Ke nel o leading al e na i es Elimina e domina ed al e na i es Elimina e domina ed al e na i es Compu e dominance ma ix E Compu e dominance ma ix E Dominance ma ix E Dominance ma ix E B A A A ELECTRE De ine decision ma ix De ine decision ma ix De ine decision ma ix De ine decision ma ix Decision ma ix Decision ma ix De ine weigh s De ine weigh s De ine weigh s De ine weigh s De i e pa ial alues wi h ec o no maliza ion De i e pa ial alues wi h ec o no maliza ion De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De ine weigh s De i e pa ial alues wi h ec o no maliza ion De i e pa ial alues wi h ec o no maliza ion Weigh s ec o wm Weigh s ec o wm Decision ma ix wi h alues Vnxm Decision ma ix wi h alues Vnxm Weigh s ec o wm Weigh s ec o wm Decision ma ix wi h alues Vnxm Decision ma ix wi h alues Vnxm Compu e weigh ed alues wj × ij Compu e weigh ed alues wj × ij Da a Da a <<localP econdi ion>> Couples o al e na i es le , which a e no compa ed ye <<localP econdi ion>> Couples o al e na i es le , which a e no compa ed ye <<localP econdi ion>> Couples o al e na i es le , which a e no compa ed ye <<localP econdi ion>> All al e na i es compa ed <<localP econdi ion>> All al e na i es compa ed <<localP econdi ion>> All al e na i es compa ed De e mine se o conco dance indices De e mine se o conco dance indices De e mine se o disco dance indices De e mine se o disco dance indices De e mine se o conco dance indices De e mine se o conco dance indices De e mine se o disco dance indices De e mine se o disco dance indices Compa e al e na i es pai wise on each c i e ion Compa e al e na i es pai wise on each c i e ion Quan i y s eng h o conco dance indices conkl Quan i y s eng h o conco dance indices conkl Quan i y s eng h o disco dance indices disckl Quan i y s eng h o disco dance indices disckl Quan i y s eng h o conco dance indices conkl Quan i y s eng h o conco dance indices conkl Quan i y s eng h o disco dance indices disckl Quan i y s eng h o disco dance indices disckl Selec pai o al e na i es Selec pai o al e na i es B Calcula e mean s eng h o disco dance Calcula e mean s eng h o disco dance Disco dance h eshold alue Disco dance h eshold alue Build disco dance dominance ma ix G Build disco dance dominance ma ix G Disco dance dominance ma ix G Disco dance dominance ma ix G Conco dance dominance ma ix F Conco dance dominance ma ix F Calcula e mean s eng h o conco dance Calcula e mean s eng h o conco dance Conco dance h eshold alue Conco dance h eshold alue Build conco dance dominance ma ix F Build conco dance dominance ma ix F Ke nel o leading al e na i es Ke nel o leading al e na i es Elimina e domina ed al e na i es Elimina e domina ed al e na i es Compu e dominance ma ix E Compu e dominance ma ix E Dominance ma ix E Dominance ma ix E B A A A Figu e 30: P ocess o he ELECTRE me hod Secondly, he s eng h o conco dance and disco dance a e de e mined o each cou- ple o al e na i es. The compa ison o wo al e na i es is conduc ed using he ou - anking ela ion S on each j- h c i e ion sepa a ely, hus i is no as s ic as he o - mal ules o he alue unc ion me hods. 68 Re e ing o he Sec ion 2, we now u n o he objec - ela ed p e equisi es, assuming he agen is buying a commodi y. This means excep o he p ice, o e s canno be di e en ia ed (se ice measu es like e ms o deli e y a e omi ed). Bu beyond p oduc cha ac e is ics, he agen conside s image and social epu a ion o a selle . Thus, h ee c i e ia a e subjec o he decision p oblem. Mo e impo an , on a supe la ge-scaled ma ke place, i is e y likely ha no image bu only a social epu a ion alue is a ailable, hus we need a compensa o y me hod which allows ade-o s be- ween c i e ia (c . 2.5.2.1). To allow compensa ion, we assume he ela ions be ween he h ee c i e ia a e independen in ou simpli ied case. I ha holds o p ice and epu a ion in e e yday li e is ques ionable – and o be s ic , in he sense o ReG eT, image exe s a sligh in luence on social epu a ion. Due o he emendous numbe o ma ke pa icipan s, we assume his e ec o be insigni ican ly small. O he wise all me hods based on addi i e u ili y assump ions would ha e o be dis ega ded. Weigh s Weigh s Aspi a ion le els Aspi a ion le els Resul Resul P e e ence in o ma ion P e e ence in o ma ion C i e ia C i e ia Independence Independence Compensa o y Compensa o y Inpu Inpu Ou pu Ou pu Inpu compliance Inpu compliance V = = Ou pu compliance Ou pu compliance   One dis inc solu ion One dis inc solu ion Se o e icien solu ions Se o e icien solu ions  Weigh s Weigh s Aspi a ion le els Aspi a ion le els Weigh s Weigh s Aspi a ion le els Aspi a ion le els Resul Resul P e e ence in o ma ion P e e ence in o ma ion C i e ia C i e ia Independence Independence Compensa o y Compensa o y Inpu Inpu Ou pu Ou pu Inpu compliance Inpu compliance VV == == Ou pu compliance Ou pu compliance   One dis inc solu ion One dis inc solu ion Se o e icien solu ions Se o e icien solu ions  One dis inc solu ion One dis inc solu ion Se o e icien solu ions Se o e icien solu ions  Figu e 33: P e equisi es o he app op ia e MCDM me hod Second, we add ess he ou pu side o he MCDM me hod: The esul o he decision-making p ocess has o be a speci ic ecommenda ion in e ms o one o e o bid o , i.e. non-in e ac i i y om he DM’s poin o iew is es- sen ial. MCDM app oaches which me ely gene a e a se o e icien solu ions a e o li le help, since hey equi e in e ac ion wi h he p incipal o con inue bidding. Those in e ac ions a e o be a oided, as hey delay he ul illmen p ocess and hus impede he sys em e iciency ( o he ace s o in e ac i i y in e ms o in e ac i e MCDM ap- p oaches see [S ew99, 10-2–10-3]). 69 Now as we ha e compiled all he p e equisi es, we need o con on hem wi h he ea u es o he discussed me hods. To acili a e he compa ison, we lis ed all ech- niques below (Table 16, 69). The dimensions o in o ma ion gi en in he o e iew a e explained in he able be o e (Table 15). Table 15: Dimensions o he compa ison able Me hod Name o ac onym o he me hod as gi en in his wo k Type MADM MADM me hod MODM MODM me hod Ou anking Ou anking me hod (Decision aid) Se o op ions Size o he se o al e na i es Fini e Bounded o a coun able numbe In ini e Un es ained and no -coun able la ge Scale le el (Scale le el equi ed) Minimum le el a which gi en in o ma ions ha e o be scaled No m (No maliza ion ) Yes/ No No malized in o ma ion equi ed Comp (Compensa o y) Yes/ No Ra he compensa o y P e (P e e ence modeling) Yes/ No Known p e e ences o he DM modeled in he me hod Ou pu (Ou pu o he MCDM me hod) 0 Ra he a single solu ion; non-in e ac i e 1 Single solu ion o se o e icien al e na i es equally possible 2 Ra he a se o e icien al e na i es Supplemen a y in o ma ion In addi ion o he decision ma ix needed in o ma ion Se o supplemen a y in o ma ion Ex en o which supplemen a y in o ma ion is needed Case Yes/ No Compu ed example p o ided in case s udy in Appendix B Re (Re e ence) Poin s o he Subsec ion o he me hod 70 Table 16: Compa ison o MCDM me hods Re 3.3.2.2 3.3.2.3 3.3.3 3.3.3 3.3.4.2 3.3.4.3 3.3.5.2 3.3.5.2 3.3.5.3 3.3.5.4 3.4.2 3.5.2 Case Yes Yes Yes No Yes Yes Yes Yes Yes Yes No Yes Se o supplemen a y in o ma ion - - m m m m m m a leas [m × (m-1) + m × n ×(n-1)] ÷2 ( h ee-le el hie a chy)a m m m Supplemen a y in o ma ion - - Aspi a ion le els Aspi a ion le els A ibu e o de o ele ance S anda ds Weigh s o a ibu es; alues de i ed om ou comes Weigh s o a ibu es; ou comes  1 Rela i e impo ance o c i e ia and al e na i es wi h espec o pa en al nodes Weigh s o a ibu es Weigh s o a ibu es; aspi a ion le els Weigh s o a ibu es Ou pu 2 0 2 2 1 1 0 0 0 0 1 2 P e No No Yes Yes Yes No Yes Yes Yes Yes Yes Yes Comp No No No Yes No No Yes Yes Yes Yes Yes No No m No Yes No No No No Yes No Yes Yesb Yes Yesb Scale le el O dinal O dinal O dinal O dinal Nominal O dinal Ca dinal Ca dinal Ca dinal Ca dinal Ca dinal O dinal Se o op ions Fini e Fini e Fini e Fini e Fini e Fini e Fini e Fini e Fini e Fini e In ini e Fini e May also be de i ed om (m × n) gi en alues Vec o no maliza ion by de elope s ecommended Type MADM MADM MADM MADM MADM MADM MADM MADM MADM MADM MODM Ou anking a b Me hod Dominance Maximin/ Maximax Sa is icing (Conjunc i e) Sa is icing (Disjunc i e) Lexicog aphic Me hods EbA SAW WPM AHP TOPSIS Goal P og amming ELECTRE (I) 71 4.2.3 Conclusion o Me hod Applica ion Wi h he help o he compa ison able and he inpu and ou pu p e equisi es, we can depic he discussed me hods on a wo-axis cha . The me hod o ou scena io should be one o he equally sui able ou in he uppe igh qua e (Figu e 34). P e e ed me hods P e e ed me hods 11 10 9 8 1 6 2 5 3 12 4 Ou pu compliance Legend (1) Dominance (2) Maximin/ Maximax (3) Conjunc i e App oach (4) Disjunc i e App oach (5) Lexicog aphic Me hods (6) EbA (7) SAW (8) WPM (9) AHP (10) TOPSIS (11) Goal P og amming (12) ELECTRE Inpu compliance 7 P e e ed me hods P e e ed me hods 1111 1010 99 88 11 66 22 55 33 1212 44 Ou pu compliance Legend (1) Dominance (2) Maximin/ Maximax (3) Conjunc i e App oach (4) Disjunc i e App oach (5) Lexicog aphic Me hods (6) EbA (7) SAW (8) WPM (9) AHP (10) TOPSIS (11) Goal P og amming (12) ELECTRE Inpu compliance 77 Figu e 34: Classi ica ion o MCDM me hods in he ligh o he scena io A his s age, we bes ow conside a ion upon he complexi y o each me hod in a nu - shell: The SAW me hod and WPM a e p obably he mos s aigh o wa d me hods and cons i u e no insu moun able obs acle in de e mining agg ega es om m×n ou - comes. The TOPSIS comp ises elici ing minimum and maximum alues o all m c i- e ia om he gi en se o n al e na i es, as well as calcula ing n dis ance ec o s. These m×n compu a ions a e manageable as well, e en o a huge se o al e na i es. A sha p con as is he AHP – wi h an inc easing numbe o n al e na i es o m c i- e ia, he numbe o pai wise compa ison ma ices, which ha e o be p ocessed, wi h each ma ix subjec o ( ) 12nn  ÷  e alua ions, soa s by he ac o o m, means in- c emen ally abou m×n² e alua ions (e.g. 100 al e na i es and h ee c i e ia al eady need 14.853 compa isons, c . p. 51) [B ug04, 310]. Hence, we elimina e he AHP om ou lis . Conce ning he emaining h ee app oaches, we choose he TOPSIS me hod o one eason: I we s o e he cu en ideal solu ion ec o s in a eposi o y da abase, we a e 72 able o ace he expe iences ou agen has made and he de elopmen he unde wen . We will explica e his in mo e de ail in Subsec ion 4.4.1. Apa om ou decision, wo o he p ac ices a e o be conside ed when sol ing a mul- iple c i e ia decision p oblem: On he one hand, we could build a sys em o ules, which il e s insu icien al e na- i es s epwise, e.g. by combining Conjunc i e and Disjunc i e app oaches. Such a sys- em would be equi alen o he way in which we decided abo e on he MCDM me hod. Tha means, we would equip he agen wi h a se o ules consis ing o anges o bounds o c i e ia alues o which we conside an al e na i e o be sa is y- ing [Oze 88, 246–247]. E en hough he agen would no seek he bes , bu me ely sa is ying solu ion, his p ocedu e may be p e e able when ex ensi e compu a ions jeopa dize he sys em’s s abili y o when p ocessing powe becomes a bo leneck; we assume his does no apply o he case o ou u u e scena io. On he o he hand, we could employ simul aneously di e en MCDM me hods, le each one de e mine he op imal solu ion, agg ega e he anked se s and syn hesize hem a e wa ds [HwYo81, 214]. Bu especially when dealing wi h a la ge numbe o c i e ia o al e na i es, his may se iously h ea en a sys em’s o e all pe o mance. We ake no e o bo h ideas he e, bu do no con empla e he implemen a ion o he abo e s a ed easons. 4.3 Scena io Speci ica ions 4.3.1 En i onmen and Ac o s Ou ALN consis s o a e y la ge numbe o indi idual compu e sys ems, each one o e ing limi ed s o age capaci y o hi e on paymen o a ee. E e y compu e sys em belongs o a p incipal and is ep esen ed by an agen , which a a pa icula ime is ei he o e ing o seeking s o age capaci y. A cen al ins i u ion collec s o e s om selle s, en iches hem wi h epu a ion in o ma ion and o wa ds hem o buye s. Be- cause his in e media y also p o ides access o he ne wo k, we call i he hub (Figu e 35). 73 ALN ALN Agen Agen (Human) P incipal (Human) P incipal Hub Hub Compu e sys em Compu e sys em is owne o ALN ALN Agen Agen (Human) P incipal (Human) P incipal Hub Hub Compu e sys em Compu e sys em is owne o Figu e 35: Scheme o he scena io 4.3.2 In e ac ion be ween Ac o s On he basis o he al eady illus a ed main p ocess in Sec ion 2 (Figu e 32, p. 66), we explain in de ail he in e ac ion o buye , selle and hub wi hin he ALN in he ollow- ing pa ag aphs ( o a UML sequence diag am see Figu e 36): Whene e an agen ecei es a demand no e o ha d disk space om his connec ed sys em, he sends ou a eques o o e s o he hub. The hub collec s cu en o e s om his o e da abase and sea ches his epu a ion da abases o imp ession en ies co esponding wi h he cu en selle s; i en ies a e a ailable, epu a ion is calcu- la ed and a ached o he o e in o ma ion. Then he hub o wa ds he in o ma ion package o he eques ing agen . A e he buye ecei es he cu en a ailable o e s om he hub, he b owses his own image da abase o p e ious expe iences wi h he p esen selle s and i a ailable, adds he image alue o he co esponding o e . Wi h his in o ma ion, he MCDM p oce- du e is ca ied ou , a bes al e na i e is de e mined and he buye submi s his p ice quo e o he selle . When nego ia ions a e success ully inished, he ansac ion is ul illed by ans e - ing paymen and accessing he ha d disk pa i ion o s o ing da a ( his s ep is sub- sumed unde he e m deli e y). 74 c ea e_en y(imp ession) ge _o e s() e u n_a ay (selle , o e ) s o e(selle , o e ) Ok=s o e() Buye Buye Buye ‘s image da abase Buye ‘s image da abase Hub Hub O e da abase o hub O e da abase o hub Repu a ion da abase o hub Repu a ion da abase o hub Selle Selle pa loop loop al b eak p o ide_o e (p ice, quan i y) eques _o e () MCDM e u n_a ay(selle , o e , ep) submi _quo e(bid) ejec () accep () paymen (bid) deli e y() eedback(imp ession) c ea e_en y(imp ession) Ok=c ea e_en y() ge _selle _ epu a ion() e u n_selle _ epu a ion( ep) e u n_ oid() al Ok=c ea e_en y() Ok= eedback() sd ge _selle _image() e u n_selle _image(img) e u n_ oid() al c ea e_en y(imp ession) ge _o e s() e u n_a ay (selle , o e ) s o e(selle , o e ) Ok=s o e() Buye Buye Buye ‘s image da abase Buye ‘s image da abase Hub Hub O e da abase o hub O e da abase o hub Repu a ion da abase o hub Repu a ion da abase o hub Selle Selle pa pa looploop looploop al al b eakb eak p o ide_o e (p ice, quan i y) eques _o e () MCDM e u n_a ay(selle , o e , ep) submi _quo e(bid) ejec () accep () paymen (bid) deli e y() eedback(imp ession) c ea e_en y(imp ession) Ok=c ea e_en y() ge _selle _ epu a ion() e u n_selle _ epu a ion( ep) e u n_ oid() al al Ok=c ea e_en y() Ok= eedback() sdsd ge _selle _image() e u n_selle _image(img) e u n_ oid() al al Figu e 36: In e ac ion wi hin he ALN 75 A e wa ds, he buye sends eedback in e ms o an imp ession uple o he hub, which s o es his in o ma ion in he associa ed epu a ion da abases. The buye si- mul aneously adds imp essions o his image da abase o u u e consul a ion. While p ospec i e buye s communica e wi h he hub, he o e da abase is ed con- inuously by selling agen s, as long as capaci y is o sale. 4.3.3 O e A ibu es The h ee dis inguishing a ibu es associa ed wi h an o e a e p ice, social epu a- ion and image (Table 17). The buying agen s i es o maximize all o hese a ib- u es, excep o he p ice. Table 17: O e a ibu es A ibu e Symbol Goal Sou ce Domain Special case P ice o o e i PRi Minimize Selle ( h ough hub) [[ 0; i PR Social epu a ion o selle o o e i SRi Maximize Hub’s SDB and IDB [] 0;1 i SR [] /   =0;1 0.5 ii SR SR Image o selle o o e i IMi Maximize Buye ’s ODB [] 0;1 i IM [] /   =0;1 0.5 ii SR SR The p ice is ini ially se by he selle and a ies wi h he numbe o o e s and eques om agen s due o he na u e o he p ice mechanism, he English auc ion: a su ging demand leads o ising p ices, a d opping one cu s p ices (c . Subsec- ion 2.4.2.3, p. 15). The pos ed p ice ela es always o a speci ied amoun o capaci y (one GB) and pe iod o which he capaci y is p o ided (e.g. one mon h). This uni o “p ice pe GB pe mon h” is assumed o be mu ually accep ed and ixed – no a i- ances a e possible and i capaci y is needed o less han a mon h o less han a GB is equi ed, he p ice will s ill ha e o be paid o he ull uni and he comple e e m. We assume ha a p ice is always posi i e and ha he e is no uppe bound. Social epu a ion is no manda o y in o ma ion: in case no eedback on he selle has been p o ided ye , no epu a ion alue exis s. The sou ces o epu a ion in o ma ion a e he SDB and he IDB, and bo h da abases a e locally main ained by hei pa en hub (c . Subsec ion 2.5.2.3, p. 22). The hub au oma ically accesses his da abases, e- 76 ie es a ailable in o ma ion and calcula es social epu a ion. The esul ing alue is no malized on an in e al om ze o o one wi h a alue o one indica ing he bes judgmen o one’s epu a ion, whe eas alues close o ze o ep esen e y bad epu a- ion. Image is simila o social epu a ion in almos all e ms excep o i s o igin. The sou ce o image is he buye ’s ODB wi h imp ession en ies om p e ious encoun e s wi h selle s (c . Subsec ion 2.5.2.3, p. 21). Al hough he buye con ols he compu a- ion o image alues, we do no examine di e en le e s o manipula ing his p oc- ess. Image is also p o ided on a scale om ze o o one, wi h he alue o one being a sign o excep ionally posi i e p e ious encoun e s, and he alue o ze o meaning he selle is leas us wo hy. Since an agen has access o exac ly one hub, he can nei he moni o a cu en o e all ma ke p ice no compu e a ma ke equilib ium [Va i06, 572]. The only key igu e one may compu e a e local mean o de ia ion measu es o he gi en o e s, bu hese igu es a e no needed he e. I an image o social epu a ion alue is no p o ided, we pu he scale mean o 0.5 in as a subs i u e o a oid unwan ed disc imina ion. 4.3.4 P incipal’s P e e ence In o ma ion The p e e ence in o ma ion equi ed o unning he scena io comp ises a weigh ec o wi h alues o each a ibu e. A he beginning he p incipal is in e oga ed o elici his p e e ence s uc u e on p ice, image and social epu a ion. The in e iew p oduces a c i e ia compa ison able (c . Subsec ion 3.2.3) and calcu- la es he ollowing esul s (Table 18): Table 18: Weigh ec o PR IM SR Sum Weigh PR 1 1/2 3/4 2.25 wPR = 0.23 = 23 % IM 2 1 3/2 4.5 wIM = 0.46 = 46 % SR 4/3 2/3 1 3 wSR = 0.31 = 31 % Sum 9.75 100 % j w=  Du ing ou expe imen we assume hese weigh s a e cons an and a e no subjec o manipula ion, nei he by he p incipal no by he agen . 77 4.4 The Ex ended TOPSIS 4.4.1 Desc ip ion o he Technique The TOPSIS c ea es e e y ime wo i ual bounds agains which all al e na i es a e anked (c . Subsec ion 3.3.5.4, p. 53). This ea u e is help ul when acking pas selec- ions and compa ing hem in he cou se o ime. The wo bounds inco po a e he ex- eme alues o a ibu es o all ecei ed al e na i es so a , hus, i se es as a “packed memo y” one may consul when anking he p e iously selec ed al e na i es. A anking o selec ed al e na i es (a “bes -o - he-bes lis ”) allows assessmen s o he pas pe o mance o he buye agen , e.g. analyzing whe he speci ic hubs p o ide equen ly male olen selle s o speci ic pe iods when demanded p ices a e unusually low. This canno be achie ed easily by applying MCDM me hods such as he WPM o he SAW me hod because hose me hods mask all bu hei syn hesized sco e alue (c . Subsec ion 3.3.5.2, p. 45). We p opose an Ex ended TOPSIS (xTOPSIS) app oach he e, which compu es he wo bounds o e he cou se o ime ins ead o ese ing he ideal solu ion ec o s a e e e y ins ance. This means, a e hei i s cons uc ion, he wo ec o s wi h he ideal solu ion a e e e ed in o hei o iginal alues and added o he se o al e na- i es e e y un be o e ca ying ou he TOPSIS p ocedu e (Figu e 37). We call hese wo ex eme poin s nega i e and posi i e ideal ec o . In o de o apply his line o ac ion we eplace he ec o no maliza ion wi h he lin- ea one as accomplished be o e by [YuCo03, 1000], [Chu02, 695]. The linea ans- o ma ion equi es me ely wo ex eme alues o scaling – and hese pa ame e s a e gi en a any ime by he wo ideal ec o s. Fu he mo e, we need o s o e h ee ec o s a e e e y un: Fi s o all, he posi i e and nega i e ideal ec o s a e sa ed in a da abase, namely he Ideal Vec o Da abase (IVD). Besides we es ablish a Pa ne Da abase (PD) consis ing o all o e s he agen success ully seized. Wi h he help o hese wo s o ages, we can align a ibu e alues o al e na i es on a single scale and compa e hem o each o he . 84 4.5.2 Selle E alua ion Selle e alua ion is no au oma ed in he p ocess o he scena io. The quali y o he s o age p o ided canno be de e mined by he buying agen , hus he p incipal is cu - en ly supposed o in e ac wi h he ALN and p o ide a eedback o he indi idual and he collec i e memo y ( he ODB and he cu en hub’s IDB and SDB). A his s age, he in e ac i i y equi emen is a bo leneck o la ge-scale applica ions since i impeds he p ocess (c . p. 68). To a oid his, we sugges he implemen a ion o a ye unspeci ied au oma ism o e alua ions. 4.5.3 Summa y Syn hesizing he esul om he compa ison o ele en MCDM app oaches wi h he p e equisi es o he en i onmen has led o h ee possible op ions: SAW, WPM and TOPSIS. We ha e chosen he la e since we saw he chance o de i e addi ional bene- i om he p o ision o ex eme ec o s compa ed o plain sco e alues. Ins ead o es ima ing new e e ence ec o s o each buying eques , we s o e all e e ences in a eposi o y and adap he wo cu en ideal solu ions du ing each un. Thus, we can judge all al e na i es by wo dynamic e e ence ec o s, and we de e - mine he alue o an o e no me ely a a ce ain ime, bu also o e se e al pe iods. Wi h ega d o his ex ension we ha e bap ized he app oach xTOPSIS. The me hod is scalable and sui able o he gi en p emises, and hus p ac ical o la ge-scale analysis. Mo eo e , i p o ides an in e ace o moni o ing he quali y o pas ansac ions as i c ea es a se o wo ec o s pe ansac ion, which can be ei he used in o e a ching esea ch on sys em pe o mance o become subjec o ade as well. A d awback wo h no ing is he missing implemen a ion o au oma ed ou come e alua ion. Since his p oblem is beyond ou objec i e o de ining a sui able MCDM me hod, we ha e no examined possible solu ions. 85 5 Conclusion 5.1 Resul s We ha e examined decision-making in ALN and concen a ed on he case o p ocess- ing epu a ion in o ma ion du ing he pu chase o goods. To au oma e he easoning p ocess o agen s be o e selec ing a supplie , we ha e analyzed he en i onmen and ex ac ed aspec s o ele ance o a sui able MCDM me hod. The p ima y objec i e o his wo k was he elabo a ion o a sui able decision-making me hod o he simula ion es bed o he eRep p ojec . We deduced an app oach called xTOPSIS om he p e equisi es o he es bed, elabo a ed he ounda ions and p esen ed a nume ical example o illus a e he p ocess. Thus he objec i e has been achie ed. In iew o he seconda y objec i es we a e able o answe he ques ions  whe he he chosen decision-making me hod can be applied o he ade o se ices and complex goods,  which assump ions o he scena io impede ans e ing he esul s o human en i onmen s, and  whe he aluable added bene i s can be d awn om he used me hod. T ading Se ices Shi ing om commodi ies o complex goods o se ices means a soa ing numbe o dis inguishing ea u es, i.e. an inc ease o c i e ia. Thus he numbe o p ocessing ope a ions ises: on he one hand because o addi ional p e e ence in o ma ion he agen needs om he p incipal, and on he o he hand because o he size o he in- o ma ion eques ed om he hub. Fo he xTOPSIS his implies g owing IVD and PD eposi o ies and a g owing numbe o compu a ions. Technically, he xTOPSIS is able o deal wi h he equi emen s o se ice p ocu e- men , bu p ac ically, one may ques ion whe he he TOPSIS philosophy is sui able o se ice p ocu emen : In con as o epu a ion, supplie s may be in he posi ion o adjus ing se ices a ibu es o balancing weaknesses in nego ia ion p ocesses. Upon e ealing a alue unc ion, buye s and selle a e able o engage in mul ia ibu e auc- 86 ion mechanisms which may be mo e help ul in his case [Bich01, 140–144]. Impeding Assump ions Du ing ou elabo a ion se e al concessions had o be made in o de o allow an e i- cien scena io modeling. Among hose, he ou aspec s below seem mos c i ical when i comes o ans e ing he esul s om he p ojec o eal li e si ua ions. Al hough he pu pose o his wo k has ne e been imposing a o mal mechanism on eal li e social s uc u es, when planing o es ablish an appealing and plausible eCom- me ce go e nance en i onmen , we ha e o emind ou sel es o he ac ha he con- sume s si ing in on o compu e sc eens a e (s ill) human beings. 1. Cons an weigh s: We can ha dly imagine human beings a ibu e he same ele ance o c i e ia in he long un. People a he adap cons an ly and change p e e ences upon expe iences. I weigh s a e o be pa ame e ized, hen an addi ional Weigh s Da abase would ha e o be implemen ed o ace he change o ela i e p e e ences. The same applies o any measu e implemen ed o enabling au oma ed selle e alua ion. 2. Lea ning: Cu en ly, nei he he selle no he buye agen e lec on pas ac- ions and imp o e hei beha io . Assuming an au oma ed e alua ion mecha- nism exis s, he buye is supposed o conside he ou come o his conduc and adap o he esul s. One idea migh be excluding speci ic hubs o pe iods which p o ided less aluable ba gains. This would be equal o a human being a oiding pa icula shopping malls o opening hou s in which she was p e i- ously no sa is ied by he ansac ion. 3. Volun a y in o ma ion dissemina ion: The ReG eT mechanism elies on p o- ided eedback om cus ome s o compu e he social epu a ion alue. I is ques ionable whe he indi iduals p o ide wo d-o -mou h o ee, assuming ansac ion cos a e ine i able. Fo example, one may conside implemen ing a deposi o e ie ed epu a ion in o ma ion, which is e u ned upon submi - ing eedback, o a ma ke mechanism encou aging indi iduals o ade hones eedback. 4. Addi i e alue unc ion: Addi i e pa ial alue unc ions a e inhe en in he TOPSIS app oaches. Bu e en in he ega ded scena io, he necessa y p econ- 87 di ion o mu ual independence be ween hose unc ions is iola ed – social epu a ion is sligh ly in luenced by he image o an agen , i he p e iously me he ega ded selle . In e e yday li e in e dependencies be ween a ibu es such as epu a ion and p ice a e also e y likely. One hough may be conside ing nonlinea alue unc ions such as he mul iplica i e one o he WPM. This lis o ou obs acles is by no means ex ensi e, and he na u e o models such as he ReG eT mechanism sugges sou ces o con lic a e e y s age o abs ac ion; we b ie ly e e o he design o sociog ams o he indi idual adap a ions o he on ologi- cal dimension o calcula ing us (c . Subsec ion 2.5.2.3, p. 22). Added bene i s Thanks o e aining p e ious ideal ec o s (in he IVD) and seized o e s (in he PD), he xTOPSIS allows in e empo al compa isons o eached ag eemen s and ideal so- lu ions. This means, o one hing we can analyze ime se ies o empo a y o e ma - ke s, o ano he one we can obse e he pe o mance o ou agen . The ideal ec o s embody ce ain ma ke s a es, since hey comp ise he ex eme al- ues o all al e na i es on he ma ke . Assuming ime s amps and iden i y o he con- nec ing hub a e a ailable as well, he da a om he IVD can p o ide g ounds o me - ics such as a e age o e quali y o co ela ion be ween p ice and epu a ion (in ela- ion o pe iods o hubs). I u he mo e allows enhancemen s o he easoning p oc- ess o an agen , e.g. compu ing h esholds, aspi a ion le els, o ese a ion alues in e e ence o he p e iously encoun e ed ma ke s. I a h eshold is no eached, he agen can be ins uc ed o eac wi h sanc ions such as swi ching he hub o ejec ing all o e s. The da abase wi h pas encoun e s enables acing he pe o mance o an agen ; scal- ing all p e ious deals wi h espec o one se o ideal ec o s makes he esul s com- pa able. We can see which o e s we e abo e o below a e age, and i we connec he esul s wi h he e alua ions om he ODB, we can y o de ine pa e ns o good and no -so-good supplie s, e.g. we may ind ou ha epu a ion is a good p edic o o quali y o o e s om ce ain hubs. One can imagine he possibili ies o analyzing pas encoun e s and de i ing p edic- ions o u u e ading. Conduc ing da a mining is possible wi h o he alue unc ion me hods as well, bu he c ucial disad an age o SAW o WPM is he necessi y o 88 s o e all ecei ed o e s wi h hei a ibu es. In con as , he TOPSIS app oach sup- po s ou sugges ed ex ension in e ms o e iciency. 5.2 Sugges ions o Resea ch and some C i ical Anno a ions Du ing he de elopmen o ou me hod se e al ma e s o in e es a ose, which we had o pos pone un il now. Fo he ield o MCDM in ALNs, we educe ou sugges- ions o u he esea ch o he ollowing issues:  How can we delega e he p ocess o e alua ing ou comes o an agen ?  Wha cons i u es he bo de be ween hose goods o which we can apply MADM me hods and hose goods o which we need o he app oaches?  To wha ex en a e human beings willing o ans e esponsibili y o agen s? E alua ing ou comes Cu en ly, he whole subp ocess o lea ning has no been speci ied. Lea ning i sel is a p oblema ic issue al eady men ioned abo e, bu pa o i includes he e alua ion o ou comes. P ocessing some ough in o ma ion can be ealized h ough compa ing ce ain se - ice le el measu es o speci ied, indi idual a ge alues (such as medium access ime, la ency o access a ailabili y). Bu in e ms o less easily quan i iable measu es, how shall an agen de i e an e alua ion? Conside s eaming a mo ie om a p o ide – hough possible om a echnical poin , bu ha dly compu able, how shall he buy- ing agen es ima e he quali y o he mo ie? How shall he de ec isual o acous ic di e ences on ime, assuming all iles use he same audio and ideo encode ? This ce ainly asks o u he esea ch on mechanisms o delega ing pa s o he e alua ion o agen s. Limi a ions o MADM me hods o compa able goods The elabo a ed me hod is su icien o he s aigh o wa d compa ison o commodi y selle s. Beyond a ibu e- ee goods, when i comes o mo e complex ones o se ices, in o ma ion on he ype o dis inguishing ea u es is necessa y. Whe eas he compa i- son o iden ical music iles o e ed may come up wi h a ew addi ional nume ical a - ibu es (such as he encoding bi a e), se ice p o ide s o e ing PDF con e sions 89 may p esen a whole a ie y o enc yp ion echniques, comp ession algo i hms, o size es ic ions. Thus, u he in es iga ions a e equi ed o de e mine he limi a ions o MADM me hods o compa ing goods wi h mul iple a ibu es. Limi s o ans e ing esponsibili y Abo e he echnical aspec s, we need o ask ou sel es in how a we wan o delega e decision-making o au onomous agen s. T ue, agen s possess he abili y o acili a e daily li e by exchanging in o ma ion and conduc ing ades o mino impo ance on behal o he p incipals. Bu o p i acy as well as sel -de e mina ion ma e s, i is ques ionable whe he indi iduals a e willing o p o ide comp ehensi e in o ma ion on hei p e e ence s uc u e o hei non-human al e ego, e en i we ake exhaus i e secu i y measu es agains abuse. The indi idual conce n o p i acy p o ec ion leads o ques ions ega ding al eady ins i u ionalized ules [Sei 86, 35–36]: The eplica ion o p e e ence s uc u es and ansac ion his o ies se e ely iola es indi iduals’ p i acy. S o ing pe sonal in o ma- ion in dis ibu ed eposi o ies appea s o in e e e in se e al ace s such as he igh o p i acy and sel -de e mina ion wi h he EC Di ec i e on p i acy and elec onic communica ions, e.g. A icles 5, 12 Di ec i e 2002/58/EC [Eu o02b], [Sei 86, 38]. Mo eo e , assuming agen s ake on mo e o less all ansac ions be ween indi iduals, we may end up asking ou sel es whe he ading is no a common pa o human be- ha io . A e we willing o o go his habi ? And can he human mind e e be app op i- a ely ep esen ed by an au onomous de ice – o will we ha e o adap ou capacious human minds g adually o he limi s o a i icially empowe ed assis an s [Lani96]? I we ag ee on he ideas o digi alizing he human mind as well as o going he human habi o ading, he gi ing up o buying and selling p o okes a decline o indi idual socializing [Sei 86, 11]. In he ex eme case he p incipals end up being socially iso- la ed, anspa en in hei consume p e e ences and elying subconsciously on ec- ommenda ions and o de s o hei agen s. A he ime mas e s and se an s ha e ex- changed hei powe s, we may emind ou sel es o he so ce e ’s app en ice om Goe he’s amous poem, wishing we could d i e ou “ he spi i s ha we called” [GoZe65, 103–109]. 90 Re e ences [Ake 70] Ake lo , G. A.: The ma ke o "lemons". The Qua e ly Jou nal o Economics, 84 (1970) 3, pp. 488–500. 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Sp inge : Be lin, Heidelbe g, New Yo k, 1991. 105 Appendix Appendix A Appendix A 1: Classi ica ion ca ego ies and op ions (based on [SaSi05, 35–41]) Concep ual model GT Game- heo y C Cogni i e In o ma ion sou ces DI Di ec in e ac ion DO Di ec obse a ion WI Wi ness in o ma ion SI Sociological in o ma ion P P ejudice Visibili y S Subjec i e p ope y G Global p ope y Model’s g anula i y CD Con ex dependen NCD Noncon ex dependen Agen beha io assump ions 0 No chea ing is conside ed 1 Biased o hidden in o ma ion possible 2 Lying is ecognized Type o exchanged in o ma ion Yes / No Boolean measu es T us / epu a ion eliabili y measu e Yes / No A ailable 106 Appendix A 2: Compa ison o epu a ion sys ems [SaSi05, 56] Concep ual model In o ma ion sou ce Visibili y Model’s g anula i y Agen beha - io assump- ions Boolean ex- changed in- o ma ion T us -Rep eliabili y measu e Model ype S. Ma sh GT DI S CD NAa NAa No T us Online Rep models GT WI G NCD 0 No Nob Rep Spo as GT WI G NCD 0 No Yes Rep His os GT DI+WIc S NCD 0 No No Rep Schillo e al. GT DI, DO, WI S NCD 1 Yes No T us A.-Rahman and Hailes GT DI, WId S CD 2 4 us alues No T us Rep Es andia y and Chand asaekha an GT DI, DO, WI, P S CD 0 No No T us Yu and Singh GT DI, WI S NCD 0 No No T us Rep Sen and Sajja GT DI, DO, WIe S NCD 2 Yes No Rep AFRAS GT DI+WIc S NCD 2 No Yes Rep Ca e e al. GT WIg G NCD 0 No No Rep Cas el anchi and Falcone C NAh S CD NAh No NAh T us ReG eT GT DI+WI+SI+Pc S CD 2 No Yes T us Rep a b c d e g h The e is no exchange o in o ma ion be ween agen s. Reliabili y is based on he numbe o a ings. The ’+’ symbol means he model combines he in o ma ion sou ces o ob ain a inal us / epu a ion alue. Di ec expe iences a e used o compa e he poin o iew o hese wi nesses wi h he di ec pe cep ion o he agen and hen be able o adjus he in o ma ion coming om hem acco dingly. Because he objec i e o his wo k was o s udy how agen s use wo d-o -mou h epu a ions o selec on o se e al pa ne s, agen s only use wi ness in o ma ion o ake decisions. Lia s a e assumed o lie consis en ly. Besides in o ma ion coming om o he use s (WI) he e is a cen al au ho i y ha moni o s he agen s’ beha io and uses ha in o ma ion o build epu a ion. In he desc ip ion o he model i is no speci ied how he agen s ob ain he in o ma ion o build hei belie s. 107 Appendix A 3: Main p ocess o buying s o age capaci y wi h xTOPSIS Main p ocess: Buying s o age capaci y wi h xTOPSIS auc ion won? [yes] Place bid Place bid In o ma ion on o e and deale In o ma ion on o e and deale Reques o e and deale in o ma ion Reques o e and deale in o ma ion Lea ning Lea ning P e e ence in o ma ion P e e ence in o ma ion Posi i e and nega i e Ideal ec o Posi i e and nega i e Ideal ec o Find new o e Find new o e Demand de ec ed Demand de ec ed Lea ning Lea ning P e e ence in o ma ion P e e ence in o ma ion Posi i e and nega i e Ideal ec o Posi i e and nega i e Ideal ec o [no] Selec op- anked al e na i e Selec op- anked al e na i e Ranking Ranking Al e na i e Al e na i e xTOPSIS xTOPSIS Main p ocess: Buying s o age capaci y wi h xTOPSIS auc ion won? [yes] Place bid Place bid In o ma ion on o e and deale In o ma ion on o e and deale Reques o e and deale in o ma ion Reques o e and deale in o ma ion Lea ning Lea ning Lea ning Lea ning Lea ning Lea ning P e e ence in o ma ion P e e ence in o ma ion Posi i e and nega i e Ideal ec o Posi i e and nega i e Ideal ec o Find new o e Find new o e Demand de ec ed Demand de ec ed Demand de ec ed Demand de ec ed Lea ning Lea ning Lea ning Lea ning Lea ning Lea ning P e e ence in o ma ion P e e ence in o ma ion Posi i e and nega i e Ideal ec o Posi i e and nega i e Ideal ec o [no] Selec op- anked al e na i e Selec op- anked al e na i e Ranking Ranking Al e na i e Al e na i e xTOPSIS xTOPSIS xTOPSIS xTOPSIS 108 Appendix B: Case S udy Si ua ion Ou DM, a new en an in a sales company, is supposed o pick a b andnew middle class ca om a lis o se en al e na i es. He decides on he basis o i e c i e ia, in which all al e na i es di e om each o he (Appendix B 1).1 Non-disc imina ing c i e ia in which all al e na i es a e equal o e y simila , a e dis- ega ded2; such aspec s include he equi ed pe ol s anda d, 95 RON3 (Eu osupe ), he emission le el (EURO IV), and he Eu o NCAP sa e y assessmen (all ca s ha e been a ed wi h i e s a s). Wi h excep ion o he unk olume, all da a is based on manu ac u e in o ma ion d awn om echnical speci ica ions on he espec i e Ge man websi e. Since unk olume appea s o di e in he no ms o measu ing, da a om ecen es s o he ADAC, he Gene al Ge man Au omobile Associa ion, is aken in o conside a ion. De- spi e he di e ence o hei uni s, all dimensions a e scaled on a a io le el. Appendix B 1: C i e ia in he ca compa ison P ice Fuel consump- ion Ca bon dioxide emission Accele a ion T unk olume C i e ion Manu ac- u e ’s lis p ice in Ge many 95 RON Eu o- supe , combined (in own, ou o own) Combined (in own, ou o own) Accele a ion ( om 0 o 100 kmph) S o age olume o he unk, wi hou olded sea s EUR L /100km g/km sec L Uni measu ed Eu os Li e s pe 100 kilome e G ams pe kilome e Seconds Li e Sou ce Manu ac u e websi es ADAC Goal Minimize Minimize Minimize Minimize Maximize The se o al e na i es includes se en models o di e en b ands which ha e been chosen in acco dance wi h a simila a ge ma ke segmen ; in e ms o p emium 1 Simila p oblems wi h di e en c i e ia and al e na i es a e p esen ed by [BMP+00, 91–93], [YoHw95, 24]. 2 Engine powe was dis ega ded because in he se o al e na i es i co ela ed s ongly wi h accel- e a ion (co ela ion coe icien o 0.7932). 3 Resea ch Oc ane Numbe 109 b ands his may be dispu ed, bu since he Fo d’s basic p ice exceeds he p ices o he Al a Romeo, he Audi A4, he Saab 9-3 and he Vol o S40, we included he Mondeo. Appendix B 2: Ca selec ion and in o ma ion sou ces Sou ce o in o ma ion B and Model All da a (excep unk olume) T unk olume Al a Romeo 159 1.8 MPI 16V [Fia 08, 3], [Fia 08, 16-17] [Thyw05c, 4] Audi A4 A ac ion 1.8TFSI [Audi08a, 4], [Audi08b] [Sipp08, 6] BMW 318i [BMW08a, 3], [BMW08b, 23-24] [Thyw05a p. 4] Fo d Mondeo Ghia 2.0l [Fo d07, 29], [Fo d08, 4] [Ruhd07a, 5] Me cedes C180 Komp esso [Daim07, 2], [Daim08, 5] [Ruhd07b, 6] Saab 9-3 1.8i M5 [Saab07, 3], [Saab08] [Thyw04b, 4] Vol o S40 1.6 [Vol 08a, 3], [Vol o08b] [Thyw04a, 4] All ca s a e ou doo s, sedan body s yle ( hough in case o he Fo d Mondeo, he se- dan is mo e expensi e han he s a ion wagon) and basic edi ions wi h manual ansmission, in o de o be compe i i e as well as compa able in all c i e ia (Appendix B 2). Decision ma ix The decision ma ix in i s ini ial appea ance is p esen ed below (Appendix B 3). Appendix B 3: Ini ial decision ma ix o ca pu chase P ice Fuel con- sump ion Ca bon dioxide emission Accele a- ion (0-100 kmph) T unk olume B and Model EUR L /100 km g/km sec L Al a Romeo 159 1.8 MPI 16V 24,550 7.6 179 10.2 445 Audi A4 A ac ion 1.8TFSI 25,900 7.1 169 10.5 380 BMW 318i 27,300 7.9 142 9.1 405 Fo d Mondeo Ghia 2.0l 26,000 7.9 189 9.9 515 Me cedes C180 Komp esso 31,089 7.6 177 9.5 350 Saab 9-3 1.8i M5 25,650 7.7 183 11.5 440 Vol o S40 1.6 21,450 7.2 171 11.9 404 We will la e apply MCDM me hods which equi e no malized a ibu es. Fo his 116 () () 1 j nw j j VA  = = wi h max j i j = () () ()( ) ()      ! ! "" ## = "" ## "" ## $%$%  0,2 0,09 0,3 0,24 0,17 L g 21,450 EUR 7.1 142 9.1 sec 515 L 100 km km 0.05744 VA VA Thi d s ep: Now we ge he sco e o he Al a aking he a io o VAl a and V(A*), () = 0.05164 0.899 0.05744 Al a V VA . Appendix B 13: Weigh ed P oduc Me hod P ice Fuel consump- ion Ca bon dioxide emission Accel- e a ion (0-100 kmph) T unk olume B and Model EUR L /100 km g/km sec L Sco e () i V VA  Al a Romeo 159 1.8 MPI 16V 0.04819 0.66656 0.99534 0.57271 2.81982 0.899 Audi A4 A - ac ion 1.8TFSI 0.04743 0.67569 0.99539 0.56874 2.74513 0.867 BMW 318i 0.04668 0.66142 0.99555 0.58861 2.77503 0.8741 Fo d Ghia 2.0l 0.04737 0.66142 0.99529 0.57683 2.89073 0.9053 Me cedes C180 Komp es- so 0.0449 0.66656 0.99535 0.58257 2.70702 0.8178 Saab 9-3 1.8i M5 0.04756 0.66482 0.99532 0.55646 2.81441 0.8581 Vol o S40 1.6 0.05018 0.6738 0.99538 0.55191 2.77386 0.8971 Al hough bo h me hods use he same weigh s, hey p oduce di e en esul s when i comes o he inal ecommenda ion: he SAW p e e s he Vol o, he WPM sugges s he Fo d. This s ems om he no maliza ion me hods – being he weakes choice in uel consump ion and ca bon dioxide emission, he Fo d’s ou come on hese dimen- sions is se o ze o in he SAW me hod; one s eng h ( unk) canno compensa e o 117 hese wo laws. The Vol o in con as has o cope wi h only one ela i ely weak a - ibu e (accele a ion). Analy ic Hie a chy P ocess Now we examine he cou se o ac ion o he Analy ic Hie a chy P ocess. Fi s , we depic he decision si ua ion in a hie a chy wi h h ee le els. The supe io goal weigh s ec o consis s o he elici ed ela i e con ibu ions o each c i e ion o he o e all goal. We ake ou weigh s ec o (Appendix B 11, p. 114) and assume i is based on pai wise compa isons; hen we a ach he weigh alues o hei espec i e edge, highligh ed in ed colo (Appendix B 14). Appendix B 14: Hie a chy o he AHP me hod (A1) Al a Romeo 159 (A2) Audi A4 (A3) BMW 318i (A4) Fo d Mondeo (A5) Me cedes C180 (A6) Saab 9-3 (A7) Vol o S40 A1 A2 A3 A4 A5 A6 A7 PR FU CO AC TV (PR) P ice (FU) Fuel consump ion (CO) Ca bon dioxide emission (AC) Accele a ion (TV) T unk olume Le el 1: Goal Le el 2: C i e ia Le el 4: Al e na i es 0.3 0.2 0.09 0.24 0.17 (A1) Al a Romeo 159 (A2) Audi A4 (A3) BMW 318i (A4) Fo d Mondeo (A5) Me cedes C180 (A6) Saab 9-3 (A7) Vol o S40 A1 A2 A3 A4 A5 A6 A7A1A1 A2A2 A3A3 A4A4 A5A5 A6A6 A7A7 PR FU CO AC TVPRPR FUFU COCO ACAC TVTV (PR) P ice (FU) Fuel consump ion (CO) Ca bon dioxide emission (AC) Accele a ion (TV) T unk olume Le el 1: Goal Le el 2: C i e ia Le el 4: Al e na i es 0.3 0.2 0.09 0.24 0.17 Secondly, we calcula e he i e weigh ec o s o he i e c i e ia (which co espond wi h blue edges be ween he le el 2 and le el 3 nodes). A ec o is de e mined by compa ing pai wise he al e na i es wi h ega d o he espec i e c i e ion, e.g. how many imes is he p ice o he Al a be e han he p ice o he Audi, and by calcula - ing he geome ic mean o each al e na i e a e wa ds4. This means we ha e h ee s eps o each c i e ion: 1. Cons uc ing a pai wise compa ison ma ix, 2. calcula ing geome ic means o each al e na i e, and 3. applying a linea ans o ma ion o no malize he means in o a weigh s ec o (Appendix B 15, whe e hese weigh s a e highligh ed in ed). 4 Al hough Saa y ecommends he use o his eigen ec o me hod, we use he simple geome ic mean calcula ion he e and omi he consis ency check. 118 The o he ou ec o s a e gi en o u he calcula ion and a e no explici ly de i ed he e (Appendix B 16). Appendix B 15: The pai wise compa ison ma ix and he weigh ec o o he p ice c i e ion 1 5 9 5 7 5 3 A7 1/51 5 1 1 1 1 A6 1/91/51 1/51/31/51/7 A5 1/51 5 1 1 1 1 A4 1/71 3 1 1 1 1/3 A3 1/51 5 1 1 1 1 A2 1/31 7 1 3 1 1 A1 A7A6A5A4A3A2A1 1 5 9 5 7 5 3 A7 1/51 5 1 1 1 1 A6 1/91/51 1/51/31/51/7 A5 1/51 5 1 1 1 1 A4 1/71 3 1 1 1 1/3 A3 1/51 5 1 1 1 1 A2 1/31 7 1 3 1 1 A1 A7A6A5A4A3A2A1 S ep 1 S ep 1 9.52975 6 0.442274.21471 A7 0.104931 A6 0.024900.23726 A5 0.104931 A4 0.079470.75731 A3 0.104931 A2 0.138561.32047 A1 No malized weigh Geom. Mean 9.52975 6 0.442274.21471 A7 0.104931 A6 0.024900.23726 A5 0.104931 A4 0.079470.75731 A3 0.104931 A2 0.138561.32047 A1 No malized weigh Geom. Mean PRPR S ep 2 S ep 2 S ep 3 S ep 3 Finally, he esul ing i e (7x1)- ec o s display he ela i e con ibu ion o each ca wi h ega d o he speci ic c i e ion; we can me ge hese i e columns in o a (7x5) ma- ix. This comes in handy o de e mining he composi e alues, because we can easily mul iply his ma ix wi h he goal ec o o he i e c i e ia (Appendix B 16). Appendix B 16: Weigh ec o s o all i e c i e ia No malized weigh s B and PR FU CO AC TV Goal weigh s Sco e i V Al a Romeo 0.1385 6 0.07269 0.07424 0.12399 0.16212 0.12011 Audi 0.1049 0.38069 0.13417 0.08729 0.0467 0.3 0.14858 BMW 0.0794 0.02942 0.51336 0.31794 0.06092 0.2 0.16259 Fo d 0.1049 0.02942 0.03554 0.16971 0.48692 u 0.09 = 0.16407 Me cedes 0.0249 0.07269 0.08685 0.24372 0.03172 0.24 0.09371 Saab 0.1049 0.06928 0.05424 0.03161 0.15071 0.17 0.0834 Vol o 0.4422 0.3458 0.10161 0.02575 0.06092 0.2275 6 (column) 1 1 1 1 1 1 1 119 We ecei e he i e sco e alues by conduc ing he ma ix mul iplica ion as men- ioned. Say, o he Al a Romeo one can compu e he sco e alue VAl a by adding he Al a’s c i e ia con ibu ions weigh ed wi h goal weigh s al eady gi en as ol- lows: ()()( )( )( ) =++++     1 PR con ibu ion FU con ibu ion CO con ibu ion AC con ibu ion TV con ibu ion 0.13856 0.3 0.07269 0.2 0.07424 0.09 0.12399 0.24 0.16212 0.17V   10.12V Thus, wi h a sco e alue o () = 70.228VA he Vol o eme ges as he bes choice. This is he same esul as in he SAW me hod, due o he simila i y o bo h me hods in summa izing he pa ial alues: The ela i e con ibu ions o he AHP can be com- pa ed o he absolu e alues o he SAW me hod. Technique o O de P e e ence by Simila i y o Ideal Solu ion We s a wi h no malizing he decision ma ix, bu his ime, we make use o he ec- o ans o ma ion which will lead o esul s di e en om he linea one (Appendix B 17). Appendix B 17: Vec o no malized decision ma ix B and Model P ice Fuel con- sump- ion Ca bon dioxide emission Accele a- ion (0-100 kmph) T unk olume Al a Romeo 159 1.8 MPI 16V 0.39380 0.37569 0.36077 0.37971 0.39786 Audi A4 1.8TFSI 0.37328 0.40214 0.38212 0.36886 0.33975 BMW 318i 0.35413 0.36142 0.45478 0.42561 0.36210 Fo d Ghia 2.0l 0.37184 0.36142 0.34168 0.39122 0.46045 Me cedes C180 Komp. 0.31097 0.37569 0.36485 0.40769 0.31293 Saab 9-3 1.8i M5 0.37691 0.37081 0.35289 0.33679 0.39339 Vol o S40 1.6 0.45071 0.39656 0.37765 0.32547 0.36121 Con inuing wi h weigh ing he esul s, we hold on o he same ade-o alues as used be o e in SAW, WPM and AHP (Appendix B 11, p. 114). Thus, we ecei e a ma- ix wi h weigh ed no malized alues (Appendix B 18). 120 Appendix B 18: Weigh ed no malized decision ma ix B and Model P ice Fuel con- sump ion Ca bon dioxide emission Accele a- ion (0-100 kmph) T unk olume Al a Romeo 159 1.8 MPI 16V 0.11814 0.07514 0.03247 0.09113 0.06764 Audi A4 1.8TFSI 0.11198 0.08043 0.03439 0.08853 0.05776 BMW 318i 0.10624 0.07228 0.04093 0.10215 0.06156 Fo d Ghia 2.0l 0.11155 0.07228 0.03075 0.09389 0.07828 Me cedes C180 Komp. 0.09329 0.07514 0.03284 0.09785 0.05320 Saab 9-3 1.8i M5 0.11307 0.07416 0.03176 0.08083 0.06688 Vol o S40 1.6 0.13521 0.07931 0.03399 0.07811 0.06140 Again, bes (and wo s ) alues a e highligh ed in blue ( ed) – hose alues comp ise he posi i e (nega i e) ideal solu ion in he nex s ep. Thus, we ecei e he ollowing wo ec o s (Appendix B 19). These wo ec o s span a con ex se o al e na i es among which ou se en ca s a e loca ed. Appendix B 19: Posi i e and nega i e ideal solu ion Re e ence poin P ice Fuel con- sump ion Ca bon dioxide emission Accele a- ion (0-100 kmph) T unk olume Posi i e ideal solu ion 0.13521 0.08043 0.04093 0.10215 0.07828 Nega i e ideal solu ion 0.09329 0.07228 0.03075 0.07811 0.05320 To de e mine he inal anking, we calcula e sepa a ion measu es S+i (S-i) o each al e na i e o hese e e ence poin s. We e ie e he closeness o he Al a Romeo o he posi i e ideal solu ion om () ()( ) ()( )( )()() = ++ =  ==++ =  + + + +   ! 5222 1 22222 0.11814 0.13521 0.06764 0.07828 0.01707 0.00529 0.00846 0.01102 0.01064 0.02501 0.03172 n Al a j Al a j j j j Al a Sw w S and compu e he simila i y measu e RAl a wi h 121  + ==  ++ 0.03172 0.55916 0.02501 0.03172 Al a Al a Al a Al a S RSS . So ing he al e na i es acco ding o he simila i y measu e, we ge a anking wi h a clea ecommenda ion o he Vol o – and he good ad ice no o conside he Me - cedes any u he (Appendix B 20). Rega ding he closeness indices, we see ha he Al a is in absolu e e ms close o he posi i e ideal solu ion, bu – due o some c i e- ia alues – also close o he nega i e ideal one. The Vol o bea s he Al a because o compensa ing o he lack o excellence in accele a ion wi h possessing ela i ely s ong igu es in e ms o p ice and uel consump ion. This indica es he simila i y be ween he SAW and TOPSIS (i.e. he addi i e compensa ion be ween c i e ia). Appendix B 20: Simila i y o posi i e ideal solu ion Closeness o… B and Model posi i e ideal solu ion nega i e ideal solu ion Simila i y Rank Al a Romeo 159 1.8 MPI 16V 0.02501 0.03173 0.55916 2 Audi A4 1.8TFSI 0.03448 0.02363 0.40659 6 BMW 318i 0.03443 0.03031 0.4682 4 Fo d Ghia 2.0l 0.02825 0.03481 0.55199 3 Me cedes C180 Komp. 0.04998 0.02005 0.28626 7 Saab 9-3 1.8i M5 0.03461 0.0243 0.41246 5 Vol o S40 1.6 0.03019 0.04341 0.58979 1 Finally, we need o come back o he no maliza ion mechanism: The choice o he echnique exe s in luence on he inal anking o de ; i we had applied he linea no maliza ion, he Audi o ins ance would ha e come ou much be e and he win- ne would ha e been he Al a (Appendix B 21). Thus, a sensi i i y analysis is compul- so y o make an en i ely sa is ac o y decision. 122 Appendix B 21: Simila i y and Ranking o linea no maliza ion B and Model Simila i y Rank Al a Romeo 159 1.8 MPI 16V 0.57131 1 Audi A4 1.8TFSI A ac ion 0.54977 3 BMW 318i 0.49529 5 Fo d Ghia 2.0l 0.51685 4 Me cedes C180 Komp esso 0.37028 7 Saab 9-3 1.8i M5 0.39788 6 Vol o S40 1.6 0.56443 2 ELECTRE Las , we use an ou anking echnique o see i we can elici a dis inc ecommenda- ion o ou case. Because i is common p ac ice o use a decision ma ix wi h ec o no malized alues and since we assume he same weigh s as be o e (Appendix B 11, p. 114), we s a wi h he weigh ed no malized decision ma ix as in he TOPSIS desc ip ion (Appendix B 18, p. 120). On he g ounds o his in o ma ion we use he ou anking ela ion S and elici he conco dance indices o assess he s eng h o sup- po o he s a emen ha one ca ou anks ano he . Wi h () {} :kj lj kl k l j ja a con con A SA w  ==  wi h {} ,1,,7kl k l! , we ecei e o he ou anking ela ion AAl aSAAudi ha he Al a 159 excels he Audi A4 in p ice, accele a ion and unk olume. The conco dance index o he s a emen ha he Al a is be e han he Audi is equal o he sum o he co esponding weigh s, hus 0.71 (wp ice= 30 %, waccele a ion= 24 %, w unk_ olume= 17 %). A e 7 × 6 = 42 compa i- sons (ou anking ela ions a e no e lexi e), we ob ain he comple e ma ix wi h con- co dance indices (Appendix B 22). 123 Appendix B 22: Conco dance indices Al a Romeo Audi BMW Fo d Me cedes Saab Vol o Al a Romeo 0.71 0.67 0.59 0.67 1 0.41 Audi 0.29 0.5 0.59 0.83 0.53 0.53 BMW 0.33 0.5 0.53 0.8 0.33 0.5 Fo d 0.41 0.41 0.67 0.47 0.41 0.41 Me cedes 0.53 0.24 0.2 0.53 0.53 0.24 Saab 0 0.47 0.67 0.59 0.47 0.41 Vol o 0.59 0.47 0.5 0.59 0.76 0.59 A e wa ds we u n o he disco dance indices, he s eng h o dissen on he s a e- men ha one ca ou anks ano he . Wi h () {} : max max kj lj jkj jlj ja a kl k l jkj jlj j wa wa dis dis A SA wa wa < ==  wi h {} ,1,,kl m k l!. we compu e he s eng h o disco dance o s a emen ha he Al a ou anks he Audi in wo s eps. Fi s , wi h ega d o he nomina o o he ac ion, we es ima e he maximum di e - ence on weigh ed no malized alues be ween he wo ca s om he subse o c i e ia in which he Al a is no ou doing he Audi, uel consump ion and ca bon dioxide emission: {} () () : max max 0.07514 0.08043 ; 0.03247 0.03439 max 0.00529; 0.00192 0.00529 Al a j Audi j jAl aj jAudij ja a wa wa < =   == In he second s ep, he denomina o , which is equi alen o a scale coe icien , is compu ed om he maximum di e ence on weigh ed no malized alues be ween he wo ca s on all c i e ia: 124 ( ) () max 0.11814 0.11198 ; 0.07514 0.08043 ; 0.03247 0.03439 ; 0.09113 0.08853 ; 0.06764 0.05776 0.00616; 0.00529; 0.00192; 0.0026; 0.00988 0.00988 jAl aj jAudij jwa wa =    = = Repea ing hese wo s eps o all 42 ma ix en ies, we de e mine he ma ix wi h dis- co dance indices (Appendix B 23). Appendix B 23: Disco dance indices Al a Romeo Audi BMW Fo d Me cedes Saab Vol o Al a Romeo 0.53559 0.92565 1 0.27023 0 1 Audi 1 1 1 0.49857 1 1 BMW 1 0.59801 1 0.22037 0.32059 1 Fo d 0.61926 0.39693 0.60878 0.15764 0.14372 1 Me cedes 1 1 1 1 1 1 Saab 1 0.84412 1 1 0.8602 1 Vol o 0.76249 0.4483 0.8295 0.71299 0.47071 0.24714 To quali y he conco dance and disco dance alues, we will now con inue wi h build- ing he conco dance dominance ma ix mm× F and he disco dance dominance ma ix mm× G . The e o e we compu e he a i hme ic mean o each ma ix as a h eshold alue – i a ma ix en y is below he h eshold, we assume he s a emen is oo weak o be aken se iously. Wi h he mean alues =0.51119con ( =0.7493dis ) o he conco dance (disco dance) indices we ecei e he conco dance dominance ma ix (Appendix B 24) and he disco dance dominance ma ix (Appendix B 25). 125 Appendix B 24: Conco dance dominance ma ix Al a Romeo Audi BMW Fo d Me cedes Saab Vol o Al a Romeo 1 1 1 1 1 0 Audi 0 0 1 1 1 1 BMW 0 0 1 1 0 0 Fo d 0 0 1 0 0 0 Me cedes 1 0 0 1 1 0 Saab 0 0 1 1 0 0 Vol o 1 0 0 1 1 1 Appendix B 25: Disco dance dominance ma ix Al a Romeo Audi BMW Fo d Me cedes Saab Vol o Al a Romeo 1 0 0 1 1 0 Audi 0 0 0 1 0 0 BMW 0 1 0 1 1 0 Fo d 1 1 1 1 1 0 Me cedes 0 0 0 0 0 0 Saab 0 0 0 0 0 0 Vol o 0 1 0 1 1 1 Finally, we agg ega e he wo ma ices in o a dominance ma ix, which can be unde - s ood as a able wi h measu es indica ing ha he ou anking s a emen be ween wo ca s is suppo ed and no ejec ed o ice e sa (Appendix B 26). We ead his able ow-wise and elimina e all ca s in columns whe e he pi o al en y is a one, namely he Audi, he BMW, he Fo d, he Me cedes and he Saab. Rega ding he emaining wo models, we canno dis inguish be ween hem: he Al a Romeo and he Vol o a e “incompa able” and hus o equal alue o he DM.