BPMSG AHP Excel Template with multiple Inputs

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1 BPMSG AP Excel Temlate wth multle Inuts Author: Klaus D. Goeel htt://bmsg.com Overvew The AP temlate works under Wndows OS and Excel verson MS Excel 2 (xlsx extenson). The workbook conssts of 2 nut worksheets for ar-wse comarsons, a sheet for the consoldaton of all udgments, a summary sheet to dslay the result, a sheet wth reference tables (random ndex, lmts for geometrc consstency ndex GCI, udgment scales) and a sheet for solvng the egenvalue roblem when usng the egenvector method (EVM). Lmtatons Maxmal number of crtera: Maxmal number of decson makers/artcants: 2 Results The result table wll show all crtera wth calculated weghts and rank, usng the EVM: Crteron Comment Weghts Rk Crteron Frst Crteron 27,9% 2 2 Crteron 2 Second Crteron 7,2% 3 3 Crteron 3 Thrd Crteron 64,9% for 9& unrotect the nut sheets and exand the queston secton On to of the table you fnd a check feld showng the convergence of the EVM calculaton usng the ower method. The value should be close to zero. EVM check: 5,24E-6 Prncal Egen value lambda and consstency ratos GCI (geometrc consstency ndex) and CR (consstency rato) are shown (see annex): Egenvalue lambda: 3, Consstency Rato,37 GCI:, CR:,% In the secton below the comarson matrx s dslayed: Matrx normalzed rncal Egenvector Crteron 5 / ,9% Crteron 2 2 /5 / ,2% Crteron ,9% ,% ,% ,% Crteron Crteron 2 Crteron 3 ow to use the temlate ,% ,% ,% ,%. Oen the Excel fle APcalc verson dd.mm.yy.xls 2. Select the worksheet Summary Page APcalc-v a.docx verson 24-Dec-23

2 3. Inut values n the green felds only: n= 3 umber of crtera (3 to ) Scale: Lnear a) umber of crtera n n= (3-) b) Scale: selected AP scale (see annex) default s scale, standard lnear to 9 AP scale = standard lnear scale to 9 2 = logarthmc 3 = Square root 4 = Invers lnear 5 = Balanced 6 = Power 7 = Geometrc ote: a) Although the most often used scale s the lnear to 9 scale, we recommend tryng as an alternatve the balanced scale, often resultng n better consstency. b) From verson onwards decmals as nut values for arwse comarsons are acceted. = 2 umber of Partcants ( to ) :,5 Consensus:,% c) umber of artcants = ( - 2) d) Alha (): threshold for accetance of nconsstency. We recommend a value between. and.2. ote: The consensus feld s an outut feld showng the AP consensus ndex (see annex).if you have more than one decson maker/artcant. The consensus ndcator ranges from % (no consensus between decsons makers) to % (full consensus between decson makers). = selected Partcant (=consol.) 3 7 Partcant e) Selected artcant default For more than artcant you can select whose artcant s result to be dslayed. Partcants are numbered from to 2 accordng the nut sheets for ar-wse comarsons. When selectng, the consoldated result for all artcants wll be shown, usng the geometrc mean of all decson matrces. Obectve Calculate weghts for arwse comarson of three crtera Author Klaus Date 8-Feb-3 EVM check: 5,24E-6 f) Obectve (text) to descrbe the roect/category g) Author (text, otonal) h) Date (date, otonal) ) The table allows you to nut the name of crtera and a comment for each crteron. Crteron Frst Crteron Crteron 2 Second Crteron Crteron 3 Thrd Crteron APcalc-v a.docx Page 2 verson 24-Dec-23

3 Par-wse comarsons. Select worksheet In In each nut sheet you can secfy the name of the decson maker/artcant, a weght for hs evaluaton and a date. Partcant ame Weght Date A weght hgher than one for examle two means that hs nut s weghted twce the nut of all other artcants. The elements of the consoldated decson matrx (all artcants) are calculated as weghted geometrc mean of all ndvdual artcants (see annex). The table below s the nut table for ar-wse comarsons Crtera more mortant? Scale A B A or B (-9) 2 Crteron Crteron 2 A 5 3 Crteron 3 B Crteron 2 Crteron 3 B For 3 crtera the frst comarson s crteron versus crteron 2. In the second last column the artcant has to select ether A (crteron more mortant than 2), or B (crteron 2 more mortant than ). A or B are not case senstve. In the last column of the table the artcant secfes the ntensty how much more mortant s comared to 2 res. 2 comared to. Vald nuts are ntegers from to 9. Imortant ote: If you use more than 8 crtera, you have to unrotect the nut sheets and exand the lnes from 49 to 65 to comlete all comarsons. After unrotectng clck on the + At the bottom of the age the exlanaton of ntenstes (scale) s shown: Intensty Defnton Exlanaton Equal mortance Two elements contrbute equally to the obectve 3 7 Moderate mortance 5 Strong Imortance Very strong mortance 9 Extreme mortance 2,4,6,8 can be used to exress ntermedate values Exerence and udgment slghtly favor one element over another Exerence and udgment strongly favor one element over another One element s favored very strongly over another, t domnance s demonstrated n ractce The evdence favorng one element over another s of the hghest ossble order of affrmaton The next comarson s then crteron versus 2, followed by 2 versus 3. For more the 3 crtera automatcally more ars wll be lsted n the table. When dong the comarsons, t mght haen that 3 lnes wll be hghlghted: APcalc-v a.docx Page 3 verson 24-Dec-23

4 A 9 A4 A 8 5 A 7 3 A9 A 6 2 A3 A 5 6 Ths s an ndcaton of nconsstent nuts. The most nconsstent udgment s marked wth. The text feld after the markng shows the deal, most consstent udgment (A4, A9 and A3 n the examle above). Partcants mght slghtly modfy the hghlghted udgments n drecton of the deal udgment, n order to mrove consstency. :. CR: 32% Consstency Rato After revewng all answers deally no lne wll be hghlghted and consstency s wthn the gven threshold to make the result relable. ote: Each nut sheets wll show the resultng rortes calculated from the arwse comarsons based on the row geometrc mean method (RGMM). The fnal calculaton usng the Egen vector method (EVM) wll only be shown n the summary sheet. n Crtera Comment RGMM Crteron 74% 2 Crteron 2 7% 3 Crteron 3 9% 4-2. For more than artcant select worksheet In2 In and nut name, date and the ar-wse comarsons for addtonal artcants. Go back to sheet Summary to see the result. Please make a reference to the author and webste, when usng the temlate n your work: Goeel, Klaus D., BPMSG AP Excel temlate wth multle nuts, verson xx htt://bmsg.com, Sngaore 23, or refer to Goeel, Klaus D. (23). Imlementng the Analytc erarchy Process as a Standard Method for Mult- Crtera Decson Makng In Cororate Enterrses A ew AP Excel Temlate wth Multle Inuts, Proceedngs of the Internatonal Symosum on the Analytc erarchy Process 23 For questons, feedback, suggestons lease contact the author under htt://bmsg.com Under htt://bmsg.com you wll also fnd other AP onlne tools for the calculaton of rortes and the handlng of comlete AP herarches and evaluaton of alternatves. APcalc-v a.docx Page 4 verson 24-Dec-23

5 Annex - Mathematcal relatons and formulas used A. Scales Intenstes x, wth x = to 9 (nteger) are transformed nto c usng followng relatons: - Lnear c x 2- Logarthmc c log 2 ( x ) 3- Root square c x 4- Inverse lnear c 9 /( x) 5- Balanced c w /( w); w.5,.55,.6,,.9 6- Power 7- Geometrc.45.5x c (.45.5x) 2 c x c 2 x c s then used as element n the ar-wse comarson matrx. For a summary and revew see: Ishzaka A., Labb A. Revew of the man develoments n the analytc herarchy rocess, Exert systems wth Alcatons, 38() , 2 B. RGMM Prortes n each nut sheet are calculated usng the row geometrc mean method (RGMM). Wth the arwse x comarson matrx A a We calculate and normalze: r ex ln( a r./ ) ( r a ) / C. Inconsstences To fnd the most nconsstent comarson, we look for the ar, wth ( a ) Consstency ratos are calculated n all nut sheets and n the summary sheet. Wth the calculated rncal egenvalue - ether based on the rorty egenvector derved from RGMM n the nut sheet or derved from EVM n the summary sheet the consstency ndex CI s gven as ( ) CI CI The consstency rato CR s calculated usng CR RI We use the Alonson/Lamata lnear ft resultng n CR: CR Alonso, Lamata, (26). Consstency n the analytc herarchy rocess: a new aroach. Internatonal Journal of Uncertanty, Fuzzness and Knowledge based systems, Vol 4, o 4, Geometrc consstency ndex GCI s calculated usng: 2 ln a ln CGI ( )( 2) Page 5 APcalc-v a.docx verson 24-Dec-23

6 D. Aggregaton of ndvdual udgments (Consoldaton of artcants) The consoldated decson matrx C (selected artcant ) combnes all k artcants nuts to get the aggregated grou result. We use the weghted geometrc mean of the decson matrces elements a (k) usng the ndvdual decson maker s weght w k as gven n the nut sheets: E. AP consensus ndcator c ex w k k ( k ) AP consensus s calculated n the summary sheet based on the RGMM results of all nuts usng Shannon alha and beta entroy. The consensus ndcator ranges from % (no consensus between decsons makers) to % (full consensus between decson makers). AP consensus ndcator S* S k ln a M ex( ) ex( ) / ex( ) ex( ) * mn mn wth M / ex( ).,, w s the,, Shannon entroy for the rortes of all K decson makers/artcants. k Shannon alha entroy Shannon gamma entroy wth Shannon beta entroy K K K ln ln We need to adust for the mum score c of the AP scale used and mn c c c ln( c ) ( ) c ln c ( K) c ln c K c c K c ln K c number of crtera, K number of decson makers/artcants. For more nformaton see: Goeel, Klaus D., Imlementng the analytc herarchy rocess as a standard method for mult-crtera decson makng n cororate enterrses a new AP excel temlate wth multle nuts. Proceedngs of the nternatonal symosum on the analytc herarchy rocess, Kuala Lumur, Malaysa, 23 (Submtted Feb. 23). APcalc-v a.docx Page 6 verson 24-Dec-23