DAME - Microsoft Excel add-in for solving multicriteria decision problems with scenarios Radomir Perzina 1, Jaroslav Ramik 2

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1 Itroductio DAME - Microsoft Excel add-i for solvig multicriteria decisio problems with scearios Radomir Perzia, Jaroslav Ramik 2 Abstract. The mai goal of every ecoomic aget is to make a good decisio, especially i ecoomic eviromet with may ivestmet alteratives ad evaluatio criteria. The Aalytic Hierarchy Process (AHP) is widely used approach for solvig decisio makig problems. There exists wide rage of computer programs that are able to help decisio makers to make good decisios. Mai disadvatage of those programs is that they are commercial ad relatively quite expesive ad thus it prevets them to be used by small compaies or idividual etrepreeurs. This paper itroduces a ew Microsoft Excel add-i amed DAME Decisio Aalysis Module for Excel. Comparig to other software products for solvig multicriteria decisio problems, DAME is free, able to work with scearios or multiple decisio makers, allows for easy maipulatio with data ad utilizes capabilities of widespread spreadsheet Microsoft Excel. Users ca structure their decisio models ito three levels - scearios, criteria ad variats. Stadard pair-wise comparisos are used for evaluatig both criteria ad variats. For each pair-wise compariso matrix there is calculated a icosistecy idex. There are provided three differet methods for the evaluatio of the weights of criteria, the variats as well as the scearios Saaty s Method, Geometric Mea Method ad Fuller s Triagle Method. All calculatios are istat so users ca easily see what happe if value of ay iput is chaged. Apart from the fial orderig of the variats there are also show all itermediate results, so it is clearly see how the sythesis was produced. The results of the decisio model are depicted by a bar chart. Capabilities of the proposed software package are demostrated o couple of illustratig examples of real life decisio problems. Keywords: aalytic hierarchy process, multi-criteria decisio makig, pair-wise comparisos, Microsoft Excel, Scearios. JEL Classificatio: C44 AMS Classificatio: 90C5 Decisio makig i situatios with multiple variats is a importat area of research i decisio theory ad has bee widely studied e.g. i [2], [3], [5], [7], [9], [0], []. There exists wide rage of computer programs that are able to help decisio makers to make good decisios, e.g. Expert Choice ( Decisios Les ( Mid Decider ( MakeItRatioal ( or Super Decisios ( Mai disadvatage of those programs is that they are commercial ad relatively quite expesive ad thus it prevets them to be used by small compaies or idividual etrepreeurs. Here we itroduce a ew Microsoft Excel add-i amed DAME Decisio Aalysis Module for Excel. Comparig to other software products for solvig multicriteria decisio problems, DAME is free, able to work with scearios or multiple decisio makers, allows for easy maipulatio with data ad utilizes capabilities of widespread spreadsheet Microsoft Excel. Users ca structure their decisio models ito three levels - scearios, criteria ad variats. Stadard pair-wise comparisos are used for evaluatig both criteria ad variats. For each pair-wise compariso matrix there is calculated a icosistecy idex. There are provided three differet methods for the evaluatio of the weights of criteria, the variats as well as the scearios - Saaty's Method [0], Geometric Mea Method [] ad Fuller's Triagle Method [2]. School of Busiess Admiistratio, Silesia Uiversity, Departmet of Mathematical Methods i Ecoomy, Uiversity Square 934/3, Karviá, Czech Republic, 2 School of Busiess Admiistratio, Silesia Uiversity, Departmet of Mathematical Methods i Ecoomy, Uiversity Square 934/3, Karviá, Czech Republic,

2 2 Software descriptio DAME works with all curret versios of Microsoft Excel from versio 97. It cosists of four idividual files: DAME.xla mai module with user iterface, it is writte i VBA (Visual Basic for Applicatios), DAME.dll it cotais special fuctios used by the applicatio, it is writte i C#, DAME.xll it cotais library for likig C# modules with Excel called Excel-DNA ( DAME.da cofiguratio file for Excel-DNA module. All four files must be placed i the same folder ad macros must be permitted before ruig the module (see Excel documetatio for details). DAME itself ca be executed by double clickig o the file DAME.xla. After executig the add-i there will appear a ew meu item DAME i the Add-is ribbo (i older Excel versios the meu item DAME will appear i the top level meu). A ew decisio problem ca be geerated by clickig o New problem item i the mai DAME meu, see figure. Figure New problem meu The there will be show a form with mai problem characteristics, see figure 2. Figure 2 New problem characteristics I the top pael there are basic settigs: Number of scearios, criteria ad variats. I case a user does t wat to use scearios, the umber of scearios should be set to oe. I the secod pael we ca set how we wat to compare scearios ad criteria either usig pairwise compariso matrix or set weights directly. I the last pael users ca chose how they wat to evaluate variats accordig to idividual criteria. There are three optios: Pairwise each pair of variats is compared idividually, Values max idicates maximizatio criterio where each variat is evaluated by sigle value, e.g. price ad Values mi idicates miimizatio criterio where each variat is evaluated by sigle value, e.g. costs. Whe user cofirms his optios a ew Excel sheet with forms is created, where user ca set ames of all elemets ad evaluate criteria ad variats usig pairwise compariso matrices as show o figure 3. Figure 3 Pairwise compariso matrix I the pairwise compariso matrix users eter values oly i the upper triagle. The values i the lower triagle are reciprocal ad automatically calculated. If criterio (variat) i the row is more importat tha the

3 criterio (variat) i the colum user eters values from 2 to 9 (the higher the value is the more importat is the criterio i the row). If criterio (variat) i the row is less importat tha the criterio (variat) i the colum user eters values from /2 to /9 (the less the value is the less importat is the criterio i the row). If criterio (variat) i the row is equally importat to the criterio (variat) i the colum user eters value or leaves it empty. I the top right corer there is calculated icosistecy idex which should be less tha 0., if it is greater we should revise our pairwise comparisos, so that they are more cosistet. I the very right colum there are calculated weights of idividual criteria (variats) based o the values i the pairwise compariso matrix ad selected evaluatio method. The weights w k based o geometric mea method are calculated usig the equatio (). w k = j= a i= j= kj / a ij /, k =,2, K, () where w k is weight of k-th criteria (variat), a ij are values i the pairwise compariso matrix, ad is umber of criteria (variats). The icosistecy idex is calculated usig the formula (2). GCI = 2 ( )( ) 2 i< j 2 w j log aij wi (2) Whe we are eterig values i idividual pairwise compariso matrices all weights are beig istatly recalculated, so we ca see immediate impact of our each idividual etry. Matrix ad graph with total evaluatio of variats is the show at the bottom of the sheet. The resultig vector of weights of the variats Z is give by the formula (3). where W 2 is the matrix (weighig vector of the criteria), i.e. ad W 32 is the m matrix: Z = W 32 W 2, (3) w( C ) W = 2 M, (4) w( C ) w( C, V ) L w( C, V ) W = 32 M L M, (5) w( C, ) (, ) Vm L w C Vm where w(c i ) is weight of the criterio C i, w(v r,c i ) is weight of variat V r subject to the criterio C i. 3 Case study Here we demostrate the proposed add-i DAME o a decisio makig situatio buyig a optimal car with 3 decisio criteria ad 3 variats. The goal of this realistic decisio situatio is to fid the best variat from 3 preselected oes accordig to 3 criteria: price (miimizatio criterio), efficiecy (pairwise) ad desig (pairwise). At this stage we do t use scearios, so umber of scearios will be set to oe. Settig of parameters ca be see o the figure

4 Figure 4 Case study settig of parameters Whe we submit the form a ew sheet is geerated. First we set ames of criteria ad variats, for simplicity we use default ames for variats (Var, Var 2 ad Var 3), see figure 5. Figure 5 Case study ames of criteria ad variats Next step is compariso of idividual criteria usig pairwise compariso matrix with elemets sayig how much more importat is criterio i the row tha the criterio i the colum, see figure 6. Figure 6 Case study criteria compariso We ca see that icosistecy idex is less tha 0. therefore we ca say that our pairwise comparisos are cosistet. I the very right colum we ca see calculated weights of idividual criteria. Fial step is evaluatio of variats accordig to idividual criteria. Variats accordig the first criterio (price) will be evaluated by actual price ad variats accordig the other two criteria (efficiecy ad desig) will be evaluated usig pairwise comparisos), see figure 7. Figure 7 Case study evaluatio of variats

5 As we ca see both pairwise compariso matrices are cosistet, because their icosistecy idexes are less tha 0.. I the top right matrix we ca see calculated weights of all variats (rows) accordig to idividual criteria (colums). At this stage sythesis is calculated ad we ca see total evaluatio of variats i the last table o figure 8 ad graphical represetatio o figure 9. Figure 8 Case study total evaluatio of variats 4 Case Study with Scearios Figure 9 Case study total evaluatio of variats - graph I real decisio situatios a decisio maker usually faces ucertaity. For example it may happe that price goes up or efficiecy is calculated based o special coditios that are far from real oes. That is why our proposed software works also with scearios. I this case study we assume two scearios optimistic ad pessimistic. First we must compare both scearios usig pairwise compariso matrix. It ca be see o figure 0. Figure 0 Case study scearios compariso Optimistic sceario is usig exactly the same etries as i the previous case study, so we eed to just evaluate variats to idividual criteria for the secod - pessimistic sceario, see figure. Figure Case study evaluatio of variats pessimistic sceario Fial evaluatio of variats for pessimistic sceario ca be see o figure

6 Figure 2 Case study fial evaluatio of variats pessimistic sceario Fially from both scearios there is calculated sythesis ad total evaluatio of variats is show o figure 3. Figure 3 Case study total evaluatio of variats Comparig to the previous case study without scearios we ca see that fial rak of variats was chaged. Now the best variat is Var 2 with weight 0.35, the Var with weight 0.34 ad the last oe Var 3 with weight Coclusios I this paper we have proposed a ew Microsoft Excel add-i DAME for solvig decisio makig problems. Comparig to other decisio support programs DAME is free, able to work with scearios or multiple decisio makers, allows for easy maipulatio with data ad utilizes capabilities of widespread spreadsheet Microsoft Excel. O two realistic case studies we have demostrated its fuctioality i idividual steps. The ew add-i could be used maily by studets, scietists ad small compaies. Ackowledgemets This research was supported by the grat project of GACR No Refereces [] Aguaro, J., Moreo-Jimeez, J.M.: The geometric cosistecy idex: Approximated thresholds. Europea Joural of Operatioal Research 47 (2003), [2] Fishbur, P. C.: A comparative aalysis of group decisio methods, Behavioral Sciece (6), 97, [3] Gass, S.I., Rapcsák, T.: Sigular value decompositio i AHP. Europea Joural of Operatioal Research 54 (2004), [4] Hor, R. A., Johso, C. R.: Matrix Aalysis, Cambridge Uiversity Press, 990. [5] Mazurek, J., Fiedor, J.: The Decisio Tool for the Ordial Cosesus Rakig Problem. I: Coferece Proceedigs of the Iteratioal Scietific Coferece ICT for Competitiveess 202. Silesia Uiversity, School of Busiess Admiistratio, Karvia, 202, [6] Ramík, J., Korviy, P.: Icosistecy of pair-wise compariso matrix with fuzzy elemets based o geometric mea. Fuzzy Sets ad Systems 6 (200), [7] Ramik, J., Perzia, R.: Fuzzy ANP a New Method ad Case Study. I: Proceedigs of the 24 th Iteratioal Coferece Mathematical Methods i Ecoomics 2006, Uiversity of Wester Bohemia, [8] Ramík, J., Vlach, M.: Geeralized cocavity i optimizatio ad decisio makig. Kluwer Publ. Comp., Bosto-Dordrecht-Lodo, 200, 305 p. [9] Saaty, T.L.: Explorig the iterface betwee hierarchies, multiple objectives ad fuzzy sets. Fuzzy Sets ad Systems, 978, [0] Saaty, T.L.: Multicriteria decisio makig - the Aalytical Hierarchy Process. Vol. I., RWS Publicatios, Pittsburgh, 99. [] Saaty, T.L.: Decisio Makig with Depedece ad Feedback The Aalytic Network Process. RWS Publicatios, Pittsburgh,

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