Slide 1

Informs Annual Meeting 2012, Phoenix, AZCaveats of Decision Rules for Comparing Alternatives under Incomplete Preference InformationAntti Punkka and Ahti SaloSystems Analysis LaboratoryDepartment of Mathematics and Systems AnalysisAalto University School of ScienceIncomplete preference information about additive value functions1 e.g., Kirkwood and Sarin (Man.Sci., 1985), Hazen (Oper.Res., 1986), Salo and Hmlinen (Oper.Res., 1992)Example

Experts apply decision rules to obtain decision recommendations

(2,1) is the maximax2 solution(1,2) is the maximin2 solution(2,1) is the weak dominance2,3 solution0.1250.1(1,2) is the weak dominance2,3 solution(2,1) is the maximin2 solution(1,2) is the maximax2 solution2 Salo and Hmlinen (IEEE Transactions on SMC-A, 2001)3 Park and Kim (EJOR, 1997)4 Sarabando and Dias (IEEE Transactions on SMC-A, 2009)(2,1) is the quasi-dominance4 solution with all tolerances in [0.1,0.125)(1,2) is the quasi-dominance4 solution...ValueValue

Where are the attribute weights?

Expert 1Expert 25 Eiselt and Laporte (EJOR, 1992)(2,1) is the domain criterion5 solution(1,2) is the domain criterion5 solutionValueValueNormalization is one possibility to choose representative value functionsStandard procedure for choosing representative value functionsRevisiting the visualizationsRepresentative value functions and ordinal comparisonsRanking intervalsRank-order alternatives with all consistent value functions

Vw10.40.7w20.60.3x2 can have ranking 1 x3 can have ranking 3x3 can have ranking 1 x1 can have ranking 4x1x2x3x4

Ranking intervals

Ranking intervals for sensitivity analysis: Academic Ranking of World Universities

exact weights

20 % interval

30 % interval

incompl. ordinalno information

Robust rankings

Different weighting wouldlikely yield a better rankingRankingUniversity10th442ndRanking intervals for project portfolio selection a case study6 revisited

Ranking intervals without any preference information about the relative values of the three attributes6 Data and case example from Knnl et al. (Technological Forecasting & Social Change, 2007)

DISCARDCHOOSECONSIDERConclusionsNormalizationNot implied by preference statementsNot needed to compare alternatives, but carried out to associate numerical values with alternativesDoes not affect results with complete preference informationWith incomplete information about relative importance of attributes, many value functions that describe different preferences are consistent with stated informationNumerical comparisons of value differences across these value functions do not provide meaningful resultsValues and value differences should always be compared with the same value functionUse dominance relations and ranking intervals