توسعه مدل رتبه بندي ترجيحي و تحليل روش هاي حل آن

چكيده انگليسي :

Development of the Preference Ranking Model and it s Solution Methods Fateme Nakhaee f nakhaee@in iut ac ir Date of Submission ۵ Department of Industrial System Engineering Isfahan University of Technology Isfahan ۴ ۵۶ IranDegree M Sc Language FarsiSupervisor Naser Mollaverdi naserm@cc iut ac irAbstractDecision making is one of the important human s characteristic and every body makes so much decisiondaily As personal and social life could be affected by correct and well timed decision making existence ofscientific methods that helps every one in this field is necessary Multi attribute decision making concerned with a finite set of alternatives The results can be expressed in the form of a selection of themost appropriate alternative a ranking of the alternatives from the best to the worst or a classification intopredefined performance classes There are different ways to allow the voters to express their preferences ona set of candidates In ranked voting systems each voter selects a subset of the candidates and ranks them inorder of preference A well known class of these voting systems are scoring rules where fixed scores areassigned to the different ranks and the candidates with the highest score are the winners One of the mostimportant issues in this context is the choice of the scoring vector since the winning candidate can varyaccording to the scores used Data envelopment analysis DEA a useful assessment tool has been used tosolve the problem of preference voting and aggregation which require the determination of the weightsassociated with different ranking places Instead of applying the same externally imposed weighting schemeto all candidates DEA models allow each candidate to choose his her own weights in order to maximizehis her own overall ratings subject to certain conditions Cook and Kress using a DEA AR model proposedto assess each candidate with the most favorable scoring vector for him her However the use of thisprocedure often causes several candidates to be efficient i e they achieve the maximum score For thisreason several methods to discriminate among efficient candidates have been proposed Each method hassome weaknesses and strengths Some of these methods aren t stable and monotonic such as Nogchi smodel This model is useful to discriminate efficient candidates but it has two drawbacks First the numberof first second kth ranks obtained by inefficient candidates may change the order of efficientcandidates On the other hand this method isn t stable Second a winning candidate can lose when he shewins some jth place ranks from inefficient candidates or equivalently a losing candidate can win whenhe she loses some jth place ranks to inefficient candidates Consequently this method is not monotonic In this paper Noguchi s model is improved through changing constraints Because of constraintscorresponding to inefficient candidates are redundant a test removed them before using the model This testis based on a transformation on the given data which makes it possible to use the definition of efficiencyinstead of AR efficiency Assurence Region efficiency Then it s became stable and monotonic Furthermore the algorithm was proposed that can rank candidates with votes of voters and managers opinion In other part of this research a nonlinear programming model was proposed that could rankcandidates with weighted classification of voters Then capability of this algorithm and models wereexamined with numerical examples The result show these methods and algorithm can rank candidateagreeably and give a full ranking of all the candidates Key wordsData Envelopment Analysis Preference Voting System Noguchi s Model Manager s Opinion Voter s Weighted Classification

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توسعه مدل رتبه بندي ترجيحي و تحليل روش هاي حل آن

سيستم هاي راي گيري ترجيحي , روش نوگوچي , آراي مديريت , طبقه بندي وزني راي دهندگان , تحليل پوششي داده ها