Group Decision Making with Dispersion in the Analytic Hierarchy Process

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• 作者：Natalie M. Scala ; Jayant Rajgopal ; Luis G. Vargas…
• 关键词：Group decisions ; Analytic Hierarchy Process ; Geometric mean ; Geometric dispersion ; Principal component analysis ; Weighted geometric mean
• 刊名：Group Decision and Negotiation
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：25
• 期：2
• 页码：355-372
• 全文大小：1,447 KB
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• 作者单位：Natalie M. Scala (1)
  Jayant Rajgopal (2)
  Luis G. Vargas (3)
  Kim LaScola Needy (4)
  
  1. Department of e-Business and Technology Management, Towson University, 8000 York Road, Towson, MD, 21252, USA
  2. Department of Industrial Engineering, University of Pittsburgh, 1048 Benedum Hall, Pittsburgh, PA, 15261, USA
  3. Katz Graduate School of Business, University of Pittsburgh, 356 Mervis Hall, Pittsburgh, PA, 15261, USA
  4. Graduate School and International Education, University of Arkansas, 213B Ozark Hall, Fayetteville, AR, 72701, USA
  
• 刊物类别：Business and Economics
• 刊物主题：Economics
  Operation Research and Decision Theory
  Social Sciences
  
• 出版者：Springer Netherlands
• ISSN：1572-9907

文摘

With group judgments in the context of the Analytic Hierarchy Process (AHP) one would hope for broad consensus among the decision makers. However, in practice this will not always be the case, and significant dispersion may exist among the judgments. Too much dispersion violates the principle of Pareto Optimality at the comparison level and/or matrix level, and if this happens, then the group may be homogenous in some comparisons and heterogeneous in others. The question then arises as to what would be an appropriate aggregation scheme when a consensus cannot be reached and the decision makers are either unwilling or unable to revise their judgments. In particular, the traditional aggregation via the geometric mean has been shown to be inappropriate in such situations. In this paper, we propose a new method for aggregating judgments when the raw geometric mean cannot be used. Our work is motivated by a supply chain problem of managing spare parts in the nuclear power generation sector and can be applied whenever the AHP is used with judgments from multiple decision makers. The method makes use of principal components analysis (PCA) to combine the judgments into one aggregated value for each pairwise comparison. We show that this approach is equivalent to using a weighted geometric mean with the weights obtained from the PCA. Keywords Group decisions Analytic Hierarchy Process Geometric mean Geometric dispersion Principal component analysis Weighted geometric mean