A new case of rank reversal in analytic hierarchy process due to aggregation of cost and benefit criteria

IF 3.7 4区 管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Abhijit Majumdar , Manoj Kumar Tiwari , Aastha Agarwal , Kanika Prajapat
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引用次数: 11

Abstract

Rank reversal in Analytic Hierarchy Process (AHP) due to introduction or removal of a new alternative is well documented in literature. However, rank reversal due to the aggregation of benefit and cost criteria has not been addressed with requisite rigour. This paper demonstrates a new type of rank reversal in AHP which can arise due to the method (ratio or difference) and approach (sum 1 or sum 2) used to aggregate the benefit and cost criteria. Numerical examples, mathematical analyses and computer simulations have been used for demonstration of results. It is found that considering the benefit and cost criteria separately (sum 2 approach) while aggregating them can yield irrational ranking. It is also demonstrated that ratio method of aggregation is untenable in additive variants of AHP as it yields identical ranking in sum 1 and sum 2 approaches. Difference method of aggregation considering the benefit and cost criteria together (sum 1 approach) is most logical and sound in additive variants of AHP. The results also counter the notion that multiplicative AHP is immune to rank reversal between ratio and difference methods of aggregation. Besides, sum 1 and sum 2 approaches produce different raking of alternatives in multiplicative AHP irrespective of the method of aggregation. Outcome of this research will be helpful while choosing the appropriate method and approach for aggregation of benefit and cost criteria in different variants of AHP.

层次分析法中由于成本和效益标准聚集而导致的等级反转的新案例
在层次分析法(AHP)中,由于引入或去除一个新的选择而导致的秩反转在文献中有很好的记录。但是,由于综合效益和成本标准而导致的排名颠倒问题尚未得到必要的严格处理。本文论证了层次分析法中一种新型的等级反转问题,这种问题是由于综合效益和成本标准所采用的方法(比率或差异)和方法(求和1或求和2)所引起的。通过数值算例、数学分析和计算机模拟对结果进行了论证。研究发现,在综合效益和成本标准的同时,单独考虑效益和成本标准(sum 2法)会产生不合理的排序。还证明了比例聚合法在AHP的加性变量中是站不住脚的,因为它在sum 1和sum 2方法中产生相同的排名。综合考虑效益和成本标准的差异聚合法(和1法)是层次分析法中最合理的方法。结果也反驳了乘法AHP不受比率和差异聚集方法之间的秩反转的观念。此外,无论采用何种聚合方法,乘法AHP的和1和和2方法都会产生不同的选择排序。本文的研究结果将有助于在不同层次分析法中选择合适的方法和途径来综合效益和成本标准。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Operations Research Perspectives
Operations Research Perspectives Mathematics-Statistics and Probability
CiteScore
6.40
自引率
0.00%
发文量
36
审稿时长
27 days
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