Annals of Operations Research

, Volume 271, Issue 2, pp 297–317 | Cite as

Interval cross efficiency for fully ranking decision making units using DEA/AHP approach

  • Qingxian An
  • Fanyong MengEmail author
  • Beibei Xiong
Original Research


Data envelopment analysis (DEA) is a popular technique for measuring the relative efficiency of a set of decision making units (DMUs). Fully ranking DMUs is a traditional and important topic in DEA. In various types of ranking methods, cross efficiency method receives much attention from researchers because it evaluates DMUs by using self and peer evaluation. However, cross efficiency score is usual nonuniqueness. This paper combines the DEA and analytic hierarchy process (AHP) to fully rank the DMUs that considers all possible cross efficiencies of a DMU with respect to all the other DMUs. We firstly measure the interval cross efficiency of each DMU. Based on the interval cross efficiency, relative efficiency pairwise comparison between each pair of DMUs is used to construct interval multiplicative preference relations (IMPRs). To obtain the consistency ranking order, a method to derive consistent IMPRs is developed. After that, the full ranking order of DMUs from completely consistent IMPRs is derived. It is worth noting that our DEA/AHP approach not only avoids overestimation of DMUs’ efficiency by only self-evaluation, but also eliminates the subjectivity of pairwise comparison between DMUs in AHP. Finally, a real example is offered to illustrate the feasibility and practicality of the proposed procedure.


Data envelopment analysis Analytic hierarchy process Interval multiplicative preference relation Consistency 



This research is supported by the National Natural Science Foundation of China under Grants (No. 71501189, 71571192), Natural Science Foundation of Hunan Province (2017JJ3397), the open project of “Mobile Health” Ministry of Education-China Mobile Joint Laboratory of Central South University, the China Postdoctoral Science Special Foundation (2015T80901), the State Key Program of National Natural Science of China (No. 71631008), Major Project for National Natural Science Foundation of China (71790615), and the China Postdoctoral Science Foundation (2014M560655).


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Authors and Affiliations

  1. 1.School of BusinessCentral South UniversityChangshaChina
  2. 2.Industrial Systems Optimization LaboratoryCharles Delaunay Institute and UMR CNRS 6281TroyesFrance
  3. 3.School of ManagementUniversity of Science and Technology of ChinaHefeiChina
  4. 4.School of Management Science and EngineeringNanjing University of Information Science and TechnologyNanjingChina

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