Annals of Operations Research

, Volume 253, Issue 1, pp 657–681 | Cite as

A novel method for selecting a single efficient unit in data envelopment analysis without explicit inputs/outputs

  • Mehdi Toloo
  • Madjid Tavana
Original Paper


Data Envelopment Analysis (DEA) is a non-parametric technique for evaluating a set of homogeneous decision-making units (DMUs) with multiple inputs and multiple outputs. Various DEA methods have been proposed to rank all the DMUs or to select a single efficient DMU with a single constant input and multiple outputs [i.e., without explicit inputs (WEI)] as well as multiple inputs and a single constant output [i.e., without explicit outputs (WEO)]. However, the majority of these methods are computationally complex and difficult to use. This study proposes an efficient method for finding a single efficient DMU, known as the most efficient DMU, under WEI and WEO conditions. Two compact forms are introduced to determine the most efficient DMU without solving an optimization model under the DEA-WEI and DEA-WEO conditions. A comparative analysis shows a significant reduction in the computational complexity of the proposed method over previous studies. Four numerical examples from different contexts are presented to demonstrate the applicability and exhibit the effectiveness of the proposed compact forms.


Data envelopment analysis (DEA) Most efficient unit Explicit inputs Explicit outputs Computational complexity 



The authors would like to thank the anonymous reviewers and the editor for their insightful comments and suggestions. The research was supported by the European Social Fund within the project CZ.1.07/2.3.00/20.0296 and the Czech Science Foundation through project No. 16-17810S. All support is greatly acknowledged.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Systems Engineering, Faculty of EconomicsTechnical University of OstravaOstravaCzech Republic
  2. 2.Business Systems and Analytics DepartmentLa Salle UniversityPhiladelphiaUSA
  3. 3.Business Information Systems Department, Faculty of Business Administration and EconomicsUniversity of PaderbornPaderbornGermany

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