Number of performance measures versus number of decision making units in DEA

  • Dariush Khezrimotlagh
  • Wade D. Cook
  • Joe ZhuEmail author
S.I.: Data Mining and Decision Analytics


Sufficient numbers of decision-making units (DMUs) in comparison to the number performance measures that are classified as inputs and outputs has been a concern when applying data envelopment analysis (DEA) in real world settings. As the number of DMUs decreases (or the numbers of inputs and outputs increases) the discrimination power and accuracy of DEA with respect to the performance of DMUs decreases. The current study proposes a technique which increases the discrimination power of DEA and allows for increasing the numbers of inputs and outputs even if the number of DMUs is relatively small. An adjusted DEA methodology is proposed which is stronger and more accurate than the routine DEA methodology, and permits one to identify the reference units for each best-practice unit (more than the DMU itself) and to distinguish the performance and rank of DMUs relative to one another, thereby enhancing the discrimination power of DEA. The scores from the adjusted methodology are logically meaningful. The pros of the new approach are demonstrated by several examples and simulation experiments in controlled environments. The results show that the proposed technique significantly improves the discrimination power over that of the conventional DEA model when the number of DMUs decreases or the number of inputs and outputs increases. In addition, the proposed technique is used to evaluate the quality-of-life related to twelve input–output combinations for two sets of DMUs, namely fifteen USA cities and five international cities, where none of the rules of thumb are satisfied.


DEA Best-practice Performance evaluation Simulation study 



We appreciate the valuable comments from the three anonymous reviewers as they aided to improve the clarity of our paper. This research is supported by Pennsylvania State University Harrisburg (No. 0206020 AC6ET), by the National Natural Science Funds of China (No. 71828101), and by the NSERC-the Natural Sciences and Engineering Research council of Canada (No. A8966).


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Authors and Affiliations

  1. 1.Department of MathematicsPennsylvania State University HarrisburgMiddletownUSA
  2. 2.Schulich School of BusinessYork UniversityTorontoCanada
  3. 3.College of Auditing and EvaluationNanjing Audit UniversityNanjingChina
  4. 4.Foisie Business SchoolWorcester Polytechnic InstituteWorcesterUSA

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