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Advances in Operations Research
Volume 2016 (2016), Article ID 7171467, 8 pages
Research Article

Finding the Most Preferred Decision-Making Unit in Data Envelopment Analysis

1Department of Mathematics, Islamic Azad University, Science and Research Branch, Tehran, Iran
2Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Iran

Received 20 June 2016; Revised 25 October 2016; Accepted 20 November 2016

Academic Editor: Konstantina Skouri

Copyright © 2016 Shirin Mohammadi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Data envelopment analysis (DEA) evaluates the efficiency of the transformation of a decision-making unit’s (DMU’s) inputs into its outputs. Finding the benchmarks of a DMU is one of the important purposes of DEA. The benchmarks of a DMU in DEA are obtained by solving some linear programming models. Currently, the obtained benchmarks are just found by using the information of the data of inputs and outputs without considering the decision-maker’s preferences. If the preferences of the decision-maker are available, it is very important to obtain the most preferred DMU as a benchmark of the under-assessment DMU. In this regard, we present an algorithm to find the most preferred DMU based on the utility function of decision-maker’s preferences by exploring some properties on that. The proposed method is constructed based on the projection of the gradient of the utility function on the production possibility set’s frontier.