Title: New approach for ranking efficient DMUs based on Euclidean norm in data envelopment analysis

Authors: Mohammad Ebrahim Bolouri; Shokrollah Ziari; Ali Ebrahimnejad

Addresses: Department of Industrial Management, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran ' Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran ' Department of Mathematics, Qaemshahr Branch, Islamic Azad University, P.O. Box 163, Qaemshahr, Iran

Abstract: Data envelopment analysis (DEA) is a widely used technique for measuring the relative efficiencies of decision-making unit (DMUs) with multiple inputs and multiple outputs. In many applications, ranking of DMUs is an important and essential procedure to decision makers in DEA, especially when there are extremely efficient DMUs. Basic DEA models usually give the same efficiency score for some DMUs. Hence, it is necessary to rank of all extreme DMUs. The main purpose of this study is to propose an appropriate method in order to overcome the drawbacks in several methods for ranking DMUs based on the DEA concept. In the present paper, we propose a model for ranking extreme efficient DMUs in DEA by super efficiency technique and Euclidean norm (ℓ₂-norm). The presented method in this paper is able to overcome the existing obstacles in some methods. As regards, the proposed model is into nonlinear programming form, a linear model is suggested to approximate the nonlinear model.

Keywords: data envelopment analysis; DEA; ranking; efficiency; extreme efficient; Euclidean norm.

DOI: 10.1504/IJOR.2020.104225

International Journal of Operational Research, 2020 Vol.37 No.1, pp.85 - 104

Received: 24 Oct 2016
Accepted: 22 Jan 2017
Published online: 23 Dec 2019 *

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