Title: A complete ranking of decision making units with interval data

Authors: Somayeh Khezri; Gholam Reza Jahanshahloo; Akram Dehnokhalaji; Farhad Hosseinzadeh Lotfi

Addresses: Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran ' Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran ' Operations and Information Management Department, Aston Business School, B4 7ET, Birmingham, UK ' Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Abstract: Interval data envelopment analysis (interval DEA) deals with the problem of efficiency assessment when the inputs and/or outputs of decision making units (DMUs) are given as interval data. This paper focuses on the problem of ranking DMUs with interval data. First, we define extreme efficient units, super efficiency score, the best and the worst efficiency (inefficiency) frontiers in the interval DEA context. Then, we propose a novel method based on the lower and upper super efficiency scores of a unit under evaluation and the distance of that unit to four developed frontiers. Our method ranks all efficient and inefficient units which is one of the main advantages of it. Our method uses several essential criteria simultaneously to rank units with interval data. These criteria increase the discrimination power of our proposed method. Potential application of this method is illustrated with a dataset consisting of 30 branches of the social security insurance organisation in Tehran.

Keywords: date envelopment analysis; DEA; interval DEA; decision making unit; DMU; ranking.

DOI: 10.1504/IJOR.2022.122335

International Journal of Operational Research, 2022 Vol.43 No.3, pp.332 - 359

Received: 08 Jun 2018
Accepted: 28 Jun 2019
Published online: 20 Apr 2022 *

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