Ranking with a Euclidean common set of weights in data envelopment analysis: with application to the Eurozone banking se
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Ranking with a Euclidean common set of weights in data envelopment analysis: with application to the Eurozone banking sector Helmi Hammami1 • Thanh Ngo2,3
•
David Tripe4 • Dinh-Tri Vo5,6
Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper provides a new method to define a Euclidean common set of weights (ECSW) in data development analysis (DEA) that (1) allows ranking both efficient and inefficient firms, (2) is more realistic in terms of determination of weights, and (3) generates rankings for banks consistent with their credit ratings. We first use DEA to determine the efficient frontier and then estimate a common set of weights that can minimize the Euclidean distance between the firms and that frontier. This process is illustrated by a simple numerical example and is extended to a real-life situation using the Eurozone banking sector. Our ECSW approach outperforms other common set of weights approaches in both numerical and real-life examples, and in terms of providing rankings consistent with banks’ credit ratings. Keywords Data envelopment analysis Common set of weights Euclidean distance Banking system Eurozone
1 Introduction Data Envelopment Analysis (DEA), which was first introduced by Charnes et al. (1978), has become a popular tool for efficiency measurement in various fields (Emrouznejad et al. 2008; Liu et al. 2013). It is based on the idea that optimal weights can be estimated for and applied to the inputs and outputs of an individual decision-making-unit (DMU), from the perspective of maximizing total output (output-oriented DEA), minimizing total input (input-oriented DEA) or both (additive, or slack-based-measure DEA) (Cooper et al. 2006). & Thanh Ngo [email protected] 1
Rennes School of Business, Rennes, France
2
School of Aviation, Massey University, Palmerston North, New Zealand
3
VNU University of Economics and Business, Hanoi, Vietnam
4
School of Economics and Finance, Massey University, Palmerston North, New Zealand
5
IPAG Business School, Paris, France
6
University of Economics Ho Chi Minh City, Ho Chi Minh City, Vietnam
123
Annals of Operations Research
The use of these weights, also referred to as virtual or shadow prices, allows DEA to be price-free, which is both a strength and a weakness. On one hand, it allows measurement of the relative efficiency of DMUs without the need for any price information or functional form (Seiford and Thrall 1990). On the other hand, different weights mean that DMUs are evaluated under different facets of the frontier, thus making it difficult to rank DMUs, whether efficient or inefficient (Sexton et al. 1986; Kao and Hung 2005; Asmild et al. 2013). Ranking these DMUs using the different (optimal) set of weights of DEA (hereafter called ‘‘dynamic set of weights’’—DSW) is therefore inappropriate, and different ranking methods should be preferred. There are different methods to rank DMUs based on DEA. Adler et al. (2002) classified the
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