Robust data envelopment analysis via ellipsoidal uncertainty sets with application to the Italian banking industry
- PDF / 2,331,223 Bytes
- 28 Pages / 439.37 x 666.142 pts Page_size
- 103 Downloads / 182 Views
bust data envelopment analysis via ellipsoidal uncertainty sets with application to the Italian banking industry Emmanuel Kwasi Mensah1 Received: 17 November 2019 / Accepted: 22 July 2020 © The Author(s) 2020
Abstract This paper extends the conventional DEA models to a robust DEA (RDEA) framework by proposing new models for evaluating the efficiency of a set of homogeneous decision-making units (DMUs) under ellipsoidal uncertainty sets. Four main contributions are made: (1) we propose new RDEA models based on two uncertainty sets: an ellipsoidal set that models unbounded and correlated uncertainties and an interval-based ellipsoidal uncertainty set that models bounded and correlated uncertainties, and study the relationship between the RDEA models of these two sets, (2) we provide a robust classification scheme where DMUs can be classified into fully robust efficient, partially robust efficient and robust inefficient, (3) the proposed models are extended to the additive DEA model and its efficacy is analyzed with two imprecise additive DEA models in the literature, and finally, (4) we apply the proposed models to study the performance of banks in the Italian banking industry. We show that few banks which were resilient in their performance can be robustly classified as partially efficient or fully efficient in an uncertain environment. Keywords Robust optimization · Ellipsoidal uncertainty set · Robust data environment analysis (RDEA) · Robust additive DEA · Italian banks efficiency JEL Classification C6 · G2
* Emmanuel Kwasi Mensah [email protected]; [email protected] 1
Department of Economics, University of Insubria, Via Monte Generoso, 71, 21100 Varèse, VA, Italy
13
Vol.:(0123456789)
E. K. Mensah
1 Introduction Data envelopment analysis (DEA) is a nonparametric optimization model for assessing the relative performance of a set of peer decision-making units (DMU) with multiple inputs and multiple outputs. Specifically, the DEA model is based on linear programming to measure the efficiency of the i-th DMU under evaluation relative to the other DMUs of the set. The model was initially proposed under the constant returns to scale assumption of a firm’s production activity by Charnes et al. (1978) and later extended to the variable returns to scale by Banker et al. (1984). The multiple advantages of the DEA make it an important analysis tool for benchmarking in various scientific areas such as operational research, decision analysis, management science, social science, etc. However, the learning procedure through which DMUs are benchmarked against each other implicitly assumes precision in data and ignores the uncertainties and noise inherent in the inputs and outputs. Hence, the traditional models as proposed in Charnes et al. (1978) and Banker et al. (1984) can be practically unsuitable in application. For instance, in many applications, some of the data are only known within specified bounds or in ordered relations while others are described vaguely such that the real values are unknown or
Data Loading...
