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.
Highlights
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
We proposed new robust DEA models based on the ellipsoidal uncertainty and interval-based ellipsoidal uncertainty sets designed in Ben-Tal and Nemirovski (1999, 2000)
By constraining the uncertain data in an ellipsoidal uncertainty sets, the models developed in this paper become less pessimistic and in contrast offer the advantage over the interval DEA models which mostly evaluate the performance of DMUs based on their extreme lower and upper bounds of efficiency
Summary
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. The approach offers to immunize the uncertain inputs and outputs data of DMUs in a user-defined uncertainty set and provides a probability guarantee for reliable efficiency scores, robust discrimination and ranking of DMUs. The RDEA is based on the robust optimization (RO) technique which was initially introduced by Soyster (1973) and extended by the likes of Ben-Tal and Nemirovski (1998, 1999, 2000) and El Ghaoui et al (1998). The authors applied the robust approach of Bertsimas and Sim (2004) and Monte Carlo simulation to compute for the range of Gamma values for the conformity of the ranking of the DMUs. Omrani (2013) introduced an RDEA to find the common set of weights (CSW) in DEA with uncertain data under a similar uncertainty set.
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