A Two-stage improved base point slacks-based measure of super-efficiency for negative data handling

Abstract

For most of the Slacks-Based Measure (SBM)-type models in Data Envelopment Analysis, the variable returns-to-scale (VRS) condition is required to become feasible and translation invariant while applied on negative data. Unlike them, the “Base Point SBM (BP-SBM)” and “Super BP-SBM” models accept negative values under four returns-to-scale (RTS) conditions; however, (i) they are not translation invariant, (ii) they are sensitive to some perturbation terms which help to translate negative data to positive data by avoiding division-by-zero irrationality, and (iii) the Super BP-SBM model suffers from infeasibility issue. To address the above limitations, this study improves the existing BP-SBM and Super BP-SBM models. The Improved BP-SBM (IBP-SBM) and Improved Super BP-SBM (ISBP-SBM) models are translation invariant under four different RTS conditions, and do not involve any perturbation terms. Although the proposed ISBP-SBM model is feasible under the four RTS conditions, it fails to provide Pareto efficient projections. Therefore, we propose a two-stage super-efficiency approach, where the ISBP-SBM model is applied on the first stage to obtain the input savings and output surpluses, which are incorporated in the IBP-SBM model to be applied on the second stage. To validate the proposed models, their results are compared with some state-of-the-art models using a benchmark dataset. Experimental findings indicate that the proposed models have overcome the limitations of the existing models while applied on negative data. Further, three real-life case studies of supplier selection, financial performance evaluation, and airline performance evaluation are used to discuss the applicability of the proposed approach.