Integrating slacks-based measure of efficiency and super-efficiency in data envelopment analysis

Tran, Trung Hieu; Mao, Yong; Nathanail, Paul; Siebers, Peer-Olaf; Robinson, Darren

Abstract

© 2018 Elsevier Ltd In this paper, we develop an integrated model for slacks-based measure (SBM) simultaneously of both the efficiency and the super-efficiency for decision-making units (DMUs) in data envelopment analysis (DEA). Unlike the traditional solution approaches in which we need to identify the efficient DMUs by the SBM model of Tone (2001) [20] before applying the super SBM model of Tone (2002) [21] for the DMUs to achieve their super-efficiency scores, our integration can obtain the efficiency scores of the inefficient DMUs and the super-efficiency scores of the efficient DMUs by solving simultaneously these two models by an one-stage approach. Therefore, it may save computational time for large-scale practical applications. Due to the non-linearity in the objective function of this integrated model, we develop a linearisation technique to deal with the non-linear model. The numerical experiments, carried out on several examples in the literature and a case study, have demonstrated the accuracy and the computational time effectiveness of our proposed model as compared with the traditional solution approaches.

Citation

Tran, T. H., Mao, Y., Nathanail, P., Siebers, P., & Robinson, D. (2019). Integrating slacks-based measure of efficiency and super-efficiency in data envelopment analysis. Omega, 85, 156-165. https://doi.org/10.1016/j.omega.2018.06.008

• Journal Article Type: Article
• Acceptance Date: Jun 11, 2018
• Online Publication Date: Jun 15, 2018
• Publication Date: 2019-06
• Deposit Date: Jun 29, 2018
• Publicly Available Date: Dec 16, 2019
• Journal: Omega
• Print ISSN: 0305-0483
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 85
• Pages: 156-165
• DOI: https://doi.org/10.1016/j.omega.2018.06.008
• Keywords: Data envelopment analysis (DEA) ; Slacks-based measure ; Efficiency ; Super-efficiency ; One-stage approach ; Linearisation
• Public URL: https://nottingham-repository.worktribe.com/output/938794
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0305048317308472?via%3Dihub