Integrating slacks-based measure of efficiency and super-efficiency in data envelopment analysis. (June 2019)

• Record Type: Journal Article
• Authors: Tran, Trung Hieu; Mao, Yong; Nathanail, Paul; Siebers, Peer-Olaf; Robinson, Darren
• Is Part Of: Omega. Volume 85(2019)
• Page Start: 156
• Page End: 165
• Publication Date: 2019-06
• Subjects: Data envelopment analysis (DEA) -- Slacks-based measure -- Efficiency -- Super-efficiency -- One-stage approach -- Linearisation; Management -- Periodicals; 658.4005
• DOI: 10.1016/j.omega.2018.06.008
• Languages: English
• ISSNs: 0305-0483

Abstract

Highlights: We build an integration of efficiency and super-efficiency slacks-based measures. We develop a linearisation technique to solve the integrated non-linear model. We use a novel scaling strategy to deal with negative and zero observed data. A case study is constructed to evaluate the model in practical applications. Several numerical experiments are carried out to test the accuracy of the model. Abstract: 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.