Super efficiencies or super inefficiencies? Insights from a joint computation model for slacks-based measures in DEA

Chien-Ming Chen

European Journal of Operational Research, 2013, vol. 226, issue 2, 258-267

Abstract: The slacks-based measure (SBM) can incorporate input and output slacks that would otherwise be neglected in the classical DEA model. In parallel, the super-efficiency model for SBM (S-SBM) has been developed for the purpose of ranking SBM efficient decision-making units (DMUs). When implementing SBM in conjunction with S-SBM, however, several issues can arise. First, unlike the standard super-efficiency model, S-SBM can only solve for super-efficiency scores but not SBM scores. Second, the S-SBM model may result in weakly efficient reference points. Third, the S-SBM and SBM scores for certain DMUs may be discontinuous with a perturbation to their inputs and outputs, making it hard to interpret and justify the scores in applications and the efficiency scores may be sensitive to small changes/errors in data. Due to this discontinuity, the S-SBM model may overestimate the super-efficiency score. This paper extends the existing SBM approaches and develops a joint model (J-SBM) that addresses the above issues; namely, the J-SBM model can (1) simultaneously compute SBM scores for inefficient DMUs and super-efficiency for efficient DMUs, (2) guarantee the reference points generated by the joint model are Pareto-efficient, and (3) the J-SBM scores of a firm are continuous in the input and output space. Interestingly, the radial DEA efficiency and super-efficiency scores for a DMU are continuous in the input–output space. The J-SBM model combines the merits of the radial and SBM models (i.e., continuity and Pareto-efficiency).

Keywords: Data envelopment analysis; Slacks-based measure; Super-efficiency; Pareto-efficiency (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:226:y:2013:i:2:p:258-267

DOI: 10.1016/j.ejor.2012.10.031

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