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

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).