Chen (2013) extended the exiting SBM approaches and developed a joint model (J-SBM) that can (1) simultaneously compute SBM scores for inefficient DMUs and super-efficiency for efficient DMUs, (2) guarantee the reference points generated by the J-SBM are Pareto-efficient, and (3) the J-SBM scores of a DMU are continuous in the input and output space. In this note, we provide a counter example which shows that the reference point generated by the J-SBM might not be Paretoefficient, and the current study has also revised the model (8) proposed by Chen (2013).

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