Closest targets in the slacks-based measure of efficiency for production units with multi-period data

The efficiency calculated from the conventional slacks-based measure (SBM) model is the minimum in terms of efficiency scores, and the corresponding target point requires more effort for an inefficient decision making unit (DMU) to become efficient. To find the closest target point to the assessed DMU, several models have been proposed via calculating the maximum efficiency. This paper proposes a set of models to measure the maximum SBM efficiency for DMUs with multi-period data. It is found that, when the non-Archimedean number is not in effective in claculating the radial efficiency, the maximum SBM efficiency is greater than or equal to the radial efficiency. The corresponding target point is easier for an inefficient DMU to reach. This efficiency is more reliable than radial efficiencies because the latter may be affected by the non-Archimedean number. Furthermore, the SBM efficiency can be decomposed into the product of the input and output efficiencies. Under the different-multiplier models, the DMU efficiency can also be decomposed into a weighted average of the individual year efficiencies. The factor and year that cause the unsatisfactory performance can thus be detected. A case of Taiwanese commercial banks is used as an illustration.