A maximum slacks-based measure of efficiency for closed series production systems

The conventional slacks-based measure (SBM) model measures efficiency based on the target point that is farthest to the decision making unit (DMU) being assessed. The result is that the efficiencies for inefficient DMUs are relatively low, and more effort is required for the DMUs to become efficient. In this research, a model is developed to calculate the SBM efficiency based on the target that is closest to the assessed DMU for a closed series production system, where the outputs of a division are the only inputs for the succeeding division. The efficiency measured from this model satisfies the monotonicity property. It is greater than that measured from the radial model. Since the target is closest to the assessed DMU, less effort is required for inefficient DMUs to become efficient. Furthermore, the efficiency of the system can be decomposed into the product of the efficiencies of the component divisions. The divisions that cause unsatisfactory system performance can thus be detected. Making improvements to these divisions can effectively increase the efficiency of the system. A case of non-life insurance companies in Taiwan with a two-division series structure is studied for illustrative purposes.