An alternative MILP-DEA model to choose efficient unit without explicit inputs

Data envelopment analysis is a nonparametric method to empirically measure the relative efficiency of a set of congeneric decision making units (DMUs) with multiple inputs and outputs. In the previous researches, diverse methods have been proposed to enhance the discrimination of efficient DMUs, which can also be viewed as an important issue of multi-criteria decision making. In 2013, based upon the concept of common set of weights, Toloo proposed a mixed integer linear programming approach to choosing efficient units without explicit inputs. The model hopes to directly reduce the number of efficient DMUs to be only one. However, the model proposed by Toloo does not guarantee that the maximum deviation of all DMUs from the efficient frontier is minimized. In other words, Toloo’s model finds an efficient frontier on which there is only one efficient DMU at a price that the maximum of the deviations of all DMUs from the frontier might not be minimized. To remedy such situation, we propose an alternative approach which guarantees that the maximum of the deviations of all DMUs from the frontier is minimized and under such precondition the number of the efficient DMUs is minimized.