Ranking of efficient units on the basis of distance from virtual ideal and anti-ideal units

Data envelopment analysis (DEA) divides the units under evaluation into two groups: 1) the efficient units; 2) inefficient units. Inefficient units can be ranked in terms of effectiveness while efficient units, because of the same efficiency score being equal to one, have the same rank. Several methods have been proposed to rank efficient decision making units (DMUs). Each of these methods have certain weaknesses such as the infeasibility of the model, instability, the lack of non-extreme DMUs ranking, computational complexity, etc. In this paper, we present an alternative method that does not have the disadvantages of existing ranking techniques. The new approach is based on the evaluation of new DMUs corresponding to the efficient DMU. Also, some theorems are provided to show that the proposed model for ranking the DMUs is feasible and bounded. For this purpose, some examples are illustrated to show its difference with other methods.