The lower limit of interval efficiency in Data Envelopment Analysis

In data envelopment analysis technique, the relative efficiency of the homogenous decision making units is calculated. These calculations are done based on the classical model of linear programming such as CCR,BCC,…. Because of maximizing the weighted sum of outputs to that in inputs of one unit under certain conditions, the obtained efficiency in all of these models is the upper limit of exact relative efficiency. In other words, the efficiency is calculated from the optimistic viewpoint. To calculated the lower limit of efficiency, i.e. the efficiency obtained from a pessimistic viewpoint forcertain weights, the existing models cannot calculate the exact lower limit and in some cases, there exist some models that show an incorrect lower limit. Through the model introduced in the present study, we can calculate the exact lower limit of the interval efficiency. The designed model can be obtained by minimizing the ratio of weighted sum of outputs to that of inputs for every unit under certain conditions. The exact lower limit can be calculated in all states through our adopted model.

Keywords:

Data envelopment analysis , Interval efficiency , Interval inefficiency , lower limit , upper limit