Closest targets and minimum distance to the efficient frontier in DEA

In this paper we propose a general approach to find the closest targets for a given unit according to a previously specified criterion of similarity. The idea behind this approach is that inefficient units can more easily learn from those that are more similar and, in addition, closer targets may show for the inefficient units how to achieve the efficiency with less effort. Similarity can be interpreted as closeness between the inputs and outputs of the assessed unit and the proposed targets, and this closeness can be measured by using either different distance functions or different efficiency measures. Depending on how closeness is measured, we develop several mathematical programming problems that can be easily solved and guarantee to reach the closest projection point on the efficient frontier. This is one of the advantages of our procedure with respect to other existing approaches, in particular those based on algorithms that need to identify all the efficient facets of the frontier, which require a very intensive computational burden.