Direct targeting of efficient DMUs for benchmarking

We propose a two-stage procedure for finding realistic benchmarks for nonparametric efficiency analysis. First, the efficient units are identified by a free disposal hull approach. These benchmarks are directly targeted by directional distance functions and the extent of inefficiency is measured along the direction towards an existing efficient unit. Two variants for finding the closest or the farthest benchmark are proposed. With this approach there is no need to use linear combinations of efficient units as benchmarks which may not be achievable in reality and also no need to accept slacks which are not reflected by the efficiency measure.