Data envelopment analysis-like models for the efficiency evaluation of hierarchically structured units

The knowledge of the internal structure of decision making units (DMUs) gives further insights with respect to the “black box” perspective when considering data envelopment analysis models. We present one-level and two-level hierarchical structures of the DMUs under evaluation. Each unit is composed of consecutive stages of parallel subunits all with constant returns to scale. In particular, the maximization of the relative efficiency of a DMU is studied. For the two-stage situation, different degrees of coordination among the subunits of the hierarchical levels are discussed. When some form of coordination has to be guaranteed, we introduce balancing constraints and we compare two different models. In both cases, we prove that the maximum relative efficiency of a DMU is assessed by comparing it with all the existing subunits.