Modeling a shared hierarchical structure in data envelopment analysis: An application to bank branches

The paper addresses the question of ensuring comparability in data envelopment analysis (DEA) in situations when units are organized in an ordered hierarchy with functions shared at different levels. In such a case, although units may have identical input-output sets that they put to use in similar production, they are not an ideally homogeneous group and their comparability in a benchmarking context is limited. The paper proposes to control explicitly the degree of comparability by a fairly flexible comparability constraint in order to obtain more informative technical efficiency scores and economically feasible targets. Furthermore, the paper develops a methodology to identify closest targets under the comparability constraint that are more attainable for inefficient units than traditional targets. These ideas are demonstrated in a case study located in the area of bank branch performance assessment from which the motivation of the paper sprouted. The case study shows for three hierarchical branch categories of a Slovak commercial bank that the comparability constraint renders closest targets more apposite, but they depend on how slacks are handled, i.e. whether they are summarized by a normalized sum or by means of a slacks-based measure.