Directional closest-target based measures of effciency: Holder norms approach

Recently, an innovative single-stage approach was developed in [J. Aparicio, J. L. Ruiz, I. Sirvent, Closest targets and minimum distance to the Pareto-effcient frontier in DEA, Journal of Productivity Analysis 28 (2006) 209 { 218], to determine the closest Pareto-effcient targets for a given ineffcient decision making unit (DMU). The purpose of this paper is to perfect this approach via integrating it with the concepts of Holder norms and directional distance function. To this purpose, rst, we introduce a furthest-target based directional, named Linear FDHDF, Holder distance function. Then, we characterize the set of Pareto-effcient points of the production possibility set dominating directionally the assessed DMU. Finally, we develop a closest-target based directional, named Linear CDHDF, Holder distance function that, as well as providing an effciency index, determines the closest targets. Comparing to the earlier approach, our approach is more general and the decision maker's preference information can be appropriately incorporated into effciency assessment and target setting. Furthermore, it is more exible in computer programming.