DIRECTIONAL CLOSEST-TARGET BASED MEASURES OF EFFICIENCY: 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-efficient frontier in DEA, Journal of Productivity Analysis 28 (2006) 209 – 218], to determine the closest Pareto-efficient targets for a given inefficient 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, first, we introduce a furthest-target based directional, named Linear FDHDF, Holder distance function. Then, we characterize the set of Pareto-efficient 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 efficiency 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 efficiency assessment and target setting. Furthermore, it is more flexible in computer programming.