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, closesttargets and minimum distance to the pareto-ecient frontier in dea, journal of productivity analysis 28(2006) 209 { 218], to determine the closest pareto-ecient targets for a given inecient decision making unit(dmu). the purpose of this paper is to perfect this approach via integrating it with the concepts of holdernorms 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-ecient points ofthe production possibility set dominating directionally the assessed dmu. finally, we develop a closest-targetbased directional, named linear cdhdf, holder distance function that, as well as providing an eciencyindex, determines the closest targets. comparing to the earlier approach, our approach is more general andthe decision maker's preference information can be appropriately incorporated into eciency assessment andtarget setting. furthermore, it is more exible in computer programming.