The directional distance function and measurement of super-efficiency: an application to airlines data

In a recent paper published in this Journal, Lovell and Rouse (LR) proposed a modification of the standard data envelopment analysis (DEA) model that overcomes the infeasibility problem often encountered in computing super–efficiency. In the LR procedure one appropriately scales up the observed input vector (scale down the output vector) of the relevant super–efficient firm thereby usually creating its inefficient surrogate. By contrast, Chen suggested a different procedure that replaces input–output bundles that are found to be inefficient in standard DEA by their efficient projections. An alternative procedure proposed in this paper uses the directional distance function and the resulting Nerlove–Luenberger measure of super–efficiency. The fact that the directional distance function combines, by definition, features of both an input–oriented and an output–oriented model, generally leads to a complete ranking of the observations and is easily interpreted. A dataset on international airlines is utilized in an illustrative empirical application.