In most applications of DEA with internal structures in the literature, the models are designed to evaluate the performance of homogeneous Decision Making Units (DMUs). In many instances, however, DMUs operating in a similar technological environment may have different internal structures. In...

It is well known that the discrimination power of data envelopment analysis (DEA) models will be much weakened if too many input or output indicators are used. It is a dilemma if decision makers wish to select comprehensive indicators, which often have some hierarchical structures, to present a...

We present a sufficient and necessary condition for the convergence of stochastic approximation algorithms, which were proposed 50 years ago, have been widely applied to various areas and intensively investigated in theory. In the literature, only various sufficient conditions are known. The...