measuring the efficiency and returns to scale in the systems with parallel network structure

Network data envelopment analysis (dea) has attracted the interest of many researchers in the dea theory and applications. in this paper we consider one class of the simplest network dea models: parallel network dea models. we address some pitfalls existing in the proposed models for parallel systems. in fact, there exist some problems in decomposition the efficiency of the whole system into the sub-system efficiency because some inefficiency might be related to allocative inefficiency. furthermore, one of the most important concepts in the standard dea models with black box structure is that of returns to scale (rts). some scholars try to develop the concept of rts into the series network dea models. there are some issues in this development as the relationship between the rts status of the whole system and the sub-system is not determined correctly. this paper discusses some existing models and points out some issues. to solve the problem of the efficiency decomposition, we develop the approach at three levels aggregation: the process, the dmu (firm), and the industry. for each level, the efficiency is computed using the directional distance function, and the efficiency of each higher level is ecomposited into exhaustive and mutually exclusive components. regarding the relationship between the rts status of the whole system and its processes, we first reallocate the resources to the processes and align the rts of the whole system and its processes.