cost efficiency estimation in network dea in the case of varying input prices

Data envelopment analysis (dea) evaluates the cost efficiency of systems with multiple inputs and multiple outputs in two scenarios, one where the input prices are the same in all decision-making units (dmus) (competitive space), and the other where the input prices differ from one dmu to another (non-competitive space). in many situations, the dmus could have a multi-stage network structure with intermediate measures. although a model has been presented for calculating the network cost efficiency in a competitive space in such cases, no method has been proposed so far to calculate the cost efficiency of such networks in a non-competitive space. the present article focuses on the concept of cost efficiency in dea for dmus with network structures and varying input prices. to this end, a cost-based production possibility set (pps) is first introduced for the network systems and their sub-systems, and after calculating the network cost efficiency, it is decomposed into efficiencies such as technical, price, and allocative efficiencies, and the reasons behind the occurrence of extra costs due to various types of inefficiency are explained.