Conflict intermediate measures in DEA models, especially in constraint and open the black box, is the main difference between traditional DEA and network DEA models. Furthermore, from the application's perspective, intermediate measures aren’t deterministic. So, for measuring the efficiency more precisely, they can be considered as imprecise data. The aim of this paper is introducing a stochastic relational model for measuring overall efficiency that deals with intermediate and outputs as stochastic data. The proposed model is applied for portfolio optimization. An actual data set of 27 Iranian stock industries is applied as numerical example. The result shows that SR-NDEA has better discriminant power than R-NDEA model. پرونده مقاله

Data Envelopment Analysis (DEA) is a mathematical programming for evaluating efficiency of a set of Decision Making Units (DMUs). One of the problems in DEA, is distinguishing outlier DMUs which have a different behavior in contrast to the general prevailing behavior of the population. The important issue is that the outlier DMUs, which are caused by the incorrect way of collecting data or other unknown factors which can be social, political and etc. , can affect the efficiency of other DMUs. Thus, recognizing and excluding them from the population or reducing their effect and proportioning their status with the population can influence the improvement of total efficiency of population. Therefore, as a result, it prevented the incorrect deduction about the population. In this paper, it is assumed that the efficiency of population must have a unimodal symmetric distribution, and a method based on the skewness of efficiency and inefficiency presented. The important contribution of this method is that it can recognize all the outlier DMUs, in different layers. پرونده مقاله