Evaluating two-stage systems with stochastic Data

Stochastic data envelopment analysis (SDEA) is suggested to measure the efficiency of decision making units (DMUs) with black box structure under uncertainty conditions. And also, Network data envelopment analysis (NDEA) is proposed to calculate the efficiency of DMUs with network structures under certainty conditions. In many problems of the real world, DMUs have network structures and information of data is imprecise. Hence, in this paper, we combine SDEA and NDEA and introduce a model that measures the stochastic efficiency of two-stage systems in presenceof random data under the variable return to scale (VRS) assumption. Then a deterministic equivalent of this model is obtained. Finally, the real data of Taiwanese non-life insurance companies is illustrated to explain the proposed model.