Stochastic Two-stage Network-structures Under P-models: A DEA Based Approach

Regular network data envelopment analysis (NDEA) models for calculating the efficiency of decisionmaking units (DMUs) with two-stage construction requires the data set to be deterministic. In the real world, however, there are many observations that have stochastic behavior. This paper proposes a network DEA with two-stage structures models by the attention to stochastic data. The stochastic two-stage network DEA models are formulated based on the P-models of chance constrained programming and leader-follower concepts. On the basis of probability distribution properties and by the assumption of stochastic single factor components of data set, the probabilistic form of models is transformed to the equivalent deterministic linear programming model. In addition, the relationship between each stage as leader or follower is discussed. A real case on 16 commercial banks in China has been clarified to confirm the applicability of the proposed approaches under different levels.