Primal-dual correspondence and frontier projections in two-stage network DEA models

The standard data envelopment analysis (DEA) procedure involves solving a pair of two types of models, multiplier model and envelopment model, and one of the most interesting features of DEA is that these two types of models are equivalent due to duality in linear programming. However, while several prominent network DEA models have been proposed in the literature in multiplier and/or envelopment forms, it is still doubtful or unclear whether and how the same primal-dual correspondence can be retained between the two types of network DEA models as in the standard DEA. To address this issue, we develop an axiomatic derivation of some two-stage network DEA models in this paper focusing on the basic two-stage serial process structure. We define the production possibility set for the basic two-stage serial process based upon some reasonable axiomatic properties. Subsequently we develop envelopment network DEA models using different distance measures, which are then shown to result in well-known existing two-stage network DEA models in the multiplier form.