Production scale-based two-stage network data envelopment analysis

We develop a new network data envelopment analysis (DEA) approach for two-stage network systems considering a match between the production scale of the substages and the intermediate measure levels. Several explicit production axioms are introduced to build a production possibility set. New models are developed based on the production possibility set and a frontier projection procedure with the production scale matching process. Unlike the existing approach which assumes the intermediate measures are free-setting decision variables, the new envelopment network DEA models project the intermediate measures of a unit using the radial projection technique. Correspondingly, the resulting multiplier network DEA models allow for weight flexibility on the intermediate measures while holding a total value flow equivalence between a unit's two stages. We show that our approach does not suffer the known network DEA pitfalls. It identifies the overall efficiency, divisional efficiencies, and frontier projection using either an envelopment or a multiplier network DEA model, i.e., the primal-dual correspondence holds in our approach. Our approach also avoids uncertainties in determining divisional efficiencies by generating a unique pair of divisional efficiencies for each unit. Additionally, the adoption of the production scale matching process explains clearly the frontier projection procedure from the practical point of view. The proposed approach is illustrated with a numerical example and compared with the existing approaches with a case study of commercial bank branches.