A Russell-based model for estimating overall and divisional efficiency in two-stage production systems with sets of convex hulls in intermediate products

Data Envelopment Analysis (DEA) research works have been recently examining production systems with a two-stage network structure. These studies consider system operations that are performed in two stages where intermediate products play dual roles: they are the outputs of the previous stage and inputs to the next stage. This dual role is incompatible with Pareto-Koopmans dominance in activity analysis. Also, disregarding intermediate products in assessing performance of two-stage systems compromises the models. The present work introduces a new production possibility set for two-stage network production systems by considering a convex hull for intermediate products. In addition, new models are introduced for evaluating overall efficiency and divisional efficiency of production units from the Pareto-Koopmans efficiency perspective. The proposed models are developed based on an enhanced Russell graph model for efficiency evaluation of two-stage network production structures with convex hulls for intermediate products. Numerical examples are further provided for illustration purposes.