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

摘要

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 thenext 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. Thepresent 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.