Pareto–Koopmans efficiency and network DEA

• Network DEA models generalize standard DEA models.
• We propose a two-phase network DEA approach from a Pareto–Koopmans perspective.
• The approach can provide information on overall efficiency status and divisional efficiency.

Standard or black-box data envelopment analysis (DEA) evaluates the efficiency of the transformation of a DMU׳s exogenous inputs into its final outputs by ignoring what is going on in its divisions (sub-DMUs). To cope with this problem, network DEA (NDEA), which can provide adequate detail to management, has been developed and applied empirically. However, we show that some of the commonly used NDEA methods are inconsistent with the notion of Pareto–Koopmans efficiency. Since the original development of DEA, Pareto–Koopmans efficiency is a fundamental property used in DEA. From a Pareto–Koopmans efficiency perspective, therefore, we propose a two-phase NDEA approach that can provide information on both each DMU׳s overall (system) efficiency status and its divisions׳ efficiency scores. The proposed novel approach is developed based on the enhanced Russell graph model or equivalently the slacks-based model. We also propose several theorems and illustrate the proposed approach using two artificial numerical examples and a real-world data set.