Two-stage additive network DEA: Duality, frontier projection and divisional efficiency

Abstract

In the previous literature, it is demonstrated that the dual equivalence of multiplier and envelopment models that exists in standard data envelopment analysis (DEA) is not necessarily true for network DEA to derive frontier projection and divisional efficiency. Multiplier network model is often used for computing the divisional efficiency while envelopment network model is often used for identifying the frontier projection for inefficient decision making units (DMUs). In this paper, we show that the duality of standard DEA can be extended to two-stage additive network DEA. We propose an improved golden section method to solve parametric linear multiplier network model. Based on the primal-dual correspondence of parametric linear programming, we subsequently develop envelopment network model in parametric linear form to determine frontier projection and to find divisional efficiency as well.