Dominance at the divisional efficiencies level in network DEA: the case of two-stage processes

We introduce in this paper the notion of dominance in the divisional efficiencies space in Network Data Envelopment Analysis. We argue that, irrespectively of the method used, a successful efficiency evaluation protocol should satisfy the dominance property at the divisional efficiencies level. In particular, there should not exist any other feasible solution in the assessment model, suboptimal in terms of the optimality criterion, that provides stage efficiencies scores at least as high as the assessed ones and higher for at least one stage. Then, we investigate the dominance property in different methods for two-stage series processes of various complexity. We prove that the additive efficiency decomposition method and the relational model provide non-dominated divisional efficiencies when they are applied to elementary two-stage processes, where nothing but the external inputs to the first stage enters the system and nothing but the external outputs of the second stage leaves the system. For more complex two-stage structures, however, we provide examples showing that these models do not comply with the dominance requirement at the divisional efficiencies level and lead to controversial results. Finally, we revisit some characteristic NDEA methods for which dominance is an inherent property.