Some variants and extensions of dominance network analysis

Abstract The aim of this paper is to extend Dominance Network (DN) analysis, a methodology that evaluates the dominance relationships among a sample of homogeneous operating units (OUs) based on the inputs they consume and the outputs they produce. The relative efficiencies of the OUs are commonly assessed using Data Envelopment Analysis (DEA). DN complements DEA providing indicators to assess the performance of not only each OU individually but also the whole set of OUs. DN also allows visualisation of multidimensional datasets that in conventional DEA can only be done for low-dimensional datasets. The methodology builds a weighted directed acyclic network, the nodes of which are the observed OUs and the links represent all the dominance relationships among the OUs. The weight of these links measures the relative inefficiency among the linked OUs. Complex Network Analysis (CNA) techniques can be applied to this type of layered network. This provides many interesting measures and indexes to characterise the individual nodes as well as the whole sample. However, existing DN applications only involve the existing OUs and hence use a non-convex DEA technology. In this paper, an approach to overcome this limitation and use other DEA technologies is proposed. Also, as a secondary objective, how the use of different inefficiency metrics affects the results of the analysis is studied.