Reformulation of Network Data Envelopment Analysis models using a common modelling framework

Network Data Envelopment Analysis (network DEA) is an extension of the conventional Data Envelopment Analysis (DEA) developed to take into account the internal structure of the Decision Making Units (DMUs). In network DEA, the DMU is considered as a network of interconnected sub-processes, where the connections indicate the flow of the intermediate measures. In this paper, we reformulate some of the basic network DEA methodologies in a common modelling framework. We show that the leader-follower approach, the multiplicative and the additive decomposition methods as well as the recently introduced min-max method and the “weak-link” approach, can all be modelled in a multi-objective programming framework, differentiating only in the definition of the overall system efficiency and the solution procedure adopted. Such a common modelling framework makes the direct comparison of the different methodologies possible and enables us to spot and underline their similarities and dissimilarities effectively. We illustrate graphically how the aforementioned methodologies locate their optimal efficiency scores on the Pareto front in the objective functions space, with an example taken from the literature.