Network activity analysis for arbitrary production structures and technologies: Generic approach with application to network DEA

Abstract

Today, production usually takes place in complex networks. An important question is how the efficiency of the whole network is related to that of its units. Respective research on this topic has been strongly growing over the past decades, as a rule using methods of data envelopment analysis that are known as “network DEA”. However, there is a lack of theoretical foundation that allows clear statements to be made for arbitrary network structures and general, possibly non-convex or even discrete production technologies. This paper develops an activity analytic approach for modelling such general production networks and measuring their efficiency. Based on work of Koopmans and embedding it into a broader framework the approach is generic as it requires rather weak premises with regard to production technology and allows the network to be simply composed from its units as subsystems. It is shown that the relationship between the efficiency of a network activity and that of the subsystems and units depends strongly on the extent of which the individual production units are free to choose their input and output quantities, i.e. whether the network is loose or tied. Especially in cases where flows of intermediate products are constrained (instead of freely disposable), the explicit modelling of their overproduction helps to analyse their influence on efficiency scores. It is furthermore shown that calculating an overall efficiency score for a decision-making unit as average of individual scores of network units is inappropriate in any case.