Industrial organisations must supply a variety of products and services, meet the needs of fragmented customer expectations, and cope with the consequences of the globalisation of world markets, all of which are producing significant levels of complexity. This study develops a new quantitative measurement of complexity for supply network based on Network Analysis, which is often used to study natural ecosystems, focussing in particular on the concept of entropy of information. The research reports advances in both theory on Supply Network Analysis problem and on its application to industrial contexts. Eight indexes based on entropy are presented. These measures provide a meaningful analysis of the level of complexity in the whole supply network mapping the exchanges of goods between the different actors in the network. The impact of possible modifications of the structure can simply be evaluated using these tools, providing a simple evaluation of the different scenarios. The proposed method takes an holistic point of view to tackle the problem of supply network optimisation. A real world application of the developed new methodology is presented.