The elementary flux modes of a manufacturing system: a novel approach to explore the relationship of network structure and function

Elementary flux modes (EFMs) are a concept from Systems Biology, where they serve as an indicator of component relevance in metabolic networks. An elementary flux mode is a functionally relevant, non-decomposable path through a given network. In this paper, we apply elementary flux mode analysis to manufacturing systems, with the aim of using the number of EFMs as a predictor for resource significance in the manufacturing system. For this, we formulate a network representation of a manufacturing process, which allows us to define the manufacturing equivalent of a stoichiometric matrix to draw an analogy between metabolic and manufacturing systems. This, in turn, allows the computation of EFMs, which we conduct in a case-study for a real manufacturing system. We further show that the change of EFMs under resource breakdown is a good indicator of the average order lateness in the manufacturing system. In this way, EFMs provide insight into the relationship of network structure and function in manufacturing.