Empirical evidence created a commonly accepted understanding that synchronisation and stability of material flows impact its productivity. This crucial link between synchronous and stable material flows by time and quantity to create a supply chain with the highest throughput rates is at the heart of lean thinking. Although this supply chain triangle has generally been acknowledged over many years, it is necessary to reach a finer understanding of these dynamics. Therefore, we will develop and study supply chains with the help of fluid dynamics. A multistage, continuous material flow is modelled through a conservation law for material density. Unlike similar approaches, our model is not based on some quasi steady-state assumptions about the stochastic behaviour of the involved supply chain but rather on a simple deterministic rule for material flow density. These models allow us to take into account the nonlinear, dynamical interactions of different supply chain echelons and to test synchronised and stable flow with respect to its potential impacts. Numerical simulations verify that the model is able to simulate transient supply chain phenomena. Moreover, a quantification method relating to the fundamental link between synchronisation, stability, and productivity of supply chains has been found. 1. Introduction Lean thinking under a manufacturing perspective has been well described in the literature over many years. Gradually the lean principles spread from the shop floor to the entire company and further on to the whole supply chain [1, 2]. A lean supply chain enables high productivity by synchronised and stable material flows across all partners [3]. Lean thinking created a commonly accepted understanding that synchronisation (e.g., just-in-time supply) and stability (e.g., levelled production) of material flows impact the effectiveness of supply chains. Although this link between synchronisation, stability, and productivity of supply chains is generally acknowledged, it is necessary to reach a finer understanding of these dynamics. The supply chain triangle provides an explanation for this transient and nonequilibrium behaviour experienced within supply chains. The specific contribution of this paper is to investigate the supply chain triangle with the help of dynamic modelling to provide a framework, or understanding, from which a firm can assess its inherent options for improving supply chains. In this paper concepts from fluid dynamics have been applied in discovering and explaining dynamical phenomena in supply chains. The mathematical tools we
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