Bifurcation analysis and synchronisation issues in a three-echelon supply chain

Abstract

In today's global marketplace, supply chains are dynamic and volatile. This dynamic and volatile nature produces various types of uncertainties along the supply chain, for example, demand uncertainty, supply uncertainty, delivery uncertainty and forecasting uncertainty. These uncertainties make supply chains complex and nonlinear systems as they propagate both upstream and downstream. This work investigates the dynamic behaviour of a three-echelon supply chain. Modelling of this structure is carried out to display its nonlinear dynamic behaviour. It is shown that the dynamics (stability) of the supply chain are very sensitive to external uncertainties. Specifically, a supply chain subjected to these uncertainties can exhibit strange and undesired states such as saturation and chaos. An adaptive algorithm for the automatic cancellation of these strange dynamics due to uncertainties is developed by re-adjusting the internal parameters of the supply chain to achieve its synchronisation. A bifurcation analysis is carried out. This analysis is essential and useful for strategic decision-makers as it allows both the visualisation and control of the states/dynamics of the entire supply chain. The internal parameters of the supply chain are used as control parameters, and various remarkable states are discovered towards the achievement of synchronisation.