A technique to develop simplified and linearised models of complex dynamic supply chain systems

• We propose a systematic method for the analysis of high-order nonlinear dynamic models.
• Nonlinear control theory is used to gain insights into system’s behaviour.
• More accurate simplified linear approximations can be found.
• These simplified models enhance the understanding of the system transient responses.
• This work is a precursor to robust analysis and design of system dynamics models.

There is a need to identify and categorise different types of nonlinearities that commonly appear in supply chain dynamics models, as well as establishing suitable methods for linearising and analysing each type of nonlinearity. In this paper simplification methods to reduce model complexity and to assist in gaining system dynamics insights are suggested. Hence, an outcome is the development of more accurate simplified linear representations of complex nonlinear supply chain models. We use the highly cited Forrester production-distribution model as a benchmark supply chain system to study nonlinear control structures and apply appropriate analytical control theory methods. We then compare performances of the linearised model with numerical solutions of the original nonlinear model and with other previous research on the same model. Findings suggest that more accurate linear approximations can be found. These simplified and linearised models enhance the understanding of the system dynamics and transient responses, especially for inventory and shipment responses. A systematic method is provided for the rigorous analysis and design of nonlinear supply chain dynamics models, especially when overly simplistic linear relationship assumptions are not possible or appropriate. This is a precursor to robust control system optimisation.