Theoretical Model-Based Cybertronics for Dynamic Supply Chain Mathematical Modeling: A Stability Analysis Approach

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Abstract
This research communication presents an analysis of dynamic supply chains (DSCs). The main goal of model-based cybertronics is to approximate, via a mathematical model from a dynamical system, the dynamics and behavior of dynamic supply chains. This considers that is at the operational level, where automation and control theory approaches take an insight —in this case, via Lyapunov stability—as a way to extend the use of mechatronic systems. Three case studies are presented: Firstly, the mathematical modeling and stability analysis of the ball-and-beam problem, as an approximation of a two echelon supply chain. Secondly, the mathematical modeling and stability analysis of a cold chain with temperature monitoring, and its relationship to inventory levels, are presented. From a theoretical perspective, applying model-based cybertronics in DSCs has direct practical implications: it improves operational control, enhances decision-making, and optimizes inventory management, particularly in cold chains. By treating high-volume supply chains as dynamical systems, managers can anticipate fluctuations and quantify efficiency. Finally, Lyapunov stability analysis ensures that models reliably reflect real-world behavior, enabling automation and predictable performance at an operational level in DSCs.

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