Dynamical Analysis and Sliding Mode Controller for the New 4D Chaotic Supply Chain Model Based on the Product Received by the Customer

Supply chains comprise various interconnected components like suppliers, manufacturers, distributors, retailers, and customers, each with unique variables and interactions. Managing dynamic supply chains is highly challenging, particularly when considering various sources of risk factors. This paper extensively explores dynamical analysis and multistability analysis to understand nonlinear behaviors and pinpoint potential risks within supply chains. Different phase portraits are used to demonstrate the impact of various factors such as transportation risk, quality risk, distortion, contingency reserves, and safety stock on both customers and retailers. We introduced a sliding mode control method that computes the sliding surface and its derivative by considering the error and its derivative. The equivalent control law based on the sliding surface and its derivative is derived and validated for control purposes. Our results show that the controller SMC can significantly enhance supply chain stability and efficiency. This research provides a robust framework for understanding complex supply chain dynamics and offers practical solutions to enhance supply chain resilience and flexibility.