Dynamical behaviors of a nonlinear production-inventory supply chain system

To analyze the dynamical behaviors of a supply chain under the influence of nonlinear restriction, a two-echelon production-inventory supply chain system was established, which consisted of one manufacturer and one retailer. The system includes three nonlinear restrictions: forbidden returning, finite supply service level, and maximum production capacity constraint, which make the model more realistic. The dynamical behaviors of the system were analyzed and shown by phase diagram. Then bifurcation map and the maximum Lyapunov Exponent were employed to explore the impact of some parameters on system dynamical behaviors. Through numerical simulation, the study demonstrates that nonlinear restrictions lead to the complex chaotic behaviors of supply chain; and production capacity and transportation lead-time have great influences on the dynamical behaviors of the system. Finally the paper offers some insights into more effective management of supply chain.