Supply-Chain Shocks as Structured Dynamical Systems: A Hamiltonian-Poisson Perspective on Inventory, Ordering, and Amplification

Supply-chain shocks are commonly analyzed using stochastic simulation, control theory, or equilibrium-based optimization. While these approaches are effective for policy design, they often obscure the structural mechanisms through which disruptions propagate, amplify, and persist across supply networks. This paper proposes a complementary framework in which supply-chain shocks are modeled as dynamical events governed by a Hamiltonian system on a Poisson manifold. Inventory deviations and ordering pressure are treated as conjugate economic variables evolving under conservation laws imposed by material balance and capacity constraints. The Hamiltonian is constructed directly from standard accounting cost components, including holding costs, stockout penalties, and lead-time-induced adjustment costs. Exogenous disruptions enter as ports, while smoothing, perishability, and managerial intervention introduce controlled dissipation. A three-tier numerical example demonstrates how a localized demand shock generates upstream amplification and prolonged recovery as a consequence of system geometry rather than forecasting error alone. The framework provides a structural explanation for the bullwhip effect and offers a principled basis for designing shock-resilient supply chains through energy shaping rather than ad hoc stabilization.