Supply chain aperiodicity, bullwhip and stability analysis with Jury's inners

Jury presents a novel method for the analysis of dynamical systems based on matrices of the coefficients of the systems transfer function and its ‘inners’. Here, we exploit his procedure for an analysis of a supply chain replenishment or ordering decision known as the order-up-to policy, We study the discrete-time case and generalize the classical order-up-to policy by the addition of two independent proportional controllers in the policy's feedback loops, The addition of the proportional controllers is well known to allow the order-up-to policy to eliminate the bullwhip problem and we quantify this herein using Jury's inners approach.