Dynamics, uncertainty and control in circular supply chains

This work introduces a prototype dynamic model of a circular supply chain based on the state-task network paradigm, and a framework for characterizing the effect of uncertainty on the system dynamics. Processing tasks are represented using transfer functions coupled with saturation functions to capture physical limitations such as inventory depletion. Physically-motivated uncertain parameters are used in the aforementioned transfer functions. Closed-form expressions are derived for the mean and variance of inventories of material in different states, showing that the variance of inventory increases over time. The results are validated via extensive simulations, complemented by an example implementation of model predictive control for tracking material inventory targets and reducing variance.