Production-Inventory System Controller Design and Supply Chain Dynamics

This paper deals with the modelling and control of aggregated production-inventory systems as described by differential equations. Hitherto, research in this area has been characterised by the approximation of production delays, by first order lags, rather than more realistic pure delays. We demonstrate the substantial qualitative differences between these two approaches and thus generate the motivation for the rest of the paper, which tackles pure delay systems. The application of some relatively new design methodologies for delay systems yields four design choices, which are tested for their performance over a range of criteria including stability robustness. The investigation is then extended to the model of a supply chain comprising many such production-inventory systems. The mechanism by which disturbances can be transmitted along the supply chain causing disruption and incurring costs to other supply chain echelons is elucidated. An heuristic feedback policy designed to adaptively tune the individual system designs in response to such disturbances is presented.