Control and Optimisation of Supply Networks

In this paper we apply concepts from dynamics and control to study structural issues that arise in the management of highly distributed supply chains. The supply chain system is represented by a graph using variables that capture seven important aspects of the supply chain management problem: the topology, transportation (more generally rate of activity), shipping/receiving and market conditions, assembly/disassembly, storage of assets, signal processing (forecasting) and performance evaluation. We use the manufacture of silicon to motivate a model for supply chain analysis which can be represented as a large scale system of differential algebraic equations. We demonstrate existence, uniqueness and stability of solutions when the routing policies are monotone. These conditions are necessary and sufficient. We also develop optimality properties that arise directly from the system structure using a decentralized control policy. We finally connect the modeling approach with a previous study on centralized control of multi-echelon, supply chain system with batch processing units. In the centralized approach we develop optimisation based schedules for routing and flow control.