A theory of supply chains

This report presents a series of lecture notes dealing with the stability and optimization of autonomous supply chains. It begins with an introduction to the terminology and notation. General weak- stability results for autonomous, pull supply chains are then developed. Duality results for "push" supply chains are next presented. The report then examines the ability or inability of autonomous algorithms to return to a steady state, track a time- dependent target, and dissipate small perturbations. A family of strongly stable autonomous algorithms, including "just-in-time" operations, is developed. The procedure for estimating total cost with both autonomous and coordinated system-optimal operations is shown. The report concludes with a presentation of autonomous, strongly stable algorithms for non-linear, multi-commodity, multi-destination networks.