Optimization of a vendor managed inventory supply chain with guaranteed stability and robustness

In this work we address the steady state optimization of a supply chain model that belongs to the class of vendor managed inventory, automatic pipeline, inventory and order based production control systems (VMI-APIOBPCS). The supply chain is optimized with the so-called normal vector method, which has specifically been developed for the economic optimization of uncertain dynamical systems with constraints on dynamics. We demonstrate that the normal vector method provides robust optimal points of operation for a number of scenarios. Since the method strictly distinguishes economic optimality, which is treated as the optimization objective, from dynamical requirements, which are incorporate by appropriate constraints, it provides a measure for the cost of stability and robustness as a desired side-effect.