Stability of Prioritized Scheduling Policies in Manufacturing Systems With Setup Times

We study the dynamic scheduling of a multi-item machine with setup times and static priorities. We consider a class of base-stock policies for this system and seek sharp stability conditions that allow us to respect the item priorities over a large region of the decision space. We show that requiring the existence of a linear Lyapunov function that decreases between production runs reduces to an intuitive stability condition, which can nevertheless be too conservative for this policy class. We then sharpen this result by showing that, if the original condition is satisfied for the highest-priority N-1 part types, the system with N items is stable. Finally, we develop stability conditions based on affine Lyapunov functions.