Stochastic Stability of a Prioritized Control Policy for Scheduling Failure-Prone Machines with Setups

This paper deals with our previously introduced Hedging Zone Policy (HZP), which is a simple-to-implement, well-behaved heuristic for scheduling machine setup changes in real time. In the HZP, a pair of parameters for each product type defines a set in surplus space called the hedging zone, and a different changeover rule is implemented depending on the location of the production surplus state with respect to this zone. When the surplus state lies outside of the hedging zone, a fixed rank ordering or prioritization is used for deciding which item to produce next. When the surplus state is inside the hedging zone, the policy may either produce the current part type at its demand rate until more demand builds up, or change over to the item that is furthest behind (in an appropriate sense). After providing some background and overview of the HZP, we present new results concerning its stability properties. In particular, we show that if a deterministic counterpart of the stochastic system satisfies an easy-to-evaluate condition, the stochastic system with exponentially distributed failure and repair times is rate stable.