Stochastic optimal control of a hybrid manufacturing system model

We consider a single-stage manufacturing system where the physical state of each job is characterized by time-driven dynamics and its temporal state by event-driven dynamics. Extending an earlier analysis of a deterministic model for this system, we study a stochastic model where there are controllable parameters that affect the service processing speed. When job arrivals are represented through a Poisson process, the service time required to attain a desired physical state is exponentially distributed (dependent on a controllable processing speed), and the cost associated with inventory level is non-decreasing convex, we show that there exists a threshold policy on the inventory level for selecting the optimal process speed. For a discrete-time model with geometrically distributed arrivals and deterministic service times, similar results are derived.