Production control in a two-stage system

Consider a two-stage production system with a significant setup time at the upstream station. A threshold production control rule is used at the upstream station, with an objective of minimizing the work-in-process level while maintaining a required busy probability at the downstream station. To characterize the system performance under this rule, a Markov model is constructed and from which the analytical performance measures are obtained. The objective function for the decision rule is found to have good analytical properties and numerical optimization can thus be performed using a simple algorithm.