A scheduling problem for two competing queues with finite capacity and non-negligible setup times

We consider a setup scheduling problem for a manufacturing system with finite buffers. Some analytical results for the infinite capacity case are also included. The system comprises a non-perfect, reliable single machine processing two part types, modeled by means of a fluid approximation. The objective of the control is to minimize an index cost under steady and transient conditions. Dynamic programming is used to derive the structure of the optimal policy and some initial analytical results are given. A symmetry assumption on part types is considered to simplify the problem.