A scheduling problem for N competing queues with finite capacity

We consider a scheduling problem for a pull manufacturing system with constant demand rates. The system comprises a reliable single machine which can provide service to N different part types, with negligible set-up times and costs. Back-logged requests and finite goods incur a cost, linear in the backlog and inventory levels which must be minimized over an infinite time interval. While the solution for the infinite buffer case is well known, this paper explores the case of finite buffers. A symmetry assumption is considered and the optimal policy is analytically derived. An example is reported to illustrate the policy obtained. The analysis of the relation between cost and throughput optimization in the case of finite buffers is also included in the paper