A scheduling problem for a pull manufacturing system: how to modify the cμ-rule for finite buffer capacities

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 two 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. If buffer capacities are infinite, a dynamic version of the well known cμ rule solves the problem: the objective of this paper is to analyze how the cμ rule must be modified to deal with the finite buffer capacity case