We consider a fluid model of an unreliable production line consisting of n machines and n fixed buffer sizes. These machines produce a single part with two different quality levels: conforming and non-conforming parts. The ratio of non-conforming parts to conforming ones is assumed to be a constant β, which may vary depending on the machine. The production line can contain inspection stations whose function is to reject the non-conforming parts from the system. It is assumed that the production line must meet a constant rate of demand for good parts.

Our research objective is to develop an approximate modeling framework and an optimization algorithm for unreliable transfer line inter machine buffer sizing, so as to minimize, under a constant demand for parts rate, the average long term combined storage and shortage costs, while accounting for parts quality and specifying the optimal location of inspection stations. Decomposition/aggregation methods developed in Sadr and Malhamé (2004) and their dynamic programming based optimization algorithm are adapted to the current model. In addition, numerical results based on the approximate theory, and those obtained from Monte Carlo simulation, are contrasted.