Decomposition/aggregation based dynamic programming optimization of partially homogeneous unreliable transfer lines

The problem of optimally controlling production in a single part unreliable, manufacturing flow line, subjected to a constant rate of demand for parts, while minimizing a given combined measure of storage and production backlog costs, is considered. A suboptimal class of decentralized hedging policies parameterized by a set of critical inventory levels, one for each machine in the transfer line, is considered. Thus, each machine strives to achieve as quickly as possible a given critical level of processed parts in the associated storage bin, which, once reached, will attempt to maintain it by producing exactly at the current rate of demand for parts until failure or starvation occurs. Once starvation ceases or the machine is repaired, it will resume the same production strategy. Our objective is to optimize the choice of the processed parts critical levels. Finally, under specific structural assumptions, qualitative properties of optimal critical levels profile for the homogeneous continuous states, but finite transfer line are derived. From these properties, homogeneous infinite transfer line behavior is inferred. Results of numerical experiments are reported.