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

The general problem of buffers sizing for mean work in process/inventory minimization in a particular class of single part unreliable manufacturing flow lines, subjected to a constant rate of demand for finished parts, is analyzed. Two variants of the problem are considered: buffers sizing for average work in process minimization when there is a fixed requirement on parts availability in the buffer next to last; minimization of an aggregate measure of average work in process and demand backlog when the complete flow line is considered. A fluid model of part production is employed. The production control policies of interest are suboptimal, strictly decentralized, and are unambiguously parameterized by the size of buffer levels. Optimization of policy parameters is based on the analysis of the structural properties of an associated dynamic program. The latter is built around an approximate, flow line decomposition based, buffer levels dependent theoretical expression of the policy performance measure. The nature of the related flow line approximations is discussed and numerical results of the dynamic programming procedure are reported. Scalability of the computations is demonstrated. The numerical results suggest that when parameters are optimal, both a form of flow line balancing and a just in time internal production principle, are in place.