Process Flexibility for Multi-Period Production Systems

We develop a theory for the design of process flexibility in a multi-period make-to-order production system. We propose and formalize a notion of "effective chaining" termed the Generalized Chaining Gap (GCG), which can be viewed as a natural extension of classical chaining structure from the process flexibility literature. Using the GCG, we prove that in a general system with high capacity utilization, one only needs a sparse flexibility structure with m plus n arcs to achieve similar performance as full flexibility, where m and n are equal to the number of plants and products in the system, respectively. The proof provides a simple and efficient algorithm for finding such sparse structures. Also, we show that the requirement of m plus n arcs is tight, by explicitly constructing systems in which even the best flexibility structure with m plus n minus 1 arcs cannot achieve the same asymptotic performance as full flexibility. The goal of this paper is to make progress towards the better understanding of the key design principles of process flexibility structures in a multi-period environment