This talk will discuss some recent findings on designing process flexibility in multi-period make-to-order production (MTO) systems. Traditionally, process flexibility has been studied in single-period systems, because one cannot compute the optimal multi-period policy due to the curse of dimensionality. To overcome this, we apply results from applied probability to propose a notion of “generalized chaining" in general asymmetric and unbalanced systems, which achieves performance that is asymptotically close to that of full flexibility. “Generalized chaining” includes the classical chaining structure from Jordan and Graves (1995) as a special case. Moreover, we provide an algorithm that produces a “generalized chaining” structure with only m+n arcs where m and n represent the number of plants and product types, respectively. We also show that the requirement of m+n arcs is tight, by explicitly constructing systems in which even the best flexibility structure with m+n-1 arcs cannot achieve the same asymptotic performance as full flexibility. Finally, using numerical simulation, we find that sparse structures designed using “generalized chaining” are very effective for small to medium size systems, even under non-asymptotic regimes.

This is joint work with Cong Shi from University of Michigan and Yehua Wei from Boston College.