Process flexibility : a distribution-free approach to long chain resilience

Abstract

Process flexibility has been a well-established supply chain strategy in both theory and practice for managing demand uncertainty. This study extends its application to mitigating supply disruptions by analyzing a long chain system. Specifically, we investigate the effectiveness of long chains in the face of random supply disruptions and demand uncertainty. We derive a closed-form, tight bound on the expected sales ratio of a long chain relative to full flexibility under random disruptions, thus providing a service-level guarantee. Our analysis shows that, when designed capacity equals expected demand, the fraction of benefits a long chain achieves relative to full flexibility increases with disruption probability; however, it decreases when capacity is instead expanded to match expected demand under disruptions. The long chain also demonstrates superior resilience, absorbing a significant portion of unexpected disruptions because of its sparsity. To generalize our findings, we introduce a moment decomposition approach that readily adapts to general piecewise polynomial performance metrics, maintaining tractability through a semidefinite program. This approach extends the traditional type II service metric (expected sales) to include a type I metric (probability of meeting full demand) and supports more flexible capacity–demand relationships. Applying this approach to the capacity configuration problem, we find that, without disruption, a long chain achieves target service levels with capacity comparable to full flexibility even with limited demand information. In contrast, disruptions significantly raise capacity requirements although long chains maintain a substantial advantage over dedicated systems. Our results highlight the resilience of long chains and the critical need to adapt capacity configuration decisions to supply disruption risks.