Process Flexibility: A Distribution-Free Approach to Long Chain Resilience

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.

Funding: The research of L. Chen was supported by the Emerging Scholar Research Fellowships, University of Sydney Business School. The research of M. Chou was supported by the National Natural Science Foundation of China [Grant 72374036]. The research of Q. Sun was supported by Hong Kong Research Grants Council [Grant 25509623].

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2023.0430.