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 that enhances responsiveness to demand uncertainty. In this study, we extend the scope of this strategy to supply disruption mitigation by analyzing a long chain system. Specifically, we investigate the effectiveness of long chains in the face of random supply disruption under ambiguous demand. Our study derives a closed-form, tight bound on the ratio of expected sales under supply disruption for the long chain relative to that of a fully flexible system. Our analysis provides a concrete analytical result demonstrating that the fraction of benefits a long chain can achieve relative to full flexibility increases in the disruption probability when supply designed capacity equals expected demand. Also, long chain demonstrates superior resilience by withstanding a non-negligible fraction of the supply disruption due to its relative sparse structure compared to a fully flexible system. To comprehensively handle supply disruption and demand ambiguity, we introduce a moment decomposition approach that easily adapts to general piecewise polynomial performance metrics, such as the type-I service level, which is a novel contribution in the existing literature. Our approach can also incorporate higher-moment information (such as skewness and kurtosis) on the random demand while maintaining tractability through a semidefinite program (SDP). To further demonstrate the strength of this approach, we apply it to study the capacity configuration problem. Our study reveals that, in the absence of supply disruption, attaining a specific service level requires a capacity level close to that of a fully flexible system, even when the demand distribution is only partially characterized. In contrast, a notable increase in capacity is required under supply disruption. Yet, long chain outperforms dedicated system significantly in capacity requirement. Our findings underscore the remarkable resilience demonstrated by long chains and the importance of adapting capacity configuration decisions to supply disruption.