Validating Worst-Case System Performance Under Multi-State System Disruptions: Evidence from Supply Chain Networks

Abstract Reliable performance of large-scale engineered systems is difficult to guarantee when components experience gradual rather than complete failures. Traditional reliability approaches based on binary operational states cannot formally validate performance under such graded disruptions. This study develops an optimization-based framework for validating worst-case system performance under multi-state disruptions with linear or exactly linearizable performance measures, polyhedral adaptive-response structures, and continuous polyhedral or discrete combinatorial disruption sets. The framework models adaptive system responses, such as rerouting and resource reallocation, through a nested optimization that captures the interplay between failures and operational decisions. A dual reformulation combined with the Reformulation–Linearization Technique transforms the resulting nonconvex validation problem into a tractable linear relaxation, providing provable upper bounds on worst-case performance. The methodology is applied to multi-echelon supply chain networks to examine performance degradation under continuous, bounded, and combinatorial disruption scenarios. Numerical analyses demonstrate that the framework efficiently identifies critical vulnerabilities, yields tight performance bounds for the tested instances where the true worst-case values can be certified, and provides computationally tractable, provable upper bounds across all tested instances. The findings extend reliability validation beyond binary failure models, offering a rigorous foundation for resilience assessment in complex service networks.