Semigroup-theoretic analysis of supply-chain disruptions and resilience.

Abstract

This paper develops a rigorous framework using finite transformation semigroups to model supply-chain state evolution under cascading disruptions and resilience interventions. Disruptions and interventions are represented as non-invertible transformations on finite configuration spaces, generating a semigroup whose structure encodes collapse conditions, equilibria, minimal collapse-inducing sets, and redundancy. We establish explicit semigroup-theoretic criteria for synchronizing collapse, idempotent stabilisation, and redundancy identification via basis-pruning algorithms. The framework is illustrated with examples spanning manufacturing, agricultural, and e-commerce logistics systems. Analytical results, algorithmic procedures, and case studies demonstrate how semigroup properties map to measurable resilience indicators, providing interpretable, computationally tractable tools for assessing shock containment strategies in real-world networks.