A Viability-Theoretic Framework for Supply Chain Resilience under Heterogeneous External Stressors: An Application to the Arabica Coffee Supply Chain

Abstract

Supply chains exposed to long-run climate stress face a governance problem that conventional resilience frameworks are not well-suited to address. This paper proposes a viability-theoretic framework for supply chains under heterogeneous external stressors, illustrated through the arabica coffee supply chain. The framework combines system dynamics with viability theory to specify a four-layer state space, physical, economic, social, and compliance, a non-compensatory constraint set, and a bounded firm-level control set. Rather than computing the viability kernel numerically, the framework establishes the structural conditions under which such computation is defined and well-posed. The Arabica coffee supply chain is used to instantiate each component with domainspecific variables, feedback structures, and control instruments. The paper concludes that stressor heterogeneity, asymmetric erosion dynamics, and margin-constrained control capacity are structural properties that composite resilience indices cannot capture, and that the viability kernel represents a more analytically adequate governance target for supply chains under prolonged climate stress than a recovery trajectory or resilience index.