A stochastic network-based framework for modelling sustainability propagation in supply chain systems

Sustainability assessment in supply chains has traditionally relied on static and firm-level metrics that fail to capture the dynamic and interdependent nature of modern supply networks. In practice, sustainability performance emerges through complex interactions among supply chain actors and evolves over time under uncertainty. This study addresses this gap by proposing a stochastic network-based framework for modelling the propagation of sustainability across multi-tier supply chains. The proposed approach represents sustainability as a dynamic state variable associated with network nodes, while interdependencies are captured through a weighted adjacency structure that reflects the intensity of cross-tier interactions. A stochastic propagation model is developed to simulate how sustainability performance evolves across the network under varying structural and uncertainty conditions. Sensitivity and scenario analyses are conducted to evaluate the robustness of the model and to identify critical nodes and links that disproportionately influence system-wide sustainability outcomes. An illustrative case study demonstrates the applicability of the framework and highlights how localised interventions can generate amplified effects across the supply chain. The results provide new insights into the dynamics of sustainability diffusion and offer a decision-support tool for managers and policymakers seeking to enhance supply chain resilience and sustainability performance under uncertainty.