Toward agri-food supply chain viability under pest spread risk

Plant pests and diseases present a formidable challenge to the agri-food industry. However, by embracing the principles of sustainability, circular economy, intertwined supply networks, and implementing risk management strategies, these threats can be transformed into opportunities. In this paper, we address the issue of viability for the circular pomegranate supply chain (SC) under pest spread risk and demand uncertainty. To realize the circular economy concept, we employ the co-pyrolysis method, which links the fruit and bio-product SC networks. We implement constraints related to water consumption and greenhouse gas emissions for sustainability considerations. Furthermore, we introduce a predetermined responsiveness level target for the SC viability. The main contribution of this article lies in modeling the dynamic pest spread and demand uncertainty in the problem of viable agri-food supply chain design. In this regards, we develop a novel approach known as the elastic $p$-robustness multi-stage stochastic programming (EPRMSSP). Additionally, we employ a method called augmented adjustable column-wise robust optimization (AACWRO) to model demand fluctuations. In order to capture the external uncertainty of the impact of pest spread on producer capacity, we introduce deep dynamic uncertainty. We conduct an actual case study in Iran to evaluate the performance of our model and proposed approaches in real-world conditions. The numerical results confirm the effectiveness of the approaches and risk measures. Specifically, our findings demonstrate that in comparison to the minimax regret robust optimization, the $p$-robustness risk measure yields lower costs in 88.8 % of scenarios. Finally, we present several valuable managerial insights.