Evaluating the resilience of a single-echelon supply chain using bilevel programming: A case study for the infant formula industry

Disruptions can adversely affect the provision of critical products, including drugs, medical supplies, and infant formula. Attacker-defender models formulated as bilevel mathematical programs are increasingly being used to predict the extent to which supply chain (SC) performance degrades after a disruptive event. We aim to contribute to this line of research by developing a model that captures the important features of a disruption that occurred in the infant formula SC in the United States in 2022, where the largest manufacturing plant was shut down for six months due to bacterial contamination. Our goal is not only to determine the most critical facilities in a SC network whose disruption causes the largest post-disruption cost increase, but also to identify the optimal reaction of the SC in terms of increasing the capacity of non-disrupted facilities by means of overtime production. The post-disruption decisions are the optimal increase in capacity using overtime and the reassignment of markets to production facilities. We perform an extensive numerical study to analyze the effect of the extent of disruption and the capacity of overtime production on the optimal solution in the case study. The results indicate that the solution is robust in terms of the disrupted facility for the worst-case damage and the level of overtime production at the non-disrupted facilities. We also define a new metric to quantify the resilience of the SC to disruptions. Using this metric, we determine the effect of the dispersion of facility locations on the SC resilience.