Where to Invest in Resilience in a Facility Network?

Much of the previous research on facility networks focuses on improving the network design, but a good design alone is not sufficient to ensure smooth operations against disruption risks. This study examines an underexplored question of where to invest in resilience in a facility network. Prior studies offered insights into this issue, with some scholars recommending a focus on critical nodes, while others emphasize the importance of critical paths that are sequences of adjacent nodes and edges. Yet the node and path perspectives have not been fully integrated and optimized for facility networks. Motivated by real problems from Cainiao Network, this study reconciles the debate over node versus path and solves the problem of resilience investment to maximize expected max-flow through the network. The analysis reveals that investing in high-capacity nodes is optimal under rare disruptions, whereas investing in nodes on entire paths is best under frequent disruptions. The problem of resilience investment is in general NP-hard, but we propose greedy algorithms inspired by the node and path perspectives to provide approximate solutions with performance guarantees. Empirical analysis using operational data from Cainiao Network supports our analytical findings.