Robust facility location considering protection and backup under facility disruptions with decision-dependent uncertainty

Designing a resilient supply chain network is crucial to mitigate the impact of disruptions on supply facilities. This paper merges the facility fortification problem into the robust facility location problem by consideration of proactive and response strategy to against supply facility disruptions and introduces a novel two-stage robust optimization (TRO) model with decision-dependent uncertainty (DDU). Within this TRO framework, facility location, protection, and backup decisions are treated as here-and-now decisions, anticipating the worst-case scenario of facility failures under disruption. Subsequent enabling backup and allocation decisions are wait-and-see decisions. Some theoretic properties on the TRO-DDU model are proposed and a decomposition method based on the nested column-and-constraint generation (NC&CG) algorithm is presented to solve the model exactly. Extensive numerical experiments are conducted to demonstrate the effectiveness of considering both protection and backup decisions and to examine their importance from the perspectives of the impact of protection budget, backup budget, total budget, disruption risk level, minimum number of facilities to open and backup cost coefficient. Also, we propose optimal budget plans for the manager based on maximizing average marginal efficiency (AME) to avoid meaningless additional budget investment. We highlight the advantages of the proposed model in random disruption scenarios compared to the one-stage robust model and one-stage model with random disruption risk. The results show how our model strategically mitigates facility disruption risks and enhances system performance.