Strengthening and protecting hubs against sequential unintentional and intentional disruptions considering decision-dependent uncertainty

This paper studies the strengthening and protection of multiple allocation hub networks subject to sequential unintentional and intentional disruptions, with the unintentional impacts occurring first, followed by the intentional impacts. We develop a two-stage stochastic bi-level programming model that incorporates decision-dependent uncertainty, where the first stage focuses on strengthening against unintentional impacts, and the second stage addresses protection against intentional impacts. The first stage determines the optimal strengthening strategy, incorporating various types to address multiple unintentional impacts, each with varying levels of intensity. The imperfect effect of strengthening and unintentional impacts makes decision-dependent uncertainty in the hub’s post-disruption operation state, which probabilistically depends on the strengthening decision and the intensity level of unintentional disruptions, and is interpreted using the contest success function. The second stage corresponds to a scenario-based bi-level hub interdiction median problem with fortification, formulated as a Stackelberg game between the defender and the attacker. To solve the proposed model, we develop a novel hybrid algorithm based on its structure, which utilizes the benefits of genetic algorithms, simulated annealing, and a greedy heuristic separation approach. We also develop a maximum-likelihood sampling method as a core component of the proposed hybrid algorithm to enhance its performance. Experimental results demonstrate the effectiveness of our proposed model and hybrid algorithm. The results also analyze the impact of the discount factor and strengthening budget on the expected network cost. Additionally, the results highlight the advantage of our model in incorporating multi-level disruption intensity, decision-dependent uncertainty, and sequential disruptions.