A bi-level programming model for protection of hierarchical facilities under imminent attacks

•The paper extends the r-interdiction median problem to consider hierarchical facilities•A mixed integer bi-level programming is provided for protection of hierarchical facilities•Three metaheuristic algorithms based on VDNS, SA and hybrid SA-VDNS are developed.•Numerical studies are conduced to test the model and the metaheuristic algorithms.

Disorders caused by deliberate sabotage and terrorist attacks have always been considered as a major threat by the governments. Hence, identifying and planning for strengthening of critical facilities have become a priority for more security and safety. This paper presents a bi-level formulation of the r-interdiction median problem with fortification for critical hierarchical facilities. In the developed bi-level formulation, the defender, as the leader, decides to protect a certain number of facilities in each level of the hierarchical system in order to minimize the impact of the most disruptive attacks to unprotected facilities. On the other hand the attacker, as the follower, with full information about protected facilities, makes his interdiction plan to maximize the total post-attack cost incurred to the defender. We develop three metaheuristic algorithms and an exhaustive enumeration method to solve the introduced problem. Extensive computational tests on a set of randomly generated instances demonstrate the effectiveness of the developed algorithms.