Presentation of a Tri-level Covering Fortification Model in Order to Protect Facility Against Disturbance in r-interdiction Median Problem with the Approach of Stackelberg Game

In this paper, a tri-level defense facility location model for full coverage in r-interdiction median problem is delivered. The purpose of this model is to design a proper service system in a way that after a worst case scenario of disturbance, they can utilize their full capacity of providing services. Hence, we have considered the defense facilities to provide extra protection for service facilities, and the goal is to optimally locate these facilities. The tri-level model is proposed based on leader-follower games as defender-attacker-defender framework. After the disturbance caused by the attacker, with the purpose of ensuring the operation of service facilities, the defender tries to establish a number of defense facilities in potential locations. Locating these facilities is carried with respect to the establishment of fixed cost of facilities and system’s current cost. It should be noted that each service facility must be at least within the coverage range of at least one defense facility (first level).So, system’s current costs can be defined based on the worst-case scenario of disturbance caused by the attacker. The problem is modeled as a static Stackelberg game between the attacker (level 2) and defender (level 3). In order to solve the model, two approaches have been used. In the first approach, explicit enumeration method is used for the first and second levels and an exact approach is used for the third level. In the second approach, hybrid methods consisting of genetic algorithm, explicit exact enumeration and exact approach have been used to solve the problem in a reasonable time. Comparing the proposed meta-heuristic to the exact approach in some samples, the numerical results show a quite satisfactory of this algorithm.