عنوان مقاله [English]
The importance of locating and fortifying hierarchical facilities in the face of sabotage operations has encouraged many researchers to make appropriate decisions. In this paper, a bi-level programming model has been introduced, which, considering the interdiction operations and failure of hierarchical facilities at two levels, selects appropriate strategies to locate and fortify them. Depending on available location resources, service demand, and the worst-case scenario of facility failure at both levels, the decisions as to the allocation, location, and fortification of existing facilities are determined. The concepts of capacity and budget have been used to bring the hierarchical system closer to reality. The model aims at minimizing the location cost as well as service distance between demand points and facilities at both levels. In the following, a number of numerical examples of the problem have been presented and solved with two-level combined approaches based on genetic and particle swarm algorithms for the first level and the exact method for the second level problem.