A bi-level model and solution methods for partial interdiction problem on capacitated hierarchical facilities

•The paper provides a mixed integer bi-level programming model for partial interdiction of nested capacitated hierarchical facilities.•Interdictor has budget limitation and different levels of interdiction will incur different facilities' capacity lost.•A new heuristic algorithm is developed to solve mixed integer bi-level programming.•Numerical studies are conducted to test the model and the heuristic algorithms. Due to the importance of gaining high levels of customer satisfaction in today's competitive world, making appropriate decisions in the face of malicious attacks is valued highly by many organizations. In this paper, to predict and handle the destructive effects of an intentional attack on capacitated nested hierarchical facilities, a bi-level partial interdiction problem is proposed. In this problem, there is an interdictor who can attack facilities partially in different levels. Subsequently, the system defender could respond to the customers’ demand in two different ways, namely through the remaining system facilities and the outsourcing option. The goal of the defender is to minimize the satisfaction cost of all customers’ demand under the interdictor's attacking scenario. This problem can be modeled as a bi-level programming model in which an interdictor and the system defender play the role of the leader and the follower, respectively. Due to the inherent complexity of the bi-level programming models, we develop a heuristic approach, namely “FDS”, to obtain near optimal solutions within a reasonable running time. In each iteration of the FDS, an interdiction scenario is produced heuristically and, thereupon CPLEX solver is called to solve the lower level of the model. To evaluate the effectiveness of the proposed model, a comparison between the cost of customers’ demand satisfaction in both absence and presence of the bi-level model is drawn. Computational results show that for those instances in which the optimal solutions are available, the proposed model can, on average, achieve a saving of 7.94%.