Locating and protecting interdependent facilities to hedge against multiple non-cooperative limited choice attackers

Abstract

This paper studies an interdependent facility location and protection problem against multiple non-cooperative limited choice attackers. In a supply network, the defender and attackers have completely opposite objectives by optimizing their respective patterns. This interaction is represented with a game-theoretic bilevel framework. The defender as a leader in the upper-level makes location and protection decisions while the attackers as followers in the lower-level carry out attack strategies following a limited choice rule. A real supposition is that the effects of protection and attack are imperfect, making the decision-dependent uncertainty in the post-disruption states of the facilities. We incorporate the uncertainty into a two-stage model and formulate the resulting model as a two-stage stochastic bilevel programming problem. The first stage problem involves a bilevel defender–attacker model that locates and protects facilities against attacks, while the second stage problem involves allocation decisions around customers that optimizes a scenario-based minimization problem of allocating demand capacity. Due to the NP-hardness of the considered problem, we develop a hybrid solution method based on genetic algorithm and column generation to solve the model. Computational experiments show the efficiency of the proposed algorithm and demonstrate the effects of limited choice and risk propagation on the optimal solutions.