A stochastic bilevel model for facility location-protection problem with the most likely interdiction strategy

Abstract

This paper studies a capacitated facility location and protection problem against the boundedly rational attacker that merges probabilistic fortification and interdiction, and decision-dependent uncertainty in the post-interdiction capacity of the facilities. The defender decides the location and fortification of the facilities, whereas the attacker uses the minimum information approach to determine the amount of interdiction exerted for facilities based on the interdiction exertion probability. The defender and attacker’s strategy decisions influence the capacity of facilities, making decision-dependent uncertainty. The problem is formulated as a two-stage stochastic bilevel model. The first stage involves a bilevel game formulation where the defender and attacker make decisions sequentially at the outer and inner-level, respectively. The second stage is to optimize the assignments of the facilities with decision-dependent uncertain capacity state probability. A novel hybrid genetic algorithm is developed to solve the proposed model. Also, an analytic hierarchy process and a multinomial logistic regression are embedded into the algorithm for estimating the probability of interdiction exertion and uncertain post-interdiction capacity state, respectively. Computational experiments are provided to illustrate the validity of the proposed model.