A risk-averse tri-level stochastic model for locating and recovering facilities against attacks in an uncertain environment

This paper presents a risk-averse tri-level stochastic game-theoretic model between the defender and the attacker in application to the supply networks. A real supposition is that the facility capacity and attack effect are uncertain, which is interpreted in stochastic programming. In the presence of uncertainties, the Conditional-Value-at-Risk (CVaR) is incorporated into the model to control the risk associated with extreme scenarios. The model is to minimize the CVaR cost of the defender and allows for locating facilities with capacity backups at different levels so as to recover disrupted facilities against the worst-case attacks. We reformulate the tri-level programming based on a master-subproblem framework and implement a customized column-and-constraints generation to solve it. Numerical results demonstrate that the optimal solutions are sensitive to budgetary limitations and backup levels. Results also draw attention to the need of considering the impacts of the recovery strategy and risk-averseness.