Preemptive facility interdiction under damage uncertainty

Abstract

The preemptive facility interdiction problem aims to disable or diminish future threats from adversaries by proactively targeting their critical facilities. This research generalizes a preemptive facility interdiction problem with capacitated facilities. The problem is formulated as a bi-level optimization problem in which the interdictor, at the upper level, decides to attack several facilities to maximize the supply cost of the adversary (defender) force at the lower level. We make a realistic assumption that the magnitude of damage after the attack decisions is uncertain, leading to the partially available capacity for the defender to supply some of the demand points. The network defender may allow for a demand shortage while having the option to reallocate some of the demands to alternative facilities at a fixed cost and potentially higher transportation costs. The defender reacts to the attack to keep the supply network operational at the minimum expected cost.

This problem is NP-hard and computationally intensive to solve, particularly on a large scale. We have designed a cutting plane incorporating (1) optimality cuts to guide us towards an optimal solution and (2) so-called minus-k cuts devised based on the dominant solutions to improve efficiency. We have conducted extensive experiments on our facility interdiction problem to address the practical aspects of the problem by sensitivity analysis and the computational aspects of the solution method by solving relatively large instances with a small optimality gap. Furthermore, we draw some practical insights into how the decision-making process is affected in such an interdiction problem.