A decomposable resource allocation model with generalized overarching protections

This paper considers a defensive resource allocation problem in which a defender protects a set of assets either individually or collectively using overarching protections. An overarching protection refers to an option that protects multiple assets at the same time, e.g., emergency response, border security and counter intelligence. Most of the defensive resource allocation models with overarching protections assume that there is only one option that protects all targets. However, this may not be realistic considering that, for example, emergency response investment may cover only a certain region. In this paper, we develop a new resource allocation model to accommodate generalized overarching protections against intentional attacks. The model also considers multiple natural disaster types. We show that the proposed optimization model is a convex optimization problem and therefore can be solved to optimality in polynomial time. Furthermore, the overall country-level resource allocation problem can be decomposed into smaller city-level subproblems, thus resulting in a more efficient algorithm. The numerical experiments demonstrate the performance of the proposed approach.