Optimal Allocation of Protective Resources in Shortest-Path Networks

We develop a game theoretic approach for allocating protection resources among the components of a network so as to maximize its robustness to external disruptions. Specifically, we consider shortest-path networks where disruptions may result in traffic flow delays through the affected components or in the complete loss of some elements. We develop a multi-level program which identifies the set of components to harden so as to minimize the length of the shortest path between a supply node and a demand node after a worst-case disruption of some unprotected components. We propose an implicit enumeration algorithm to solve the multi-level problem to optimality and streamline the approach by solving the lower level interdiction problem heuristically at each node of the

enumeration tree. We also propose some variable fixing rules which reduce the dimension of the lower level problems. A thorough computational investigation demonstrates that the proposed solution method is able to identify optimal protection strategies for networks

of significant size. We also study the sensitivity of the proposed approach to variations of the problem parameters, such as the level of offensive and defensive resources, and the distribution of the arc lengths and delays.