Analysis of Facility Protection Strategies Against Uncertain Numbers of Attacks: The Stochastic R-Interdiction Median Problem with Fortification

We present the Stochastic R-Interdiction Median Problem with Fortification (S-RIMF). This model optimally allocates defensive resources among facilities to minimize the worst-case impact of an intentional disruption. Since the extent of terrorist attacks and malicious actions is uncertain, the problem deals with a random number of possible losses. A max-covering type formulation for the S-RIMF is developed. Since the problem size grows very rapidly with

the problem inputs, we propose pre-processing techniques based on the computation of valid lower and upper bounds to expedite the solution of instances of realistic size. We also present heuristic approaches based on heuristic concentration-type rules. The heuristics are able to

find an optimal solution for almost all problem instances considered. Extensive computational testing shows that both the optimal algorithm and the heuristics are very successful at solving the problem. A comparison of the results obtained by the two methods is provided as is a

discussion of the importance of recognizing the stochastic nature of the number of possible attacks.