116 Scaparra, Church.PDF

Vulnerability to sudden service disruptions due to deliberate sabotage and terrorist attacks is one of the major threats of today. Whereas the design of reliable supply networks has received considerable attention in the last few decades, few authors have addressed the issue of optimizing security investments for existing, but vulnerable, systems. In this paper we consider a simple service/supply system with p facilities and a set of costumers, where each customer receives service from its closest facility. In this paper, we assume that there is an antagonist who will attempt to do the most harm to the service system and that our objective is to efficiently allocate security investments so that the effects of a worst-case attack are minimized. As this represents a problem with two different and opposing goals (one of protection and one of inflicting harm), we have cast this problem as a bilevel programming model where the top level problem involves the decisions about which facilities to secure or harden and the lower level problem entails the interdictor response on which unprotected facilities to attack. We solve the bilevel problem through an implicit enumeration algorithm, based on a binary tree search. The algorithm involves solving iteratively r-interdiction median (RIM) models. We show how the original RIM formulation can be streamlined through a process of variable reduction and consolidation and this significantly reduces the computing time needed to solve the bilevel fortification/interdiction model. Extensive computational results are reported, including comparisons with earlier results obtained by a single-level approach to the problem.