Optimal Placement of Detectors to Minimize Casualties in an Intentional Attack

This article proposes a mathematical model to optimally locate a set of detectors in such a way that the expected number of casualties in a given threat area can be minimized. The reliability of a detector is often a function of the duration that the threat remains within the effective radius. To accurately detect any threat event and to avoid any false alarm, in this article, two sets of detectors, primary and secondary, are utilized; the primary detectors rely on the secondary set as reinforcement to confirm or deny that a threat is present. The problem is formulated as a nonlinear binary integer programming model and then solved as a linearized branch and bound algorithm. A number of sensitivity analyses are performed to illustrate the robustness of the model and to draw key managerial insights. Experimental results reveal that a two-layer detection system will significantly minimize the expected number of casualties in a given threat area as opposed to a one-layer detection system.