Optimal Placement of Detectors to Minimize Casualties on a Manmade Attack

Abstract

This study 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. Detectors may not be perfectly reliable, which is often a function of how long an attacker would stay within the detectors effective detection radius. To accurately detect any threat event and to avoid any false alarm, we assume that a set of backup/secondary detectors are available to support the primary detectors. 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 will significantly minimize the expected number of casualties in a threat area over a one-layer detection problem.