  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.

Systems and Control;Systems and Control;Optimization and Control