Optimal Placement of Detectors to Minimize Casualties on a Manmade Attack

TL;DR

This paper develops a nonlinear binary integer programming model to optimally place detectors in threat areas, incorporating reliability and backup detectors, to minimize casualties in manmade attack scenarios.

Contribution

It introduces a novel mathematical model for detector placement that accounts for reliability and backup support, solved via linearized branch-and-bound methods.

Findings

Two-layer detection significantly reduces expected casualties.

Model demonstrates robustness through sensitivity analyses.

Backup detectors improve detection reliability and effectiveness.

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.