Optimal Placement of Suicide Bomber Detectors

Abstract

This paper develops upon the work by Kaplan and Kress [1], which considers the operational eectiveness of suicide bomber (SB) detector schemes. Here, we consider the optimal placement of detectors in a threat area where the potential targets are known. The threat area is divided into grids for the purpose of our analysis and can have several entrances. We assume that a SB would detonate at a potential explosive grid centroid. The number of individuals near every potential explosive grid is assumed to be given by a spatial Poisson process, with the density being a function of the specific potential explosive grid. It is assumed that the SB would take the shortest path from one of the entrances to the grid centroid where he/she intends to detonate. SB detectors are not perfectly reliable, with the probability of detection being a function of how long the SB would stay in the eective detection area. We choose the objective of minimizing the expected number of casualties. The problem is formulated as a nonlinear integer program and properties are derived to gain insights into the model as well as to develop ecient solution methods. Later, a greedy adding heuristic and a branch and bound algorithm are proposed. A base case is analyzed to illustrate the application of the model. We also perform a sensitivity analysis for a number of key factors as well as an investigation of the performance of the greedy heuristic procedure.