Optimal Placement of Suicide Bomber Detectors

This paper develops upon the work by Kaplan and Kress [7], which considered the operational effectiveness 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 will explode 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 different for each such grid. It is assumed that the SB will take the shortest path from one of the entrances to the grid centroid where he/she intends to explode. SB detectors are not perfectly reliable, with the probability of detection being a function of how long the SB will stay in the effective 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 efficient 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 study sensitivity due to a number of key factors as well as an investigation of the efficiency of the greedy heuristic procedure.