Optimal placement of suicide bomber detectors
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abstract
This paper develops upon the work by Kaplan and Kress (2005), which considers 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 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 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 perform a sensitivity analysis for a number of key factors as well as an investigation of the performance of the greedy heuristic procedure.
