Enterprise Resource Location-Allocation for Intruder Detection and Interdiction

Security systems must effectively detect and intercept would-be intruders with an efficient use of limited assets. For the organization of security operations, these operations are often decomposed into spatially distinct stages to organize efforts and facilitate localized management of assets. Given two respective sets of detection resources and interdiction resources, each having different types of resources with heterogeneous capabilities, this research addresses the problem of locating and allocating them over a sequence of spatially defined stages to effectively detect and intercept an intruder. Moreover, the threat of intrusion may arise suddenly (e.g., when geopolitical events motivate unauthorized intrusions into another country), so it is important to identify high-quality enterprise solutions rapidly, allowing time for implementation. We set forth a mixed-integer nonlinear mathematical programming model and seven alternative variants to address the underlying problem using a leading commercial solver for global optimization. Empirical testing evaluates and compares the effect of alternative model variants on the efficacy and efficiency of the solver to identify global optimal solutions over multiple synthetic instances for a set of scenarios corresponding to specific problem feature settings. Subsequently, a designed experiment examines the impact of selected problem features on the ability of the leading commercial solver to address increasingly sized instances of the underlying problem, portending its utility for larger applications. The testing results reveal that the number of types of detection and interdiction resources significantly affect the relative optimality gap identified, and the number of defender stages is a significant predictor for the required computational effort required when solving a scenario instance. Ultimately, the superlative model variant is identified via two phases of empirical testing and performs well with regard to both solution quality (measured by relative optimality gap identified) and required computational effort over various sizes of scenarios, identifying solutions within 0.005% of the global optimum for 77.2% of the 900 instances tested, and only terminating due to the imposed time limit of 900 seconds for 56.8% of the same instances. The research concludes with a description of the extensions to which these results will be applied.