We describe two stochastic network interdiction models for thwarting nuclear smuggling. In the first model, the smuggler travels through a transportation network on a path that maximizes the probability of evading detection, and the interdictor installs radiation sensors to minimize that evasion probability. The problem is stochastic because the smuggler's origin-destination pair is known only through a probability distribution at the time when the sensors are installed. In this model, the smuggler knows the locations of all sensors and the interdictor and the smuggler "agree" on key network parameters, namely the probabilities the smuggler will be detected while traversing the arcs of the transportation network. Our second model differs in that the interdictor and smuggler can have differing perceptions of these network parameters. This model captures the case in which the smuggler is aware of only a subset of the sensor locations. For both models, we develop the important special case in which the sensors can only be installed at border crossings of a single country so that the resulting model is defined on a bipartite network. In this special case, a class of valid inequalities reduces the computation time for the identical-perceptions model.

Abstract:Cargo ships arriving at US ports are inspected for unauthorized materials. Because opening and manually inspecting every container is costly and time-consuming, tests are applied to decide whether a container should be opened. By utilizing a polyhedral description of decision trees, we develop a large-scale linear programming model for sequential container inspection that determines an optimal inspection strategy under various limitations, improving on earlier approaches in several ways: (a) we consider mixed strategies and multiple thresholds for each sensor, which provide more effective inspection strategies; (b) our model can accommodate realistic limitations (budget, sensor capacity, time limits, etc.), as well as multiple container types; (c) our model is computationally more tractable allowing us to solve cases that were prohibitive in preceding models, and making it possible to analyze the potential impact of new sensor technologies.

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Interlaminar stresses that arise in composite laminates where gradients exist in in-plane stress fields are investigated. Two distinct mechanisms give rise to interlaminar stresses in generic problems, the presence of free edges and in-plane gradients. It is shown that the latter mechanism should be considered separately from the former and that interlaminar stresses from such in-plane gradients can be significant. A methodology to approximate these stresses through direct integration of the equilibrium equations is presented. The methodology involves the use of closed-form expressions of the in-plane stress field obtained by solving two-dimensional elasticity problems using homogenized material properties. As an example, the methodology is applied to the case of a laminate with a circular hole through which the importance of interlaminar stresses from in-plane gradients is demonstrated. The results show that the characteristics of the interlaminar stresses from in-plane gradients are very different from those of interlaminar stresses arising from free edges. Specifically, the parameters that affect the decay rates and magnitudes of the interlaminar stresses from the two mechanisms are found to be different. The current investigation provides new insights into interlaminar stress problems, in general, and offers a simple method for calculating the interlaminar stresses due to in-plane gradients.

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