A large-scale linear programming model for finding optimal container inspection strategies

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.