| Container inspection is vital to maintaining secure ports-of-entry and preventing undesired cargo from entering the United States. The inspection process can be generalized as the collection and analysis of information obtained from multiple sensors. Formulating a mathematical model of container inspection allows for evaluation and improvement of the process. The performance of the system under a specified policy is evaluated using one or more objectives such as misclassification errors (false accept and false reject), costs associated with these errors, inspection cost, inspection time, and others. The main contributions of this research are the modeling, formulation, and optimization of inspection policies under different conditions. Furthermore, the dissertation introduces a new class of problems in scheduling theory in which the allocation of inspections is not defined and appears as a decision variable in the solution.;In the initial model, the overall system decision is a Boolean function of the individual station decisions. Under these conditions we define an optimal sequence of stations with respect to the expected cost of inspection and solve simultaneously for the threshold level values and sequence of stations that produce a minimum total cost. This optimization is extended to include the time for inspection as an objective and a multi-objective optimization approach is developed. Next we introduce an independent error term that accounts for measurement error contributed by the sensor and propose some strategies, including repeat inspection, to improve the system's performance. We investigate an approach to approximating the efficient frontier for three objectives.;We then consider distinct risk categories and due times for containers. Approaches are developed to determine the optimal allocation and scheduling of inspection operations to minimize false acceptance and tardiness objectives. The problem is presented as a variation of the open shop scheduling problem with no predefined operations. A solution approach to this simultaneous allocation and scheduling problem is proposed and its performance is compared with an enumerative approach. The results show that the proposed approach produces near-optimal solutions in a much shorter time than full enumeration and is capable of solving large problems for which the enumerative approach is intractable. |
