A Bi-Level Modeling Approach to Mitigate Illicit Trafficking of Nuclear and Radioactive Materials

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After the dissolve of the Soviet Union, a lot of nuclear facilities became vulnerable to theft in the former Soviet Union countries. Many programs and organization were established (e.g. Second Line of Defense (SLD), National Nuclear Security Administration (NNSA), International Atomic Energy Agency (IAEA), Nuclear Threat Initiative (NTI)) to counter the spread of nuclear and radioactive materials. Even though the number of countries storing these dangerous martials has dropped, many funded terrorist organizations have declared their intent to pursue materials for weapon of mass destruction. The dissertation addresses two main challenges addressed in one of the NNSA reports.par The first problem is combating illicit traffic of nuclear and radioactive materials. Most papers studied interdiction of nuclear and radioactive materials from the receptive of placing sensors in the country border. The study view the possible global network for the illicit nuclear and radioactive materials that could used. The objective of nuclear smuggling detection and deterrence program is to detect and interdict nuclear and radioactive materials as far away from the United States. This could be achieved by partnering up with other countries to provide radiation detection equipment and support. Various public data sets were collected in order to establish shipping network through ground, sea and air. The NTI nuclear security index is used to assess countries and territories security and deterrence capabilities of nuclear and radioactive materials. The problem is formulated as min-max problem, the smuggler tries to maximize the probability to traverse the network while the interdictor tries to minimize the probability of smuggler traversing the network by placing detection equipment in partnered countries. The smuggler original point and destination are assumed to be stochastic. The objective of the study to find which countries/regions to partner with and which work as transition hub for the smugglers. Due to expensive cost of installing sensors in all airports, seaports or land borders, the study found the possible candidate for partnership and later the possible smuggling method (air, sea and land) that could be used to go in or out of the country. The second problem is detection and deterrence of nuclear and radioactive materials ground shipping using fixed radiation portal monitors (RPM) and dynamic mobile detection systems (MDS). Most of the interdiction problems in the literature consider the resources or commodities used for interdiction as static that could be placed on arc or node but in reality, some of these resources are dynamic. They move from one arc or node to another. The objective of the study is to find the best assignment of RPM and MDS in a road network to minimize the chance of an illicit transport of nuclear and radioactive materials. The problem is formulated as min-max problem with multiple interdiction resources. A new evader's model based or reliability path problem is developed to handle multiple interdiction strategies. Two new formulations for the interdictor’s model were developed. The first formulation assumes that the $N$ patrolling paths for MDS is given as an input. The $N$ patrolling are generated from a model that is a variant to travel salesman problem with customer selection. The second formulation assumes that each MDS is given limited number of hours to be assigned to limited arcs. Later a vehicle routing model will find the best patrolling path that cover the security requirement from the second interdictor's model. The city of Piedmont, California, USA drive network is used as an example to test the two developed models. The first model is found to be fast in solving the problem but the second model gave better solution even though it was solved for optimal solution. For a small-scale problem, the secon