The seriousness of this risk is apparent by the installation of SNM detectors in major international and domestic portals. Initially, the primary concern regarding the origin of SNM material was a result of the collapse of the Soviet Union and the accompanying economic depression that placed nuclear and radioactive materials into lower-security installations. However, the number of countries that have or may have gained access to SNM has grown recently and pose an ever-increasing risk of obtainment by those eager to smuggle it into possible target destinations and use it as a weapon. In order to ship the nuclear materials from a source location with SNM productions to a target city, the smugglers must employ the global and domestic transportation network in different modes, such as air cargo, container ships, and freight trucks.

According to container port traffic statistics provided by the World Bank [1], there are about 470 million twenty-foot equivalent container units (TEU) shipped globally each year by these modes of travel, and 40 million containers enter the U.S. every year by land, sea, and air. This vast volume of containers is simply too large to practically and thoroughly search and screen.Even with the existence of advanced network interdiction methodologies, the detection of SNM smuggling activities is very difficult. The smugglers can come from different countries, target different cities, and use many different routes and modes within the global transportation network.

Improving system-wide observability of nuclear material smuggling flow in multimodal transportation networks, subject to available budgetary constraints, is an extremely challenging task that requires Drug_discovery a seamless and complex integration of cyber and GSK-3 physical processes. The inability to quantify the information gain and system-wide impacts of individual detectors in a heterogeneous sensor network becomes a critical bottleneck in the evaluation of various promising detection scenarios.1.1. Literature Review1.1.1. Network Interdiction ModelsA number of optimization-based network interdiction models have been developed in the past few decades. In the well-known deterministic network interdiction model proposed by Wood [2], a smuggler attempts to maximize flow through a capacitated network while an interdictor tries to minimize this maximum flow by reducing flow on network arcs using limited resources. Wood��s study first proves that the network interdiction model is NP-hard, so it is computationally intensive even for solving its simplified form.