Selective catalytic reduction system

Abstract

We study the interdiction of smuggling network that arranging the activities of the police in order to successfully interdict criminals in smuggling goods. This work contributes to the literature of maximum flow network interdiction problems by addressing asymmetric information, uncertain conditions, multi commodity, and with multiple sources (origins) and sinks (destinations). Information Asymmetry realistically occurs due to incomplete information of interdictor (police) and operator (smuggler) about each other's performance, which is adapted from the real-world condition. We propose two mixed-integer programming models by reformulating a Min–Max bi-level mathematical model. In the first model, the type of interdiction is discrete (zero and one), while in the second model, the interdiction is assumed continuous, meaning that the partial interdiction is possible. The asymmetry type of the smuggler's information towards the police have formulated through a linear function while the asymmetry of the police information to the smuggler is formulated using an uncertain parameter through a two-stage stochastic programming framework. To solve the first model, an innovative exact hybrid method is proposed combining of a Decomposition Method and Progressive Hedging Algorithm (DM-PHA). An augmented Karush-Kuhn-Tucker (KKT) method is also used to solve the second model. Several sensitivity analyses are then conducted, and the results demonstrate the applicability and effectiveness of the proposed models as well as the solving approach. It is also shown that the proposed models can be used as a suitable approach in uncertain environment and under asymmetric information to determine the optimal interdiction decisions of police to prevent further smuggling.