Given a marine area of interest (e.g., water-ways, ports), this paper attempts to efficiently allocate sonar sensors (utilized for under water detection) within a limited budget to achieve a reasonable amount of coverage, thereby keeping ports and waterways under surveillance against impending threats. Though total coverage of the entire area of interest is desired, priority is given to the criticality/importance attached to specific locations within the area of interest, on a grid-based system. We present two optimization models to detect potential threats by placing underwater sonars within a port or waterway of interest. The first model (mixed integer linear programming model) developed maximizes the detection coverage based on the importance attached to a sub-region. The second model is a mixed integer nonlinear programming model that is designed to achieve optimal detection based on a desired detection probability threshold. Both models satisfy a budget constraint that limits number of sonars to be deployed.
