Locating a surveillance infrastructure in and near ports or on other planar surfaces to monitor flows

A safety and security issue of concern for traffic managers and homeland security is the monitoring of flows on " planar surfaces," such as ports and border areas. This article addresses the problem of locating surveillance radars to cover a given target surface that may have barriers through which radar signals cannot penetrate. The area of coverage of a radar is assumed to be a disc, or a partial disc when there are barriers, with a known radius. The article shows that the corresponding location problems relate to two well studied problems: the set-covering model and the maximal covering problem. In the first problem, the minimum number of radars is to be located to completely cover the target area; in the second problem a given number M of radars are to be located to cover the target area as much as possible. Based on a discrete representation of the target area, a Lagrangian heuristic and a two-stage procedure with a conquer-and-divide scaling are developed to solve the above two models. The computational experiences reported demonstrate that the developed method solves well the radar location problems formulated here.