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.