Scheduling beams with different priorities on a military surveillance radar

The problem of scheduling the searching, verification, and tracking tasks of a ground based, three-dimensional military surveillance radar is studied. Although the radar is mechanically steered in the sense that a servomechanism rotates the antenna at a constant turn rate, it has limited electronic steering capability in azimuth. The scheduling problem arises within a planning period during which the antenna scans a given physical range. A task/job corresponds to sending a transmission beam to hit a particular target. Targets are allowed to be hit with an angular deviation up to a predetermined magnitude. The steering mechanism of the radar helps alter these deviations by imposing a scan-off angle from broadside on the transmission beam. A list of jobs along with their priority weights, processing times, and ideal beam positions are given during a predetermined planning period. The ideal beam position for a given job allows hitting the corresponding target with zero deviation. Each job also has a set of available scan-off angles. It is possible to map the antennas physical position, beam positions, scan-off angles, and angular deviations to a time scale. The goal is to select the subset of jobs to be processed during the given planning period and determining the starting time and scan-off angle for each selected job. The objectives are to simultaneously minimize the weighted number of unprocessed jobs and the total weighted deviation. An integer programming model and two versions of a heuristic mechanism that relies on the exact solution of a special case are proposed. Results of a computational study are presented.