We present a new approach to automatically generate complete stereotactic radiosurgery treatment plans for Gamma Knife⃝R PerfexionTM that combines sector-duration optimiza- tion and isocentre location optimization in one large mixed-integer linear model. Sampling techniques are used for tractability. We employ two types of voxel (a cube of patient tissue) sampling to reduce the number of constraints and to simplify the objective function, and an isocentre sampling method to reduce the number of integer variables, which represent the decision to use or not use an isocentre. We also propose a heuristic method of bounding the number of isocentres needed for each target in a treatment plan. The effects of sampling and bounding the number of isocentres is tested on seven clinical radiosurgery cases, with results showing that our method obtains quality treatment plans with computational effort varying predictably with the sampling and bounding scenarios.