The optimization over long time horizons in order to consider long-term effects is of paramount importance for effective sensor scheduling in multi-sensor systems like sensor arrays or sensor networks. Determining the optimal sensor schedule, however, is equivalent to solving a binary integer program, which is computationally demanding for long time horizons and many sensors. For linear Gaussian models, two efficient long-term sensor scheduling approaches are proposed in this report. The first approach determines approximate but close to optimal sensor schedules via convex optimization. The second approach combines convex optimization with a branch-and-bound search for efficiently determining the optimal sensor schedule. Both approaches are compared by means of numerical simulations.