Assume that a set of Demand Response Switch (DRS) devices are deployed in smart meters for autonomous demand side management within one house. The DRS devices are able to sense and control the activity of each appliance. We propose a set of appliance scheduling algorithms to 1) minimize the peak power consumption under a fixed delay requirement, and 2) minimize the delay under a fixed peak demand constraint. For both problems, we first prove that they are NP-Hard. Then we propose a set of approximation algorithms with constant approximation ratios. We conduct extensive simulations using both real-life appliance energy consumption data trace and synthetic data to evaluate the performance of our algorithms. Extensive evaluations verify that the schedules obtained by our methods significantly reduce the peak demand or delay compared with naive greedy algorithm or randomized algorithm.