In this paper we present and analyze online and offline scheduling models for the determination of the maximum power consumption in a smart grid environment. The proposed load models consider that each consumer's residence is equipped with a certain number of appliances of different power demands and different operational times, while the appliances' feature of alternating between ON and OFF states is also incorporated. Each load model is correlated with a scheduling policy that aims to the reduction of the power consumption through the compression of power demands or the postponement of power requests. Furthermore, we associate each load model with a proper dynamic pricing process in order to provide consumers with incentives to contribute to the overall power consumption reduction. The evaluation of the load models through simulation reveals the consistency and the accuracy of the proposed analysis. (C) 2014 Elsevier Ltd. All rights reserved.