In this paper, we consider a two-hop communication system model, where a source is able to harvest energy and a relay is non-EH half-duplex node over a fading channel. We address the throughput maximization problem for the proposed system model with and without delay tolerant. Two effective algorithms are proposed to solve the joint power allocation and transmission time scheduling problems. The performance of the proposed schemes is evaluated via simulation and the results demonstrate that a network with delay tolerant ability provides better performance in term of throughput.