In this paper, we obtain the optimal resource allocation scheme in order to maximize the achievable rate region in a dual-hop system that consists of two independent source-destination pairs sharing a single half-duplex relay. The relay decodes the received information and possesses buffers to enable storing the information temporarily before forwarding it to the respective destination. We consider both non-orthogonal transmission with successive interference cancellation at the receivers and orthogonal transmission. Also, we consider Gaussian block-fading channels and we assume that the channel state information is known and that no delay constraints are required. We show that, with the aid of buffering at the relay, joint user-and-hop scheduling is optimal and can enhance the achievable rate significantly. This is due to the joint exploitation of multiuser diversity and multihop diversity in the system. We provide closed-form expressions to characterize the average achievable rates in a generic form as functions of the statistical model of the channels. Furthermore, we consider sub-optimal schemes that exploit the diversity in the system partially and we provide numerical results to compare the different schemes and demonstrate the gains of the optimal one. © 2014 IEEE.