This paper studies resource allocation in wireless-powered orthogonal-frequency-division multiplexing (OFDM) amplify-and-forward (AF) or decode-and-forward (DF) relay networks with time-switching (TS) based relaying. Our objective is to maximize end-to-end achievable rates by optimizing TS ratios of energy transfer (ET) and information transmission (IT), power allocation (PA) over all subcarriers for ET and IT as well as subcarrier pairing (SP) for IT. The formulated resource allocation problem is a mixed integer programming (MIP) problem, which is prohibitive and fundamentally difficult to solve. To simplify the MIP problem, we firstly provide an optimal ET policy and an optimal SP scheme, and then obtain a nonlinear programming problem to optimize TS ratios and PA for IT. Nevertheless, the obtained nonlinear programming problem is non-convex and still hard to tackle directly. To make it tractable, we transform the non-convex problem into a fractional programming problem, which is further converted into an equivalent optimization problem in subtractive form. By deriving the optimal solution to the equivalent optimization problem, we propose a globally optimal resource allocation scheme which bears much lower complexity as compared to the suboptimal resource allocation in the literature. Finally, our simulation results verify the optimality of our proposed resource allocation scheme and show that it outperforms the existing scheme in literature.