A high-speed railway system equipped with moving relay stations placed on the middle of the ceiling of each train wagon is investigated. The users inside the train are served in two hops via orthogonal frequency-division multiple-access (OFDMA) technology. In this paper, we first focus on minimizing the total downlink power consumption of the base station (BS) and the moving relays while respecting specific quality-of-service (QoS) constraints. We first derive the optimal resource-allocation solution, in terms of OFDMA subcarriers and power allocation, using the dual decomposition method. Then, we propose an efficient algorithm based on the Hungarian method to find a suboptimal but low-complexity solution. Moreover, we propose an OFDMA planning solution for high-speed trains by finding the maximal inter-BS distance, given the required user data rates to perform seamless handover. Our simulation results illustrate the performance of the proposed resource-allocation schemes in the case of Third-Generation Partnership Project (3GPP) Long-Term Evolution Advanced (LTE-A) and compare them with previously developed algorithms, as well as with the direct transmission scenario. Our results also highlight the significant planning gain obtained, owing to the use of multiple relays instead of the conventional single-relay scenario.