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In this paper, we study the joint data gathering and energy harvesting (JoDGE) problem in rechargeable wireless sensor networks (RWSNs) with a mobile sink. In RWSNs, the sensor nodes are equipped with RF circuit to harvest energy from a mobile sink that moves along a pre-defined path, and at the same time, transmit gathered sensor data to the sink. Given that the consumed and harvested energy at a sensor node is proportional and inversely proportional to the square of transmission distance, a far-relay approach is proposed to select the sensor nodes closer to the path to assist the data transmission of the farther sensor nodes. Under the far-relay approach, we formulate a network utility maximization problem (NUM), and propose an optimal scheduling scheme (Opt-JoDGE), which jointly considers the power allocation, relay selection and time slot scheduling policies. By employing the Lyapunov drift theory …