Wireless power transfer via radio-frequency (RF) radiation is regarded as a potential solution to energize energy-constrained users, who are deployed close to the base stations (near-by users). However, energy transfer requires much more transmit power than normal information transfer, which makes it very challenging to provide the quality of service in terms of throughput for all near-by users and cell-edge users. Thus, it is of practical interest to employ non-orthogonal multiple access (NOMA) to improve the throughput of all network users, while fulfilling the energy harvesting requirements of the near-by users. To realize both energy harvesting and information decoding, we consider a transmit time-switching (transmit-TS) protocol. We formulate two important beamfoming problems of users' max-min throughput optimization and energy efficiency maximization under power constraint and energy harvesting thresholds at the nearly-located users. For these problems, the optimization objective and energy harvesting are non-convex in beamforming vectors. Thus, we develop efficient path-following algorithms to solve them. In addition, we also consider conventional power splitting (PS)-based energy harvesting receiver. Our numerical results confirm that the proposed transmit-TS based algorithms clearly outperform PS-based algorithms in terms of both, throughput and energy efficiency.