This paper studies an intelligent reflecting surface (IRS)-assisted wireless-powered communication network (WPCN), where a hybrid access point (HAP) broadcasts energy signals to multiple devices for their energy harvesting in the downlink (DL) and then the devices use the harvested energy to transmit information signals to the HAP in the uplink (UL) with the help of an IRS. In particular, we propose three types of IRS beamforming configurations, namely fully dynamic IRS beamforming (FDBF), partially dynamic IRS beamforming (PDBF), and static IRS beamforming (SBF), to strike a balance between the system performance and signaling overhead as well as implementation complexity. Moreover, we adopt a practical non-linear energy harvesting (EH) model, and leverage a power-splitting (PS) EH receiver architecture with multiple rectifiers to avoid the input radio frequency power to get stuck into the saturation regime. We aim to minimize the transmit energy consumption at the HAP by jointly optimizing the DL/UL time allocation, the HAP/devices transmit power, the PS factor, and IRS phase shifts, subject to a set of minimum throughput requirements for individual devices. To address the resulting non-convex optimization problems, a successive convex approximation (SCA) based alternating optimization algorithm is proposed. Moreover, we study the case with the ideal linear EH model and two algorithms, namely SCA-based algorithm and semidefinite relaxation (SDR) algorithm, are proposed. Simulation results demonstrate the effectiveness of our proposed designs over various benchmark schemes and also unveil the importance of the joint design of IRS beamforming and PS rectifiers for achieving energy efficient WPCNs in practice.