WP-MEC (wireless powered-mobile edge computing) combines mobile edge computing and wireless power transfer technologies. It aims to address the challenges of insufficient computing power and continuous energy supply for mobile devices. However, the heterogeneous power supply and computational capabilities of different edge servers in WP-MEC, as well as the varying delay tolerance times of mobile devices and the time-varying wireless channels between devices and servers, create significant challenges in system resource allocation and task processing. To address these challenges, research has been conducted from the perspective of joint optimization of heterogeneous server selection, computation offloading, and resource allocation in WP-MEC networks. In order to improve the effective computation rate of the system, WADT_CD(weighted average of delay-sensitive tasks-based coordinate descent) joint scheduling algorithm was proposed. First, a heterogeneous server selection strategy was designed based on WADT(weighted average of delay-sensitive tasks), taking into account the time-varying wireless channel gain, heterogeneous task latency, transmit power, and computational capability of edge servers. Second, CD (coordinate descent) algorithm was developed, based on one-dimensional time-variable binary search, to solve the mobile device offloading decision and time resource allocation problems. Finally, the proposed method was validated through simulation experiments, which compare its performance with various algorithms, and the effectiveness of the proposed algorithm was also analyzed at different scales of edge devices and heterogeneous task ratios.