Wireless sensor network （WSN） is constrained by limited battery energy and insufficient computing power， and the limited battery life hinders its widespread deployment. In this paper， wireless power transmission （WPT） and multi-access edge computing （MEC） technologies are used to solve the problem of limited energy consumption of sensor nodes. By jointly optimizing the decision of the node offloading， wireless power supply duration and bandwidth resource allocation， the average task completion delay of sensor nodes is minimized to the greatest extent possible. The optimization problem is modeled as a mixed integer programming problem. In order to adapt to the complex and dynamic channel environment， a deep reinforcement learning delay minimization （DrlDM） algorithm based on soft actor critic （SAC） is proposed. The original optimization problem is modeled as a Markov decision process （MDP）. Simulation results show that compared with three baseline experiments， the average delay of the DrlDM algorithm proposed in this paper is reduced by 62.11 %， significantly shortening the average task completion time of nodes.