Devices in Internet of Things (IoT) networks are required to execute tasks such as sensing, computation and communication. These devices, however, have energy limitation, which in turn bounds the number of tasks they can execute and their tasks execution time. To this end, this paper considers energy delivery, tasks assignment and execution in a Radio Frequency (RF) IoT network with a Hybrid Access Point (HAP) and RF-powered devices. We outline a novel Mixed-Integer Linear Program (MILP) to assign tasks to devices, and also to optimize the HAP’s charging duration. We also propose a heuristic algorithm called Energy Saving Task Assignment (ESTA), and two Model Predictive Control (MPC) approaches called MPC-MILP and MPC-ESTA; both of which use channel estimates over a given window or time horizon. Our results show that MPC-MILP and MPC-ESTA respectively consume up to 74.27% and 63.71% less energy as compared to competing approaches. Moreover, MPC-MILP with a small window has better performance. This is because a small window allows MPC-MILP to execute all tasks sooner as opposed to waiting idly for incorrectly estimated good channel conditions.