Using drones to monitor construction site is a flexible approach with low manpower costs. Researchers study a drone scheduling problem in which a drone flies on a fixed path over a construction site. The flying speed of the drone is optimized to ensure that the drone spends the most time monitoring areas of the construction site that deserve the most attention while ensuring that the drone completes the route within a certain time and without depleting its battery. Researchers propose a nonlinear optimization model for the problem and develop a dynamic programming algorithm to solve the model. A case study is carried out to demonstrate the applicability of the proposed drone scheduling model.