This paper proposes a novel framework for humanoid robots to execute inspection tasks with high efficiency and millimeter-level precision. The approach combines hierarchical planning, time-optimal standing position generation, and integrated \ac{mpc} to achieve high speed and precision. A hierarchical planning strategy, leveraging \ac{ik} and \ac{mip}, reduces computational complexity by decoupling the high-dimensional planning problem. A novel MIP formulation optimizes standing position selection and trajectory length, minimizing task completion time. Furthermore, an MPC system with simplified kinematics and single-step position correction ensures millimeter-level end-effector tracking accuracy. Validated through simulations and experiments on the Kuavo 4Pro humanoid platform, the framework demonstrates low time cost and a high success rate in multi-location tasks, enabling efficient and precise execution of complex industrial operations.