In agriculture irrigation management, irrigation scheduling is typically performed in an open-loop fashion and is done only once at the beginning of a growing season. In this work, we study whether closed-loop scheduling with closed-loop control can lead to improved performance in terms of crop yield and water conservation in agriculture irrigation. The interaction between soil, water, crop (maize in this work), and atmosphere is described by an agro-hydrological model, which is a partial differential equation. In the proposed scheduling and control scheme, both the scheduler and the controller are designed using model predictive control (MPC). The scheduler uses a long horizon (with a sampling period of 1 day) that covers the entire crop growth season, and the horizon shrinks as time moves. The primary objective of the scheduler is to maximize the crop yield. The controller uses a much shorter prediction horizon and a much finer sampling period. The primary objective of the controller is to track the soil moisture reference calculated by the scheduler. To alleviate the computational complexity of the scheduler and the controller, a linear parameter varying (LPV) model is identified for the scheduler and controller, respectively. The performance of the closed-loop scheduling scheme is evaluated against the traditional open-loop scheduling scheme under different scenarios.