Abstract: To address the challenges of strong multi-timescale coupling and complex coordination between computing workload scheduling and cooling control in high-density data centers, a bi-level full-stack synergistic optimization method for computing and cooling resources is proposed based on model predictive control (MPC). The approach leverages a multi-physics coupled simulation system that integrates key components including server heat generation, cooling loops, and heat exchange components. The framework employs a hierarchical control architecture: the upper layer performs day-ahead economic dispatch at an hourly timescale, generating optimal reference trajectories for server power load ratio and inlet cooling flow rate by jointly considering time-of-use electricity pricing and outdoor temperature; the lower layer executes minute-level rolling optimization to dynamically adjust cooling actuators and load allocation, ensuring precise tracking of references while maintaining chip temperature safety. The simulation results show that, while guaranteeing task completion and equipment safety, the proposed strategy reduces the average power usage effectiveness (PUE) of the data center from 1.18 to 1.14 and lowers total operational cost by 13.3%. Furthermore, when the service level agreement violation (SLAV) rate, which is defined as the proportion of tasks failing to meet their deadline, is incorporated as an additional objective in the multi-objective optimization, the average violation rate is reduced by 34% with only a 0.42% increase in energy consumption. These results confirm that the proposed framework effectively enhances the energy efficiency, economic performance, and quality of service of data centers.