Abstract We optimize the design and time-varying operation of a CO 2 -capture-enabled power station burning coal and natural gas, subject to a CO 2 emission intensity constraint. The facility consists of a coal-fired power plant and an amine CO 2 capture system, which is powered by a combined-heat-and-power auxiliary gas-fired subsystem. The detailed design of the CO 2 capture system, the detailed heat integration of the facility, and time-varying operations schedule across all hours of the year are determined in a single optimization problem. This problem is formulated as a bi-objective mixed integer nonlinear program: objectives include minimizing total capital requirement (TCR) and maximizing net present value (NPV). Because the Aspen Plus model used for the CO 2 capture system is too computationally intensive to use directly in optimization runs, we develop a statistical proxy model of the capture system that reproduces Aspen Plus results but is several hundred times faster. The integrated proxy model includes statistical submodels for the CO 2 absorption and solvent regeneration blocks, as well as simple physical models of other system components. Incorporating the detailed CO 2 capture system in the optimization provides important design information such as the optimal number of CO 2 capture trains required. Two scenarios are considered, based on historical data for Texas and India. Results show that the choice of objective function can have a strong effect on planned operating profile (constant or variable operations). Similarly, hourly electricity price variability strongly affects design and plant scheduling. In the West Texas scenario, which has high price variability, the maximum NPV objective favors variable operations, with a CO 2 capture system utilization factor of 65.9% (out of a maximum of 85%), while the minimum TCR objective favors constant operations. In contrast, because of low electricity price variability in the India scenario, there is little value in time-shifting the demand for capture heat, so constant operations are favored in this case for both objectives.