This study proposes an integrated framework of scheduling and Real-Time Optimization (RTO) of a Refrigerated Gas Plant (RGP). At the top layer, a high fidelity dynamic model of RGP is subjected to scheduling of plant operating mode from natural gas liquids to sales gas and vice-versa. Set points from mode scheduling are passed down to the steady-state RTO layer. Modeling mismatch is minimized by rigorously exchanging values of key variables between dynamic and steady-state models. Optimal trajectories of set points are obtained using sequential quadratic programming algorithm with constraints. These trajectories are disjointedly implemented by Model Predictive Control (MPC) scheme and Proportional-Integral (PI) controllers for comparison. Four case studies for each mode scheduling are performed to illustrate efficacy of the proposed approach.