Optimal scheduling of charging and discharging in V2G systems constitutes a highly complex optimization problem due to its nonlinear, mixed-integer, and multi-objective nature. This article proposes a hybrid local-global optimization methodology for scheduling charging/discharging processes in the context of Vehicle-to-Grid (V2G). The proposed methodology integrates a global convex optimization stage, which guarantees feasibility and optimization with respect to the constraints of the entire system (charging limits and energy cost minimization), with a local optimization stage, which adjusts the charging schedules of each vehicle based on personalized constraints (individual battery status and user preferences). The methodology explicitly incorporates scalability for short-term scheduling horizons relevant to daily and intraday operation. A comparative analysis is conducted across local and global methods under an operating scenario.