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The vehicle electrification will have a significant impact on the power grid due to the increase in electricity consumption. It is important to perform intelligent scheduling for charging and discharging of electric vehicles (EVs). However, there are two major challenges in the scheduling problem. First, it is challenging to find the globally optimal scheduling solution which can minimize the total cost. Second, it is difficult to find a distributed scheduling scheme which can handle a large population and the random arrivals of the EVs. In this paper, we propose a globally optimal scheduling scheme and a locally optimal scheduling scheme for EV charging and discharging. We first formulate a global scheduling optimization problem, in which the charging powers are optimized to minimize the total cost of all EVs which perform charging and discharging during the day. The globally optimal solution provides the globally minimal total cost. However, the globally optimal scheduling scheme is impractical since it requires the information on the future base loads and the arrival times and the charging periods of the EVs that will arrive in the future time of the day. To develop a practical scheduling scheme, we then formulate a local scheduling optimization problem, which aims to minimize the total cost of the EVs in the current ongoing EV set in the local group. The locally optimal scheduling scheme is not only scalable to a large EV population but also resilient to the dynamic EV arrivals. Through simulations, we demonstrate that the locally optimal scheduling scheme can achieve a close performance compared to the globally optimal scheduling scheme.