This PhD Thesis is composed by two papers with contributions on operations research applied to smart grid theory. The first paper highlights the economic and security benefits of an enhanced system operation with the advent of a smart grid technology by introducing a novel model, which is a joint energy and reserve scheduling that incorporates the network capability to switch transmission lines as a corrective action to enhance the system capability to circumvent contingency events. The main goal is to reduce operating costs and electric power outages, by adjusting the network connectivity when a contingency occurs. In such a framework, results show that, with a limited number of corrective switches, the system operator is able to circumvent a wider range of contingencies, while resulting in lower operational costs and reserve levels. In our context, a grid that is capable to adjust its generation and also its topology through post-contingency line switching is called a self-healing grid, and its importance in network security and operating costs is demonstrated in this work. The graph structure is explored in the algorithmic solution of the post-contingency transmission switching problem. Numerical results demonstrate a significant reduction in total load shedding and operating cost. It has been also illustrated an expressive improvement in terms of security and operating cost, in comparison to the transmission switching models previously published. The second paper is an application of a modified Benders decomposition to the post-contingency transmission switching problem. The decomposition is an attempt to deal with the NP-hard optimization problem created by the transmission switching and unit commitment variables. The major contribution is the application of a new benders decomposition approach to the problem of transmission switching, in which the first and second stages problems are a mixed-integer program. To deal with this issue, it is used a Branch and Bound (B&B) procedure for the first-stage problem and a sequential convexification procedure for the second-stage problem.