In this paper, we present an optimization-based control strategy for coordinating multiple electric automated vehicles (AVs) in confined sites. The approach focuses on obtaining and keeping energy-efficient driving profiles for the AVs while avoiding collisions in cross-intersections, narrow roads, and merge crossings. Specifically, the approach is composed of two optimization-based components. The first component obtains the energy-efficient profiles for each individual AV by solving a Nonlinear Program (NLP) for the vehicle's complete mission route. The conflict resolution, which is performed by the second component, is accomplished by solving a time-scheduling Mixed Integer Linear Programming (MILP) problem that exploits the application characteristics. We demonstrate the performance of the algorithm through a non-trivial comparative simulation example with an alternative optimization-based heuristic.