This paper proposes a Branch-and-Cut algorithm for network operators and providers to propose a full coverage hole in the context of Cloud Radio Access Networks (C-RAN). In this context, and to optimize the network coverage when reducing interferences, network operators need new algorithms that enable to consolidate and re-optimize the antennas radii. This paper provides an NP-Hardness complexity proof of the full coverage hole problem and proposes a deep Branch-and-Cut algorithm based on the description of new cutting planes to accelerate the convergence time even for large problem sizes. Simulation results and comparison to the state of the art highlight the eciency and the usefulness of our approach.