In this work, we address the wireless network design problem, i.e., the problem of configuring a set of transmitters to provide service coverage to a set of receivers. It is well-known that natural formulations of this problem are sources of numerical instabilities and make the optimal resolution challenging for state-of-the-art solvers, even in small-sized instances. We tackle this limitation from a computational perspective by suggesting two implementation procedures capable of speeding the resolution of the instances of this problem. The first one consists of the employment of an extremely effective branching rule for a compact reformulation of this problem. The second one is the use of presolve operations to manage numerical instability. The approaches are validated using LTE instances kindly provided by Fondazione Ugo Bordoni. The proposed implementation techniques have proved capable of significantly accelerating the resolution of the problem, beating the performance of a standard resolution.