This paper addresses the optimal design of wireless networks through the site and power assignment problem. Given a set of candidate transmitters, this problem involves choosing optimal transmitter locations and powers to provide service coverage over a target area. In the modern context of increasing traffic, establishing suitable locations and power emissions for the transmitters in wireless networks is a relevant and challenging task due to heavy radio spectrum congestion. Traditional network design formulations are very ill-conditioned and suffer from numerical inaccuracies and limited applicability to large-scale practical scenarios. Our contribution consists of speeding up the solution of the problem under consideration by addressing its drawbacks from a modeling point of view. We propose valid cutting planes and various presolve operations to reduce the problem size and strengthen existing formulations, along with a reduction scheme based on reduced cost fixing to reduce the sources of numerical inaccuracies. Our proposals prove effective, allowing us to achieve optimality on large-scale instances obtained from a real 4G LTE network in solution times aligning well with planning windows.

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