You may have a look at our recent work based on Benders decomposition, for the discrete Maximum Coverage Facility Location problem. It works very well if the number of facilities is relatively small, but the number of customers can run in millions…
J.F. Cordeau, F. Furini, I. Ljubic: Benders Decomposition for Very Large Scale Partial Set Covering and Maximal Covering Problems, European Journal of Operational Research 275(3):882-896, 2019
You can donwload the preprint from here.
The code is open-source.
