Which algorithm does the location-allocation Maximize Coverage problem type use? I already found on the ArcGIS help that location-allocation uses a vertex substitution heuristic to solve the p-median problem (Teitz and Bart), but I didn't find, which algorithm the Maximize Coverage uses. Is it also solved as a p-median problem (Teitz and Bart)?
esri normally doesn't specify which algorithms they use, but you could try going to help file link for a topic and on the bottom right, there is a "Provide Feedback link". You could send a message there stating that you would like to see a reference to the describe the method used for the tool. They may respond... otherwise, you are left with doing a trial and error should there be alternatives. I would check your reference link to see if the methodology is applicable in different scenarios.