PLEASE HELP For my System analysis and design class, I have to write a paper on which project management methodology would be most appropriate for a given scenario. My problem is that I do not understand what "project management methodology" really is. The following paragraph is the chosen problem statement, and yes it is silly.

The Emperor has told you to build the Death Star. (Yeah, Episode IV is my favorite.) These plans were drawn up three months ago, and now you must make this project happen. At your disposal are more than 10,000 workers, 1,000 subcontractors, and 1.5 Trillion Credits. You must implement life support, power generation, and most importantly - a megadeath laser beam, within three years.

I do not need a paper written for me, I just need to know which project management methodology would be most appropriate for this scenario. I can do the "Why it's better" once I know what a project management methodology is.