The Pentagon has a Zombie Apocalypse plan

If they can like a proper military, yes. Unfortunately, that doesn't make for an exciting zombie story/game, so they have be given the Idiot Ball or suffer from contrived problems that nerf them sufficiently so that they can't just curbstomp the zombie menace.

I would be disappointed if the Pentagon in the States, or the Ministry of Defence in London didn't have a zombie apocalypse plan somewhere in the cupboard.

FYI the only film where you see the army doing a proper job on the zombie scum is Shaun of the Dead, where they pull a Big Damn Heroes moment and save the protag, his girlfriend and the only other smart girl of the group.