There was someone complaining about this mentioned in a kotaku article 2 days ago.
http://kotaku.com/fallout-4-has-lots-of-bugs-reviewers-say-1741472178
That is the article I saw, the guy there says he had reports of a guy with elevators simply not working, here is the part pulled from article:
"Pretty much everyone who’s played the game, Suellentrop included, says they’ve run into glitches and bugs ranging from minor (framerate drops) to major (total crashes). One piece, published on The Verge by Kotaku friend Chris Plante, stands out. “Nine hours into Fallout 4,” he writes, “http://www.theverge.com/2015/11/9/9696186/fallout-4-bugs.” As it turns out, elevators are totally broken in his playthrough, and even after loading an earlier save, he just keeps getting stuck.
UPDATE (5:13pm): Turns out Plante hadn’t actually downloaded the latest PS4 system update. Whoops! After updating his copy of the game, he now says elevators are working."
So maybe go to the homescreen, hit options button on FO4, hit "check for updates" and see if maybe your PS4 didn't update the game with the day 1 patch and make sure to come back to post results for others having issues. If update checks don't work, maybe back up the save file on a thumbdrive (just to be sure) and delete/redownload the game data with the patch.