There is no real need to cut your hair at all if you don't want to. There are a hundred different ways to put your hair up even if it is long and thick.
Quick question though. When you say you need to have your hair "up" do you mean that it needs to be completely up and off your shoulders/constricted close to your head or do you mean that it just needs to be secured and not flying loose for health inspection reasons?
When I was waiting tables, they just wanted us to have our hair contained in some way where it wasn't flying around and getting into the food on the trays as we carried it out. I would do a twisted bun like one of the other posters mentioned or I would do a braided ponytail (pull it back in a ponytail and then braid it), or I would do what I called a folded ponytail (you start like you are going to do a regular ponytail but the last couple of rounds, you don't pull the tail of your hair all the way through, so it is trapped under the band and essentially "folds" your ponytail in half). Because my hair is about as long as yours, I generally do a double folded pony, where I trap the ends twice. The folded pony doesn't generally look quite as "finished" as the other styles though.