How do you handle customers that think they own you at work?

I'm customer service person at this place (I don't want to give too many details) and I have to make sure no one brings food or drinks in. Well today, I told someone not to bring any drinks in and they said "Nah I'm going to" and just walked in Another guy (A few days later) I told not to bring food or drinks in walked in and went "What are you gonna do? I'm a lot bigger than you, are you going to fight me? This guy is pathetic, let's go." I mean how do you handle these people? I have to just let them have their way because I can't do anything physical to them or I'll get fired on the spot and my boss is usually busy anyways. Oh I'm also a very shy person. What are your opinions?