I'm all out of fucks to give when it comes to pushy-ass employees at work

Every year it's the same thing: people bitching to me about their mail they need when it comes in, that they say they need right away. I recently sent out an email to all employees reminding everyone how busy the procurement department is this time of year and to please be patient with us, that delivering packages and mail tends to be a slow process due to the literal truckloads we tend to get every day, but we will get everything out as promptly as we can. Even after I sent that out, people still get pushy and impatient with us! I've tried being professional about this and I personally am just over it already. I've already had to snap at a couple of employees for their BS and if they have a problem with it, they can go report it to HR. See if I give a shit. We've got a lot of work to do in my department and it's stressful enough without a bunch of entitled fuckheads riding our asses when we're trying to be as fast as we can over here.