"Food, water, medicine, this way." signs will make it possible to direct the people that didn't make any preparations to another city where they can die while making the journey.

What you want to do is prepare signs in advance that say two things, that help is coming and that a refugee center is in the next city. These signs can point people in various directions and the goal is to either direct them into an area they will die or keep them perpetually wandering instead of attacking people for food and stuff.

You can make a general big professional sign pre-collapse that says "Refugee center this way! Looters will be denied aid, aerial surveillance is in effect." then glue a map of the area to it with a route drawn to the supposed destination from the spot you place it.

People can travel 20 miles a day walking with food and water. But how long people can go without water varies with conditions.

You can also distribute poisoned food to rival groups to kill them while pretending to help them from the outset, then they won't be attacking you later and you can acquire whatever territory they previously had by going through and killing the rest, which you can do safely by walking through their area screaming, "everyone died, is anyone there" making them think it happened to your people too before shooting them or poisoning them again.