Conveyor belts? 2D

If this was posted multiple times, I'm sorry, I wasn't logged in when I first tried, and it's not showing up now, so hopefully this is the only version.

I'm trying to work out all the mechanics for a tycoon style game, like Prison Architect or Factorio. One item I feel is pretty important is some form of item movement besides workers. In Factorio one of them is conveyor belts, a farily simple thing in theory. I can think of three main ways to make them work.

1. A very limited pathfinding system for items placed on conveyor belts where items determine their path from the start. Not sure how to deal with belts being removed mid-movement though or how to do one-way nodes if using something like A*.

2. Items checking each tile they're on to see what direction to go. This seems like the most likely but when there are hundreds or more items moving it seems like it might bog the system down

3. Physics based, which seems not as useful in case the items might fall off?

If anyone has done something like this, or has any ideas, please let me know! I've searched a bunch but I keep finding only 3D physics based ones which don't really suit me needs :(