Conveyor and Counter Project
Your project is pretty simple, and Arduino can handle it easilly. (Pretty much any microcontroller could do it) It's true that only ome program can be run at a time on Arduino (same as on 99% of other microcontrollers) but that one program can handle all three conveyors at the same time. Though I suggest using 3 different Arduinos and separating the systems. If somethig goes wrong on one conveyor it will not affect other ones. Price of Arduino is very low in comparison to price of industrial conveyors. (I didn't believe how much a meter of conveyor costs when you setup a facory line)