Assign IP Address to Each Port

I'm trying to figure out how to setup networking for an array of industrial devices.

There are 200 of these devices, each identical. My hope is that I can have these devices automatically assigned an ip address based on what switch port they are plugged in to. This way, I can infer physical location (important for the operation of these devices) from the ip address, and if I have to replace a faulty unit, it will be a plug and play affair.

I think what I want is a Cisco Layer 3 switch?

I don't know the right words to search for to figure out how to approach this problem. Pointers to keywords, topics, or tutorials would be greatly appreciated!