Routing of an ASIC chip - time taken?
Routing or PNR takes the longest time as they have to match the timing. It usually finishes the last as they are the recipient of all the chip blocks (typically from various departments). Once all the blocks are received they make sure that the blocks are placed optimally so that the timing is met. 

The team also generates huge data (~700GB in my case per scenario). Once the best timing is achieved other scenarios are removed and best one is kept.

The team may also have to do an IR drop analysis so that every part of the chip gets enough current.