The c0cky answer is they don't - the pilot is just a bus driver with an ATPL, who steps onto the plane and somebody hands him a pack containing the route (the flight plan has already been filed, of course), the weather, etc. Everything has been worked out by the ops department.
I know at least some operations use a Jeppesen product called Jetplanner. I tried to find out more from Jepp once, but made the mistake of asking about the cost, and their attitude was that if I need to ask I can't afford it and they stopped the communications.
Jetplanner seems to do just about everything for upper airway route planning including whether it's worth filling up at different places versus fuel costs etc etc etc.
You will get a better answer posting the Q in some airline forum.
OTOH some corporate jet pilots have to do everything themselves.