Let us take CI 0 as an example for clarity: CI 0=minimum fuel
(CI 19 will be the same idea, but ofcourse less pronounced)
Then:
Climb will give you max rate of climb: around 250 kt.
Descent will give us green dot.
For minimum fuel you want to be at your cruise-level in the minimum time, hence the max ROC climb speed.
Green dot will give you the best glide angle, so at the same time also the earliest possible TOD in idle.
In other words:
descent=most fuel efficient flight phase (idle)
cruise=2nd most fuel efficient flight phase
climb=least fuel efficient flight phase (high thrust)
So we want to
minimise our time in CLB,
maximise our time in Descent and just accept the cruise bit in between.
Cheers