Use airbrake / speed-brake early to achieve or regain the required flight path. This does not use more fuel; - if you are already above the required path / speed profile (a reducing energy level), you have already expended the fuel energy - its lost. Thus the earlier that stable conditions can be achieved, maximising the time spent at the lowest ‘energy rate’ should equate to the final min fuel profile (aircraft / config / ATC dependent).
No airbrake does not save fuel, but use of airbrake might save face by avoiding an overrun.
Minimum fuel used is not minimum cost; that is achieved by avoiding the grass at the end of the runway.
Use ‘gate’ checkpoints to monitor the approach - slide 8; a mental model of how-goes-it, referenced from memory.
https://www.dropbox.com/s/o9jkpmtwrt...Final.pdf?dl=0