LIDO, Jeppesen and many more offer the airlines ways to optimise predicted fuel burns. But each comes with its own limitations and so forth.
Most importantly, is how good and dedicated your operations staff is to maintain and use correctly all the figures provided, including route restrictions (intermediate level off altitudes), which can be great discrepancy creators.
Here are some of the common but not always incorporated items for accuracy:
* Individual airframe corrections versus a new aircraft
* Accurate route profiling, vertically
* Optimising lateral routings
* Inclusion of runway specific fuel burns for a single SID STAR
* Operational information for higher/lower levels fuel/time penalties/gains
* Accurate use of statistical taxi times runway specific if needed
In terms of accuracy: ~50 kgs each sector, <1%
on both of todays ~2:30h flights which were predicted with LIDO, using the correct registration, incorrect FL for 1st route (as not tankering as much as LIDO suggested thus operating lighter and able to climb taking advantage of additional tailwind), correct runway usage, etc...