Most aircraft have a bit of a drag bucket which leads to whatever speed being the preferred nil-wind situation for a given set of conditions. Unless there is a good reason not to do so, an airline will seek to operate at the preferred speed for dollar reasons. Slow down or speed up and the drag goes up and fuel costs as well. Target Mach will be set as accurately as reasonably possible - certainly to better than ± 0.005 (for want of a number) and, generally, considerably better depending on the equipment. At the risk of hanging myself out to dry, you probably could expect accuracy in the vicinity of 0.001-0.002.
Some considerations which will lead to a varying of the target speed -
(a) individual aircraft differences which are monitored by inflight data recording for ops engineering backroom number crunching
(b) strong tailwind - slow down a bit
(c) strong headwind - speed up a bit
(d) curfew/schedule - speed up/down as appropriate
(e) while fuel costs are a significant driver, the airline should be looking to minimise overall cost. Sector length, capital costs, maintenance costs then start to be a noticeable component in the equations.
Generally, jets are operated within a narrow altitude band unless other constraints dictate (eg ATC, weather) so it all gets a tad rigid.
Back 20-30 years ago and earlier we had a reasonable discretion regarding speed and, on occasion, it was clacker all the way - several fond recollections of having to get an aircraft to another port ASAP for whatever reason with nil pax/cabin folk
. These days, with the mighty dollar reigning, fuel burn control (mainly speed driven) dictates a far more rigid approach to the conduct of the operation.