daveonhols:
The Cost Index mentioned is generally for newer generation aircraft with flight management computers. The computer flight plan fashioned by flight control/management is prioritized by the company for their benefit, balanced by the operating costs and the need to keep the airplane on schedule.
When I was last at the airline I flew the classic 747's (100/200). The airplane had both .84M, .86M and long range cruise charts. After 16 years on the airplane, I found that the 747 seemed to be most comfortable at .85M to .855M, and my fuel burns vs the CFP data burns confirm that. Anything slower than .84M caused a higher body attitude and more drag and all the negatives that result. The Whale didn't like slow. .86M and higher sucked down fuel at a prodigious rate, so those speeds were reserved for making time and service on mostly rare occasions.
Over the North Pacific between Alaska and Japan, where I commonly flew, the common Mach was .84-.86M for the large widebodies. The 767 flew at .80-.82M, resulting in separation issues.
The other issue in cruise is optimum flight level for a particular weight, taking into account ISA deviation (temperature deviation from standard). Flying at this flight level resulted in the best efficiency. The -100 @ 660,000# had an optimum cruise flight level of 330 and the -200 optimum was 40,000# above that weight at FL330. Optimum cruising flight level increased 1,000' for every 25,000# of fuel burned (about an hour). As a result, my rule was to maintain .85M and go to the optimum flight level for the weight if ATC allowed the profile.
There a few other variables, but constant Mach and optimum altitude were generally the targets for long overwater flights.