Calculation of fuel cost vs. other costs(crew variable costs, time related costs of components, on time performance, etc).
Flying faster than your most efficient speed for the flight(adjusted for head/tail winds) burns additional gas. The company calculates the other costs and benefit of on time performance/connections and issues a CI to use.
However, that's a predicted CI for when the paperwork is generated and the anticipated 'off' time for the flight. If we have a different 'off' time then planned we do not get an updated CI, that is based on our actual off time, to use. Then it's back to the 'old school'/common sense method. If you're airborne ahead of the estimated 'off' time you don't need to be using a high CI. If you're airborne later then the flight plan estimate, and saving time will allow people to make connections or get the entire crew/plane/system back on schedule, flying faster(burning additional gas) makes sense.