I flew P-3s for years, which are based on the L-188 commercial turboprop airliner. To use the minimum of fuel for a given distance, we flew max range airspeed. That results in maximum miles per gallon fuel. Slowing down below max range airspeed would result in lower fuel burned per hour, but more fuel burned per mile flown. Another way of looking at it is to maximize range (which is to say maximize miles per gallon) increase speed until the per cent increase in fuel flow equals the per cent increase in airspeed. This assumes a no wind scenario. There are factors to adjust for head or tail wind.
Because we had a patrol mission and needed to stay "on station" for the maximum period, we routinely slowed down to max endurance airspeed which resulted in minimum fuel burn per hour. As we burned down our fuel and got light enough, we'd shut down one engine to save fuel. On some missions we'd shut down two engines. We always used all four engines for the return flight.
So in summary, we used max range airspeed to get to our on-station location, then used max endurance airspeed to stay on station, and then used max range airspeed to get back home.