It is known that - for example - LaMia Airlines Flight 2933 needed to travel 1,605 nautical miles (2,972 km), which exceeds the range of the Avro RJ85 at 1,600 nautical miles (2,963 km). At what point in flight planning does the airline calculate and determine if an aircraft has enough fuel/range for its intended flight?
The spec-sheet range is not a fixed value—
- The range of the RJ85 (BAe 146-200) is 1,570 NM with standard fuel capacity.
- Range values are only valid for certain (marketable) payload/fuel levels.
- If you have less payload and/or more fuel, you increase the range. Example here.
- If there is tailwind, the [air] distance to destination is reduced (apparent range is increased). That's why marketed range circles are not circles, as shown below. Example here.
The wind may provide a head- or tailwind component, which in turn will increase or decrease the fuel consumption by increasing or decreasing the air distance to be flown.— Wikipedia
Corrected distance (after the average-wind is taken into consideration) is checked in the flight planning phase, and the plane is loaded accordingly (fuel and payload). If the aircraft can't reduce the payload to reach its destination, then a technical stop to refuel is planned.
Google Flights shows all the airlines stopping at least once on the way.
The accident happened less than 24 hours ago, and any talk of fuel exhaustion at this stage is simply speculation.
The answer to your question is the pilots check if they have enough fuel to make the destination before every single flight. As others have said, the actual range of the aircraft is dependant on so many variables, that the quoted figure is effectively just a guideline for marketing purposes.