I am sitting at the airport and I was wondering if there is an optimal number of passengers to try to board a plane through an interesting fare.
Flying an empty plane is obviously the worst situation: you have fixed costs and fuel costs that depend on the weight of the plane. For an empty plane your gain is 0% (all loss, 100% would mean breaking even and anything above that is pure gain).
As you start to add passengers, their weight is added (say, 110 kg per passenger and their luggage), which means more fuel to buy. But you also get some income so you are raising up from 0%.
Is the relationship
gain(number_of_passengers_boarded) such that the weight passengers add is insignificant, semi-significant, or a key factor? Is the curve always raising (which means the more passengers - the better, until all space is exhausted)? This will certainly depend on the plane, so with two reasonable extremes (a typical regional jet vs a long-haul jet) are there key differences?
In other words: is it always interesting to lower the fare as the start date approaches? (purely from a gain perspective, I am not taking into account ways to optimize this for a passenger by, say, waiting until the last moment)