  We consider the airplane refueling problem, where we have a fleet of
airplanes that can refuel each other. Each airplane is characterized by
specific fuel tank volume and fuel consumption rate, and the goal is to find a
drop out order of airplanes that last airplane in the air can reach as far as
possible. This problem is equivalent to the scheduling problem $1||\sum w_j (-
\frac{1}{C_j})$. Based on the dominance properties among jobs, we reveal some
structural properties of the problem and propose a recursive algorithm to solve
the problem exactly. The running time of our algorithm is directly related to
the number of schedules that do not violate the dominance properties. An
experimental study shows our algorithm outperforms state of the art exact
algorithms and is efficient on larger instances.
