A Fast Exact Algorithm for Airplane Refueling Problem

TL;DR

This paper introduces a recursive algorithm for the airplane refueling problem that efficiently finds the optimal refueling order, outperforming existing methods especially on larger problem instances.

Contribution

The paper presents a novel recursive exact algorithm leveraging dominance properties to solve the airplane refueling problem more efficiently than previous approaches.

Findings

Algorithm outperforms state-of-the-art exact methods.

Efficient on larger problem instances.

Reveals structural properties of the problem.

Abstract

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.