Solving the Flight Radius Problem

In this article, we present the flight radius problem on the condensed network. This problem consists of locating in the network what routes represent business opportunities that are attractive regarding time or cost criteria, and passing through a specific flight. We introduce a regret function to model the regret compared to the optimal value of such criteria. We work with a startup company specialized in air transportation. The company has developed a decision tool for airline managers to analyze and simulate a new market. Our problem is derived from this application. Thus, we start by formulating the problem as finding a maximal sub-graph such as for each node, there exists a valid path by the regret function. Then, we propose two methods for solving the problem. One using procedures of the graph database Neo4j where the condensed network is stored. The second one is a new algorithm based on Dijkstra algorithm. Finally, we have been able to report results on a set of real-world instances, based on different (OD) pairs and various values of the regret, studying the impact of considering different combinaison of node's type: Hub & Spoke.