Shortest path in the presence of obstacles: An application to ocean shipping

This paper presents the problem of determining the estimated time of arrival (ETA) at the destination port for a ship located at sea. This problem is formulated as a shortest path problem with obstacles, where the obstacles are modelled by polygons representing the coastlines. An efficient solution algorithm is proposed to solve the problem. Instead of generating a complete visibility graph and solving the problem as an ordinary shortest path problem, the algorithm constructs arcs to the ship node during the solution process only when needed. This greatly enhances the algorithmic performance. Computational results based on test problems from an actual dry-bulk shipping operation are provided. The proposed algorithm is implemented in a decision support system for the planning of ship operations and it has successfully been applied on several real life problems.