Maritime transportation plays a central role in international trade, being responsible for the majority of long-distance shipments in terms of volume. One of the key aspects in the planning of maritime transportation systems is the routing of ships. While static and deterministic vehicle routing problems have been extensively studied in the last decades and can now be solved effectively with metaheuristics, many industrial applications are both dynamic and stochastic. In this spirit, this paper addresses a dynamic and stochastic maritime transportation problem arising in industrial shipping. Three heuristics adapted to this problem are considered and their performance in minimizing transportation costs is assessed. Extensive computational experiments show that the use of stochastic information within the proposed solution methods yields average cost savings of 2.5% on a set of realistic test instances.