The air pollution caused by the use of heavy fuel oil in shipping is a growing problem that is drawing increased attention. Methods have been developed to reduce air emissions from ships, more or less aimed at the choice of fuel and the related air emissions. However, the emissions of particulates, sulphur and carbon dioxide, which contribute to the greenhouse effect are not only related to the choice of fuel but also to the amount of fuel consumed in the combustion engines. This paper proposes an additional method that can contribute to the reduction of the air pollution from ships by decreasing the fuel consumption. This is done by specifying the amount of fuel that can be consumed on a specific ocean crossing and by computing a minimal-time route for that given amount of fuel, so decreasing the fuel consumption in a verifiable way.

Under some circumstances, dependent on a ship's velocity, the wave period and wave direction, certain courses induce heavy rolling and must be avoided. This paper proposes a computational method for the solution of optimal control problems in ship routing for ships with such limited manoeuvrability. Known results for the control problem of Bolza with additional constraints are interpreted in terms of this new problem. This approach is equivalent to the application of Pontryagin's maximum principle. The method is an extension of an earlier method dealing with the meteorological navigation of ships with unrestricted manoeuvrability and gives a more realistic picture of what really could happen in practice.