Ship Speed Optimisation with Time-Varying Draft Restrictions

Fuel consumption for a ship can be approximated by a cubic function of the ships speed, and fuel can account for over half of the total cost of maritime transportation (Ronen, 2011). With rising fuel prices in recent years, there has been increased interest in maritime routing and scheduling problems with variable ship speed, which can be used to minimise fuel consumption and therefore reduce shipping costs (Norstad et al., 2011). The draft of a ship the distance between the waterline and the keel, which is a function of the amount of cargo loaded can also affect feasible ship speeds by changing the time windows when the ship can sail past a draft-restricted waypoint. However, most maritime transportation literature does not consider draft restrictions, or only models them as static, rather than varying over time, see for instance Rakke et al. (2011).