Adaptive ship routing through stochastic ocean currents: General formulations and empirical results

Technological advances in satellite altimetry offer the potential for providing timely ocean current information which could be used when optimizing strategic ship routes. However, the time to collect and process the raw data and deliver the processed information to the end user makes the information an inaccurate description of the actual current patterns that would be encountered by a ship in areas of dynamic current activity. We, therefore, develop an optimization approach that explicitly addresses the uncertainty that results from these time lags. We formulate the routing problem as an adaptive, probabilistic dynamic program. Our formulation incorporates three information elements: (i) aged synoptic ocean current information; (ii) localized information encountered by the ship; and (iii) state transition probabilities of current changes derived from historical data. The solution provides a set of optimal policies that minimizes a ship's expected fuel consumption. We conduct a simulated, numerical study to compare the performance of our adaptive, probabilistic formulation to that of its deterministic counterpart in an area of the Gulf Stream. For the eastbound (‘with current’) voyages investigated, our approach consistently outperformed the deterministic approach. For the westbound (‘against current’) voyages, our approach performed equally well for time lags of 5 days or less and slightly better for longer time lags. These numerical results indicate the promise of our stochastic, adaptive formulation for the current routing problem.