Inverse Control Constrained Optimization of Vessel Speed Decisions Under Environmental Risk: Evidence from Arctic Shipping

Understanding how decision makers balance operational efficiency with environmental and ecological risks is central to vessel navigation. We model vessel speed as a control variable in a constrained optimization framework in which vessel operators balance multiple competing objectives, including transit efficiency, ice related navigational risk, and whale related ecological risk. The underlying risk parameters are estimated using over 14 million Automatic Identification System (AIS) observations from the United States Arctic (2010-2019), together with environmental covariates and spatially explicit whale density estimates. The framework incorporates a nonlinear risk objective, vessel heterogeneity, and regularization to ensure stable and interpretable results. The inferred trade offs reveal distinct decision making patterns across vessel groups and navigational statuses. Vessel types such as Tug Tow and Cargo balance operational speed with environmental and ecological considerations. In contrast, several vessel groups, including Fishing, Passenger, and Unspecified vessels, are strongly influenced by ice related risk, while Pleasure Craft and Tankers exhibit higher sensitivity to whale related risk. Across navigational status categories, similar heterogeneity is observed. The dominant status, under way using engine, displays a clear trade off, whereas other statuses, such as aground and undefined, are strongly shaped by ice related constraints. Statuses including restricted maneuverability and engaged in fishing exhibit higher estimated sensitivity to whale related risk, though with substantial uncertainty. Sensitivity analysis indicates that increasing whale-related risk weighting produces limited changes in model-implied optimal speed, whereas increasing ice-related risk leads to more consistent reductions.