Robust liner ship routing and scheduling schemes under uncertain weather and ocean conditions

•An optimal liner ship routing and scheduling model in the mixed integer linear programming form is proposed, particularly taking into account schedule-sensitive demand and late-arrival penalty.•Two robust optimization counterparts of the deterministic ship routing and scheduling model are constructed for finding solutions in the uncertain weather and ocean conditions along the Northern Sea Route (NSR).•The value of robust optimization techniques in worst cases, the impact of revenue rate and demand sensitivity on solutions, the relationship between the order of a visited port and the weight of its uncertainty budget, and the relationship between the solution robustness and the variation tendency of uncertainty budgets, are exhibited.