Containership scheduling with transit-time-sensitive container shipment demand

•Propose the concept of transit-time-sensitive demand.•Containership schedule with transit-time-sensitive demand.•Branch-and-bound based ε-optimal solution methodology.

This paper examines the optimal containership schedule with transit-time-sensitive demand that is assumed to be a decreasing continuous function of transit time. A mixed-integer nonlinear non-convex optimization model is first formulated to maximize the total profit of a ship route. In view of the problem structure, a branch-and-bound based holistic solution method is developed. It is rigorously demonstrated that this solution method can obtain an ε-optimal solution in a finite number of iterations for general forms of transit-time-sensitive demand. Computational results based on a trans-Pacific liner ship route demonstrate the applicability and efficiency of the solution method.