Liner ship scheduling with time-dependent port charges

Abstract

Port operators provide attractive port charges, and liner shipping companies make decisions on ship scheduling, in accordance with port charges. This paper proposes a liner ship scheduling problem with time-dependent port charges. Empirical studies on the ship arrival time distribution basically show a periodic phenomenon, which can be used to support the reasonability and validity of our time-dependent port charge scheme. To address our problem under different scenarios, we propose two mixed-integer nonlinear programming models, where the nonlinear objective functions can be linearized by using an outer approximation method. Numerical experiments are provided to analyze the effectiveness of our port charge scheme.