the vessel scheduling problem in a liner shipping route with heterogeneous fleet

Increasing volumes of the international seaborne trade force liner shipping companies to improve efficiency of their operations to remain competitive. many of liner shipping companies continue increasing size of their vessels, as larger vessels provide lower voyage costs per container due to their economies of scale. larger vessels also allow liner shipping companies more efficiently share the demand with the alliance partners. nowadays, many of liner shipping routes are served by vessels of different types (e.g., small, medium, large). however, the key assumption of studies on vessel scheduling, conducted to date, is homogeneous nature of the vessel fleet (i.e., all vessels in the fleet, serving a given liner shipping route, have the same technical characteristics). this study proposes a novel mathematical model for the vessel scheduling problem with heterogeneous fleet. the objective of a mixed integer non-linear model is to minimize the total vessel turnaround cost. due to high non-linearity of the proposed mathematical model a non-linear optimization solver is used to solve it. numerical experiments are performed to evaluate efficiency of the proposed solution approach and the novel methodology. results demonstrate a computational efficiency of the adopted solution approach. furthermore, vessel schedules are found to be more sensitive to introduction of larger vessels in the fleet as compared to increase in the unit bunker cost.