A comprehensive multi-objective optimization model for the vessel scheduling problem in liner shipping

The international seaborne trade volumes have been continuously increasing over the last years. Many liner shipping companies started consolidation to form stronger alliances and attract new customers. In order to remain competitive and avoid potential monetary losses, liner shipping companies have to improve efficiency of their vessel schedules. Some of the decisions that have to be made by liner shipping companies are conflicting in their nature. However, the existing vessel scheduling models generally combine the conflicting objectives into one objective function, which aims to minimize the total route service cost. Such approach imposes limitations for liner shipping companies in the analysis of tradeoffs between the conflicting objectives. To avoid the latter drawback, this study proposes a multi-objective mixed integer nonlinear optimization model for the vessel scheduling problem, which accounts for all major route service cost components reported in the literature and separates them in two conflicting groups. The original mixed integer nonlinear model is linearized by discretizing the vessel sailing speed reciprocal, and the Global Multi-Objective Optimization Algorithm is developed to solve the linearized model. A set of numerical experiments are conducted for the Asia-Mediterranean Express Service liner shipping route. Results demonstrate that negotiation of both vessel service time windows and handling rates between liner shipping companies and marine container terminal operators may significantly reduce the total route service cost components. Furthermore, vessel schedules are found to be more sensitive to the unit fuel cost as compared to the unit carbon dioxide emission cost.