Decisions on sailing frequency and ship type in liner shipping with the consideration of carbon dioxide emissions

Abstract

To find the optimal sailing frequency and optimal ship type of container liner operation under low carbon environment, a mixed integer nonlinear programming model is proposed, in which the ship load capacity constraint is considered. The objective of the proposed model is to minimize voyage total cost consisting of carbon dioxide emissions cost, voyage shipping cost(fuel costs, port charges, operating costs) as well as shipper’s inventory cost in a certain operation period. It is shown from theoretical analysis that the proposed model can be solved by Kuhn–Tucker condition and Enumeration method. A numerical example is given to demonstrate the effectiveness of the proposed model, and analyze the impacts of carbon tax levels, fuel prices, ship size and the sailing frequency on total cost and environmental cost. The results show that as the size of the ship increases, the ship total cost decreases first and then increases, the percentage of carbon emission cost in total ship cost increases. As the sailing frequency increases, the ship total cost decreases first and then increases, the percentage of carbon emission cost in total ship cost decreases. The results indicate that the shipping companies can improve economic performance and environment performance simultaneously by employing reasonable sailing frequency and ship type decisions.