Green vessel scheduling in liner shipping: Modeling carbon dioxide emission costs in sea and at ports of call

Considering a substantial increase in volumes of the international seaborne trade and drastic climate changes due to carbon dioxide emissions, liner shipping companies have to improve planning of their vessel schedules and improve energy efficiency. This paper presents a novel mixed integer non-linear mathematical model for the green vessel scheduling problem, which directly accounts for the carbon dioxide emission costs in sea and at ports of call. The original non-linear model is linearized and then solved using CPLEX. A set of numerical experiments are conducted for a real-life liner shipping route to reveal managerial insights that can be of importance to liner shipping companies. Results indicate that the proposed mathematical model can serve as an efficient planning tool for liner shipping companies and may assist with evaluation of various carbon dioxide taxation schemes. Increasing carbon dioxide tax may substantially change the design of vessel schedules, incur additional route service costs, and improve the environmental sustainability. However, the effects from increasing carbon dioxide tax on the marine container terminal operations are found to be very limited.