The green vessel scheduling problem with transit time requirements in a liner shipping route with Emission Control Areas

Increasing volumes of the international seaborne trade and new regulations on vessel emissions require liner shipping companies to enhance efficiency of their operations to remain competitive and in the meantime comply with the established restrictions on emissions that are produced by vessels. This paper presents a novel mixed integer nonlinear mathematical programming model for the green vessel scheduling problem with transit time requirements in a liner shipping route with “Emission Control Areas”, which not only enforces constraints on the quantity of emissions that are produced by vessels within “Emission Control Areas”, but also captures the cargo transit time requirements. The model's objective aims to minimize the overall route service cost. A number of linearization techniques are proposed for linearizing the original nonlinear problem. The dynamic secant approximation procedure is used to solve the linearized problem. A set of numerical experiments are performed to evaluate the efficiency of the proposed solution approach and assess the effect of introducing both emission constraints and cargo transit time requirements on design of vessel schedules.