Bunker fuel cost and freight revenue optimization for a single liner shipping service

This paper aims to maximize the freight revenue minus bunker fuel cost for a single liner shipping service. This optimization contains the determination of the sailing speeds, bunkering strategy, and shipment strategy. We first formulate this optimization problem as a mixed-integer nonlinear programming model and then make some transformations to linearize the nonlinear terms. The transformed model is a mixed-integer linear programming model and provides an upper bound for the original model. We then construct another mixed-integer linear programming model and prove that its any optimal solution can be transformed into a feasible solution of the original model. In case studies, the proposed models are applied to two real liner service routes and the computational results demonstrate the efficiency and effectiveness of our solution method. Some insights from numerical experiments are provided in the end. (C) 2019 Elsevier Ltd. All rights reserved.