Joint planning of fleet deployment, speed optimization, and cargo allocation for liner shipping

In this paper, we study a comprehensive model that addresses fleet deployment, speed optimization, and cargo allocation jointly, so as to maximize total profits at the strategic level. Our model considers a general fuel consumption function that depends on speed and load. To overcome intractability caused by nonlinear terms, we further separate fuel cost into two terms associated with ship speed and load to obtain a mixed integer linear programming formulation for approximation. Based on column generation techniques, we develop an iterative search algorithm that adaptively reorganizes the approximated formulation. We conduct extensive experiments using generated data sets from actual liner shipping services in different regions of the world to show the effectiveness of our approach as well as the significant impact of speed-load factors on fuel consumptions. Managerial insights are obtained by testing the model under different scenarios, which may greatly assist decision makers in the liner shipping industry.