The rest of this paper is organised as follows. In Section, the ship speed optimisation problem is described. This is followed by presenting the nonlinear programming and the linear programming formulations in Sections 3 and 4, respectively. A case study is presented in Section 5, with a view to serving as a basis for a comparative quantitative assessment of the nonlinear programming and the linear programming formulations. The paper is concluded in Section 5, with a general comparative assessment of the aforesaid formulations, and recommendations for future research.