where b0, b1, and b2 are regression parameters. Psaraftis and Kontovas4,5 have discussed at length the nature of the variation of ship speed consumption (per unit time) with ship speed, showing its complexity in view of its dependence on many factors, and pointing out4 that “It is known from basic naval architecture that fuel consumption depends non-linearly on both ship speed and ship payload”, and concluding that11 “the function f can be a complex function which may not even be defined in complex form”. It is worth noting that assuming that this function is convex, then the optimal solution is one where ship speed is uniform19; however, the convexity assumption may not hold in practice, as for example when different ship fuel consumption rate – ship speed curves are used for different fuels, as is the case in the case study which is presented in Section 5. In almost all work reported on ship speed optimisation problem variants the cubic function is employed to represent the variation of ship fuel consumption rate (per unit time) with ship speed. However, there is one notable exception which has not been used in the ship speed optimisation literature, namely that of Brown et al.10, whereby, instead of using ship speed as a decision variable, a ship speed level mix is selected a priori and time spent in each ship speed level (which is known) is defined as the decision variable. In the next two Sections, the nonlinear programming and linear programming models, respectively, are formulated for the ship speed optimisation problem variant for a ship voyage between two ports, wherby it is required to minimise ship fuel consumption and having a due arrival date at destination port.