Ship speed optimisation has a number of
variants, depending on the objective of the problem under consideration,
such as ship scheduling, ship routing, ship fleet sizing, and ship fuel
bunkering13,14. All ship speed optimisation problem
variants require in their mathematical formulation, in the objective and
or in the constraints, a relation expressing the variation of ship fuel
consumption rate (per unit time) with ship speed. This relation may be
determined employing the Holtrop-Menen procedure15,16(in two steps) to determine the relation between ship fuel consumption
rate (per unit time) and ship power propulsion rate (per unit time).
From data describing the relation between ship propulsion rate (per unit
time) and ship speed, the required variation of ship fuel consumption
rate (per unit time) with ship speed is finally obtained. This variation
is nonlinear, typically in the form