The optimal (economic) speed of oceangoing vessels has become of increased importance due to the combined effect of low freight rates and volatile bunker prices. We examine the problem for vessels operating in the spot market in a tramp mode. In the case of known freight rates between origin destination combinations, a dynamic programming formulation can be applied to determine both the optimal speed and the optimal voyage sequence. Analogous results are derived for random freight rates of known distributions. In the case of independent rates the economic speed depends on fuel price and the expected freight rate, but is independent of the revenue of the particular voyage. For freight rates that depend on a state of the market Markovian random variable, economic speed depends on the market state as well, with increased speed corresponding to good states of the market. The dynamic programming equations in our models differ from those of Markovian decision processes so we develop modifications of standard solution methods, and apply them to small examples.
The purpose of this paper is to clarify some important issues as regards ship speed optimization at the operational level and develop models that optimize ship speed for a spectrum of routing scenarios in a single ship setting. The paper’s main contribution is the incorporation of those fundamental parameters and other considerations that weigh heavily in a ship owner’s or charterer’s speed decision and in his routing decision, wherever relevant. Various examples are given so as to illustrate the properties of the optimal solution and the various trade-offs that are involved.
Different procedures for estimation of the extreme global wave hydroelastic responses in ships are discussed. Firstly, stochastic procedures for application in detailed numerical studies (CFD) are outlined. The use of the First Order Reliability Method (FORM) to generate critical wave episodes of short duration, less than 1 minute, with prescribed probability content is discussed for use in extreme response predictions including hydroelastic behaviour and slamming load events. The possibility of combining FORM results with Monte Carlo simulations is discussed for faster but still very accurate estimation of extreme responses. Secondly, stochastic procedures using measured time series of responses as input are considered. The Peak-over-Threshold procedure and the Weibull fitting are applied and discussed for the extreme value predictions including possible corrections for clustering effects.