Various deterministic models for economic ship speed optimisation exist in the literature, but none considered the time charter contract, and in particular the influence of the redelivery time. This paper studies the economic optimal speed of a ship on a (time) charter contract through the development of an Operational Research (OR) optimisation model. The ship charterer’s objective is to maximise the Net Present Value (NPV) of a cash-flow function of the ship’s activities over a relevant future horizon $H$, where $H$ can be interpreted as any possible day within the redelivery time window as specified in the time charter clause. We develop a general time charter contract model P${}_M\left(H\right)$, and three special cases P${}_1$, P${}_{\infty }$ and P${}_M(H\to \infty )$, each model mapping onto different contractual contexts, and present algorithms to each of these models for finding optimal ship speeds for any journey structure. While ships on time charter contracts may travel to any series of ports during the charter contract, examining the models’ behaviour when the ship repeatedly executes a roundtrip journey allows us to reach some important general insights about the impact of contract type for any journey structure. In particular, economic speeds in P${}_M\left(H\right)$ follow a very different pattern than those in the classic models from the literature, as well as in the recent class of NPV models $\mathcal{P}$ ($n,m,G_o$) from Ge et al., (2021). We prove that P${}_1$ and P${}_{\infty }$ map quite generally to the classes $\mathcal{P}$ ($1,n,0$) and $\mathcal{P}$ ($\infty ,n,-$), respectively, while $\mathcal{P}$ ($n,m,0$) shows behaviour in approximation equal to the special case P${}_M(H\to \infty )$. We prove that two main strands of speed optimisation models from the literature, which did not consider the contract type nor used the NPV approach, show equivalence under mild conditions to P${}_1$ and P${}_{\infty }$, respectively. These results facilitate matching models to contract types. None of these models, however, matches the general time charter contract model P${}_M\left(H\right)$ introduced in this paper. In general, the paper demonstrates how optimal economic speed is dependent on the (time) charter contract type, and that this should thus be reflected in the speed optimisation model developed.

文献中存在各种经济船速优化的确定性模型，但都没有考虑定期租船合同，特别是还船时间的影响。本文通过开发运筹学 (OR) 优化模型，研究了（定期）租船合同船舶的经济最优航速。船舶承租人的目标是在相关的未来范围内最大化船舶活动的现金流量函数的净现值 (NPV)$H$， 在哪里$H$可以解释为在定期租船条款中指定的重新交付时间窗口内的任何可能的日期。我们开发了一个通用的定期租船合同模型 P${}_{米}\left(H\right)$, 和三个特例 P${}_{\mathrm{1个}}$, 磷${}_{\infty }$和P${}_{米}(H\to \infty )$，每个模型映射到不同的合同上下文，并为每个模型提供算法，以找到适合任何旅程结构的最佳船速。虽然定期租船合同的船舶可能在租船合同期间前往任何系列的港口，但检查模型在船舶反复执行往返旅程时的行为使我们能够获得关于合同类型对任何旅程结构的影响的一些重要的一般见解。特别是 P 中的经济速度${}_{米}\left(H\right)$遵循与文献中经典模型以及最近一类 NPV 模型中的模式截然不同的模式$\mathcal{P}$($n,米,G_o$) 来自 Ge 等人，(2021)。我们证明 P${}_{\mathrm{1个}}$和P${}_{\infty }$非常普遍地映射到类$\mathcal{P}$($\mathrm{1个},n,0$） 和$\mathcal{P}$($\infty ,n,-$), 分别而$\mathcal{P}$($n,米,0$) 显示近似等于特殊情况 P 的行为${}_{米}(H\to \infty )$. 我们证明文献中的两个主要速度优化模型，不考虑合同类型也不使用 NPV 方法，在温和条件下显示等价于 P${}_{\mathrm{1个}}$和P${}_{\infty }$， 分别。这些结果有助于将模型与合同类型相匹配。然而，这些模型都不符合一般定期租船合同模型 P${}_{米}\left(H\right)$本文介绍。总的来说，本文论证了最佳经济速度如何取决于（定期）租船合同类型，因此这应该反映在开发的速度优化模型中。