Sailing Speed Optimization Research Articles

Ship sailing speed optimization considering dynamic meteorological conditions

Sailing speed optimization is a cost-effective strategy to improve ship energy efficiency and a viable way to fulfill emission reduction requirements. This study develops a novel ship sailing speed optimization method that considers dynamic meteorological conditions. We first develop an artificial neural network model for vessel fuel consumption rate (FCR) prediction based on a fusion dataset of ship noon reports and public meteorological data. Then, based on the predicted FCRs, the method repeatedly formulates a multistage graph based on the most recent forecasts, and optimal speeds for the remaining voyage are obtained until the vessel reaches the destination port. The computational efficiency of the optimization process is enhanced by progressively removing nodes without connections to successor nodes, starting from the penultimate stage. We examine the proposed method on two 11-day voyages of a dry bulk carrier. Results show that the proposed method demonstrates significant reductions in fuel consumption by 5.35% compared with a constant sailing speed scheme and by 7.34% compared with a static speed optimization model. In addition, the proposed model achieves similar fuel savings to those achieved by speed optimization based on actual meteorological conditions, enabling shipping companies to optimize ship sailing speeds in the absence of actual meteorological conditions. The proposed method can be applied to various types of vessels due to its flexibility and adaptability, making it a valuable tool for the shipping industry to reduce greenhouse gas (GHG) emissions, thereby supporting the International Maritime Organization (IMO)’s goal of reaching net-zero GHG emissions by around 2050.

Managing port disruption through sailing speed optimization for sustainable maritime transportation

Ports, as nodes in maritime transportation, frequently face disruptions leading to congestion, adversely affecting the efficiency and sustainability of the global supply chain. This study considers the speeding-up strategy to alleviate port congestion. We model the transportation network as a closed Jackson network and adopt a tailored mean-value analysis algorithm to solve the model. To deliver the increased sailing speed, we further put forward a bi-section search algorithm. Our numerical analysis results demonstrate the feasibility of increasing speed to alleviate port congestion. However, when port congestion exceeds a certain threshold, the system faces collapse, rendering the increase in speed ineffective. Additionally, we recommend shipping companies consider using clean energy when employing the speeding-up strategy to mitigate congestion, thus safeguarding the environment. Our study combines theoretical methodologies and analytical models, providing insights regarding speeding up the vessels. The findings of this study offer guidelines for real-world sustainable maritime practice.

Comparison of deterministic and ensemble weather forecasts on ship sailing speed optimization

Ship sailing speed optimization models are constructed based on prediction of ship fuel consumption, whose accuracy is highly influenced by the quality of sea and weather information. In this study, we develop two fusion methods for combining external meteorological data with ship noon report data, including the rhumb line based fusion method and the direct fusion method, and compare them in terms of accuracy in providing meteorological data. Next, we propose a framework based on the better data fusion strategy for comparing the impacts of deterministic and ensemble weather forecasts on ship speed optimization performance, enabling the evaluation of ship fuel consumptions under different speed plans based on weather forecast data available before departure. Results show that speed optimization based on ensemble weather forecasts has greater potential than that based on deterministic weather forecasts to diminish ship fuel consumption and thus to reduce greenhouse gas emissions.

A unified operation decision model for dry bulk shipping fleet: ship scheduling, routing, and sailing speed optimization

A unified operation decision model for dry bulk shipping fleet: ship scheduling, routing, and sailing speed optimization

A Stochastic Sailing Speed Optimization and Vessel Deployment Problem in Liner Shipping

In this research, we consider the stochastic sailing speed optimization and vessel deployment problem and examine the trade-off between sailing speed and the number of vessels required to provide a certain service in international liner shipping. Solving this kind of stochastic program is a challenging task. To address this issue, we construct a mathematical formulation based on Ng (1) and Ng (2) and enhance the linearization techniques from Wang and Meng (3) so that problem instances of an even larger scale can be solved. The proposed formulation has been numerically applied to solve realistic cases, and the empirical results show that the proposed framework is effective in solving this stochastic programming problem. The managerial insights from our work can help liner shipping companies determine bunker consumption and vessel deployment strategies.

Liner sailing speed optimization considering wind and waves

This paper proposes a new sailing speed optimization problem considering sea conditions such as wind and waves for a container shipping company. Since wind and waves, as exterior factors, can reduce speed, more power is employed as compensation to maintain regular service frequency and avoid delay, resulting in additional bunker consumption and higher cost. Hence, it is necessary to optimize the sailing speed according to the wind and waves. A power model was built to determine the reduced speed caused by the wind and waves for quantifying the speed reduction. On the basis of the proposed model, we developed a mixed-integer nonlinear programming model for a sailing speed optimization problem considering the wind and waves. In view of the complexity of the function for determining the speed reduction, a discrete method is proposed to transform the proposed mixed-integer nonlinear programming model into a mixed-integer linear programming model. Finally, a numerical experiment was conducted to verify and validate the applicability.

Flexible Optimization of International Shipping Routes considering Carbon Emission Cost

Carbon emissions cost is a potential effective measure to restrict hydrocarbon pollution in the international shipping trade. The minimization of the total cost is pursued by ship operators, whereas voyage cost is increasingly involving the replacement of clean fuel and changing the cost of the shipping route. A flexible optimization method focusing on maximizing the total profit is developed in terms of sailing speed optimization and single port skips integrate carbon emission influence. An actual ocean shipping route from Shanghai to Rotterdam is applied to validate the effectiveness of the proposed models. The results have shown that the shipping route profit is volatile along with the sailing speed and the number of port calls. However, the profit will be maximized when applying the single port skip and will slow down the sailing speed at the same time. The demand of planned skip port can be supported by a short line container. A system composed of ocean container liner and short line container can improve the profit by 4.05% and reduce the carbon emission by 19.70%. Furthermore, sensitive results show that the profit is less affected by the changing of the carbon emission cost. A small size container has enough ability to solve the short transportation demand in adjacent ports and convert extraberthing cost into profit. These findings can provide reliable support for the shipping route decision process considering future carbon emission costs.

Impact analysis of different container arrival patterns on ship scheduling in liner shipping

ABSTRACT Different transportation modes interrelate in intermodal transportation. Previous researches on intermodal transportation mainly investigate policy, network design, cargo routing or drayage operations. In order to explore the coordination between two connected transportation modes, this paper considers the connection between inland transportation and maritime container transportation. By making use of different container arrival patterns resulted from inland transportation, this paper focuses on liner ship scheduling with sailing speed optimization, as well as considering the container storage cost at each port. The studied problem is formulated as a mixed-integer nonlinear programming model, which is efficiently solved by using an outer-approximation method. Numerical results show that the optimal ship schedule varies with different container arrival patterns, and this influence is also related to the container storage cost and the bunker price.

Holistic tactical-level planning in liner shipping: an exact optimization approach

Effective liner shipping is important for the global seaborne trade. The volume of cargoes transported by liner shipping has been increasing over the past decades. Liner shipping companies face three levels of decision problems, including strategic, tactical, and operational problems. The tactical-level decisions are commonly made every three to 6 months. These decisions include: (1) port service frequency determination; (2) fleet deployment; (3) sailing speed optimization; and (4) vessel schedule design. Most of the concurrent liner shipping studies have addressed the tactical-level decision problems separately. Even though a few studies have proposed joint planning models that capture multiple decision problems at the same time, none of the conducted studies has integrated all the four tactical-level decision problems. To address this gap in the state-of-the-art, this study presents a holistic optimization model that addresses all the tactical-level liner shipping decision problems, aiming to maximize the total profit obtained from liner shipping services. The key route service cost components, found in the liner shipping literature, are considered in this study, which include: (1) vessel operational cost; (2) vessel chartering cost; (3) port handling cost; (4) port late arrival cost; (5) fuel consumption cost; (6) container inventory costs in sea and at ports of call; and (7) emission costs in sea and at ports of call. An exact optimization approach is adopted for the developed mathematical model. The computational experiments, conducted for a set of Asia-North America liner shipping routes, showcase the efficiency of the proposed approach and offer some important managerial insights.

Sailing Speed Optimization Model for Slow Steaming Considering Loss Aversion Mechanism

This paper analyses loss aversion mechanism (LAM) of the shipping company’s decision-makers about the risk-based decision (RBD) for slow steaming and generalizes a novel optimization model for the sailing speed through the trade-off between fuel consumption, SOx emissions and delivery delay. The value functions against the benchmark speed were constructed based on physiological expected utility (PEU) to reveal the features of loss aversion, and the objective function was derived from these value functions with the aim to optimize the sailing speed. After that, a Genetic Algorithm (GA) solution with fitness function and special operators was built to solve the proposed model. Finally, the model was applied to pinpoint the PEU for the optimal sailing speed against the benchmark speed, and the sensitivity of the model was discussed with different benchmark speeds, value function weights and input parameters. The analysis shows that the proposed model can assist the slow steaming RBD based on the inner feelings of the shipping company’s decision-makers, offering a novel tool for sailing speed optimization.

Integrated Liner Shipping Network Design and Scheduling

In global liner shipping networks, a large share of transported cargo is transshipped at least once between container vessels, and the total transportation time of these containers depends on how well the corresponding services are synchronized. We propose a problem formulation that integrates service scheduling into the liner shipping network design problem. Furthermore, the model incorporates many industry-relevant modeling aspects: it allows for leg-based sailing speed optimization, it is not limited to simple or butterfly-type services, and it accounts for service-level requirements such as cargo transit time limits. The classic liner shipping network design problem is already a hard problem, and to solve the extended version, we propose a column-generation matheuristic that uses advanced linear programming techniques. The proposed method solves LINER-LIB instances of up to 114 ports and, if applied to the classic liner shipping network design problem, finds new best solutions to all instances, outperforming existing methods reported in the literature. Additionally, we analyze the relevance of scheduling for liner shipping network design. The results indicate that neglecting scheduling and approximating transshipments instead may result in the design of liner shipping networks that underestimate cargo transit times and their implications.

An Expected Utility-Based Optimization of Slow Steaming in Sulphur Emission Control Areas by Applying Big Data Analytics

This paper analyses the operator's risk-based decision (RBD) company for slow steaming, and creates a sailing speed optimization model for slow steaming (SSOM-SS), aiming to balance the expected utility-based objectives (EUO) of fuel consumption, SOx emissions and delivery delay. Considering the limitations of existing theoretical fuel consumption functions under uncertainties in voyages, the authors applies big data analytics (BDA) techniques like data fusion and feature selection to provide the SSOM-SS with accurate and suitable data on fuel consumption. In addition, a solver is built based on the genetic algorithm (GA) to solve the SSOM-SS. The effectiveness of the SSOM-SS is verified through a case study on the RBD for slow steaming of an Orient Overseas Container Line (OOCL) containership sailing across the sulphur emission control areas (SECAs) in Chinese coastal regions. The results show that the SSOM-SS can facilitate the RBD for slow steaming, and provide a novel tool for sailing speed optimization.

Joint Ship Schedule Design and Sailing Speed Optimization for a Single Inland Shipping Service with Uncertain Dam Transit Time

Inland shipping has received extensive attention in practice and is a high energy-consuming service sensitive to the river streamflow speed and the uncertain lock traversing time of dams. In this study, we propose a joint ship schedule design and sailing speed optimization problem for a single inland shipping service by incorporating the effects of nonidentical streamflow speed and the uncertain dam transit time. A bi-objective programming model is developed for the proposed problem to simultaneously minimize the total bunker consumption and the ship round-trip time with service level constraints. The service level at each port call is captured by the punctual arrival probability of the ship not less than a predefined value. By introducing the term of buffer times, we analytically derive the Pareto optimal solutions of the ship sailing speeds and schedule. The theoretical method is extended to the case with an arbitrary number of dams and the uncertain port service and leg voyage time. We also examine the relationship between the Pareto optimal solution in this study and the solutions of the previous joint sailing speed and schedule optimization problems in the liner shipping service design. Numerical experiments based on the Yangtze River are conducted. The online appendix is available at https://doi.org/10.1287/trsc.2017.0808 .

Sailing speed optimization for tramp ships with fuzzy time window

This paper studies the problem of the sailing speed optimization for tramp ships. The transportation time requirements which are associated with shippers’ satisfaction are considered by a fuzzy membership function. A bi-objective model is proposed in which the minimum operation cost and the maximum shippers’ satisfaction are optimized simultaneously. The optimal speed on each leg of a given ship route is determined. A fast elitist non-dominated sorting genetic algorithm (NSGAII) is improved to solve the problem. To test the performance of the proposed model and algorithm, a numerical experiment is designed. The results show that the proposed algorithm has good convergence property and convergence speed.

A polynomial-time algorithm for sailing speed optimization with containership resource sharing

The sailing speed optimization problem aims to determine the optimal cruising speeds of ships by balancing the number of ships required on services, the fuel consumption, and the level of service provided for customers. The level of service can be incorporated into a sailing speed optimization model from the perspective of supply chain management or from the perspective of shipping lines. We design a polynomial-time algorithm workable to solve the two models based on bi-section search methods. The novelties of the algorithm include constructing a new parameter on which the bi-section search will be executed and deriving a near-optimal solution by taking advantage of the problem structure. We also provide theoretical results that guarantee the validity of the polynomial-time algorithm.

Fundamental properties and pseudo-polynomial-time algorithm for network containership sailing speed optimization

In container liner shipping, bunker cost is an important component of the total operating cost, and bunker consumption increases dramatically when the sailing speed of containerships increases. A higher speed implies higher bunker consumption (higher bunker cost), shorter transit time (lower inventory cost), and larger shipping capacity per ship per year (lower ship cost). Therefore, a container shipping company aims to determine the optimal sailing speed of containerships in a shipping network to minimize the total cost. We derive analytical solutions for sailing speed optimization on a single ship route with a continuous number of ships. The advantage of analytical solutions lies in that it unveils the underlying structure and properties of the problem, from which a number of valuable managerial insights can be obtained. Based on the analytical solution and the properties of the problem, the optimal integer number of ships to deploy on a ship route can be obtained by solving two equations, each in one unknown, using a simple bi-section search method. The properties further enable us to identify an optimality condition for network containership sailing speed optimization. Based on this optimality condition, we propose a pseudo-polynomial-time solution algorithm that can efficiently obtain an epsilon-optimal solution for sailing speed of containerships in a liner shipping network.

Sailing speed optimization in voyage chartering ship considering different carbon emissions taxation

Considering ship carbon emission, demurrage and dispatch in voyage chartering ship, the sailing speed optimization issues are presented. The sailing speed decision models under three different forms of carbon emission taxation (no carbon emission tax, taxing emissions that exceed a certain threshold, and taxing emissions based on carbon emission) are developed. An example is given to demonstrate the effectiveness of the proposed models and analyze the impact of different carbon emission taxation on shipowner’s profit and ship carbon emission. It is shown that the model considering taxing carbon emissions that exceed a certain threshold is superior to the model considering taxing emissions based on carbon emission. Some useful insights are drawn from the numerical analysis.

Formula omitted] policy model for liner shipping refueling and sailing speed optimization problem

This work expounds on implementing an effective dynamic (s,S) policy to solve a liner shipping refueling and speed determination problem under both bunker prices and consumption uncertainties. While solving an optimization model which incorporates a continuous distribution is extremely challenging, we use sample average approximation method to solve it. However, the resulting problem is still a very large-scaled problem. Therefore, we propose two variations of the progressive hedging algorithm to tackle it. Numerical results show that our solution method is efficient and, in addition, our dynamic (s,S) policy model has significant cost reduction potential compared to stationary models.

Optimizing ship speed to minimize fuel consumption

Owing to high fuel costs and environmental regulations, the optimization of ship speed to minimize fuel consumption and reduce carbon emissions has become a hot issue in the maritime industry. In this paper, we study the sailing speed optimization problem for a ship operating on a route having a specified sequence of calling ports with time windows for calling time. The considered problem can be formulated as a non-linear program. We derive the intrinsic properties of the problem and develop an optimal algorithm based on the properties. Computational experiments show that the developed algorithm in this paper is efficient in finding an optimal solution.

Bulk ship routing and scheduling: solving practical problems may provide better results

Scheduling shipments of bulk cargoes when multiple cargoes may be on board a vessel simultaneously is an especially complicated task. Most research on such bulk ship routing and scheduling problems has focused on solving a simplified version of the real problem, which we denote as the basic problem. However, practical problems often pose additional complexities and opportunities that are not considered in the basic problem. We present the basic bulk ship routing and scheduling problem and three practical extensions to it: (1) flexible cargo quantities, (2) split cargoes, and (3) sailing speed optimization. Consolidating results from various sources we show that, although the problems become harder to solve when introducing these practical extensions, significantly better solutions can be obtained by using advanced heuristics. Each of these extensions may increase profit contribution by 5–25% compared to solutions of the basic problem. These methods have been incorporated into a commercial software product used by several shipping companies. Thus, such fleet operators have the opportunity to significantly improve their financial results.