Liner Shipping Route Research Articles

Analysis of the Liner Shipping Network Structure of the Asia–Europe Main Trunk Route Using Social Network Analysis

Due to COVID-19, the shipping market has faced uncertainty, and the possibility of changes in port routes has increased. The purpose of this study was to analyze the network of container liner shipping routes between Asia and Europe. In particular, this research focused on a global risky situation—the COVID-19 pandemic. The data examined encompassed Asia–Europe route schedules from January 2018 to October 2021, which exhibited significant fluctuations due to the COVID-19 pandemic originating in 2019. To access this problem, utilizing concepts of centrality from social network analysis (SNA), namely degree centrality and betweenness centrality, this analysis incorporated route capacity as a weighted factor. The findings revealed that the port of Rotterdam held the highest degree of centrality in 2018, 2019, and 2021, while Shanghai claimed the highest degree of centrality in 2020. Singapore exhibited the highest betweenness centrality. Asian ports wielded greater influence during the COVID-19 pandemic compared to European ports. Furthermore, Singapore emerged as a pivotal mediator in the Asia–Europe routes, playing a significant role within the global supply chain. Results showed that the port could be put into an unstable situation. Therefore, the managers of port and shipping companies should be ready to minimize risk. From an academic perspective, it is difficult to integrate and analyze container liner schedules as they are monthly updated. This study therefore analyzed continuous schedules to examine dynamic changes in schedules. By adopting SNA, we presented changes in connectivity over multiple periods. This study addressed questions stakeholders may have had about route changes during the global crisis, contributing to sustainable container transportation. This study provides a general understanding of Asia–Europe container scheduling for decision makers. Using market schedules, this research analyzed the connections, and evaluated and compared each port.

Multi-Scale Higher-Order Dependencies (MSHOD): Higher-Order Interactions Mining and Key Nodes Identification for Global Liner Shipping Network

Liner shipping accounts for over 80% of the global transportation volume, making substantial contributions to world trade and economic development. To advance global economic integration further, it is essential to link the flows of global liner shipping routes with the complex system of international trade, thereby supporting liner shipping as an effective framework for analyzing international trade and geopolitical trends. Traditional methods based on first-order global liner shipping networks, operating at a single scale, lack sufficient descriptive power for multi-variable sequential interactions and data representation accuracy among nodes. This paper proposes an effective methodology termed “Multi-Scale Higher-Order Dependencies (MSHOD)” that adeptly reveals the complexity of higher-order interactions among multi-scale nodes within the global liner shipping network. The key step of this method is to construct high-order dependency networks through multi-scale attributes. Based on the critical role of high-order interactions, a method for key node identification has been proposed. Experiments demonstrate that, compared to other methods, MSHOD can more effectively identify multi-scale nodes with regional dependencies. These nodes and their generated higher-order interactions could have transformative impacts on the network’s flow and stability. Therefore, by integrating multi-scale analysis methods to mine high-order interactions and identify key nodes with regional dependencies, this approach provides robust insights for assessing policy implementation effects, preventing unforeseen incidents, and revealing regional dual-circulation economic models, thereby contributing to strategies for global, stable development.

Perishables Liner Bunkering Strategy and Route Optimization Considering Carbon Tax and Sulfur Emissions

For the issue of perishable goods liner shipping route selection and bunkering strategy, this paper gives full consideration to the characteristics of perishable goods, in the context of the carbon tax and the setting of emission control zones, constructs a mixed-integer nonlinear planning model with the goal of minimizing the total weekly cost of liner service, designs a segmented linear approximation algorithm for model solution, and conducts an arithmetic analysis based on the actual liner voyage as an example, which provides a reference for the actual operation of shipping.

Allocation and trading schemes of the maritime emissions trading system: Liner shipping route choice and carbon emissions

In September 2020, the European Union (EU) decided to include the maritime industry into the EU emissions trading system to effectively control carbon emissions from ships, namely the maritime emissions trading system (METS). Various allocation and trading schemes are adopted in practice. This paper investigates a comparison of allocation and trading schemes of the METS from the perspective of liner shipping carriers and regulators, respectively. We explore how to determine the optimal allocation and trading scheme of the METS and how the liner shipping route (LSR) choice decision (following or avoiding the METS) and carbon emissions will be affected. For liner shipping carriers, we use a mixed-integer linear programming model that aims to reduce carriers’ costs to formulate our problem. For regulators, we present a bi-level programming model that aims to reduce carbon emissions. In numerical experiments, we further analyze the impact of joining the METS on the scheme choice, LSR choice and emissions by considering the European Economic Area and the Red Sea being covered by the METS. Numerical experiments are provided to show the effectiveness of our proposed models.

Liner shipping network design model with carbon tax, seasonal freight rate fluctuations and empty container relocation

In response to the challenges posed by the shipping carbon tax resulting from the low-carbon environmental policy, the seasonal fluctuation of freight rates in the container liner shipping market, and the reduced flexibility in fleet adjustment, we develop a bi-level programming model to maximize the average revenue per container ship and the total revenue of the fleet.The upper-level model selects the optimal shipping networks for both the off-season and peak season, while also designing the liner fleet for these two networks. The lower-level model optimizes the slot allocation scheme and the empty container storage and transportation scheme to evaluate the revenue of the network calculated by the upper-level model. Three meta-heuristic algorithms are proposed. We take the China-West Europe liner shipping route as the research object, and conduct numerical experiments on different optimization objectives and liner types. Results demonstrate that maximizing the average revenue per container ship involves reducing the carbon tax cost, simplifying the trunk route structure, and increasing the number of feeder routes. These changes lead to reduced satisfaction rates for transportation demands in both China and Europe. If the company seeks to maximize total revenue, they may achieve the opposite result. Therefore, liner companies should reasonably set optimization goals, adjust the network structure and liner operation status in a timely manner, and scientifically allocate container ship and empty containers to achieve the operational goals of reducing carbon emissions and maximizing revenue to cope with the volatile market and the low-carbon regulations.

Robust liner ship routing and scheduling schemes under uncertain weather and ocean conditions

Since sailing along the Northern Sea Route (NSR) through the Arctic Ocean comes into reality, commercial shipping developments including opening new liner services along this route have been put on the agenda. However, uncertainties within weather and ocean conditions in this region, especially during temperature-varying seasons, may cause failure to on-time arrivals, resulting unignorable or even unaffordable monetary losses. As a result, these uncertainties will inevitably affect cargo shippers’ willingness of choosing this being-explored route, even if on average its shipping time is much shorter than that of the traditional Asia-Europe shipping lines. In this context, the present paper describes a liner ship routing and scheduling problem considering schedule-sensitive demand and late-arrival penalty for operating incoming NSR shipping lines in the future. By using two types of uncertainty sets, bounded and budget-bounded uncertainty sets, we construct and solve two robust counterparts of this problem. The deterministic model and bounded robust model can be seen as special cases of the budget-bounded robust model when the uncertainty budget is set to null and full, respectively. A multifaceted case study of planning liner shipping routes and schedules along the NSR is conducted to validate the efficacy and efficiency of the proposed models and identify the effects of uncertainty bounds and budgets on the solution performance. The following facts and conclusions are revealed from the optimization results of the case study: The budget-bounded robust model functions the best in the worst condition; low revenue rate and high demand sensitivity are the major factors for excluding a candidate port from the route; the order of a visited port in the route decides the weight of its uncertainty budget on the entire shipping line; setting the uncertainty budget in a decelerative way will enhance the scheduling robustness of solutions.

Vessel Scheduling and Bunker Management With Speed Deviations for Liner Shipping in the Presence of Collaborative Agreements

Vessels face uncertain factors during a voyage, such as bad weather and harsh sea conditions along a route in container liner shipping. As such, the real vessel speed during each leg of a voyage often deviates from the planned one, which may lead to fluctuations in vessel schedule and bunker consumption. This paper investigates the problem of vessel scheduling and bunker management with speed deviations (VSBMSD) for liner shipping in the presence of collaborative agreements. By establishing the worst-case scenario of the maximum bunker consumption function with vessel sailing speed as an independent variable, we develop a mixed-integer nonlinear programming model to minimize the total liner shipping route service cost. A piecewise linear secant approximation method is designed, and then a CPLEX solver is used to solve the problem. The results of the computational experiments conducted for the AEMX route indicate that VSBMSD in the presence of collaborative agreements can enable shipping companies to design vessel schedules reasonably and reduce the total cost of liner shipping route service by at least 2.95% compared to the results from similar studies.

Integrated Optimization of Port Rotation Direction and Fleet Deployment for Container Liner Shipping Routes

This paper provides an integrated planning methodology for the optimization of port rotation direction and fleet deployment for container liner shipping routes with consideration of demand uncertainty. We first consider a special case that demand is deterministic. A multicommodity flow network model is developed via minimizing the total network-wide cost. Its decisions are the selection of port rotation direction and fleet deployment and container routings in the shipping network. Afterward, we address the generic case that uncertain demand is considered, which is represented by potentially realizable demand scenarios. We develop a minimax regret model to procure the least maximum regret across all the demand scenarios. The proposed models are applied to an Asia-Europe-Oceania liner shipping network with 46 ports and 12 ship routes. Results could provide the liner company with a comprehensive decision tool to simultaneously determine port rotation direction and fleet deployment when tackling uncertain demand.

Vessel Schedule Recovery in Liner Shipping: Modeling Alternative Recovery Options

Disruption occurrences in liner shipping operations affect schedule reliability and may increase the total cost of delivering cargoes at ports. If a vessel experiences disruption occurrences either at ports of call or in sea, the liner shipping company is required to decide on the schedule recovery action to execute in order to recover the resulting delays. This study formulates a novel mathematical model for the vessel schedule recovery problem (VSRP) in liner shipping. The objective aims to minimize the total profit loss, suffered by the liner shipping company due to disruption occurrences at a given liner shipping route. A total of four recovery strategies are considered in the model, which include: (1) vessel sailing speed adjustment; (2) vessel handling rate adjustment; (3) port skipping without container diversion; and (4) port skipping with container diversion. The proposed mathematical formulation for the nonlinear VSRP model is solved to the global optimality using BARON. A set of computational experiments are further performed for the Middle East/Pakistan/India-West Mediterranean (WM3) route, which is served by the OOCL liner shipping company, for various scenarios of disruption occurrences in sea and at ports. The results from the performed analyses demonstrate potential benefits for liner shipping companies from using the proposed methodology for various realistic scenarios of disruptions.

Stochastic Programming for Liner Ship Routing and Scheduling under Uncertain Sea Ice Conditions

It is anticipated that in the foreseeable future the Northern Sea Route (NSR) will be able to serve commercial shipping as an alternative transportation shortcut between East Asia and Europe, especially in the summer season. The sailing time, however, is heavily subject to the variation of sea ice conditions along this route. Any participating shipping company must consider how to mitigate the ill effects on itinerary planning caused by sailing time and cost uncertainty. Finding a good trade-off between the benefit from a tight schedule and the risk caused by an unexpected delay is a key element in relevant routing and scheduling decisions, and may be beyond the reach of traditional deterministic planning models. With the aim of maximizing profit over all possible shipping environment scenarios, this article proposes a two-stage stochastic nonlinear integer programming model for liner ship routing and scheduling with uncertain shipping time and cost, the nonlinearity of which arises from the coexistence of schedule-sensitive shipping demand and uncertain arrival time variables in the objective function. The model is converted into an equivalent linear integer programming counterpart by introducing a set of nominal delay variables, and Benders decomposition is applied to solve the linearized problem. Numerical experiments and sensitivity analyses are conducted to validate the efficacy and effectiveness of the model, the results of which suggest several managerial insights that can be used to guide liner ship route and schedule planning under uncertain shipping conditions.

Deploying, scheduling, and sequencing heterogeneous vessels in a liner container shipping route

Previous studies on liner container shipping operations usually assume identical container ships deployed in the same shipping route. However, in real operations, this assumption does not always hold considering the distinct capacities, ages, fuel efficiencies, cost structures, etc. of these ships. These distinctions significantly influence the number of containers transported, the bunker fuel consumption, and the operating cost of a shipping route. In this regard, this paper considers the joint ship deployment, sequencing, and scheduling problem for a fleet of heterogeneous vessels in a shipping route. A mixed integer programming model is developed to select the optimal ships from a set of candidate ships together with their sequences, schedules, and sailing speeds in the shipping route to minimize the total cost. A tailored solution algorithm is subsequently developed to calculate the global optimal solution. Numerical experiments demonstrate that this algorithm significantly outperforms the classical branch-and-cut algorithm in solving the model. In addition, by applying our model in a real-case shipping route, we find that the model is able to reduce the total cost by 5% compared with that considering homogeneous vessels. Finally, several managerial insights are obtained to guide the operations of a liner shipping route.

An integrated optimization method for tactical-level planning in liner shipping with heterogeneous ship fleet and environmental considerations

The maritime transportation flows and container demand have been increasing over time, although the COVID-19 pandemic may slow down this trend for some time. One of the common strategies adopted by shipping lines to efficiently serve the existing customers is the deployment of large ships. The current practice in the liner shipping industry is to deploy a combination of ships of different types with different carrying capacities (i.e., heterogeneous fleet), especially at the routes with a significant demand. However, heterogeneous fleets of ships have been investigated by a very few studies addressing the tactical liner shipping decisions (i.e., determination of service frequency, ship fleet deployment, optimization of ship sailing speed, and design of ship schedules). Moreover, limited research efforts have been carried out to simultaneously capture all the major tactical liner shipping decisions using a single solution methodology. Therefore, this study proposes an integrated optimization model that addresses all the major tactical liner shipping decisions and allows the deployment of a heterogeneous ship fleet at each route, considering emissions generated throughout liner shipping operations. The model’s objective maximizes the total turnaround profit generated from liner shipping operations. A decomposition-based heuristic algorithm is presented in this study to solve the model proposed and efficiently tackle large-size problem instances. Numerical experiments, carried out for a number of real-world liner shipping routes, demonstrate the effectiveness of the proposed methodology. A set of managerial insights, obtained from the proposed methodology, are also provided.

Simultaneous Optimization of the Liner Shipping Route and Ship Schedule Designs with Time Windows

This paper proposes to address the problem of the simultaneous optimization of the liner shipping route and ship schedule designs by incorporating port time windows. A mathematical programming model was developed to minimize the carrier’s total operating cost by simultaneously optimizing the port call sequence, ship arrival time per port of call, and sailing speed per shipping leg under port time window constraints. In view of its structure, the nonlinear nonconvex optimization model is further transformed into a mixed-integer linear programming model that can be efficiently solved by extant solvers to provide a global optimal solution. The results of the numerical experiments performed using a real-world case study indicated that the proposed model performs significantly better than the models that handle the design problems separately. The results also showed that different time windows will affect the optimal port call sequence. Moreover, port time windows, bunker price, and port efficiency all affect the total operating cost of the designed shipping route.

Utilization of a deep learning-based fuel consumption model in choosing a liner shipping route for container ships in Asia

Designating the ideal shipping route can spare expenses, enlarge profits and improve the competitiveness of shipping companies. Liner shipping route choice is mainly contingent on fuel cost, which always contributes the major proportion of the ship's operating cost. Although many studies on this topic have been carried out, none are based on the fuel consumption forecast model designed by the advanced machine learning method. This paper provides a platform idea for selecting the optimal operating route for container ships to minimize fuel cost by using an asymmetric traveling salesman problem (ATSP) algorithm solution, in which the fuel consumption model for the route is estimated based on the deep-machine learning method. Five input variables are given in the model including average velocity, sailing time, ship's capacity, wind speed, and wind direction. The mean absolute percentage error (MAPE) of the model is 5.89%, indicating that the predictive result obtains a very high accuracy, close to 95%. The optimal model is thus applied in combination with ATSP to address the optimal solution for a certain route.

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.

Vessel scheduling in liner shipping: a critical literature review and future research needs

Liner shipping plays a major role for freight transportation and international seaborne trade. The economic development of different countries is significantly dependent on the movement of a containerized cargo. One of the most challenging decision problems, tackled by liner shipping companies, is the design of vessel schedules. At the vessel scheduling stage, the liner shipping company aims to determine vessel sailing speeds at voyage legs of a given liner shipping route, port times, vessel handling rates at ports, the minimum number of vessels required in order to provide the agreed service frequency at ports, and other factors. Considering the existing pollution levels, the environmental impacts of liner shipping have to be captured in the vessel scheduling models as well. This study conducts a comprehensive survey of the existing research on vessel scheduling in liner shipping. The collected vessel scheduling studies are classified into different categories, including general vessel scheduling, uncertainty in liner shipping operations, collaborative agreements, vessel schedule recovery, and green liner shipping. Based on a detailed analysis of the collected literature, findings are discussed, and limitations in the state-of-the-art are identified for each category of studies. The study concludes with a number of future research opportunities, taking into account the recent developments and trends in liner shipping.

A Vessel Schedule Recovery Problem at the Liner Shipping Route with Emission Control Areas

Liner shipping is a vital component of the world trade. Liner shipping companies usually operate fixed routes and announce their schedules. However, disruptions in sea and/or at ports affect the planned vessel schedules. Moreover, some liner shipping routes pass through the areas, designated by the International Maritime Organization (IMO) as emission control areas (ECAs). IMO imposes restrictions on the type of fuel that can be used by vessels within ECAs. The vessel schedule recovery problem becomes more complex when disruptions occur at such liner shipping routes, as liner shipping companies must comply with the IMO regulations. This study presents a novel mixed-integer nonlinear mathematical model for the green vessel schedule recovery problem, which considers two recovery strategies, including vessel sailing speed adjustment and port skipping. The objective aims to minimize the total profit loss, endured by a given liner shipping company due to disruptions in the planned operations. The nonlinear model is linearized and solved using CPLEX. A number of computational experiments are conducted for the liner shipping route, passing through ECAs. Important managerial insights reveal that the proposed methodology can assist liner shipping companies with efficient vessel schedule recovery, minimize the monetary losses due to disruptions in vessel schedules, and improve energy efficiency as well as environmental sustainability.

Minimizing the Total Liner Shipping Route Service Costs via Application of an Efficient Collaborative Agreement

Increasing size of vessels and formation of alliances are the common strategies, which have been widely used by liner shipping companies over the last years, aiming to serve the growing demand for the international seaborne trade efficiently. However, without a proper design of vessel schedules liner shipping companies may incur substantial monetary losses. This paper proposes a novel collaborative agreement, according to which multiple vessel arrival time windows, start and end times for each time window, and multiple handling rates during each time window are offered by the marine container terminal operator to the liner shipping company at each port of the given liner shipping route. The vessel scheduling problem is formulated as a mixed integer nonlinear programming model, where the total liner shipping route service cost is minimized. A set of linearization techniques are applied to the original model, and the linearized model is solved using CPLEX. A number of computational experiments are performed for the Pacific Atlantic 1 liner shipping route, served by the NYK liner shipping company. Results showcase effectiveness of the adopted solution methodology. Moreover, the proposed collaborative agreement outperforms the existing collaborative agreements, where either vessel arrival time windows or handling rates are offered to the liner shipping company at ports, in terms of the total route service cost on average by 10.9% and 6.6%, respectively. Therefore, the proposed collaborative agreement can be considered as an efficient alternative for improving the liner shipping operations.

The Panama Canal Expansion and Its Impact on East–West Liner Shipping Route Selection

Through an empirical study of ocean-borne trade between Hong Kong and New York, we combined qualitative and quantitative analysis to examine route selection decisions in a post-expansion era of the Panama Canal. A two-stage methodological framework was developed to assess the competitiveness of the three route alternatives, namely the Panama and Suez canals and the US intermodal system. In the first stage, a combination of literature review and expert knowledge was employed to identify the determinants of route selection. In the second stage, fuzzy theory and the multi-criteria decision-making technique were used to evaluate the criteria and the route alternatives. The results indicate that transportation cost is the most important factor in choosing a route, followed by transportation time, reliability, and route characteristics. The “all water route” via the Panama Canal is preferred over the Suez and U.S. intermodal options.

Liner shipping single service design problem with arrival time service levels

We introduce three mathematical models of increasing complexity for designing liner shipping services that guarantee the punctual arrival of vessels at a specified service level. On-time reliability is an important performance indicator for many liner carriers, but current approaches for creating new routes in liner shipping networks do not consider data-driven uncertainty. We perform an empirical analysis of vessel travel times in a real liner shipping network to develop probability distributions that we use within novel, chance-constrained mathematical models for liner shipping service design. Our models are also the first to support variable vessel speeds for service design. In our experiments, we use real-world data from 22 liner shipping routes and evaluate the designed services using a simulation procedure that demonstrates the effectiveness of our approach for reducing lateness. We show that our models can be effectively used for decision support at a tactical level not only for designing services, but also potentially for negotiating maximum demand transit times and prices with customers.