Liner Shipping Network Research Articles

Modelling the impact of liner shipping network perturbations on container cargo routing: Southeast Asia to Europe application

Understanding how container routing stands to be impacted by different scenarios of liner shipping network perturbations such as natural disasters or new major infrastructure developments is of key importance for decision-making in the liner shipping industry. The variety of actors and processes within modern supply chains and the complexity of their relationships have previously led to the development of simulation-based models, whose application has been largely compromised by their dependency on extensive and often confidential sets of data. This study proposes the application of optimisation techniques less dependent on complex data sets in order to develop a quantitative framework to assess the impacts of disruptive events on liner shipping networks. We provide a categorization of liner network perturbations, differentiating between systemic and external and formulate a container assignment model that minimises routing costs extending previous implementations to allow feasible solutions when routing capacity is reduced below transport demand. We develop a base case network for the Southeast Asia to Europe liner shipping trade and review of accidents related to port disruptions for two scenarios of seismic and political conflict hazards. Numerical results identify alternative routing paths and costs in the aftermath of port disruptions scenarios and suggest higher vulnerability of intra-regional connectivity.

Liner container assignment model with transit-time-sensitive container shipment demand and its applications

This paper proposes a practical tactical-level liner container assignment model for liner shipping companies, in which the container shipment demand is a non-increasing function of the transit time. Given the transit-time-sensitive demand, the model aims to determine which proportion of the demand to fulfill and how to transport these containers in a liner shipping network to maximize the total profit. Although the proposed model is similar to multi-commodity network-flow (MCNF) with side constraints, unlike the MCNF with time delay constraints or reliability constraints that is NP-hard, we show that the liner container assignment model is polynomially solvable due to its weekly schedule characteristics by developing two link-based linear programing formulations. A number of practical extensions and applications are analyzed and managerial insights are discussed. The polynomially solvable liner container assignment model is then applied to address several important decision problems proposed by a global liner shipping company.

Time constrained liner shipping network design

We present a mathematical model and a solution method for the liner shipping network design problem. The model takes into account coordination between vessels and transit time restrictions on the cargo flow. The solution method is an improvement heuristic, where an integer program is solved iteratively to perform moves in a large neighborhood search. Our improvement heuristic is applicable as a real-time decision support tool for a liner shipping company. It can be used to find improvements to the network when evaluating changes in operating conditions or testing different scenarios. Computational results on the benchmark suite LINER-LIB are reported.

The liner shipping berth scheduling problem with transit times

In this paper speed optimization of an existing liner shipping network is solved by adjusting the port berth times. The objective is to minimize fuel consumption while retaining the customer transit times including the transhipment times. To avoid too many changes to the time table, changes of port berth times are only accepted if they lead to savings above a threshold value. Since the fuel consumption of a vessel is a non-linear convex function of the speed, it is approximated by a piecewise linear function. The developed model is solved using exact methods in less than two minutes for large instances. Computational experiments on real-size liner shipping networks are presented showing that fuels savings in the magnitude 2–10% can be obtained. The work has been carried out in collaboration with Maersk Line and the tests instances are confirmed to be representative of real-life networks.

Minimax Regret Model for Liner Shipping Fleet Deployment with Uncertain Demand

This paper proposes a minimax regret model for liner shipping fleet deployment with uncertain demand. The minimax regret model does not need the probability distribution function of the demand, and the model is consistent with how network planners are evaluated. However, the model is large because of the incorporation of all possible demand scenarios. A dynamic scenario inclusion method is proposed for efficiently solving the minimax model with only a small subset of the demand scenarios. A case study based on an Asia–Europe–Oceania liner shipping network demonstrates the applicability of the proposed model and method.

Shipping log data based container ship fuel efficiency modeling

Container shipping lines have been initiating various ship fuel efficiency management programs because bunker fuel costs always dominate the daily operating costs of a container ship. As the basis of these kinds of programs, we develop a viable research methodology for modeling the relationship between the fuel consumption rate of a particular container ship and its determinants, including sailing speed, displacement, sea conditions and weather conditions, by using the shipping log data available in practice. The developed methodology consists of an outlier-score-based data preprocessing procedure to tackle the fuzziness, inaccuracy and limited information of shipping logs, and two regression models for container ship fuel efficiency. Real shipping logs from four container ships (two with 13000 TEUs and two with 5000 TEUs) over a six-month sailing period are used to exhibit the applicability and effectiveness of the proposed methodology. The empirical studies demonstrate the performance of three models for fitting the fuel consumption rate of a ship and the industrial merits of ship fuel efficiency management. In addition, we highlight the potential impacts of the models developed in this study on liner shipping network analysis, as these models can serve as base models for additionally considering the influence of displacement and weather conditions on ship fuel efficiency and exhaust emissions.

Simultaneous Optimization of Container Ship Sailing Speed and Container Routing with Transit Time Restrictions

We introduce a decision support tool for liner shipping companies to optimally determine the sailing speed and needed fleet for a global network. We incorporate cargo routing decisions with tight transit time restrictions on each container such that we get a realistic picture of the utilization of the network. Furthermore, we show that it is possible to extend the model to include optimal time scheduling decisions such that the time associated with transshipments is also reflected accurately. To solve the speed optimization problem, we propose an exact algorithm based on Benders decomposition and column generation that exploits the separability of the problem. Computational results show that the method is applicable to liner shipping networks of realistic size and that it is important to incorporate cargo routing decisions when optimizing speed. The online appendix is available at https://doi.org/10.1287/trsc.2018.0818 .

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.

Liner shipping cargo allocation with service levels and speed optimization

The cargo allocation problem is a key strategic problem that determines the profitability of a liner shipping network. We present a novel mixed-integer programming model for this problem that introduces service levels for transit time requirements and optimizes the vessel speed on each leg of a service. These extensions to the cargo allocation problem greatly increase its realism and value for carriers. We evaluate our model on realistic data from the LINER-LIB and perform a sensitivity analysis of transit times versus bunker costs. Furthermore, we show how carriers can use our model to make data driven decisions in their operations.

Solving the Liner Shipping Fleet Repositioning Problem with Cargo Flows

We solve a central problem in the liner shipping industry called the liner shipping fleet repositioning problem (LSFRP). The LSFRP poses a large financial burden on liner shipping firms. During repositioning, vessels are moved between routes in a liner shipping network. Liner carriers wish to reposition vessels as cheaply as possible without disrupting cargo flows. The LSFRP is characterized by chains of interacting activities with a multicommodity flow over paths defined by the activities chosen. Despite its industrial importance, the LSFRP has received little attention in the literature. We introduce a novel mathematical model and a simulated annealing algorithm for the LSFRP with cargo flows that makes use of a carefully constructed graph; we evaluate these approaches using real-world data from our industrial collaborator. Additionally, we compare the performance of our approach against an actual repositioning scenario, one of many undertaken by our industrial collaborator in 2011. Our simulated annealing algorithm is able to increase the profit from $18.1 to $31.8 million using only a few minutes of CPU time. This shows that our algorithm could be used in a decision support system to solve the LSFRP.

The time constrained multi-commodity network flow problem and its application to liner shipping network design

The multi-commodity network flow problem is an important sub-problem in several heuristics and exact methods for designing route networks for container ships. The sub-problem decides how cargoes should be transported through the network provided by shipping routes. This paper studies the multi-commodity network flow problem with transit time constraints which puts limits on the duration of the transit of the commodities through the network. It is shown that for the particular application it does not increase the solution time to include the transit time constraints and that including the transit time is essential to offer customers a competitive product.

Robust bunker management for liner shipping networks

Abstract This paper examines the sailing speed of containerships and refueling of bunker in a liner shipping network while considering that the real speed may deviate from the planned one. It develops a mixed-integer nonlinear optimization model to minimize the total cost consisting of ship cost, bunker cost, and inventory cost, under the worst-case bunker consumption scenario. A close-form expression for the worst-case bunker consumption is derived and three linearization techniques are proposed to transform the nonlinear model to a mixed-integer linear programming formulation. A case study based on the Asia–Europe–Oceania network of a global liner shipping company demonstrates the applicability of the proposed model and interesting managerial insights are obtained.

Liner shipping fleet deployment considering decision makers’ psychological behavior

Decision makers in liner shipping (i.e., liner shipping planners) are risk-averse in that they aim to minimize the adverse effect under the least desirable scenario. To take this behavior into account, we propose a minimax regret model for fleet deployment with uncertain container shipment demand. The minimax regret model reflects how in reality network planners are evaluated. A dynamic scenario inclusion method is proposed to solve the model to optimality using a limited number of demand scenarios. A case study based on a real liner shipping network is carried out to demonstrate the applicability of the proposed model.

Segment-based alteration for container liner shipping network design

Container liner shipping companies only partially alter their shipping networks to cope with the changing demand, rather than entirely redesign and change the network. In view of the practice, this paper proposes an optimal container liner shipping network alteration problem based on an interesting idea of segment, which is a sequence of legs from a head port to a tail port that are visited by the same type of ship more than once in the existing shipping network. In segment-based network alteration, the segments are intact and each port is visited by the same type of ship and from the same previous ports. As a result, the designed network needs minimum modification before implementation. A mixed-integer linear programming model with a polynomial number of variables is developed for the proposed segmented-based liner shipping network alternation problem. The developed model is applied to an Asia–Europe–Oceania liner shipping network with a total of 46 ports and 11 ship routes. Results demonstrate that the problem could be solved efficiently and the optimized network reduces the total cost of the initial network considerably.

Profit-based maritime container assignment models for liner shipping networks

We propose the problem of profit-based container assignment (P-CA), in which the container shipment demand is dependent on the freight rate, similar to the “elastic demand” in the literature on urban transportation networks. The problem involves determining the optimal freight rates, the number of containers to transport and how to transport the containers in a liner shipping network to maximize the total profit. We first consider a tactical-level P-CA with known demand functions that are estimated based on historical data and formulate it as a nonlinear optimization model. The tactical-level P-CA can be used for evaluating and improving the container liner shipping network. We then address the operational-level P-CA with unknown demand functions, which aims to design a mechanism that adjusts the freight rates to maximize the profit. A theoretically convergent trial-and-error approach, and a practical trial-and-error approach, are developed. A numerical example is reported to illustrate the application of the models and approaches.

Port connectivity study: An analysis framework from a global container liner shipping network perspective

This paper introduces an analysis framework for port connectivity from a global container liner shipping network perspective: it is defined in terms of the impact on the transportation network when the transshipment service is not available at the evaluated port. Under this framework, two models for port connectivity are introduced from transportation time and capacity. Compared with existing measures, the strength of our framework and models is not only that it provides scientific methods to compute port connectivity, but it is able to capture a global effect on how port connectivity contributes to the overall network for given shipping services.

Empirical analysis of the container liner shipping network on the East-West corridor (1995–2011)

The shipping network plays an important role in the operation of container liner shipping. It provides a system on which transportation activities take place. This article aims to study the topological structure of the shipping network on the East-West corridor from 1995 to 2011. The theoretical background is based on graph theory, statistical techniques, social network analysis, and transportation network structure. Data is deployed from the service information published in Containerisation International Yearbooks and processed by designated computer programs. The expansion of the shipping network to adapt to the growth of global trade is displayed by the increase of deployed fleet, the number of served ports and weekly calls. Major features of arcs on the network are identified in respect of nautical distance, travelling time and assortativity. Port strength on the network is evaluated on the basis of degree centrality with the majority of the largest degree ports located in East Asia. The power law distribution of port degree indicates the existence of many small degree ports and only a few high degree ones. Highly positive correlation coefficients between port degree and throughput express the causal link between them. The dynamics of regional networks is observed through network indicators. A salient trend is the de-concentration process happening in many regions during which secondary ports grown strongly and have lowered the centrality of bigger ones.

A matheuristic for the liner shipping network design problem

We present an integer programming based heuristic, a matheuristic, for the liner shipping network design problem. This problem consists of finding a set of container shipping routes defining a capacitated network for cargo transport. The objective is to maximize the revenue of cargo transport, while minimizing the cost of operating the network. Liner shipping companies publish a set of routes with a time schedule, and it is an industry standard to have a weekly departure at each port call on a route. A weekly frequency is achieved by deploying several vessels to a single route, respecting the available fleet of container vessels. The matheuristic is composed of four main algorithmic components: a construction heuristic, an improvement heuristic, a reinsertion heuristic, and a perturbation heuristic. The improvement heuristic uses an integer program to select a set of improving port insertions and removals on each service. Computational results are reported for the benchmark suite LINER-LIB 2012 following the industry standard of weekly departures on every schedule. The heuristic shows overall good performance and is able to find high quality solutions within competitive execution times. The matheuristic can also be applied as a decision support tool to improve an existing network by optimizing on a designated subset of the routes. A case study is presented for this approach with very promising results.

Traffic consolidation in East Asian container ports: A network flow analysis

The proliferation of hub-and-spoke operations in maritime container transportation has resulted in the widespread consolidation of traffic flows. Utilising liner shipping network configurations, this paper assesses the impact of freight traffic consolidation in the container port industry by exploring the spatial pattern of traffic flow movements and identifying the variety of roles that container ports play within this context. On the basis of the network concept, the spatial inequality of freight traffic consolidation is determined by the density and direction of all meaningful connections (i.e. significant flows) identified by applying Multiple Linkage Analysis (MLA) to an initial traffic flow matrix.The effectiveness of the chosen methodology is tested empirically using a sample comprising the 18 major container ports in East Asia, together with another 21 important container ports located on the East–West trading route. Based on this sample network, the spatial structure of traffic flow consolidation reveals the nature and structure of hub-and-spoke operations within a port system, the relative hub-dependence of ports, the variety of roles which individual ports play within the overall structure of inter-port interactions and the hierarchical configuration of the port industry structure. The paper concludes that MLA offers new insights into the distributional inequality of traffic flows, the spatial and economic interactions between ports and the extent to which hinterlands overlap. Furthermore, the analysis clearly shows that inter-port relationships can no longer be evaluated as isolated phenomena; any change in a specific port’s competitiveness will directly impact upon the structure of the whole maritime transportation system. Port authorities and terminal operators will need, therefore, to carefully analyse and disentangle specific inter-port relationships in order to provide the most appropriate basis for their decision making.

A novel hybrid-link-based container routing model

Container routing determines how to transport containers from their origins to their destinations in a liner shipping network. Container routing needs to be solved a number of times as a subproblem in tactical-level decision planning of liner shipping operations. Container routing is similar to the multi-commodity flow problem. This research proposes a novel hybrid-link-based model that nests the existing origin-link-based and destination-link-based models as special cases. Moreover, the hybrid-link-based model is at least as compact as the origin-to-destination-link-based, origin-link-based and destination-link-based models in the literature.