Reversing port rotation directions in a container liner shipping network

Reversing port rotation directions of ship routes is a practical alteration of container liner shipping networks. The port rotation directions of ship routes not only affect the transit time of containers, as has been recognized by the literature, but also the shipping capacity and transshipment cost. This paper aims to obtain the optimal port rotation directions that minimize the generalized network-wide cost including transshipment cost, slot-purchasing cost and inventory cost. A mixed-integer linear programming model is proposed for the optimal port rotation direction optimization problem and it nests a minimum cost multi-commodity network flow model. The proposed model is applied to a liner shipping network operated by a global liner shipping company. Results demonstrate that real-case instances could be efficiently solved and significant cost reductions are gained by optimization of port rotation directions.     

A joint optimization model for liner container cargo assignment problem using state-augmented shipping network framework

This paper proposes a state-augmented shipping (SAS) network framework to integrate various activities in liner container shipping chain, including container loading/unloading, transshipment, dwelling at visited ports, in-transit waiting and in-sea transport process. Based on the SAS network framework, we develop a chance-constrained optimization model for a joint cargo assignment problem. The model attempts to maximize the carrier’s profit by simultaneously determining optimal ship fleet capacity setting, ship route schedules and cargo allocation scheme. With a few disparities from previous studies, we take into account two differentiated container demands: deterministic contracted basis demand received from large manufacturers and uncertain spot demand collected from the spot market. The economies of scale of ship size are incorporated to examine the scaling effect of ship capacity setting in the cargo assignment problem. Meanwhile, the schedule coordination strategy is introduced to measure the in-transit waiting time and resultant storage cost. Through two numerical studies, it is demonstrated that the proposed chance-constrained joint optimization model can characterize the impact of carrier’s risk preference on decisions of the container cargo assignment. Moreover, considering the scaling effect of large ships can alleviate the concern of cargo overload rejection and consequently help carriers make more promising ship deployment schemes.     

Liner shipping network design with emission control areas: A genetic algorithm-based approach

To curb emissions, containerized shipping lines face the traditional trade-off between cost and emissions (CO₂ and SO_x) reduction. This paper considers this element in the context of liner service design and proposes a mixed integer linear programming (MILP) model based on a multi-commodity pickup and delivery arc-flow formulation. The objective is to maximize the profit by selecting the ports to be visited, the sequence of port visit, the cargo flows between ports, as well as the number/operating speeds of vessels on each arc of the selected route. The problem also considers that Emission Control Areas (ECAs) exist in the liner network and accounts for the vessel carrying capacity. In addition to using the MILP solver of CPLEX, we develop in the paper a specific genetic algorithm (GA) based heuristic and show that it gives the possibility to reach an optimal solution when solving large size instances.     

Increased energy efficiency in short sea shipping through decreased time in port

According to a range of assessments, there exists a large cost-effective potential to increase energy efficiency in shipping through reduced speed at sea enabled by shorter time in port. This means that the energy needed can be reduced whilst maintaining the same transport service. However, the fact that a large cost-effective potential has been identified that is not being harnessed by decision-makers in practice suggests that there is more to this potential to understand. In this paper, the possibilities for increasing energy efficiency by reducing waiting time in port are explored and problematised through a case study of a short sea bulk shipping company transporting dry bulk goods mainly in the North and Baltic seas. Operational data from two ships in the company’s fleet for one year showed that the ships spent more than 40% of their time in ports and that half of the time in port was not productive. The two most important reasons for the large share of unproductive time were that ports were closed on nights and weekends and that ships arrived too early before the stevedores were ready to load or unload the cargo. Reducing all of the unproductive time may be difficult, but the results also show that even a conservative estimate of one to four hours of reduced time per port call would lead to a reduction in energy use of 2–8%. From in-depth interviews with employees of the shipping company, ports and ship agencies, a complex picture is painted when attempting to understand how this potential arises. Aspects such as a lack of effective ship-shore-port communication, little time for ship operators, an absence of means for accurately predicting energy use of voyages as a function of speed, perceived risk of arriving too late, and relationships with third-party technical management may all play a role.     

Container liner fleet deployment: A systematic overview

Container liner fleet deployment (CLFD) is the assignment of containerships to port rotations (ship routes) for efficient transport of containers. As liner shipping services have fixed schedules, the ship-related operating cost is determined at the CLFD stage. This paper provides a critical review of existing mathematical models developed for the CLFD problems. It first gives a systematic overview of the fundamental assumptions used by the existing CLFD models. The operating characteristics dealt with in existing studies are then examined, including container transshipment and routing, uncertain demand, empty container repositioning, ship sailing speed optimization and ship repositioning. Finally, this paper points out four important future research opportunities: fleet deployment considering ship surveys and inspections, service dependent demand, pollutant emissions, and CLFD for shipping alliances.     

Liner ship route schedule design with port time windows

This paper examines a practical tactical liner ship route schedule design problem, which is the determination of the arrival and departure time at each port of call on the ship route. When designing the schedule, the availability of each port in a week, i.e., port time window, is incorporated. As a result, the designed schedule can be applied in practice without or with only minimum revisions. This problem is formulated as a mixed-integer nonlinear nonconvex optimization model. In view of the problem structure, an efficient holistic solution approach is proposed to obtain global optimal solution. The proposed solution method is applied to a trans-Atlantic ship route. The results demonstrate that the port time windows, port handling efficiency, bunker price and unit inventory cost all affect the total cost of a ship route, the optimal number of ships to deploy, and the optimal schedule.     

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.     

Liner container seasonal shipping revenue management

This paper proposes a liner container seasonal shipping revenue management problem for a container shipping company. For a given weekly multi-type shipment demand pattern in a particular season, the proposed problem aims to maximize the total seasonal shipping profit by determining the number of multi-type containers to be transported and assigned on each container route, the number of containerships deployed on each ship route, and the sailing speed of containerships on each shipping leg subject to both the volume and capacity constraints of each containership. By adopting the realistic bunker consumption rate of a containership as a function of its sailing speed and payload (displacement), we develop a mixed-integer nonlinear programing with a nonconvex objective function for the proposed liner container seasonal shipping revenue management problem. A tailored branch and bound (B&B) method is designed to obtain the global ε-optimal solution of the model. Numerical experiments are finally conducted to assess the efficiency of the solution algorithm and to show the applicability of the developed model.     

A tailored branch-and-price approach for a joint tramp ship routing and bunkering problem

This paper deals with a practical tramp ship routing problem while taking into account different bunker prices at different ports, which is called the joint tramp ship routing and bunkering (JSRB) problem. Given a set of cargoes to be transported and a set of ports with different bunker prices, the proposed problem determines how to route ships to carry the cargoes and the amount of bunker to purchase at each port, in order to maximize the total profit. After building an integer linear programming model for the JSRB problem, we propose a tailored branch-and-price (B&P) solution approach. The B&P approach incorporates an efficient method for obtaining the optimal bunkering policy and a novel dominance rule for detecting inefficient routing options. The B&P approach is tested with randomly generated large-scale instances derived from real-world planning problems. All of the instances can be solved efficiently. Moreover, the proposed approach for the JSRB problem outperforms the conventional sequential planning approach and can incorporate the prediction of future cargo demand to avoid making myopic decisions.     

In Search of the Link between Ship Size and Operations

Abstract

Since 1990s the liner shipping industry has faced a period of restructuring and consolidation, and been confronted with a continuing increase in container vessel scale. The impact of these changes is noticeable in trade patterns, cargo handling methods and shipping routes, in short ‘operations’. After listing factors influencing size, growth in container ship size is explained by economies of scale in deploying larger vessels. In order to quantify economies of scale, this paper uses the liner service cash flow model. A novelty in the model is the inclusion of +6000-20-foot Equivalent Unit (TEU) vessels and the distinction in costs between single and twin propeller units on ships. The results illustrate that scale economies have been – and will continue to be – the driving force behind the deployment of larger container vessels. The paper then assesses the link between ship size and operations, given current discussions about the increase in container vessel scale. It is found that (a) ship size and operations are linked; (b) optimal ship size depends on transport segment (deep-sea vs. short-sea shipping, SSS), terminal type (transhipment terminals vs. other terminals), trade lane (East-West vs. North-South trades) and technology; and (c) a ship optimal for one trade can be suboptimal for another.     

Ship emissions and their externalities in cruise ports

This paper presents an estimation and analysis of ship exhaust emissions and their externalities in the popular cruise destinations of Dubrovnik (Croatia) and Kotor (Montenegro) along the eastern coast of the Adriatic Sea. To this extent, the recent record (2012–2014) of cruise ships calling at these ports is used to model and estimate the ship exhaust emission inventories and externalities within the associated bays and ports.The results indicate that cruise ship traffic produces continuously increasing air pollution in both ports over recent years. More importantly, however, the analysis of the ship operating characteristics reveals that for any given ship traffic involving specific vessels using marine fuel of a given quality, the presence of other factors (e.g. berth availability, berth accessibility etc) can also influence the ship emission levels. This is particularly evident in the case of the port of Kotor where berth space insufficiency dictates the need for ship anchorage thus leading to increased air pollution and costs of associated damage.The application and results of the aforementioned ship activity-based methodology to the ports of Dubrovnik and Kotor improves our understanding of ship emissions in cruise bays and ports, and contributes toward the implementation of port policies for the effective control of air quality in such environmentally sensitive locations.     

Containership scheduling with transit-time-sensitive container shipment demand

This paper examines the optimal containership schedule with transit-time-sensitive demand that is assumed to be a decreasing continuous function of transit time. A mixed-integer nonlinear non-convex optimization model is first formulated to maximize the total profit of a ship route. In view of the problem structure, a branch-and-bound based holistic solution method is developed. It is rigorously demonstrated that this solution method can obtain an ε-optimal solution in a finite number of iterations for general forms of transit-time-sensitive demand. Computational results based on a trans-Pacific liner ship route demonstrate the applicability and efficiency of the solution method.     

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.     

Game-theoretical models for competition analysis in a new emerging liner container shipping market

This paper develops three game-theoretical models to analyze shipping competition between two carriers in a new emerging liner container shipping market. The behavior of each carrier is characterized by an optimization model with the objective to maximize his payoff by setting optimal freight rate and shipping deployment (a combination of service frequency and ship capacity setting). The market share for each carrier is determined by the Logit-based discrete choice model. Three competitive game strategic interactions are further investigated, namely, Nash game, Stackelberg game and deterrence by taking account of the economies of scale of the ship capacity settings. Three corresponding competition models with discrete pure strategy are formulated as the variables in shipment deployment are indivisible and the pricing adjustment is step-wise in practice. A ɛ -approximate equilibrium and related numerical solution algorithm are proposed to analyze the effect of Nash equilibrium. Finally, the developed models are numerically evaluated by a case study. The case study shows that, with increasing container demand in the market, expanding ship capacity setting is preferable due to its low marginal cost. Furthermore, Stackelberg equilibrium is a prevailing strategy in most market situations since it makes players attain more benefits from the accommodating market. Moreover, the deterrence effects largely depend on the deterrence objective. An aggressive deterrence strategy may make potential monopolist suffer large benefit loss and an easing strategy has little deterrence effect.     

Essential elements in tactical planning models for container liner shipping

Tactical planning models for liner shipping problems such as network design and fleet deployment usually minimize the total cost or maximize the total profit subject to constraints including ship availability, service frequency, ship capacity, and transshipment. Most models in the literature do not consider slot-purchasing, multi-type containers, empty container repositioning, or ship repositioning, and they formulate the numbers of containers to transport as continuous variables. This paper develops a mixed-integer linear programming model that captures all these elements. It further examines from the theoretical point of view the additional computational burden introduced by incorporating these elements in the planning model. Extensive numerical experiments are conducted to evaluate the effects of the elements on tactical planning decisions. Results demonstrate that slot-purchasing and empty container repositioning have the largest impact on tactical planning decisions and relaxing the numbers of containers as continuous variables has little impact on the decisions.     

From hierarchy to networking: the evolution of the “twenty-first-century Maritime Silk Road” container shipping system

ABSTRACT

Container shipping gives a rise of international trade since the 1960s. Based on navigation data start from the mid-1990s to 2016, this paper empirically analyses the spatial pattern of China’s international maritime linkages along the “twenty-first-century Maritime Silk Road”. We interpret such evolutionary dynamics in terms of growth, hierarchical diffusion and networking phases. Networking is a new stage of the evolution of the port system, which is approached based on the graph theory, complex network methods and geomatics, the paper discusses the networking’s basic characteristics: multi-hub spatial agglomeration, the connection of the network develops across space, functional differentiation and a division of labour appear among ports. Our results show that, while the scope of China’s maritime linkages had expanded overtime, more foreign ports become connected to the “Maritime Silk Road”. In addition, the external linkages of domestic ports tend to be dispersed, reflecting upon the decline of Pearl River Delta ports and the rise of Yangtze River Delta ports, with mixed evidence for the Bohai Rim region. Lastly, the analysis underlines the emergence of a polycentric shipping system, from the Hong Kong dominance to the more diversified Shanghai/Ningbo/Shenzhen configuration. Academic and managerial implications are included.     

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.     

The multi-port berth allocation problem with speed optimization and emission considerations

The container shipping industry faces many interrelated challenges and opportunities, as its role in the global trading system has become increasingly important over the last decades. On the one side, collaboration between port terminals and shipping liners can lead to costs savings and help achieve a sustainable supply chain, and on the other side, the optimization of operations and sailing times leads to reductions in bunker consumption and, thus, to fuel cost and air emissions reductions. To that effect, there is an increasing need to address the integration opportunities and environmental issues related to container shipping through optimization. This paper focuses on the well known Berth Allocation Problem (BAP), an optimization problem assigning berthing times and positions to vessels in container terminals. We introduce a novel mathematical formulation that extends the classical BAP to cover multiple ports in a shipping network under the assumption of strong cooperation between shipping lines and terminals. Speed is optimized on all sailing legs between ports, demonstrating the effect of speed optimization in reducing the total time of the operation, as well as total fuel consumption and emissions. Furthermore, the model implementation shows that an accurate speed discretization can result in far better economic and environmental results.     

Liner ship route capacity utilization estimation with a bounded polyhedral container shipment demand pattern

This paper aims to estimate capacity utilization of a liner ship route with a bounded polyhedral container shipment demand pattern, arising in the liner container shipping industry. The proposed maximum and minimum liner ship route capacity utilization problems are formulated as a linear programming model and a min–max model, respectively. We examine two fundamental properties of the min–max model. These two nice properties enable us to develop two ε-optimal global optimization algorithms for solving the min–max model, which find a globally ε-optimal solution by iteratively cutting off the bounded polyhedral container shipment demand set with a cut. The latter algorithm overcomes non-convexity of the remaining feasible demand set generated by the former algorithm via a novel hyperplane cut. Each hyperplane cut can assure that the current vertex of the polyhedral demand set is cut off, whereas solutions that may improve the current one by more than a factor of ε are retained. Extensive numerical experiments for problems larger than those encountered in real applications demonstrate the computational efficacy of the latter algorithm.