Sailing speed optimization for container ships in a liner shipping network

This paper first calibrates the bunker consumption - sailing speed relation for container ships using historical operating data from a global liner shipping company. It proceeds to investigate the optimal sailing speed of container ships on each leg of each ship route in a liner shipping network while considering transshipment and container routing. This problem is formulated as a mixed-integer nonlinear programming model. In view of the convexity, non-negativity, and univariate properties of the bunker consumption function, an efficient outer-approximation method is proposed to obtain an ε-optimal solution with a predetermined optimality tolerance level ε. The proposed model and algorithm is applied to a real case study for a global liner shipping company.     

Liner ship fleet deployment with container transshipment operations

This paper proposes a liner ship fleet deployment (LSFD) problem with container transshipment operations. The proposed problem is formulated as a mixed-integer linear programming model which allows container transshipment operations at any port, any number of times, without explicitly defining the container transshipment variables. Experiments on the Asia-Europe-Oceania shipping network of a global liner shipping company show that more than one third (17-22 ports) of the total of 46 ports have transshipment throughputs. Computational studies based on randomly generated large-scale shipping networks demonstrate that the proposed model can be solved efficiently by CPLEX.     

Risk management in liner ship fleet deployment: A joint chance constrained programming model

This paper provides a tangible methodology to deal with the liner ship fleet deployment problem aiming at minimizing the total cost while maintaining a service level under uncertain container demand. The problem is first formulated as a joint chance constrained programming model, and the sample average approximation method and mixed-integer programming are used to deal with it. Finally, a numerical example of a liner shipping network is carried out to verify the applicability of the proposed model and solution algorithm. It is found that the service level has significant effect on the total cost.     

Measuring the perceived container leasing prices in liner shipping network design with empty container repositioning

This paper aims to measure the perceived container leasing prices at different ports by presenting a two-stage optimization method. In stage I, we propose a practical liner shipping network design problem with empty container repositioning. The proposed problem further considers the use of foldable containers and allows the mutual substitution between empty containers to decrease the number of empty containers to be repositioned. In stage II, the inverse optimization technique is used to determine the perceived container leasing prices at different ports, based on the solution obtained in stage I. Based on a set of candidate liner shipping service routes, a mixed-integer nonlinear programming model is built for the proposed problem in stage I. The nonlinear terms are linearized by introducing the auxiliary variables. Numerical experiments based on a realistic Asia-Europe-Oceania liner shipping network are carried out to account for the effectiveness of our two-stage optimization method.     

The container shipping network design problem with empty container repositioning

This paper addresses the design of container liner shipping service networks by explicitly taking into account empty container repositioning. Two key and interrelated issues, those of deploying ships and containers are usually treated separately by most existing studies on shipping network design. In this paper, both issues are considered simultaneously. The problem is formulated as a two-stage problem. A genetic algorithm-based heuristic is developed for the problem. Through a number of numerical experiments that were conducted it was shown that the problem with the consideration of empty container repositioning provides a more insightful solution than the one without.     

A robust optimization approach to the integrated berth allocation and quay crane assignment problem

This paper investigates the integrated berth allocation and quay crane assignment problem in container terminals. A deterministic model is formulated by considering the setup time of quay cranes. However, data uncertainties widely exist, and it may cause the deterministic solution to be infeasible. To handle the uncertainties, a robust optimization model is established. Furthermore, to control the level of conservativeness, another robust optimization model with the price constraints is proposed. A genetic algorithm and an insertion heuristic algorithm are suggested to obtain near optimal solutions. Computational experiments indicate that the presented models and algorithms are effective to solve the problems.     

Estimating attributes importance for container shipping industry by closing the listening gap with maximum convergent validity

This paper estimates the relationship of attributes importance (AI) to prospect purchase intention by closing the listening gap between customers and managers of container shipping companies. A proposition of minimum cross entropy is proposed to find a solution to the problem with maximum convergent validity, and this proposition is used to estimate AI, in which both opinions about AI of customers and managers of container shipping companies are included. Results indicate that price, discount, personal selling, and word of mouth, are the most important attributes to prospect purchase intention, within the industry. In addition, managerial implications are also discussed.     

The effect of multi-scenario policies on empty container repositioning

This paper addresses a container maritime-repositioning problem where several parameters are uncertain and historical data are useless for decision-making processes. To address this problem, we propose a time-extended multi-scenario optimization model in which scenarios can be generated taking into account shipping company opinions. We then show that multi-scenario policies put shipping companies in the position of satisfying empty-container demands for different values that may be taken by uncertain parameters.     

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.     

A novel modeling approach for the fleet deployment problem within a short-term planning horizon

This paper is concerned with model development for a short-term fleet deployment problem of liner shipping operations. We first present a mixed integer nonlinear programming model in which the optimal vessel speeds for different vessel types on different routes are interpreted as their realistic optimal travel times. We then linearize the proposed nonlinear model and obtain a mixed integer linear programming (MILP) model that can be efficiently solved by a standard mixed integer programming solver such as CPLEX. The MILP model determines the optimal route service frequency pattern and take into account the time window constraints of shipping services. Finally, we report our numerical results and performance of CPLEX on randomly generated instances.     

Study on China-EU container shipping network in the context of Northern Sea Route

The emerging Northern Sea Route (NSR) represents change to the existing liner network for China-EU container shipping. It is necessary to re-examine the container network in this context and assist liner companies in decision-making. This paper assesses the potential of the NSR based on designing a multi-port multi-trip liner service by establishing a two-stage optimization model. Based on the estimated data of NSR shipping, ship routing schemes on both the NSR and conventional routes are proposed. It is determined that container service along the NSR is largely influenced by ice-breaking charge, seasonality, and cargo volume, which makes NSR more likely to act as a supplementary line of the liner network in the short or medium term. The results also indicate that use of NSR may drive the redeployment of shipping network and hub ports in the long term. This study's conclusions may prove useful for strategic planning by liner companies, port authorities, and governments to assess the operation of liner service via the NSR.     

A strategic network choice model for global container flows: specification, estimation and application

Container flows have been booming for decades. Expectations for the 21st century are less certain due to changes in climate and energy policy, increasing congestion and increased mobility of production factors. This paper presents a strategic model for the movement of containers on a global scale in order to analyse possible shifts in future container transport demand and the impacts of transport policies thereon. The model predicts yearly container flows over the world’s shipping routes and passing through 437 container ports around the world, based on trade information to and from all countries, taking into account more than 800 maritime container liner services. The model includes import, export and transhipment flows of containers at ports, as well as hinterland flows. The model was calibrated against observed data and is able to reproduce port throughput statistics rather accurately. The paper also introduces a scenario analysis to understand the impact of future, uncertain developments in container flows on port throughput. The scenarios include the effects of slow steaming, an increase in land based shipping costs and an increased use of large scale infrastructures such as the Trans-Siberian rail line and the opening of Arctic shipping routes. These scenarios provide an indication of the uncertainty on the expected port throughputs, with a particular focus on the port of Rotterdam in the Netherlands.     

Terminal and yard allocation problem for a container transshipment hub with multiple terminals

This paper presents an integer programming model for the terminal and yard allocation problem in a large container transshipment hub with multiple terminals. The model integrates two decisions: terminal allocation for vessels and yard allocation for transshipment container movements within a terminal as well as between terminals. The objective function aims to minimize the total inter-terminal and intra-terminal handling costs generated by transshipment flows. To solve the problem, we develop a 2-level heuristic algorithm to obtain high quality solutions in an efficient way. Computational experiments show the effectiveness of the proposed approach.     

Optimal network flows for containerized imports to the United States

This paper analyzes the intermodal transportation network of containerized imports to the United States. An optimization model is developed that integrates international and North America inland transport networks. The results indicate optimal ship size, route, port, and interior shipping corridor and are highly reflective of observed shipments. Sensitivity analyzes were performed to evaluate impacts of congestion on capacity constraints as well as the prospective impacts of the alternative routes that are emerging. Results indicate that Prince Rupert is highly competitive for shipments to some markets, but the expansion of the Panama Canal would have lesser impacts on container flows.     

Shipping efficiency comparison between Northern Sea Route and the conventional Asia-Europe shipping route via Suez Canal

The continuous retreat of Arctic sea ice and seemingly appealing cost competitiveness of transarctic shipping routes are expected to boost shipping activities in the region. However, in reality, the number of Arctic transits remains meagre compared with major shipping routes. This study first develops a profit estimation model for containership sailing from an original port to a destination port with multiple port calls and a cost estimation model for oil tanker sailing from an origin port to a destination port. The authors then proceed to compare the shipping efficiency between the Northern Sea Route (NSR) and the Asia-Europe shipping route via Suez Canal by using the developed models and real shipping operational data. The results demonstrate that NSR shipping is not economically favored compared to traditional one in container shipping, but may be only appealing to small or medium-size tanker operators.     

A combinatorial benders’ cuts algorithm for the quayside operation problem at container terminals

The quayside operation problem is one of the key components in the management system for a container terminal. In this paper, the integrated models proposed in the previous studies to address the quayside operation problem are examined and one of the potential frameworks is identified. A new method called combinatorial benders’ cuts algorithm is developed to solve the berth-level model in the framework. The computational experiment conducted in this research shows that the proposed approach is more efficient than the branch and cut algorithm embedded in CPLEX.     

The effect of high fuel costs on liner service configuration in container shipping

For shipping activities, not least container shipping, bunker fuel is a considerable expense. In the last 5 years, bunker prices have risen considerably. An increasing bunker price in container shipping, especially in the short term, is only partially compensated through surcharges and will therefore affect earnings negatively. This paper deals with the impact of increasing bunker costs on the design of liner services on the Europe–Far East trade. The paper assesses how shipping lines have adapted their liner service schedules (in terms of commercial speed, number of vessels deployed per loop, etc.) to deal with increased bunker costs. The paper also includes a cost model to simulate the impact of bunker cost changes on the operational costs of liner services. The cost model demonstrates for a typical North Europe–East Asia loop that the current bunker prices have a significant impact on the costs per TEU even when using large post-panamax vessels. The model also shows shipping lines are reacting quite late to higher bunker costs. The reasons that explain the late adaptation of liner services relate to inertia, transit time concerns, increasing costs associated with fixing schedule integrity problems and fleet management issues.     

Urban gravity in the global container shipping network

While the spatial and functional relationships between ports and cities have been put in question in the last decades, the continued importance of urbanization and maritime transport in global socio-economic development motivates deeper research on their interaction. The global trade network is often studied at the country level and all transport modes included, concluding that distance remains a strong counterforce to exchange. This article wishes to detect whether the global container shipping network obeys similar properties at the city level. More than 2 million inter-port vessel movements between 1977 and 2016 are assigned to about 9000 ports and 4600 cities to run a gravity model on two different network topologies. Gravitational properties are found, as larger cities connect more with each other but less at distance. The degree of distance effects negatively expanded in 40 years, confirming the “puzzling” or reinforcing effect of distance, yet it varies greatly depending on node aggregation and network topology. We conclude that ports and cities continue to share important interdependencies, but these often rest on a detrimental physical transformation. A discussion is proposed about the underlying operational and theoretical mechanisms at stake. Keywords container shipping; gravity model; maritime trade; port cities; spatial interaction; world city networks.     

A hybrid parallel genetic algorithm for yard crane scheduling

This paper aims at postulating a novel strategy in terms of yard crane scheduling. In this study, a dynamic scheduling model using objective programming for yard cranes is initially developed based on rolling-horizon approach. To resolve the NP-complete problem regarding the yard crane scheduling, a hybrid algorithm, which employs heuristic rules and parallel genetic algorithm (PGA), is then employed. Then a simulation model is developed for evaluating this approach. Finally, numerical experiments on a specific container terminal yard are used for system illustration. Computational results suggest that the proposed method is able to solve the problem efficiently.     

Container fleet sizing and empty repositioning in liner shipping systems

This paper considers the joint container fleet sizing and empty container repositioning problem in multi-vessel, multi-port and multi-voyage shipping systems with dynamic, uncertain and imbalanced customer demands. The objective is to minimize the expected total costs including inventory-holding costs, lifting-on/lifting-off costs, transportation costs, repositioning costs, and lost-sale penalty costs. A simulation-based optimization tool is developed to optimize the container fleet size and the parameterized empty repositioning policy simultaneously. The optimization procedure is based on Genetic Algorithms and Evolutionary Strategy combined with an adjustment mechanism. Case studies are given to demonstrate the results.