Laden Containers Research Articles

Liner fleet deployment and empty container repositioning under demand uncertainty: A robust optimization approach

This paper investigates a robust optimization problem concerning the integration of fleet deployment and empty container repositioning in a shipping line network, where a fleet of vessels is dispatched to transport both laden and empty containers, aiming to fulfill a predetermined set of requests over a defined time horizon. The sizes of customer demands are uncertain and are characterized by a budgeted uncertainty set. This study aims to ascertain the vessel types assigned to each shipping route, the routing of laden containers, and the repositioning of empty containers in a manner that minimizes the total cost. Simultaneously, it ensures the feasibility of all transportation plans for any realization of demand within the uncertainty set. We introduce a path-based two-stage robust formulation for addressing the problem. In the first stage, the assignment of vessel types to each shipping route is determined, and the second stage focuses on establishing the routing of laden containers and repositioning of empty containers under a worst-case scenario. We propose the Column-and-Constraint Generation algorithm for solving the proposed robust formulation. To address large-scale size instances, we propose an acceleration technique, i.e., the piece-wise affine policy, which reduces the dimensions of the uncertainty set while maintaining a bounded compromise in solution quality. Comprehensive numerical experiments derived from real-world industries, such as the Shanghai port and CMA CGM, are conducted to validate the proposed formulation and solution methodologies.

Tactical vessel deployment and empty container repositioning considering container turnover times

Global trade imbalances lead to the common occurrence of empty container flows from export-dominated to import-dominated ports in container shipping networks. Efficient strategies for repositioning empty containers are essential for addressing deficits at major ports. Existing studies often assume an arbitrary supply of empty containers at a port before repositioning. However, the actual quantity depends on laden containers shipped and turnover times. Considering this interdependence is crucial for reliable repositioning plans, especially at the tactical planning level.This paper explores an integrated problem of vessel deployment and empty container repositioning, aiming to deploy vessels along a route and periodically reposition empty containers, accounting for turnover times. We present an integer programming model minimizing operational and container shortage costs. A novel branch-and-price algorithm is developed, efficiently solving the master problem at each branching tree node using a novel approach that combines column generation and Lagrangian relaxation. Performance evaluation and computational experiments on instances generated from container port turnover statistics and shipping line operational data demonstrate the algorithm’s efficacy. The study highlights the impact of container turnover times on repositioning decisions, emphasizing the need for a comprehensive understanding of this dynamic in strategic planning.

Liner shipping hub location and empty container repositioning: Use of foldable containers and container leasing

Considering the influence of economies of scale and ship capacity on empty container repositioning, using foldable containers and container leasing may be effective ways to save the operating costs of liner shipping companies. Considering the minimization of the transportation costs of empty and laden containers, this paper studies a liner shipping hub location problem with empty container repositioning (LSHLPECR) considering foldable containers. We propose a mixed integer linear program (MILP) for the formulation of the LSHLPECR. In terms of the optimal solution of our MILP, this paper further explores the container leasing pricing problem (CLPP), where our aim is to obtain perceived container leasing prices (PCLPs) utilizing the inverse optimization technique. Numerical experiments verify the effectiveness of the studied problems.

The dynamic programming model for optimal allocation of laden shipping containers to Nigerian seaports

In highly competitive shipping market environment, container network operators-Freight forwarders, shipping companies etc. are concerned about design, development and deployment of optimized allocation model to achieve cost savings through improved container storage yard operations, crane productivity, outbound container allocation/distribution to seaport terminals and hence reduction in ships’ waiting times. In this paper, we developed two models, the Dynamic programming model and optimal allocation policy (model), for the optimal allocation of units of outbound laden cargo containers of sizes: 20ft and 40ft to six (6) major seaports in Nigeria. The distributions of the laden containers were allocated as follows: Port-Harcourt, Tincan Island, Onne, and Calabar seaports were allocated with 1,064 units of stuffed containers each. Apapa seaport was allocated with 2,128 units of laden containers, and zero allocation was made to Warri seaport. These results were arrived at through the implementation of the optimal allocation policy. The zero units allocation made to Warri seaport could be attributed to poor shipper patronage and hence the low frequency of ship visits. Apapa seaport was allocated double the number of containers moved to the remaining ports because it attracted more shipper patronage and hence more ship visits. Hence, freight forwarding companies will be assured of cargo spaces and make more profit by allocating more containers. Policy implications of the developed models were discussed.

Distribution-Free Approaches for an Integrated Cargo Routing and Empty Container Repositioning Problem with Repacking Operations in Liner Shipping Networks

Cargo (laden container) routing and empty container repositioning are crucial components in liner shipping, which are closely relevant. However, most existing works focus on cargo routing and empty container repositioning separately, which cannot optimize the global shipping cost. In addition, (1) appropriate repacking operations for laden containers can curtail the total handling costs, and (2) the perfect information for uncertain laden and empty container demands may be difficult to obtain due to insufficient historical data. This work investigates an integrated cargo routing and empty container repositioning problem with repacking operations in which only partial information about uncertain laden and empty container demands is known. The objective is to minimize the total costs including repacking operation cost and laden and empty container transportation costs. For the problem, a new chance-constrained programming model based on moment-based ambiguous sets is formulated. Then, four distribution-free solution approaches are adopted to solve the investigated problem. Numerical experiments are conducted to compare the proposed methods.

A Multi-Stage Approach for Empty Container Repositioning Under Coordination Among Liner Carriers

This paper studies the empty container repositioning (ECR) problem considering the exchange of slots and empty containers among liner shipping companies. It is common for an individual shipping company to seek an optimal solution for ECR and cargo routing to maximize its own benefits. To achieve cooperation among shipping companies, a multi-stage solution strategy is proposed. With the inverse optimization technique, the guide leasing prices of slots and empty containers among shipping companies are derived considering the schedule of vessels and cargo routing. Based on the guide leasing price, a cooperative model is formulated to minimize the total cost, which includes the transportation cost for laden containers, the inventory holding cost, the container leasing cost, and the repositioning cost. All the involved shipping companies are expected to follow the best solution of ECR and cargo routing to achieve a cooperative and stable optimum. A real-world shipping network operated by three liner shipping companies is used as a case study with promising numerical results.

Leasing or repositioning empty containers? Determining the time-varying guide leasing prices for decision making

ABSTRACT Repositioning empty container and leasing container from leasing company are mainly the outcomes of imbalance in trade flows. How to make decision on repositioning or leasing remains a challenge in running shipping service efficiently and economically. To address such challenge, this study aims to derive guide leasing prices. If the realistic leasing price is lower than the guide price, shipping companies should consider leasing containers from leasing company; otherwise repositioning empty container is a more economical option. Both time-varying short-term and long-term guide leasing prices are determined in a shipping network with consideration of empty container devanning and laden container transportation. A two-stage approach is applied to model development. At the first stage, an empty container repositioning model is proposed with consideration of holding, transportation and lifting-on/off costs. Then, inverse optimization technique is applied to deriving the second model in order to determine the guide leasing prices. A realistic shipping network is adopted to compare long-term guide leasing prices among different ports and short-term guide leasing prices on different paths between a pair of ports. The results show that short-term guide leasing prices at a deficit port vary on different paths and they are correlated to the schedule of vessels.

Tactical and Operational Cooperative Empty Container Repositioning Optimization Model Based on Business Flow and Initial Solutions Generation Rules

Due to the special role of empty containers in the container transportation process, empty container repositioning is a focal point in the shipping industry. For this problem, highly efficient and feasible optimization models are critical in improving the benefit for shipping companies and increasing their market competitiveness. Operational decisions are affected by tactical ones. Aimed at this point, we propose a tactical and operational cooperative empty container repositioning optimization model. To cut the search space and obtain the optimal solution quickly, several initial solutions generation rules are extracted, based on business flow. Furthermore, the reachable shipping distance may change when the calling sequence is different. An algorithm which calculates the reachable shipping distance matrix between ports is presented to solve this problem. Simulated cases are used to test the proposed model and algorithm. The results show that the cases can cope with the tactical and operational cooperative empty container repositioning optimization model. Moreover, some interesting conclusions also are deduced about the relationships among number of calling ports, total profits, leasing cost, calling port fee, number of Empty Containers Repositioned (ECR), and laden containers. All these can guide and assist the various decisions to be made. According to the homepage of Symmetry, its subject areas include Mathematics, Computer Science, Theory, and Methods. Their branches include information theory, computer-aided design, and so on. The topic of our paper is to solve this engineering application problem by using a mathematical optimization model and computer methods. That is, applying mathematical theory and computer methods to make decision results for the empty container repositioning problem in the shipping industry. It has certain economic value and practical significance. Obviously, it is consistent with the theme of Symmetry.

A Multiojective Programming Model for Container Shipping of Sea-Carriage

The paper uses multiobjective programming to build the modal of optimization of choosing shipping container routing. In the model, the first objective function is to maximize the profit of container transport. The second objective function is to minimize the shortage cost of laden container. And the constraints to the model include meeting the need of containers, the limit to transport ability and the number of empty container supported. We transfer the multiobjective model into a linear programming. Then the linear model is solved by Lingo9.0. The loss produced by choosing unreasonable route can be reduced effectively by use of the method in the paper. The aim of the paper is to provide a reasonable project of choosing shipping container route, so the profit of a shipping company can be maximized.

A method for solving the classification problem with stability in small clinical samples

Container inventory imbalance (or under/over balanced, i.e. one carrier can be in an excess situation while the other will be in deficit) is a severe problem that adds a substantial expense on ocean freight. The ocean containers are built for continuous transportation with cargo. However, due to the imbalance in world trade and other inherent characteristics of shipping the import volumes and export volumes of laden containers in a port are not equal. This variation leads carriers reposition empty containers from excess ports to elsewhere that the empty containers are in demand. If carriers retain containers in a port pending exports demands the sole purpose of containers cannot be met. Thus, it may add storage cost and wear and tear that makes the container shipping uneconomical. This paper appraises the potential of the container exchange and its practical aspects using real container data. Further, it focuses on several factors that may influence container exchange among carriers. Finally, it concludes that the organizational factors play the key role in container exchange thus recommends for further research based on statistical analysis of this paper.

The reality of container exchange between shipping lines: Clearing the pathway to virtual container yard

Container inventory imbalance (or under/over balanced, i.e. one carrier can be in an excess situation while the other will be in deficit) is a severe problem that adds a substantial expense on ocean freight. The ocean containers are built for continuous transportation with cargo. However, due to the imbalance in world trade and other inherent characteristics of shipping the import volumes and export volumes of laden containers in a port are not equal. This variation leads carriers reposition empty containers from excess ports to elsewhere that the empty containers are in demand. If carriers retain containers in a port pending exports demands the sole purpose of containers cannot be met. Thus, it may add storage cost and wear and tear that makes the container shipping uneconomical. This paper appraises the potential of the container exchange and its practical aspects using real container data. Further, it focuses on several factors that may influence container exchange among carriers. Finally, it concludes that the organizational factors play the key role in container exchange thus recommends for further research based on statistical analysis of this paper.

Direct shipping service routes with an empty container management strategy

This paper presents an investigation of an empty container management strategy in a two-way four-echelon container supply chain for bilateral trade between two countries. The strategy reduces high maritime transportation costs and long delivery times due to transshipment. The impact of direct shipping was investigated to determine the number of empty containers to be repositioned among selected ports, number of leased containers, and route selection to satisfy the demands for empty and laden containers for exporters and importers in two regions. A hybrid solution procedure based on accelerated particle swarm optimization and heuristic is presented, and corresponding results are compared.

Containership Traffic Optimization on Feeder Shipping Line

AbstractThis article is devoted to feeder containership traffic optimization on the trunk and feeder shipping lines. The optimization is fulfilled in case of the necessity of laden containers delivery between fixed pairs of ports as well as in case of the requirement not to exceed the vessel's capacity, taking into account her residual value during transition between feeder port lines. The paper takes into account uneven distribution of empty container equipment in ports of line and the solution is suggested considering the estimation of the empty TEU’s number which is subject to reposition.

Operational shadow pricing in back haul container shipping

Minimum acceptable rates for back haul cargo are difficult for carriers to establish in practice. They depend on complex factors such as availability of empty containers in the vicinity, cost of repositioning empties and container on-hiring decisions. A shadow pricing and “shadow credit” approach is proposed and applied to an inland network. Such a model can help carriers undertake yield management at the operational level to improve financial performance in a post-conference era. Results also suggest a positive relationship between variability in the imbalance situation of laden containers in a particular trade and volatility of short-term back haul freight rates.

Reprint of “Enhancing green supply chain initiatives via empty container reuse”

In this paper, the maritime industry’s commitment to green supply chain has been analyzed. The objective of this study is to show that the reuse of empty containers not only adds value to a firm, but leads to waste reduction in the supply chain. The novelties of this article include (i) empty and laden containers are treated in accordance with a shipping company’s green effort; (ii) both the volume and weight of containers are introduced to indicate a potential constraint on green effort; (iii) empty container storage costs are included as a value-added component which stem from green effort.

Enhancing green supply chain initiatives via empty container reuse

In this paper, the maritime industry’s commitment to green supply chain has been analyzed. The objective of this study is to show that the reuse of empty containers not only adds value to a firm, but leads to waste reduction in the supply chain. The novelties of this article include (i) empty and laden containers are treated in accordance with a shipping company’s green effort; (ii) both the volume and weight of containers are introduced to indicate a potential constraint on green effort; (iii) empty container storage costs are included as a value-added component which stem from green effort.

Dynamic Container Deployment: Two-Stage Robust Model, Complexity, and Computational Results

Containers are widely used in the shipping industry mainly because of their capability to facilitate multimodal transportation. How to effectively reposition the nonrevenue empty containers is the key to reduce the cost and improve the service in the liner shipping industry. In this paper, we propose a two-stage robust optimization model that takes into account the laden containers routing as well as the empty container repositioning, and define the robustness for this model with uncertainties in the supply and demand of the empty containers. Based on this definition, we present the robust formulations for the uncertainty sets corresponding to the ℓp-norm, where p = 1, 2, and ∞, and analyze the computational complexities for all of these formulations. The only polynomial-time solvable case corresponds to the ℓ1-norm, which we use to conduct the numerical study. We compare our approach with both the deterministic model and the stochastic model for the same problem in the rolling horizon simulation environment. The computational results establish the potential practical usefulness of the proposed approach.

A Stochastic Programming Optimization Model of Container Shipping of Sea-Carriage

The paper dose research about the optimization of container shipping of sea carriage for meeting the goods transport requirement by use of stochastic programming. Both laden and empty containers are combined into a system. In particular, the effect of special laden container shipping capacity on the shipping plan is investigated. In the model, the objective function is to maximize the total profit of container shipping. The profit caused by laden container shipping minus the cost caused by both laden and empty container shipping equal to the total profit. The constraints to the model include meeting the need of both laden and empty containers, shipping limit to both common and special laden containers, the number of empty container supported. The number of empty containers is stochastic and the model is transmitted to an integer programming. Lingo9.0 is used to solve the model and shipping methods in varied parameters are shown by simulation. The aim of the paper is to provide a reasonable plan of container shipping of sea-carriage, so the container shipping cost of a shipping company can be reduced and the its profit made by container shipping are maximized.

Long-haul liner service route design with ship deployment and empty container repositioning

This paper proposes a single liner long-haul service route design problem including route structure design, ship deployment and empty container repositioning. The objective of this problem is to minimise the total cost incurred from a liner long-haul service route, including ship related costs, fuel consumption costs, port related costs, laden containers and empty container inventory-in-transition costs. We propose a three-stage optimisation method to tackle the problem. We introduce the notions of topological structure and ship load factors, which lead to a classification of shipping route structures and the relationships between the container flow pattern and the route structure. This greatly simplifies the route structure design decisions at the first stage and enables us to develop an efficient heuristic algorithm to reposition empty containers at the second stage. The ship deployment problem concerning the number of ships and their capacity and sailing speeds is considered at the third stage. The model takes advantage of the characteristics of the existing route structures and can solve the service route design problems effectively from the practical perspective. In addition, the established relationships between the load factors and the route structure provide useful insights into ship utilisation and route structure choice. Case studies are presented to show efficiency and applicability of the proposed research methodology.

An Integer Programming Optimization Model of Container Shipping of Sea-Carriage

The paper dose research about the optimization of container shipping of sea –carriage for meeting the goods transport requirement by use of integer programming. Both laden and empty containers are combined into a system. In particular, the effect of special laden container shipping capacity on the shipping plan is investigated. In the model, the objective function is to maximize the total profit of container shipping. The profit caused by laden container shipping minus the cost caused by both laden and empty container shipping equal to the total profit. The constraints to the model include meeting the need of both laden and empty containers, shipping limit to both common and special laden containers , the number of empty container supported. Lingo9.0 is used to solve the model and shipping methods in varied parameters are shown by simulation. The aim of the paper is to provide a reasonable plan of container shipping of sea-carriage, so the container shipping cost of a shipping company can be reduced and the its profit made by container shipping are maximized.