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.

Do Foldable Containers Enhance Efficient Empty Container Repositioning under Demand Fluctuation?—Case of the Pacific Region

This study considers the empty container repositioning problem of shipping companies that use standard and 3-in-1 foldable containers with more advanced designs. A mathematical model is developed to compare the total management costs of container repositioning of various patterns in different cargo shipping demand scenarios. Numerous scenario analyses and simulations of empty container repositioning were conducted, focusing on a liner shipping service in the Pacific Islands where empty containers are likely to be present because of the imbalance between inbound and outbound flows of containers, including static analysis and consecutive analysis with demand fluctuation in different approaches. Results show that with the introduction of foldable containers, depending on the growth rate of container cargo shipping demand, the total management costs of empty container repositioning can be reduced. However, introducing a large number of foldable containers may increase the total management costs of container repositioning. Moreover, the cost reduction effect of adding another containership increases in cases where future cargo shipping demand increases substantially. Furthermore, the introduction of foldable containers not only effectively reduces the management costs of empty containers, but also makes costs more stable and predictable.

Optimization on the Multi-period Empty Container Repositioning Problem in Regional Port Cluster Based upon Inventory Control Strategies

Within the area of regional port clusters, this paper establishes a multi-period mixed integer programming model to optimize the empty container repositioning between public hinterlands and ports, comprehensively considering the quantitative and periodic inventory control strategy. By using Markov decision process combined with dynamic programming method, this paper dynamically optimizes the empty container inventory threshold (D;U) under quantitative strategy and S under periodical strategy at each port within the regional port clusters. On this basis, this paper optimizes the empty container repositioning scheme between public hinterlands and ports. Meanwhile, Liaoning coastal regional port cluster and its northeast hinterland are selected as the objects to solve this model and the results show that the total cost of shipping company can be saved by 14.16% and 11.92% respec- tively by the quantitative and periodical inventory control strategy. Selecting the quantity of public hinterland terminals, the empty container demand of public hinterland terminals and ports, the inventory threshold of empty containers and other factors, this paper carries on the sensitivity analysis. This paper validates inventory control strategy can weaken the shipping company in the influence of the external environment changes. And the quantitativeinventory control strategy can reduce the total cost value to a greater extent and more effective in cost control than periodical strategy.

Research on the Optimization of Empty Container Repositioning of China Railway Express in Cooperation with International Liner Companies

Both China Railway Express (CRE) companies and international liner companies are faced with the problem of empty container repositioning. In order to reduce empty container repositioning cost and realize their sustainable development, this paper studies the optimization problem of empty container repositioning under the condition of their cooperation. To minimize the cost, three optimization models of empty container repositioning are established, which are based on the single repositioning and cooperative repositioning. Numerical experiments are carried out to analyze the three empty container repositioning optimization models solved by CPLEX. The results show that the total cost could be greatly reduced by the cooperative repositioning. The effects of cooperation become more obvious with the unit storage cost or repositioning cost increases and become weaker with the unit mutual rental cost increase. When the demand fluctuation is in a certain range, the cooperation is still effective, which can reduce the cost. But when it is beyond a certain range, the benefits will be greatly reduced. In reality, for the sustainability of their cooperation, both sides should pay attention to the proportion of supply and demand and set reasonable mutual rental cost.

Fuzzy inventory model for NVOCC’s returnable containers under empty container repositioning with leasing option

At present, the entire globe gets engaged in importing and exporting the products for promoting their business in which supply chain management is playing a vital role. The main aspect of any effective supply chain management is the transportation of cargoes. To avoid the damages of cargoes during transportation and for minimizing the cost, the returnable containers are used. The present research deals with an inventory model of Non-Vessel Operating Common Carrier (NVOCC) for returnable containers with price dependent demand under fuzzy environment. In this study, it is presumed that the import of cargoes is less than the export. The Empty Container Repositioning (ECR) and the leasing options are utilized to replace the deficit containers which prevent shortages. The proportion of the used containers returned, the proportion of the repositioned containers and the fraction of repairable from the returned containers are considered as Triangular Fuzzy Numbers [TFNs]. Fuzzy inventory model is framed for the purpose of attaining optimal length of the screening, the repositioning cycle and the leasing cycle which are used to minimize the expected total cost and the proposed model is illustrated with the numerical example. The sensitivity analysis is performed to show the effect of fuzziness of return rate, repositioning rate and repairable percentage along with the changes in parameters.

Coordinating Pricing and Empty Container Repositioning in Two-Depot Shipping Systems

This paper studies joint decisions on pricing and empty container repositioning in two-depot shipping services with stochastic shipping demand. We formulate the problem as a stochastic dynamic programming model. The exact dynamic program may have a high-dimensional state space because of the in-transit containers. To cope with the curse of dimensionality, we develop an approximate model where the number of in-transit containers on each vessel is approximated with a fixed container flow predetermined by solving a static version of the problem. Moreover, we show that the approximate value function is [Formula: see text]-concave, thereby characterizing the structure of the optimal control policy for the approximate model. With the upper bound obtained by solving the information relaxation–based dual of the exact dynamic program, we numerically show that the control policies generated from our approximate model are close to optimal when transit times span multiple periods.