Liner Shipping Network Design Research Articles

Optimization in liner shipping

Seaborne trade is the lynchpin in almost every international supply chain, and about 90% of non-bulk cargo worldwide is transported by container. In this survey we give an overview of data-driven optimization problems in liner shipping. Research in liner shipping is motivated by a need for handling still more complex decision problems, based on big data sets and going across several organizational entities. Moreover, liner shipping optimization problems are pushing the limits of optimization methods, creating a new breeding ground for advanced modelling and solution methods. Starting from liner shipping network design, we consider the problem of container routing and speed optimization. Next, we consider empty container repositioning and stowage planning as well as disruption management. In addition, the problem of bunker purchasing is considered in depth. In each section we give a clear problem description, bring an overview of the existing literature, and go in depth with a specific model that somehow is essential for the problem. We conclude the survey by giving an introduction to the public benchmark instances LINER-LIB. Finally, we discuss future challenges and give directions for further research.

Analyzing complex service structures in liner shipping network design

One of the most important strategic decisions of a liner shipping company is the design of a set of cyclic routes, services, for container vessels to provide transport for goods from origins to destinations. This problem is called the liner shipping network design problem (LSNDP). The cyclic nature of the services as well as the possibility of transshipping cargoes between services makes the problem difficult to solve for large instances. Therefore, it is common to make assumptions regarding the structure of the services. We analyze the effect of different structures ranging from simple ones visiting a port once in a service, to butterfly services where one port can be visited twice in a service and a more general structure where every port in a service can be visited more than once. To perform these analyses, we have developed a new mathematical model for the LSNDP where there are no limitations on the number of visits to each port. The model is solved by a branch-and-price method, where we for the sake of computational time have reduced the number of visits per port on a service to a maximum of two. The computational study shows that complex service structures can create more cost-efficient networks and that the objective value can be improved by allowing general service structures even for small sized instances.

Formulating cargo inventory costs for liner shipping network design

ABSTRACTThis study examines how to incorporate the inventory costs of containerized cargoes into existing liner service planning models such that the designed networks could be improved while not causing extra modeling/computational burden. Two approaches are compared: (i) not considering the inventory costs at all and (ii) incorporating the inventory costs associated with onboard time and those related to transshipment by assuming a fixed connection time. The two models are compared with the ideal model capturing the exact inventory costs on a route choice problem and a capacity planning problem based on extensive randomly generated and practical numerical experiments. The results show that: first, ignoring the inventory costs in service planning models may lead to network design with much higher costs (poor network design decisions); second, in service planning models assuming weekly frequency, the inventory costs associated with onboard time could be formulated exactly, and those related to the connection time of weekly services could be approximated by assuming fixed connection time of 3.5 days for ports with 1 day’s minimum connection time and 4.5 days for ports with 2 days’ minimum connection time.

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.

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 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.

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.

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.

Global intermodal liner shipping network design

This paper presents a holistic analysis for the network design problem of the intermodal liner shipping system. Existing methods for liner shipping network design mainly deal with port-to-port demand. However, most of the demand has inland origins and/or destinations. Thus, it is necessary to cope with inland origin–destination (OD) pairs involving a change in transport mode from inland transportation to maritime shipping. A method is first proposed to convert inland OD demand to port-to-port demand. Then, a framework for global intermodal liner shipping network design is proposed. Finally, the proposed methodology is applied to and numerically verified by a large-scale network example.

A service flow model for the liner shipping network design problem

Global liner shipping is a competitive industry, requiring liner carriers to carefully deploy their vessels efficiently to construct a cost competitive network. This paper presents a novel compact formulation of the liner shipping network design problem (LSNDP) based on service flows. The formulation alleviates issues faced by arc flow formulations with regards to handling multiple calls to the same port. A problem which has not been fully dealt with earlier by LSNDP formulations. Multiple calls are handled by introducing service nodes, together with port nodes in a graph representation of the problem, and by introducing numbered arcs between a port and a novel service node. An arc from a port node to a service node indicate whether a service is calling the port or not. This representation allows recurrent calls of a service to a port, which previously could not be handled by LSNDP models. The model ensures strictly weekly frequencies of services, ensures that port-vessel draft capabilities are not violated, respects vessel capacities and the number of vessels available. The profit of the generated network is maximized, i.e. the revenue of flowed cargo subtracted operational costs of the network and a penalty for not flowed cargo. The model can be used to design liner shipping networks to utilize a container carrier’s assets efficiently and to investigate possible scenarios of changed market conditions. The model is solved as a Mixed Integer Program. Results are presented for the two smallest instances of the benchmark suite LINER-LIB-2012 presented in Brouer, Alvarez, Plum, Pisinger, and Sigurd (2013).

Methods for strategic liner shipping network design

In this paper the combined fleet-design, ship-scheduling and cargo-routing problem with limited availability of ships in liner shipping is considered. A composite solution approach is proposed in which the ports are first aggregated into port clusters to reduce the problem size. When the cargo flows are disaggregated, a feeder service network is introduced to ship the cargo within a port cluster. The solution method is tested on a problem instance containing 58 ports on the Asia–Europe trade lane of Maersk. The best obtained profit gives an improvement of more than 10% compared to the reference network based on the Maersk network.

Liner shipping network design with deadlines

It is crucial for a liner shipping company to design its container shipping network. Given a set of port-to-port container shipment demands with delivery deadlines, the liner shipping company aims to design itineraries of portcalls, deploy ships on these itineraries and determine how to transport containers with the deployed ships in order to maximize its total profit. In this paper we first demonstrate NP-hardness of this problem and subsequently formulate it as a mixed-integer non-linear non-convex programming model. A column generation based heuristic method is proposed for solving this problem. Numerical experiments for container shipping on the Asia–Europe trade lane show that the proposed solution algorithm is efficient to find good quality solutions.

A Base Integer Programming Model and Benchmark Suite for Liner-Shipping Network Design

The liner-shipping network design problem is to create a set of nonsimple cyclic sailing routes for a designated fleet of container vessels that jointly transports multiple commodities. The objective is to maximize the revenue of cargo transport while minimizing the costs of operation. The potential for making cost-effective and energy-efficient liner-shipping networks using operations research (OR) is huge and neglected. The implementation of logistic planning tools based upon OR has enhanced performance of airlines, railways, and general transportation companies, but within the field of liner shipping, applications of OR are scarce. We believe that access to domain knowledge and data is a barrier for researchers to approach the important liner-shipping network design problem. The purpose of the benchmark suite and the paper at hand is to provide easy access to the domain and the data sources of liner shipping for OR researchers in general. We describe and analyze the liner-shipping domain applied to network design and present a rich integer programming model based on services that constitute the fixed schedule of a liner shipping company. We prove the liner-shipping network design problem to be strongly NP-hard. A benchmark suite of data instances to reflect the business structure of a global liner shipping network is presented. The design of the benchmark suite is discussed in relation to industry standards, business rules, and mathematical programming. The data are based on real-life data from the largest global liner-shipping company, Maersk Line, and supplemented by data from several industry and public stakeholders. Computational results yielding the first best known solutions for six of the seven benchmark instances is provided using a heuristic combining tabu search and heuristic column generation.

Mathematical expressions for the transit time of merchandise through a liner shipping network

Recent publications on the design of liner shipping networks are limited in their treatment of the level of service (LoS) experienced by shippers. We propose the use of inventory holding costs—a function of merchandise transit time—as a proxy for LoS. We assume the existence of a two-tier optimization model, where fleet deployment, vessel routing, and vessel speed are determined in the higher tier. Merchandise flows and transshipment quantities are determined in the lower tier. We partition the total merchandise transit time into time spent in open waters, time spent during port calls, and time spent dwelling in the terminal yard. Using the notions of service frequency and service phase, we develop mathematical expressions for the three aforementioned quantities within the lower tier of the optimization model. We arrive at a bilinear expression for overall inventory holding costs that is suitable for liner shipping network design.

Hub location problems in transportation networks

In this paper we propose a 4-index formulation for the uncapacitated multiple allocation hub location problem tailored for urban transport and liner shipping network design. This formulation is very tight and most of the tractable instances for MIP solvers are optimally solvable at the root node. While the existing state-of-the-art MIP solvers fail to solve even small size instances of problem, our accelerated and efficient primal (Benders) decomposition solves larger ones. In addition, a very efficient greedy heuristic, proven to be capable of obtaining high quality solutions, is proposed. We also introduce fixed cost values for Australian Post (AP) dataset.

Study on a Liner Shipping Network Design Considering Empty Container Reposition

Empty container allocation problems arise due to imbalance on trades. Imbalanced trade is a common fact in the liner shipping,creating the necessity of repositioning empty containers from import-dominant ports to export-dominant ports in an economic and efficient way. The present work configures a liner shipping network, by performing the routes assignment and their integration to maximize the profit for a liner shipping company. The empty container repositioning problem is expressly taken into account in whole process. By considering the empty container repositioning problem in the network design, the choice of routes will be also influenced by the empty container flow, resulting in an optimum network, both for loaded and empty cargo. The Liner Shipping Network Design Program (LS-NET program) will define the best set of routes among a set of candidate routes, the best composition of the fleet for the network and configure the empty container repositioning network. Further, a network of Asian ports was studied and the results obtained show that considering the empty container allocation problem in the designing process can influence the final configuration of the network.