Liner Shipping Network Design Problem Research Articles

Approximate dynamic programming for liner shipping network design

AbstractThe global containerised trade heavily relies on liner shipping services, facilitating the worldwide movement of large cargo volumes along fixed routes and schedules. The profitability of shipping companies hinges on how efficiently they design their shipping network; a complex optimization problem known as the liner shipping network design problem (LSNDP). In recent years, approximate dynamic programming (ADP), also known as reinforcement learning, has emerged as a promising approach for large-scale optimisation. This paper introduces a novel Markov decision process for the LSNDP and investigates the potential of ADP. We show that ADP methods based on value iteration produce optimal solutions to small instances, but their scalability is hindered by high memory demands. An ADP method based on a deep neural network requires less memory and successfully obtains feasible solutions. The quality of solutions, however, declines for larger instances, possibly due to the discrete nature of high-dimensional state and action spaces.

Liner shipping network design problem in modern transportation system of Russia

The liner shipping network design problem is considered in the paper. This problem is particularly relevant in the current global political and economic conditions, where finding optimal solutions for business becomes crucial for survival. State-of-the-art formulations and methods for solving the problem in domestic and international scientific papers are discussed. Four types of liner services such as simple service, “butterfly”, “pendulum” and complex service are described. A simple service that can be reduced to the traveling salesman problem is primarily focused on. Our own formulation of the problem is proposed and an example of liner shipping network description, based on the proposed formulation, is provided. In the example, presented in the paper, a container line, based on a single domestic seaport (Vladivostok) and four seaports in China, is demonstrated. It should be noticed, that the problem includes several optimization sub-problems (such as multi-commodity flow problem), solving which is important for finding best solutions for the designed shipping line, but is outside the bounds of this research. The liner services as a sequence of vessel calls to ports are described; and some results of the foregoing generation process are discussed. The optimal solution is selected from the set of generated solutions. It represents a particular case that simultaneously has the lowest costs for implementing the container line and the highest number of serviced container flows. It is noted that this solution is optimal only within the generated solution space and may not be optimal for the considered example of the problem.

A branch-and-price algorithm for solving the single-hub feeder network design problem

In liner shipping, containers are generally transshipped in major hub ports in each region, between larger inter-region vessels and smaller feeder vessels. In this paper, we study the problem of designing the feeder vessel network, transporting containers between a regional hub and the surrounding feeder ports. The problem, as modelled, has many similarities with the split delivery vehicle routing problem, but with additional characteristics such as simultaneous pickups and deliveries and weekly departures. The problem also includes fleet sizing with a heterogeneous fleet and allows demand rejection at a penalty cost. We present a branch-and-price framework to solve the problem, where the subproblem is solved by enumerating vessel routes and subsequently assigning commodities by solving a min-cost flow problem for each commodity. The algorithm is tested on instances with up to 12 ports, which are all solved to optimality. Since the problem is similar to the liner shipping network design problem but without transshipments, we further study selected instances from the LINER-LIB instance suite. The Baltic instance is solved to proven optimality and we find the best known solution to the West Africa instance, significantly improving on what can be found in the literature.

Container liner shipping network design with shipper’s dual preference

This paper addresses the container liner shipping network design by explicitly taking into account shipper's inertia preference and non-inertial preference. Firstly, using the double-constrained gravity model and Newton calibration method to predict the future OD demand matrix which is considered as the input of the model, and then the liner shipping company profit maximization is taken as the objective function to optimize the ship shipping routes, ship type and ship speed. A hybrid genetic algorithm is designed to solve CLSNDP (Container Liner Shipping Network Design Problem). We validate the proposed model by employing a real liner shipping network on the trade shipping route between Asia and West Europe. Through sensitivity analysis, it is found that the service level and market share of container liner shipping company can be improved by considering the dual preference of shippers. In the non-inertia preference of shippers, when cost preference of shippers is greater than time preference, using large ships (over 7000TEU) can achieve greater profits and realize the scale economies of lager ships.

A Branch-and-Price Algorithm for the Liner Shipping Network Design Problem

Maritime transportation is the backbone of the global economy and one of its most important segments is liner shipping. To design a liner shipping network is notoriously difficult but also very important since an efficient network can be the difference between prosperity and bankruptcy. In this paper, we propose a branch-and-price algorithm for the liner shipping network design problem, which is the problem of designing a set of cyclic services and to deploy a specific class of vessels to each service so that all demand can flow through the network at minimal cost. The proposed model can create services with a complex structure and correctly calculate the transshipment cost. The formulation of the master problem strengthens a known formulation with valid inequalities. Because of multiple dependencies between ports that are not necessarily adjacent and no defining state at any of the ports, the subproblem is formulated and solved as a mixed integer linear program. Strategies to improve the solution time of the subproblem are proposed. The computational study shows that the algorithm provides significantly tighter lower bounds in the root node than existing methods on a set of small instances.

Integrated Liner Shipping Network Design and Scheduling

In global liner shipping networks, a large share of transported cargo is transshipped at least once between container vessels, and the total transportation time of these containers depends on how well the corresponding services are synchronized. We propose a problem formulation that integrates service scheduling into the liner shipping network design problem. Furthermore, the model incorporates many industry-relevant modeling aspects: it allows for leg-based sailing speed optimization, it is not limited to simple or butterfly-type services, and it accounts for service-level requirements such as cargo transit time limits. The classic liner shipping network design problem is already a hard problem, and to solve the extended version, we propose a column-generation matheuristic that uses advanced linear programming techniques. The proposed method solves LINER-LIB instances of up to 114 ports and, if applied to the classic liner shipping network design problem, finds new best solutions to all instances, outperforming existing methods reported in the literature. Additionally, we analyze the relevance of scheduling for liner shipping network design. The results indicate that neglecting scheduling and approximating transshipments instead may result in the design of liner shipping networks that underestimate cargo transit times and their implications.

A new formulation for the liner shipping network design problem

AbstractThe liner shipping network design problem (LSNDP) is an important problem within liner shipping because a good network can reduce costs and increase profits. Given sets of ports, vessel classes, and demands between the ports, the problem is to design a network of cyclic routes and assign a vessel class to each route so that all demands can flow through the network at minimal cost. In this paper, we analyze a new formulation of the LSNDP based on a two‐layer network structure. The formulation takes into account the cost of transshipment and allows for complex service structures. Valid inequalities and a novel approach of inner representations of low‐dimensional polyhedra are proposed. A new set of small instances with up to 12 ports has been developed and the formulation has been tested on these instances. Instances with up to 10 ports are solved to optimality, but the largest instances are not, confirming that the LSNDP is a very complex problem. The proposed improvements of the formulation are also shown to have a positive effect.

Competitive Liner Shipping Network Design

We present a solution method for the liner shipping network design problem which is a core strategic planning problem faced by container carriers. We propose the first practical algorithm which explicitly handles transshipment time limits for all demands. Individual sailing speeds at each service leg are used to balance sailing speed against operational costs, hence ensuring that the found network is competitive on both transit time and cost. We present a matheuristic for the problem where a MIP is used to select which ports should be inserted or removed on a route. Computational results are presented showing very promising results for realistic global liner shipping networks. Due to a number of algorithmic enhancements, the obtained solutions can be found within the same time frame as used by previous algorithms not handling time constraints. Furthermore, we present a sensitivity analysis on fluctuations in bunker price which confirms the applicability of the algorithm.

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.

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.

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.

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).

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.