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.

Liner companies face a complex problem in determining the optimal routing and deployment of a fleet of container vessels. This paper presents a model and an algorithm to address the two problems jointly. The model captures the revenues and operating expenses of a global liner company, and allows for the representation of vessel types with different cost and operating properties, transhipment hubs and associated costs, port delays, regional trade imbalances and the possibility of rejecting transportation demand selectively. Benchmark tests demonstrate that the proposed algorithm achieves good solutions quickly. The proposed algorithm is applied in a case study with 120 ports of call distributed throughout the globe. The case study explores the sensitivity of optimal fleet deployment and routing to varying bunker costs. Maritime Economics & Logistics (2009) 11, 186–208. doi:10.1057/mel.2009.5

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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.