Hub-and-spoke network design and fleet deployment for string planning of liner shipping

Shahin Gelareh*, Nelson Maculan, Philippe Mahey, Rahimeh Neamatian Monemi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


All shipping liner companies divide their service regions into several rotations (strings) in order to operate their container vessels. A string is the ordered set of ports at which a container vessel will call. Each port is usually called at no more than twice along one string, although a single port may be called at several times on different strings. The size of string dictates the number of vessels required to offer a given frequency of service. In order to better use their shipping capacity, groups of Liner Service Providers sometimes make a short term agreement to merge some of their service routes (in a certain region) into one main ocean going rotation and p feeder rotations. In order to minimize the weighted sum of transit time, and fixed deployment costs, this paper proposes a mixed integer linear programming model of the network design, and an allocation of proper capacity size and frequency setting for every rotation. Given that none of the existing general-purpose MIP solvers is able to solve even very small problem instances in a reasonable time, we propose a Lagrangian decomposition approach which uses a heuristic procedure and is capable of obtaining practical and high quality solutions in reasonable times. The model will be applied on a real example, and we shall present some of the results obtained by our model which show how it facilitates a better use of assets and a significant reduction in the use of fuel, therefore allowing a more environmentally friendly service.

Original languageEnglish
Pages (from-to)3307-3321
Number of pages15
JournalJournal of Applied Mathematical Modelling
Issue number5
Publication statusPublished - 1 Mar 2013
Externally publishedYes


  • Decomposition
  • Environment and emission
  • Integer programming
  • Lagrangian relaxation
  • Liner shipping
  • Transportation


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