Liner hub-and-spoke shipping network design

•Investigate container transshipment operations when designing feeder ship routes.•Ship route design with fleet deployment, due to the transit time constraints.•Present a genetic algorithm embedded with a multi-stage decomposition approach.

This paper proposes a liner hub-and-spoke shipping network design problem by introducing the concept of a main port, as well as some container shipping constraints such as multi-type container shipment and transit time constraints, which are seldom considered in the previous studies. It develops a mixed-integer programming model with nonconvex multi-linear terms for the proposed problem. An efficient genetic algorithm embedded with a multi-stage decomposition approach is developed to solve the model. Numerical experiments are carried out to assess the effectiveness of the proposed model and the efficiency of the proposed algorithm.