A variable neighbourhood decomposition search approach applied to a global liner shipping network using a hub-and-spoke with sub-hub structure

This paper presents a new concept for a hub-and-spoke network structure, called "sub-hub", applied to global operations of liner shipping. Hub-and-spoke networks are widely used in transportation due to the economy of scale offered to the demands between hubs. However, efficient network structures require more than an economy of scale with regard to transport costs. This study therefore, aims to demonstrate that lower transport costs are achievable by a hub-and-spoke with sub-hub structure because the economy of scale this model provides is combined with shorter alternative paths. A short sea operation in liner shipping is a circular route at cluster level (the hub and its allocated spokes). A deep sea operation functions as a direct connection between hubs. A sub-hub is an intersection point between two regional (cluster) routes, thereby allowing the transshipment of goods, for certain demands, without using hub nodes. Hubs and sub-hubs are selected between the existing ports (nodes), and installation costs are not included for these models. A cutting plane approach was implemented. Although the computation results of the models, which are classified as hub location-routing problems, were compared on small instances, a Variable Neighbourhood Decomposition Search (VNDS) was implemented to test large instances.