Hub location and routing problem with alternative paths

In the actual scenario of international trade, shipping industry is responsible for carrying the largest volume of goods and the liner shipping is the way what provides more stability because of its published and stable rates for long periods. Moreover, it is based on a fixed and published schedule in which vessels operate cyclic routes. This paper introduces a new hub and spoke network structure for regular cyclic vessel routes. The network structure, representing a deap sea operations and short sea operations of liner shipping, is a hierarchical hub and spoke structure that offers alternative paths for flow between nodes through hub-route and sub-route and whose sub-routes could have a sub-hub linking them. A mathematical model which integrates a hub location problem with multiple allocations and with routing problem is presented to optimize the network design global cost.