Liner shipping service network design with empty container repositioning

This paper proposes a liner shipping service network design problem with combined hub-and-spoke and multi-port-calling operations and empty container repositioning. It first introduces a novel concept - segment - defined as a pair of ordered ports served by one shipping line and subsequently develops a mixed-integer linear programming model for the proposed problem. Extensive numerical experiments based on realistic Asia-Europe-Oceania shipping operations show that the proposed model can be efficiently solved by CPLEX for real-case problems. They also demonstrate the potential for large cost-savings over pure hub-and-spoke or pure multi-port-calling network, or network without considering empty container repositioning.