Cargo allocation and vessel scheduling on liner shipping with synchronization of transshipments

A mixed integer linear programming model is presented for the operational level cargo al- location and vessel scheduling problem of a liner shipping company in Turkey, where flow- dependent port-stay lengths, transit times and transshipment synchronizations are consid- ered. The proposed model aims to assign shipments to routes to decrease total tardiness and construct partial vessel schedules for establishing coordination with port authorities to comply with the berthing time windows. In addition to the mathematical model, novel valid inequalities and benders decomposition algorithm are implemented. Performance of the developed algorithm is evaluated on real-life problem instances. The results show that benders decomposition with valid inequalities yields the best performance.