Network design and capacity exchange for liner alliances with fixed and variable container demands

In liner shipping, liner carriers operate and cooperate as an alliance by sharing (or exchanging) ship capacities in order to compete with other liner carriers. Because of the long-term or short-term shipment contracts signed by shippers, the container demands transported by liner carriers can be classified as fixed demands or variable demands, respectively. We present an integrated mixed-integer linear programming model to solve the relevant problems on liner alliances including shipping network design with ship fleet deployment, allocation of the variable demands, capacities exchanged among liner carriers, and container routing. In our model, liner carriers are guided to pursue an optimal collaborative solution. As an added incentive, the capacity exchange costs are paid to liner carriers for sharing capacities and following the optimal collaborative solution. The computation of capacity exchange costs is obtained by using the inverse optimization technique. Finally, the numerical experiments for Asia-Europe-Oceania shipping services are discussed.