Heterogeneous vessel fleet co-management for liner alliances under profit-sharing agreement and weekly-dependent demand

As the oversupply of shipping capacity and the competition within the shipping industry intensifies, liner alliances have emerged as the prevailing mode of cooperation. The members in a liner alliance often have different shipping resources, indicating that they have to coordinate the shipping resources with each other, in order to achieve smooth cooperation. During the coordination, the fairness of members cannot be ignored as it forms the foundation of cooperation stability. Meanwhile, the vessel fleet is often heterogeneous in practice, not homogeneous assumed in most of existing studies. Therefore, this research explores the joint optimization problem of heterogeneous vessel fleet co-management (including fleet co-deployment, vessel co-scheduling, vessel co-sequencing, slot co-chartering and slot co-allocation), taking into account profit-sharing agreement and weekly-dependent demand. In response to this problem, a mixed-integer nonlinear program is first formulated with the goal of maximizing the overall profit reached by the alliance. We then linearize this nonlinear program, and subsequently develop a solution method to identify the optimal solution for the linearized model. Various numerical tests are performed to examine the validity of the proposed model. Furthermore, several managerial insights that support the operation of liner alliance are delivered.