Joint optimization of slot and empty container co-allocation for liner alliances with uncertain demand in maritime logistics industry

With the growth traffic of containerized shipping worldwide, container liners have seen increasing cooperation. Slot co-allocation has drawn wide attention as a way of cooperation within liner alliances. However, due to the need for liner alliances to predict uncertain future demands to formulate empty container scheduling plans, empty container repositioning and co-allocation are essential but seldom considered. In response to this, this paper jointly optimizes the slot and empty container co-allocation issues by considering slot and empty container sharing. First, we proposed a two-stage stochastic programming model to minimize the total cost of the liner alliance. To solve the high-dimensional stochastic programming problem, we then proposed two new hybrid stochastic learning algorithms, which utilize the network structure while adaptively approximating the objective function by learning from historical data. Finally, we tested our algorithm in the real route data of the Ocean Alliance between South Asia and Southeast Asia. Computational results indicate that the proposed algorithms exhibit effective and efficient performance for joint optimization of slot and empty container co-allocation for liner alliances with uncertain demand, and some interesting managerial insights can be drawn from the rolling-horizon experiments.