Integrated optimization of vessel dispatching and empty container repositioning considering turnover time uncertainty

The global trade disproportion results in the accumulation of containers in import-dominated ports and shortages in export-dominated ports, causing congestion and high freight costs, thus hindering maritime shipping economy development. To address these issues, this study develops a stochastic programming model considering uncertain container turnover times. The model integrates decisions for vessel deployment and empty container repositioning over multiple planning periods through a two-stage decision process, aiming to minimize the total cost, including vessel deployment, container leasing, and penalty costs for unfulfilled demand. By formulating the scenario selection problem as a p-median problem, we effectively reduce the model size. We propose an accelerated Benders decomposition algorithm which leverages the independence of sub-problems in the second stage to enable parallel computation. Numerical experiments show that our Benders decomposition algorithm improves solution speed by over 63% compared to the Gurobi optimization solver. Furthermore, our integrated optimization approach proves to be more cost-effective than the reactive method used by shipping lines, achieving an average cost savings of 0.72%. Additionally, our method of constructing turnover time scenarios to address uncertainty saves approximately 0.45% in costs compared to using the probability distribution of container turnover time.