A model for container stowage planning considering stability constraints

The growth in global trade has led to the deployment of mega-container ships to meet increasing transportation demands. However, the larger vessel sizes pose significant challenges for planners in arranging container loading. This study addresses the container stowage planning problem for near-sea routes, incorporating stability constraints, container types, and technical limitations related to stack weight and stress. We propose a mixed integer linear programming model to describe this problem and generate load plans that minimize total costs associated with re-stowing and bending moments (BM). To solve the model efficiently, we design a dynamic weight and time-varying particle swarm optimization (PSO) algorithm, which combines particle classification and time-varying acceleration constants. The effectiveness of the model and the efficiency of the algorithm are validated through extensive numerical experiments. The results demonstrate that our proposed algorithm outperforms the traditional PSO algorithm in both solution quality and computation time. Additionally, sensitivity analyses are conducted to derive potentially useful managerial insights for supporting shipping liners’ decision-making. This study highlights the benefits of particle classification and time-varying acceleration constants, and reveals the influence of container bay capacity and permitted frame BM.