A decision framework for decomposed stowage planning for containers

Stowage planning is crucial to the efficiency of loading containers onto vessels, which can affect the competitiveness of ports. In this paper, we study the stowage problem and consider the storage locations of containers in the yard. A decision framework is proposed to optimize the stowage, which is decomposed into three phases: allocating storage locations to container blocks, the stacking slots of vessel bays, and the stowing sequences through which containers are stowed. We formulate mixed integer programming models to minimize container relocations, the moving distances from blocks to bays, and operation times of containers in the proposed decision framework. An adaptive large neighborhood search (ALNS) algorithm based on heuristic rules is then designed to solve the optimization problem. Numerical experiments with different scales are conducted to verify the models and algorithm. Comparisons of various methods such as CPLEX and particle swarm optimization, also demonstrate the effectiveness of the ALNS algorithm in terms of its solution performance. A sensitivity analysis of the relocation and bay utilization rates is also conducted, which can provide port operators with managerial insights. Robustness is tested by comparing the objective value gaps when encountering deviations in container weight and size between the actual and expected information. There is a small gap of less than 2% in the solutions, which are solved from the models with parameter deviations. Port operators can develop stowage plans according to the classification of container attributes, and the stowing can achieve fewer relocations within the optimal operation time.