The multiport container ship stowage problem consists in determining the position of the containers on board a ship along its route with the objective of minimizing the number of unproductive moves required in the loading and unloading operations at each port. This paper presents an integer programming model for the problem and proposes several sets of valid constraints that bring its LP-relaxation closer to an integer solution. Moreover, it presents a GRASP algorithm that generates stowage plans with a minimal number of unproductive moves in a high percentage of medium and large-size instances. An extended computational analysis has been performed in which, to the best of the authors’ knowledge, the efficiency of integer programming models for the problem is tested for the first time. With respect to GRASP, the computational results show that it performs well on different sized datasets.
The container pre-marshalling problem involves the sorting of containers in stacks so that there are no blocking containers and retrieval is carried out without additional movements. This sorting process should be carried out in as few container moves as possible. Despite recent advancements in solving real world sized problems to optimality, several classes of pre-marshalling problems remain difficult for exact approaches. We propose a branch and bound algorithm with new components for solving such difficult instances. We strengthen existing lower bounds and introduce two new lower bounds that use a relaxation of the pre-marshalling problem to provide tight bounds in specific situations. We introduce generalized dominance rules that help reduce the search space, and a memoization heuristic that finds feasible solutions quickly. We evaluate our approach on standard benchmarks of pre-marshalling instances, as well as on a new dataset to avoid overfitting to the available data. Overall, our approach optimally solves many more instances than previous work, and finds feasible solutions on nearly every problem it encounters in limited CPU times.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.