We focus on a simplified container stowage planning problem where containers of different size and weight must be loaded and unloaded at multiple ports while maintaining the stability of the ship. We initially investigate how the difficulty in solving the problem changes with and without the consideration of container sizes and weight constraints. For this purpose, we provide integer programming formulations for the general problem as well as some special cases with identical container size and/or identical weights and evaluate their performance in randomly generated small- and medium-scale instances. We develop a matheuristic procedure, namely, an insert-and-fix heuristic, exploiting the special structure of the proposed formulations. The Insert-and-Fix method, in combination with a constructive algorithm that gives the solver an initial solution in each iteration, provides solutions with a low number of rehandles for instances with up to 5000 TEUs.
