An Integrated Optimization Model for the Multi-Port Stowage Planning and the Container Relocation Problems

This paper introduces a new optimization model that integrates the multi-port stowage planning problem with the container relocation problem. This problem is formulated as a binary mathematical programming model that must find the containers' move sequence so that the number of relocations during the whole journey of a ship, as well as the associated port yards is minimized. Modeling by binary variables to represent the cargo status in a ship and yards makes the problem very complex to be solved by exact methods. To the best of our knowledge, this integrated model has not been developed yet as that such problems are always addressed in a partitioned or hierarchical way. A demonstration of the benefits of an integrated approach is given. The model is solved in two different commercial solvers and the results for randomly generated instances are presented and compared to the hierarchical approach. Two heuristics approaches are proposed to quickly generate feasible solutions for warm-starting the model. Extensive computational tests are performed and the results indicate that the solution approaches can reach optimal solutions for small sized instances and good quality solutions on real-scale based instances within reasonable computation time. This is a promising model to support decisions in these problems in an integrated way.