Stowage Container Planning: A Model for Getting an Optimal Solution

In this paper a mathematical programming model for the container stowage problem is shown; the binary decision variables determine, for each port, the container unloading and loading sequence. In fact, the solution indicates successively which container will be handled, and from or to which cell in the ship. Unless for some constraint linearisations (related to ship safety parameters), the proposed model finds, from the theoretical point of view, an optimal global solution for the stowage problem. Nevertheless, this combinatorial problem is NP-HARD and cannot be solved for commercial ship sizes in reasonable processing time using the available computer software and hardware. The basic features of this model were used for the development of an implicit enumeration procedure for solving the container stowage problem. In spite of the computational complexity of this approach, some heuristic rules are proposed to explore the combinatorial tree in an intelligent way and produce good, if not optimal, solutions for the problem in a reasonable processing time.