Computational evaluation of a MIP model for multi-port stowage planning problems

In this paper, we consider the problem of determining stowage plans for containers into ships having to visit a given number of ports in their circular route. The problem is denoted Multi-Port Master Bay Plan Problem (MP-MBPP). In practice, the MP-MBPP consists in determining how to stow a given set of containers, split into different groups, according to their size, type, class of weight and destination, into bay locations, either on the deck or in the stow. Some structural and operational constraints, related to the containers, the ship and the maritime terminals, have to be satisfied. The single port MBPP is a NP-hard optimization problem, and has been proposed in the literature from 2001. From then, some variants of the problem have been presented, together with the related solution methods, mainly aimed at including in the corresponding models realistic features, required as a consequence of the naval gigantism. As a novel issue, in the present work, we look for stowage plans where the set of containers to be loaded on board at each port of the route consists of standard, reefer and open top ones. Hatches positions in the ships are considered too. We present a new mixed integer programming (MIP) model for the MP-MBPP able to manage realistic scenarios and find stowage plans for containerships up to 18,000 TEUs. The model is finalized to be solved with a commercial MIP solver. The reported computational experimentation shows that the model is very efficient and could be fruitfully used for facing real-size instances of the problem.