An efficient representation scheme of candidate solutions for the master bay planning problem

Abstract

The master bay planning problem (MBPP) arises in the context of maritime transportation. In particular, MBPP consists of determining an efficient plan to stowage the containers into the containership such that the total loading time is minimized. This problem is classified as NP-hard due to the large number of possible solutions generated by the combination of assigning containers to locations in the containership. These solutions are both feasible and infeasible, which increases even more the hardness of MBPP. To deal with this problem, there are several exact and heuristic approaches that are well documented in the literature. One of the most important exact methods is in the form of an integer linear programming (ILP) formulation. However, the number of variables and constraints generated by this ILP model is very large. In this chapter, we propose a new exact algorithm based on a branch and bound (B&B) approach. The main feature is the usage of an efficient representation structure of candidate solutions. We test the proposed B&B on a set of small-sized instances. Experimental results demonstrate that, within this set of instances, our B&B is competitive with respect to the ILP model from the literature.