This thesis, after presenting recent advances obtained for the two-dimensional bin packing problem, focuses on the case where guillotine restrictions are imposed.
A mathematical characterization of non-guillotine patterns is provided and the relation between the solution value of the two-dimensional problem with guillotine restrictions and the two-dimensional problem unrestricted is being studied from a worst-case perspective.
Finally it presents a new heuristic algorithm, for the two-dimensional problem with guillotine restrictions, based on partial enumeration, and computationally evaluates its performance on a large set of instances from the literature.
Computational experiments show that the algorithm is able to produce proven optimal solutions for a large number of problems, and gives a tight approximation of the optimum in the remaining cases
