Generating unconstrained two-dimensional non-guillotine cutting patterns by a Recursive Partitioning Algorithm

In this study, a dynamic programming approach to deal with the unconstrained twodimensional non-guillotine cutting problem is presented. The method extends the recently introduced recursive partitioning approach for the manufacturer’s pallet loading problem. The approach involves two phases and uses bounds based on unconstrained two-staged and non-staged guillotine cutting. Since a counterexample for which the approach fails to find known optimal solutions was not found, it is conjectured that it always finds an optimal unconstrained non-guillotine cutting. The method is able to find the optimal cutting pattern of a large number of problem instances of moderate sizes known in the literature. For the instances that the required computer runtimes is excessive, the approach is combined with simple heuristics to reduce its running time. Detailed numerical experiments show the reliability of the method.