Exactly solving packing problems with fragmentation

We improve the theoretical understanding of the problem and we introduce new models by exploiting only its combinatorial nature. We design new exact solution algorithms and heuristics based on these models. We consider also variants from the literature with different objective functions and the option of handling weight overhead after splitting. We present experimental results on both datasets from the literature and new, more challenging, ones. These show that our algorithms are both flexible and effective, outperforming by orders of magnitude previous approaches from the literature for all the variants considered. By using our algorithms we could also assess the impact of explicitly handling split overhead, in terms of both solutions quality and computing effort.