Improved flow-based formulations for the skiving stock problem

•Two new ILP formulations (loss arcflow and reflect) for the skiving stock problem are introduced.•The strength of the corresponding LP relaxations is discussed from a theoretical point of view.•A wide variety of benchmark instances for the SSP is described.•Based on extensive computational tests, especially the reflect formulation is shown to perform much better (on average) compared to state-of-the-art flow-based approaches.