Advanced constraint programming formulations for additive manufacturing machine scheduling problems

In comparison with traditional subtractive manufacturing techniques, additive manufacturing (AM) enables fabricating complex parts through a layer-by-layer process. AM makes it possible to produce one-piece and lightweight functional products, which are traditionally made from several parts. This paper introduces constraint programming (CP) models to minimise makespan in single, parallel identical and parallel unrelated AM machine scheduling environments for selective laser melting. Alternative CP formulations are explored to improve efficiency. The proposed CP model significantly benefits from the introduction of interval variables to replace binary assignment variables, and pre-definitions to narrow the search space, resulting in increased search performance. A computational study has been conducted to compare the performance of our proposed CP model with both a mixed-integer programming and a genetic algorithm from existing literature, evaluating improvements made to its search capability. Computational results indicate that the proposed CP model can obtain high-quality solutions in a timely manner even for several large-size instances.