Including mechanical requirements in a bi-objective nesting and scheduling model for additive manufacturing

Following the increasing relevance of Additive Manufacturing (AM) as Manufacturing-as-a-service (Maas), the AM scheduling (and related nesting) problem has been increasingly investigated. Due to their business nature, Maas companies are interested in minimizing both the makespan and the total tardiness; however, most of the literature focuses only on one of them. This work fills this gap proposing a mixed-integer linear programming (MILP) model that minimizes both makespan and total tardiness. In doing so, for the first time in the literature, considerations on parts’ strength are included. During nesting procedures, indeed, parts can be oriented in different ways, with this choice affecting not only the total processing time (as considered by the literature) but also the strength achievable: if this is lower than what planned, parts might fail unexpectedly with detrimental consequences. Thus, this work ensures that parts are produced with the required strength. In doing so, we focus on a parallel unrelated AM batch scheduling problem for metallic parts. Considering the multi-objective and NP-hard nature of the problem, an ε-constraint algorithm and a non-dominated sorting genetic algorithm-II (NSGA-II) are developed to solve the problem. Four different problem-specific decoding mechanisms are integrated into the NSGA-II to improve its search capability and solution-building performance. Their performances are evaluated through computational experiments, showing that the integrated mechanisms improve the performance of the NSGA-II. Finally, through numerical instances and analysis of the super Pareto front, we derive managerial insights on the impact of strength requirements and machines’ number and features on the objectives.