A multi-objective optimization approach for exploring the cost and makespan trade-off in additive manufacturing

Additive manufacturing (AM) suggests promising manufacturing technologies, which complement traditional manufacturing in multiple areas, such as biomedical, aerospace, defense, and automotive industries. This paper addresses the production planning problem in multi-machine AM systems. We consider all relevant physical and technological parameters of the machines and the produced parts, for using direct metal laser sintering (DMLS) technology. In DMLS technology, each machine produces jobs, where each job consists of several parts arranged horizontally on the build tray. Starting a new job requires a setup operation. We address the simultaneous assignment of parts to jobs and jobs to the machines, while considering the cost and makespan objectives. A unified mixed-integer linear-programming (MILP) formulation that can minimize the above objectives separately and simultaneously is suggested, along with analytical bounds and valid inequalities. Experimentation demonstrates the effectiveness of the proposed formulation with single objectives versus similar formulations from the literature. An efficient frontier approach is applied to the multi-objective problem while generating a diverse set of exact non-dominated solutions. The trade-off between the objectives is analyzed via experimentation. Results show that when identical machines are used, the trade-off is relatively small, and hence the decision-maker can use any of the single objectives. However, when non-identical machines are used, it is important to consider both objectives simultaneously. Moreover, the trade-off increases with the number of machines and heterogeneity of the system, with respect to the size and settings of the machines.