Considering the striking achievement of additive manufacturing (AM) as a revolutionary technology, it has increasingly attracted the attention of academia and industrial communities in recent years. Scheduling and production planning in AM play an essential role in the efficient and economical manufacturing of customized products through the saving of time and cost. In this paper, an AM scheduling problem is taken into account with different order specifications, especially the material type and due date on non-identical parallel machines. To formulate the problem, a bi-objective mixed-integer linear programming (MILP) model is proposed to minimize the makespan and the total tardiness penalty. Assuming parts with different material types necessitates the consideration of sequence-dependent setup time that depends on the material type of the current and previous jobs on an AM machine. Finally, an augmented $$ \varepsilon $$–constraint method is applied for the problem to achieve a Pareto-optimal front in an illustrative instance.