This paper studies the customer order scheduling problem in the context of additive manufacturing. The study discusses an integrated problem involving the nesting of parts as well as the scheduling of batches of nested parts onto unrelated parallel machines. A mixed-integer programming model is presented, based on existing formulations from the literature, that integrates different materials and sequence-dependent setup times. Additionally, a metaheuristic based on an iterated local search is proposed for the problem configuration under consideration. Focusing on minimizing the total weighted tardiness of orders, the efficiency of the heuristic approach is evaluated using comprehensive test data. Further, we show the importance of the considered order-related objective by using qualitative analysis.