© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.Additive manufacturing (AM) is a candidate to be one of the future general-purpose technologies. AM is called with 3D printing, Rapid Prototyping, Direct Digital Manufacturing, layered manufacturing, and/or additive manufacturing. Today, AM is a tool for producing customized small products with small lot sizes. Tomorrow, it will be possible for AM to enter every home and to be used for general purposes. The literature about AM has focused mainly on the technology to decrease the cost of AM, to increase the speed of AM machines, and to increase the common availability of those machines. There are so few papers investigating AM machines in view of scheduling problems. This paper considers a single AM machine that produces multiple parts in batches and then these parts are assembled to produce desired goods. Most AM machines have limitations because of the area of the machine tray and the height of the machine. Therefore, products are separated into small parts considering the area and height of the machine. Then, these separated small parts are assembled to produce the desired goods. In view of scheduling problems, the proposed problem includes single machine batch scheduling and assembly operations. In this paper, we propose a mixed-integer programming (MIP) model and a fast heuristic method with a simple local search mechanism for the problem. We investigate two cases for the same problem. In the first, we consider only the one-dimensional assignment of parts to baches and we just design our solution approaches to assign parts to the batch, if the total area of parts is less than or equal to the machine tray's area. In the second, we modify our solution approaches to consider parts' lengths and widths while assigning parts to batches in a 2D assignment. In the end, we compare the proposed heuristic with the proposed MIP by using some test problems within time limits for all cases. Experimental results show that the proposed heuristic provides promising results.