## 2 Literature Review  
The emphasis within the AM community recently shifted from rapid prototyping (RP) toward end-use parts, which is evident in the terminology frequently used for 3 DP and AM, such as rapid tooling, rapid manufacturing, and solid freeform fabrication. There are seven main categories of AM, as classified by the American Society for Testing and Materials [20]: (1) photopolymer vat, (2) ME, (3) powder-bed fusion, (4) sheet lamination, (5) directed energy deposition, (6) binder jetting, and (7) material jetting. The top three AM processes surveyed by [PERSON] [2] belong to the ME, photopolymer vat (i.e., SLA), and powder-bed fusion (i.e., SLS) categories. In this study, we analyzed these three AM technologies, as shown in Figure 1a-c, for ME, SLA, and SLS, respectively. Several advantages of and challenges facing AM were detailed by various researchers [21; 22; 23; 24]. In their national roadmap to define future AM research for the United States, [PERSON] et al. [21] noted the need for design, process modeling, and control to aid process and production engineers. [PERSON] [22] suggested that while traditional machining processes are constrained by geometries, resulting in parts with more weight and material than are needed, the geometric build capabilities of AM could deliver near-complete design freedom. The documented advantages of AM are inclusive of reduced tooling, reduction in inventory, part consolidation, and a decentralized supply chain. On the other hand, challenges are related to the quality assurance, effective support structures, orientation of parts, location on the printer, cost of machines and materials, 3D printer selection, production and process planning, AM supply chain, and logistics [2]. Unlike that of traditional manufacturing, the first tier of the supply chain for AM involves web-based retailers, where an end customer orders a 3D-designed part via a web-based transaction (e.g., see 3D Hubs [25] and Shapeways [26]). Thus, the supply chain structure shifts from the traditional supply chain network toward a retail-production-distribution model [27]. Given multiple orders from web-based retail transactions, production scheduling and logistical planning become an important issue for a complex AM supply chain with various AM printers, in which customers' due dates and satisfaction need to be met. A lack of systematic planning will not only cause the under-utilizationof AM printers but also affect the overall economic aspect of a company. Thus, a tool to support decision-making is desired to aid a decision-maker or production planner involved in AM process planning. The strategic, tactical, and operation planning levels of an AM supply chain are shown in Figure 2. In particular, Figure 2 illustrates the AM supply chain's strategic level planning at a macro level and the proposed tactical/operation level at the production stage. That is, the production stage consists of three related modules, which are part-to-printer assignment, part orientation, and part location. Initially, parts to be printed will be assigned to each printer based on the properties of the printer, part characteristics, and customer requirements. Then, the proper orientation of each part assigned to a printer will be decided upon. Next, given an assigned printer and proper orientation of the parts, an appropriate location on a printer chamber will be selected for part placement and printing. In this study, our focus was on the first module of the part-to-printer assignment problem. The use of the build chamber is an important aspect for the process planning of AM. [PERSON] et al. [28] suggested that increasing the AM batch size can help to mitigate production costs and time. Several researchers (e.g., [11; 12; 13; 14]) studied part orientation and printer utilization problems. For example, [PERSON] et al. [13] developed a model for SLA where the orientation of each part to be printed is selected such that it exhibits a good quality, uses minimal support material, and requires a low time to print in the first stage.