Medical innovations and patient expectations are pushing healthcare toward personalized medicine. In orthopedics, the concept of patient-specific implants could be economically realized with the use of additive manufacturing. Knee and hip replacements are some of the most common musculoskeletal procedures performed in the United States. Joint replacement implants are typically offered in standard sizes and geometries. The mass customization of theses prostheses, however, can improve patient outcomes and reduce medical costs. Mass customization is not economically feasible with traditional manufacturing methods because of the high fixed tooling costs for each geometry. The freedom of design offered by additive manufacturing presents a viable production alternative for unique personal geometry. The objective of this paper is to develop two new analytic models that can be used to investigate a complex additive manufacturing supply chain. The focus of the model is to provide planning tools and a methodology for the direct production of customized orthopedic implants using electron beam melting, an additive manufacturing technology. First, a production model for an additive manufacturing-based system is created. Next, resource planning for a single customized implant system is performed using a simulation model. A queuing model is developed for rapid systems analysis. The staffing requirement predictions of the two models align closely for production of a singular, customized implant. A detailed systems analysis of an additive manufacturing supply chain is conducted to illustrate the use of these models. The queueing model is analytically tractable, so it is extended to describe the production of standard and customized versions of multiple implant families.