This study proposed a utility-driven two-stage stochastic mixed-integer linear programming model to understand how the patient preferences impact the additive manufacturing (AM) supply chain design decisions. The goal of the mathematical model is to maximize the utilities derived from the customer preferences by appropriately allocating the AM facilities in the targeted region under customer decision and demand uncertainty. The mathematical model is visualized and validated by developing a real-life case study that utilizes the biomedical implants data for Mississippi. Several sensitivity analyses are conducted to understand how the patients' behavioral decisions (e.g., price-centric versus time- or quality-centric customers) to purchase biomedical implants impact the AM supply chain design decisions. Experimental results reveal that AM supply chain is sensitive to the utility of the patients. For instance, it is observed that in addition to opening a facility in Lamar County, an additional AM facility is opened in Washington County to serve the rural patients in our test region Mississippi. The results revealed vital managerial insights that healthcare service providers and interested stakeholders could utilize to provide quality healthcare services by managing patient-centric AM facility siting decisions.